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IMA Newsletter #375

January 2008

2007-2008 Program

Mathematics of Molecular and Cellular Biology

See http://www.ima.umn.edu/2007-2008 for a full description of the 2007-2008 program on Mathematics of Molecular and Cellular Biology.

News and Notes

Opportunities at the IMA: There is still time to apply for one of the IMA General Membership, New Directions Professorship or Postdoctoral Fellowship positions in connection with the 2008-2009 thematic program: Mathematics and Chemistry. The deadline for applying for the postdoc positions is January 4, 2008 and the deadline for the New Directions Research Professorships is January 15, 2008. You can find the applications for these positions at our Applications site.

IMA is seeking a new associate director: The IMA is looking for a new associatae director to begin September 1, 2008.

New Directions Short Course: The IMA is currently accepting applications for the 2008 New Directions Short Course - Mathematical Neuroscience, June 16 - 27, 2008, taught by G. Bard Ermentrout and Jonathan E. Rubin.

Neuroscience is becoming increasingly quantitative and the need for theoreticians interested in collaborating with experimental neuroscientists is on the rise. The proposed short course will introduce the participants to basic concepts in cellular and systems neuroscience with an emphasis on the underlying equations and dynamics. Participation is by application only. Application deadline: April 1, 2008.

IMA Events

IMA Tutorial

Mathematics of Proteins

January 10-11, 2008

Organizers: Patrice Koehl (University of California), Michael Levitt (Stanford University)

IMA Annual Program Year Workshop

Protein Folding

January 14-18, 2008

Organizers: Ken A. Dill (University of San Francisco), Sorin Istrail (Brown University), Michael Levitt (Stanford University)
Schedule

Tuesday, January 1

All DayNew Year's Day. The IMA is closed.

Tuesday, January 8

11:15a-12:15pAn experimental perspective on miscibility phase transitions and their biological applicationsBenjamin Stottrup (Augsburg College)Lind Hall 409 PS

Wednesday, January 9

11:15a-12:15pThe solution of the distance geometry problem for protein modelingZhijun Wu (Iowa State University)Lind Hall 409 MMCB

Thursday, January 10

8:15a-8:50aRegistration and coffeeEE/CS 3-176 T1.10-11.08
8:50a-9:00aWelcome to the IMADouglas N. Arnold (University of Minnesota)EE/CS 3-180 T1.10-11.08
9:00a-10:00aLecture 1: Fundamental forces and molecular architectureMichael Levitt (Stanford University)EE/CS 3-180 T1.10-11.08
10:00a-10:30aBreakEE/CS 3-176 T1.10-11.08
10:30a-11:30aThe geometry of biomolecular solvation. Part 1: HydrophobicityPatrice Koehl (University of California)EE/CS 3-180 T1.10-11.08
11:30a-1:30pLunch T1.10-11.08
1:30p-2:30pPart 2: ElectrostaticsPatrice Koehl (University of California)EE/CS 3-180 T1.10-11.08
2:30p-3:00pBreakEE/CS 3-176 T1.10-11.08
3:00p-4:00pLecture 2: Simulating molecular motionMichael Levitt (Stanford University)EE/CS 3-180 T1.10-11.08
4:00p-4:30pSecond chancesPatrice Koehl (University of California)
Michael Levitt (Stanford University)
EE/CS 3-180 T1.10-11.08

Friday, January 11

8:30a-9:00aCoffeeEE/CS 3-176 T1.10-11.08
9:00a-10:00aPart 3: Protein shape descriptorsPatrice Koehl (University of California)EE/CS 3-180 T1.10-11.08
10:00a-10:30aBreakEE/CS 3-176 T1.10-11.08
10:30a-11:30aLecture 3: Simulating protein foldingMichael Levitt (Stanford University)EE/CS 3-180 T1.10-11.08
11:30a-2:00pLunch T1.10-11.08
2:00p-2:30pGeometric simulation of protein flexibilityIleana Streinu (Smith College)EE/CS 3-180 T1.10-11.08
2:30p-3:00pKnot theory and proteins Isabel K. Darcy (University of Iowa)EE/CS 3-180 T1.10-11.08
3:00p-3:30pBreakEE/CS 3-176 T1.10-11.08
3:30p-4:00pAn introduction to multigrid techniquesBobby Philip (Los Alamos National Laboratory)EE/CS 3-180 T1.10-11.08

Monday, January 14

All DayMorning Theme: Force fields & simulations
Afternoon Theme: Design, predictions, and optimization
W1.14-18.08
8:15a-9:00aRegistration and coffeeEE/CS 3-176 W1.14-18.08
9:00a-9:15aWelcome to the IMADouglas N. Arnold (University of Minnesota)EE/CS 3-180 W1.14-18.08
9:15a-9:45aAssessing the performance of Poisson-Boltzmann continuum solvation models Nathan A. Baker (Washington University School of Medicine)EE/CS 3-180 W1.14-18.08
9:50a-10:20aSimple models for simulating replica exchange simulations of protein folding and bindingRonald M. Levy (Rutgers University)EE/CS 3-180 W1.14-18.08
10:25a-10:55aAlpha-helical topology and tertiary structure prediction of globular proteinsChristodoulos A. Floudas (Princeton University)EE/CS 3-180 W1.14-18.08
10:55a-11:40aCoffeeEE/CS 3-176 W1.14-18.08
11:40a-12:10pChallenges in generation of conformational ensembles for peptides and small proteinsCarlos L. Simmerling (SUNY)EE/CS 3-180 W1.14-18.08
12:15p-12:30pWhat is a transition path? Robert D. Skeel (Purdue University)EE/CS 3-180 W1.14-18.08
12:30p-2:00aLunch W1.14-18.08
2:00p-2:30pEngineering protein structure and function with theoretical protein designJeffery G. Saven (University of Pennsylvania)EE/CS 3-180 W1.14-18.08
2:35p-2:50pModeling ensembles of transmembrane beta-barrel proteinsJérôme Waldispühl (Massachusetts Institute of Technology)EE/CS 3-180 W1.14-18.08
2:55p-3:25pCoffeeEE/CS 3-176 W1.14-18.08
3:25p-3:40pExact methods for simplified protein modelsRolf Backofen (Albert-Ludwigs-Universität Freiburg)EE/CS 3-180 W1.14-18.08
3:40p-4:10pDiscussion forumEE/CS 3-180 W1.14-18.08
4:10p-4:25pGroup Photo W1.14-18.08
4:30p-6:00pReception and Poster SessionLind Hall 400 W1.14-18.08
Topological analysis of DNA-binding protein complexesSoojeong Kim (University of Iowa)
Overall rotation due to internal motions in the N-body dynamics of protein moleculesFlorence J. Lin (University of Southern California)
Simulating protein conformations by a geometric modelAntonio Mucherino (Seconda Università di Napoli)
Protein folding by ZAM & FRODASefika Banu Ozkan (Arizona State University)
Computing conformational free energy by deactivated morphingSanghyun Park (Argonne National Laboratory)
Minima Hopping within an all-atom framework for biomolecular structure predictionShantanu Roy (Universität Basel)
Investigation of the unfolding pathway of Cyt2Aa2 toxinAnchanee Sangcharoen (Mahidol University )
Configuration-dependent diffusion can shift the kinetic transition state and barrier height of protein foldingJin Wang (SUNY)
Mathematical methods for implicit solvent models Guowei Wei (Michigan State University)
The Dynamic Nature of the Folded and Unfolded States of the Villin Headpiece Helical Subdomain: An ultrafast folding proteinLauren Wickstrom (SUNY)
A novel method for protein folding shape descriptionJiaan Yang (MicrotechNano)
Temperature dependence of Trp-cage folding kinetics from replica exchange simulationsSichun Yang (University of Chicago)

Tuesday, January 15

All DayMorning Theme: Systems modeling
Afternoon Theme: Conformational exploration, routes, and searching
W1.14-18.08
8:30a-9:00aCoffeeEE/CS 3-176 W1.14-18.08
9:00a-9:30aSimulation methods for stochastic chemical systems that arise from a random time change representationDavid F Anderson (University of Wisconsin)EE/CS 3-180 W1.14-18.08
9:35a-10:05aCoarse-grained parameterizations of biomolecular systemsPeter R. Kramer (Rensselaer Polytechnic Institute)EE/CS 3-180 W1.14-18.08
10:10a-10:40aFrom chemical reaction systems to cellular states: A computational approachHong Qian (University of Washington)EE/CS 3-180 W1.14-18.08
10:40a-11:10aCoffeeEE/CS 3-176 W1.14-18.08
11:10a-11:40aComputational experiments in coarse-graining atomistic simulationsYannis G. Kevrekidis (Princeton University)EE/CS 3-180 W1.14-18.08
11:40a-1:30pLunch W1.14-18.08
1:30p-2:00pUsing motion planning to study molecular motionsNancy M. Amato (Texas A & M University)EE/CS 3-180 W1.14-18.08
2:05p-2:35pGeometrical methods for the efficient exploration of protein conformation spaceEvangelos A. Coutsias (University of New Mexico)EE/CS 3-180 W1.14-18.08
2:40p-3:10pNetwork models for protein dynamics and allostery: Application to GroEL-GroESIvet Bahar (University of Pittsburgh)EE/CS 3-180 W1.14-18.08
3:10p-3:40pCoffeeEE/CS 3-176 W1.14-18.08
3:40p-4:10pStructural control of motions?Robert L. Jernigan (Iowa State University)EE/CS 3-180 W1.14-18.08
4:15p-4:45pThe network of sequence flow between protein structuresRon Elber (University of Texas)EE/CS 3-180 W1.14-18.08
4:50p-5:20pDiscussion forumEE/CS 3-180 W1.14-18.08

Wednesday, January 16

All DayMorning Theme: Nonequilibrium & single molecules
Afternoon Theme: Nucleic acids & genomes
W1.14-18.08
8:30a-9:00aCoffeeEE/CS 3-176 W1.14-18.08
9:00a-9:30aExploring global energy landscape of lattice protein models via Monte Carlo methodsSamuel Kou (Harvard University)EE/CS 3-180 W1.14-18.08
9:35a-10:05aMathematical models of folded and unfolded protein ensemblesGregory S. Chirikjian (Johns Hopkins University)EE/CS 3-180 W1.14-18.08
10:10a-10:25aCurrent issues in understanding complex biological networksHans G. Othmer (University of Minnesota)EE/CS 3-180 W1.14-18.08
10:30a-11:15aCoffeeEE/CS 3-176 W1.14-18.08
11:15a-11:45aImproving nonequilibrium free energy estimates by enhancing phase space overlapChristopher Jarzynski (University of Maryland)EE/CS 3-180 W1.14-18.08
11:45a-2:00aLunch W1.14-18.08
2:00p-2:30pThe electrostatic free energy landscape for nucleic acid folding - beyond the Poisson-Boltzmann equationShi-Jie Chen (University of Missouri)EE/CS 3-180 W1.14-18.08
2:35p-2:50pAnnotated tertiary interactions in RNA structures reveal new interactions, correlations in motifs and composite motifsChristian E. Laing (New York University)EE/CS 3-180 W1.14-18.08
2:50p-3:20pCoffeeEE/CS 3-176 W1.14-18.08
3:20p-3:35pMapping evolutionary pathways of HIV-1 drug resistance using conditional selection pressureChristopher J. Lee (University of California)EE/CS 3-180 W1.14-18.08
3:40p-4:10pDiscussion forumEE/CS 3-180 W1.14-18.08

Thursday, January 17

All DayMorning Theme: Protein folding & low-resolution modeling
Afternoon Theme: Protein design and interactions
W1.14-18.08
8:30a-9:00aCoffeeEE/CS 3-176 W1.14-18.08
9:00a-9:30aFree energies and kinetics of protein folding from coarse master equationsGerhard Hummer (National Institutes of Health (NIH))EE/CS 3-180 W1.14-18.08
9:35a-10:05aEntropic and enthalpic barriers in cooperative protein foldingHue-Sun Chan (University of Toronto)EE/CS 3-180 W1.14-18.08
10:10a-10:40aThe energy landscape for folding and molecular motorsJosé Nelson Onuchic (University of California, San Diego)EE/CS 3-180 W1.14-18.08
10:40a-11:25aCoffeeEE/CS 3-176 W1.14-18.08
11:25a-11:55aTransition states in protein foldingThomas Weikl (Max Planck Institute for Colloids and Interfaces)EE/CS 3-180 W1.14-18.08
12:00p-12:15pProbing the diversity of unfolding pathways by simulated thermal denaturationAndrew J. Rader (Indiana University-Purdue University)EE/CS 3-180 W1.14-18.08
12:30p-2:00aLunch W1.14-18.08
2:00p-2:30pStructure-based maximal affinity model predicts small-molecule druggabilityAlan C. Cheng (Amgen Cambridge Research Center)EE/CS 3-180 W1.14-18.08
2:35p-2:50pCluster optimization in protein dockingJulie C. Mitchell (University of Wisconsin)EE/CS 3-180 W1.14-18.08
2:50p-3:20pCoffeeEE/CS 3-176 W1.14-18.08
3:20p-3:50pMultistage optimization for protein-protein dockingSandor Vajda (Boston University)EE/CS 3-180 W1.14-18.08
3:55p-4:25pDiscussion forumEE/CS 3-180 W1.14-18.08
6:30p-8:30pWorkshop DinnerCaspian Bistro
2418 University Ave SE
Minneapolis, MN 55414
612-623-1133
W1.14-18.08

Friday, January 18

All DayTheme: Big Simulations of atomically detailed models W1.14-18.08
8:30a-9:00aCoffeeEE/CS 3-176 W1.14-18.08
9:00a-9:30aThe limitations of temperature replica exchange (T-REMD) for protein foldingJed W. Pitera (IBM Research Division)EE/CS 3-180 W1.14-18.08
9:35a-10:05aSimulations on BlueGene of a fast folding mutant of lambda(6-85)William Swope (IBM)EE/CS 3-180 W1.14-18.08
10:05a-10:50aCoffeeEE/CS 3-176 W1.14-18.08
10:50a-11:20aSimulations of peptide folding and dynamicsKrzysztof Kuczera (University of Kansas)EE/CS 3-180 W1.14-18.08
11:25a-11:55aDiscussion forumEE/CS 3-180 W1.14-18.08
11:55a-12:10pConcluding remarks Ken A. Dill (University of San Francisco)
Sorin Istrail (Brown University)
Michael Levitt (Stanford University)
EE/CS 3-180 W1.14-18.08
2:30p-3:20pProtein folding physics and computational modelingKen A. Dill (University of San Francisco)402 Walter Library Compbio

Monday, January 21

All DayMartin Luther King holiday. The IMA is closed.

Tuesday, January 22

11:15a-12:15pBrownian dynamics simulations of polymer behavior in nanofluidic and microfluidic systemsSatish Kumar (University of Minnesota)Lind Hall 409 PS

Wednesday, January 23

11:15a-12:15pAnalyzing the protein-protein interaction networkRobert L. Jernigan (Iowa State University)Lind Hall 409 MMCB

Tuesday, January 29

11:15a-12:15pSyzygies of algebraic varietiesMilena Hering (University of Minnesota)Lind Hall 409 PS

Wednesday, January 30

11:15a-12:15pCombinatorial rigidity and the molecular conjectureBrigitte Servatius (Worcester Polytechnic Institute)Lind Hall 409 MMCB

Event Legend:

CompbioComputational Biology Seminar
MMCBMathematics of Molecular and Cellular Biology Seminar
PSIMA Postdoc Seminar
T1.10-11.08Mathematics of Proteins
W1.14-18.08Protein Folding
Abstracts
Nancy M. Amato (Texas A & M University) Using motion planning to study molecular motions
Abstract: Protein motions, ranging from molecular flexibility to large-scale conformational change, play an essential role in many biochemical processes. For example, some devastating diseases such as Alzheimer's and bovine spongiform encephalopathy (Mad Cow) are associated with the misfolding of proteins. Despite the explosion in our knowledge of structural and functional data, our understanding of protein movement is still very limited because it is difficult to measure experimentally and computationally expensive to simulate. In this talk we describe a method we have developed for modeling protein motions that is based on probabilistic roadmap methods (PRM) for motion planning. Our technique yields an approximate map of a protein's potential energy landscape and can be used to generate transitional motions of a protein to the native state from unstructured conformations or between specified conformations. We also describe new analysis tools that enable us to extract kinetics information, such as folding rates or to identify and study the folding core. For example, we show how our map-based tools for modeling and analyzing folding landscapes can capture subtle folding differences between protein G and its mutants, NuG1 and NuG2. More information regarding our work, including an archive of protein motions generated with our technique, are available from our protein folding server: http://parasol.tamu.edu/foldingserver/
David F Anderson (University of Wisconsin) Simulation methods for stochastic chemical systems that arise from a random time change representation
Abstract: Chemical reaction systems with a low to moderate number of molecules are typically modeled as continuous time Markov chains. More explicitly, the state of the system is modeled as a vector giving the number of molecules of each species present with each reaction modeled as a possible transition for the state. The model for the kth reaction is determined by a vector of inputs specifying the number of molecules of each chemical species that are consumed in the reaction, a vector of outputs specifying the number of molecules of each species that are created in the reaction and a function of the state that gives the rate at which the reaction occurs. To understand how the probability distribution of the system changes in time one could attempt to solve the Chemical Master Equation (CME), however this is typically an extremely difficult task. Therefore, simulation methods such as the Stochastic Simulation Algorithm (Gillespie Algorithm) and tau-leaping have been developed so as to approximate the probability distribution of the system via Monte Carlo methods. I will demonstrate how using a random time change representation for these models leads naturally to simulation methods that achieve greater efficiency and stability than existing methods.
Rolf Backofen (Albert-Ludwigs-Universität Freiburg) Exact methods for simplified protein models
Abstract: Due to the inherent complexity of the associated problems, investigations of the basic principles of protein folding and evolution are usually restricted to simplified protein models. Our group has developed methods and programs for exact and complete solving of problems typical for studies using HP-like 3D lattice protein models. Addressed tasks are the prediction of globally optimal and listing of suboptimal structures, sequence design, neutral network exploration, and degeneracy computation. The used methods are based on fast and non-heuristic techniques (constraint programming) instead of following stochastic approaches, which are not capable of answering many fundamental questions. Thus, we are able to find optimal structure for HP-sequences of length greater than 200, including a proof of optimality. We have used these methods to find unique folding sequences, to investigate neutral nets and to design low-degenerated sequences for given structures.
Ivet Bahar (University of Pittsburgh) Network models for protein dynamics and allostery: Application to GroEL-GroES
Abstract: Two groups of studies recently proved to provide insights into such intrinsic, structure-induced effects: elastic network models that permit us to visualize the cooperative changes in conformation that are most readily accessible near native state conditions, and information-theoretic approaches that elucidate the most efficient pathways of signal transmission favored by the overall architecture. Using a combination of these two approaches, we highlight, by way of application to the bacterial chaperonin complex GroEL-GroES, how the most cooperative modes of motion play a role in mediating the propagation of allosteric signals. A functional coupling between the global dynamics sampled under equilibrium conditions and the signal transduction pathways inherently favored by network topology appears to control allosteric effects.
Nathan A. Baker (Washington University School of Medicine) Assessing the performance of Poisson-Boltzmann continuum solvation models
Abstract: Continuum electrostatics methods have become increasingly popular due to their ability to provide approximate descriptions of solvation energies and forces without expensive sampling required by explicit solvent models. In particular, the Poisson-Boltzmann equation (PBE) provides electrostatic potentials, solvation energies, and forces by modeling the solvent as a featureless, dielectric material, and the mobile ions as a continuous distribution of charge. In this talk, I will provide a review of PBE-based and new apolar continuum solvation methods as well as approaches for assessing their performance by comparison with explicit solvent simulations. In particular, I will focus on the ability of these continuum solvent models to describe solvation forces on proteins and nucleic acids and will comment on strengths and weaknesses of these implicit solvent approaches.
Hue-Sun Chan (University of Toronto) Entropic and enthalpic barriers in cooperative protein folding
Abstract: Many small single-domain proteins undergo cooperative, switch-like folding/unfolding transitions with very low populations of intermediate, i.e., partially folded, conformations. The phenomenon of cooperative folding is not readily accounted for by common notions about driving forces for folding. I will discuss how common protein chain models with pairwise additive interactions are insufficient to account for the folding cooperativity of natural proteins, and how models with nonadditive local-nonlocal coupling may rationalize cooperative folding rates that are well correlated with native topology. The traditional formulation of folding transition states entails a macroscopic folding free energy barrier with both enthalpic and entropic components. I will explore the microscopic origins of these thermodynamic signatures in terms of conformational entropy as well as desolvation (dewetting) effects. Notably, the existence of significant enthalpic folding barriers raises fundamental questions about the validity of the funnel picture of protein folding, because such enthalpic barriers appear to imply that there are substantial uphill moves along a microscopic folding trajectory. Using results from extensive atomic simulations, I will show how the paradox can be resolved by a dramatic entropy-enthalpy compensation at the rate-limiting step of folding. In this perspective, the height of the enthalpic barrier is seen as related to the degree of cooperativity of the folding process.
Shi-Jie Chen (University of Missouri) The electrostatic free energy landscape for nucleic acid folding - beyond the Poisson-Boltzmann equation
Abstract: Multivalent ions (Mg2+) in RNA tertiary structure folding can be strongly correlated and thus cannot be treated by mean-field theories such as the Poisson-Boltzmann equation. We recently developed a statistical mechanical model (TBI) to account for ion correlation by considering ensemble of discrete ion distributions. Experimental tests show that the TBI model gives improved predictions for nucleic folding folding stability over the Poisson-Boltzmann equation, which generally underestimates the (multivalent) ion-dependent folding stability due to ignoring the ion correlation. Using the TBI theory, we investigate the folding energy landscape for a simple system with loop-tethered short DNA helices and find that Na+ and Mg2+ play contrasting roles in helix–helix assembly. High [Na+] (>0.3 M) causes a reduced helix–helix electrostatic repulsion and a subsequent disordered packing of helices, while Mg2+ of concentration > 1 mM is predicted to induce a more compact and ordered helix–helix packing. Mg2+ is much more efficient in causing nucleic acid compaction and is predicted to induce a collapse transition around 1mM of [Mg2+].
Alan C. Cheng (Amgen Cambridge Research Center) Structure-based maximal affinity model predicts small-molecule druggability
Abstract: Lead generation is a major hurdle in small-molecule drug discovery, with an estimated 60% of projects failing from lack of lead matter or difficulty in optimizing leads for drug-like properties. It would be valuable to identify these less-druggable targets before incurring substantial expenditure and effort. We discovered that a model-based approach using basic biophysical principles yields good prediction of druggability based solely on the crystal structure of the target binding site. We quantitatively estimate the maximal affinity achievable by a drug-like molecule, and we show that these calculated values correlate with drug discovery outcomes. We experimentally test two predictions using high-throughput screening of a diverse compound collection. The collective results highlight the utility of our approach as well as strategies for tacking difficult targets. I will also discuss our approach to calculating protein curvature and some potential computational approaches for difficult targets.
Gregory S. Chirikjian (Johns Hopkins University) Mathematical models of folded and unfolded protein ensembles
Abstract: This talk (and a related poster) describes Lie-group-theoretic techniques that can be applied in the analysis and modeling of protein conformations. Three topics are covered: (1) Conformational transitions between two known end states; (2) proper normalization of helix-helix crossing angle data in the PDB; (3) models of the conformational entropy of the ensemble of unfolded polypeptide conformations. Using the concept of convolution on the group of rigid-body motions, the probability density of position and orientation of the distal end of a polypeptide chain is obtained by convolving the distributions for shorter segments that make up the chain. This methodology can also be used in the analysis of loop entropy in folded proteins as well as the ensemble of unfolded conformations.
Evangelos A. Coutsias (University of New Mexico) Geometrical methods for the efficient exploration of protein conformation space
Abstract: The geometrical problem of protein folding, especially in its later stages, is composed of two types of freedom, the full torsional flexibility of loops connecting nearly rigid structural pieces (helices, beta-sheets etc), and the relative placing of such pieces. We present a method for sampling the feasible conformations of protein loops, based on Triaxial Loop Closure (TLC), a simple and highly efficient inverse kinematic (IK) method for solving the loop closure problem. TLC is easily extended to incorporate additional (i.e. position, orientation) constraints, or more general geometrical conditions. Due to its relative simplicity TLC compares favorably to more general IK robotics algorithms, both in robustness and in speed. We consider two applications: (i) An algorithm for the rapid sampling of the conformations of protein loops including three or more residues which uses quasirandom Sobol sampling of the Ramachandran regions. Ideas akin to Delauney triangulation may be employed to ensure sampling loop shapespace at a desired density. (ii) An efficient method for the sequential assembly of helical proteins via maximal hydrophobic packing. The geometrical problem of considering all possible mutual arrangements of a system of helices that are compatible with closing the corresponding loops is already too large to sample directly. We introduced a measure of hydrophobic packing by seeking to minimize the radius of gyration of the hydrophobic residues. Thus, we sequentially assemble the helices, by sampling relative orientations of pairs of them that bring specified hydrophobic residues in proximity. For the best candidates, in terms of energy and hydrophobig radius of gyration, the loops are closed using the algorithm in (i) and another helix is added to the assembly, always seeking to maximizing hydrophobic contact. We tested this iterative assembly method on 26 helical proteins each containing up to 5 helices. The method heavily samples native-like conformations. The average RMSD-to-native of the best conformations for the 18 helix bundle proteins that have 2 or 3 helices is less than 2 Angstroms with slightly worse errors for proteins containing more helices.
Isabel K. Darcy (University of Iowa) Knot theory and proteins
Abstract: Some proteins contain locally knotted structures. Many algorithms have been developed in order to detect local knotting in protein conformations. In some cases these algorithms are used to rule out computationally generated structures containing local knots as knotted proteins are rare. However, there are several types of proteins which contain local knots. I will give an overview of knotted proteins, the various methods used to define a local knot in a protein, and their potential significance.
Ken A. Dill (University of San Francisco) Protein folding physics and computational modeling
Abstract: Protein molecules are linear polymer chains that fold up into particular 3-dimensional native structures to perform the functions of the cell. We are interested in: (a) the folding code — how the 1-dimensional monomer sequence encodes the 3-dimensional fold, (b) the folding problem — how the protein searches and finds it's native structure so quickly, and (c) a folding algorithm — a computational strategy for predicting the native structure from the amino acid sequence.
Ron Elber (University of Texas) The network of sequence flow between protein structures
Abstract: Sequence-structure relationships in proteins are highly asymmetric since many sequences fold into relatively few structures. What is the number of sequences that fold into a particular protein structure? Is it possible to switch between stable protein folds by point mutations? To address these questions we compute a directed graph of sequences and structures of proteins, which is based on experimentally determined protein shapes. Two thousand and sixty experimental structures from the Protein Data Bank were considered, providing a good coverage of fold families. The graph is computed using an energy function that measures stability of a sequence in a fold. A node in the graph is an experimental structure (and the computationally matching sequences). A directed and weighted edge between nodes A and B is the number of sequences of A that switch to B because the energy of B is lower. The directed graph is highly connected at native energies with ³sinks² that attract many sequences from other folds. The sinks are rich in beta sheets. The in-degrees of a particular protein shape correlates with the number of sequences that matches this shape in empirically determined genomes. Properties of strongly connected components of the graph are correlated with protein length and secondary structure. Joint work with Leonid Meyerguz and Jon Kleinberg
Christodoulos A. Floudas (Princeton University) Alpha-helical topology and tertiary structure prediction of globular proteins
Abstract: Joint work with S. R. McAllister. The protein folding question has developed over the past four decades as one of the most challenging and potentially rewarding problems in computational biology. Three general classes of algorithms have emerged, based on the techniques of comparative modeling, fold recognition, and first principles methods. For a detailed summary of protein structure prediction methods, the reader is directed to two recent reviews [1,2]. Within the field of protein structure prediction, the packing of alpha-helices has been one of the more difficult problems. The use of distance constraints and topology predictions can be highly useful for reducing the conformational space that must be searched by deterministic algorithms to find a protein structure of minimum conformational energy. We present a novel first principles framework to predict the structure of alpha-helical proteins. Given the location of the alpha-helical regions, a mixed-integer linear optimization model maximizes the interhelical residue contact probabilities to generate distance restraints between alpha-helices [3]. Two levels of this formulation allow the prediction of both ``primary'' contacts between a helical pair as well as the prediction of ``wheel'' contacts, one helical turn beyond the primary contacts. These predictions are subject to a number of mathematical constraints to disallow sets of contacts that cannot be achieved by a folded protein. The interhelical contact prediction for alpha-helical proteins was evaluated on 26 proteins, where it identified an average contact distance below 11.0 Angstroms for the entire set. A related optimization-based approach is proposed for the prediction of alpha-helical contacts in mixed alpha/beta proteins [4]. This contact prediction is based on the maximization of the number and hydrophobicity of hydrophobic interactions. The allowable sets of contacts is restricted based on knowledge or prediction of the beta-sheet topology and a number of distance geometry rules and constraints. The interhelical contact prediction for alpha/beta proteins was evaluated on 12 test proteins, where it identified an average contact distance below 11.0 Angstroms for 11 of these proteins. The distance restraints from the interhelical contacts are then used to restrict the feasible space of the protein during the prediction of the tertiary structure using a hybrid optimization algorithm [5,6]. This tertiary structure prediction approach combines torsion angle dynamics and rotamer optimization with a deterministic global optimization technique (alphaBB) and a stochastic optimization technique (conformational space annealing) to minimize a detailed atomistic-level energy function. The tertiary structure prediction results are promising and are highlighted by the exciting, near-native blind prediction of a de novo designed 4-helix bundle protein. [1] Floudas CA, Fung HK, McAllister SR, Monningmann M, and Rajgaria R. Advances in Protein Structure Prediction and De Novo Protein Design: A Review. Chem Eng Sci. 2006;61: 966-988. [2] Floudas CA. Computational Methods in Protein Structure Prediction. Biotechnol Bioeng. 2007;97:207-213. [3] McAllister SR, Mickus BE, Klepeis JL, and Floudas CA. A Novel Approach for Alpha-Helical Topology Prediction in Globular Proteins: Generation of Interhelical Restraints. Prot Struct Funct Bioinf. 2006;65:930-952. [4] McAllister SR and Floudas CA. Alpha-helical Residue Contact Prediction in Mixed Alpha/Beta Proteins Using Mixed-Integer Linear Programming. In preparation, 2007. [5] Klepeis JL and Floudas CA. ASTRO-FOLD: A Combinatorial and Global Optimization Framework for Ab Initio Prediction of Three-dimensional Structures of Proteins from the Amino Acid Sequence. Biophys J, 2003;85:2119-2146. [6] McAllister SR and Floudas CA. An Improved Hybrid Global Optimization Method for Protein Tertiary Structure Prediction. In preparation, 2007.
Milena Hering (University of Minnesota) Syzygies of algebraic varieties
Abstract: The embedding of a projective variety in projective space can be described as the common zero locus of homogeneous polynomials in a polynomial ring. I will introduce Green's property $N_p$ and the Koszul property for embeddings of projective varieties, and present some results for toric varieties, as well as for the GIT quotient of points in $P^1$ modulo the $SL(2,C)$ action.
Gerhard Hummer (National Institutes of Health (NIH)) Free energies and kinetics of protein folding from coarse master equations
Abstract: Coarse master equations and diffusion models provide powerful tools to study the equilibrium and non-equilibrium properties of molecular systems. Maximum likelihood and Bayesian approaches have been used successfully to construct such models from the observed dynamics projected onto discrete and continuous low-dimensional sub-spaces. By using a Green's-function based formalism, issues arising from fast non-Markovian dynamics can be circumvented. The general formalism for the construction of coarse master equations and diffusion models will be illustrated with applications to peptide and protein folding.
Christopher Jarzynski (University of Maryland) Improving nonequilibrium free energy estimates by enhancing phase space overlap
Abstract: While equilibrium free energy differences can be obtained from simulations of non-equilibrium systems, such estimates are often hampered by convergence difficulties similar to those that plague traditional perturbation methods. In the nonequilibrium context, dissipation is the culprit behind poor convergence. I will discuss a general strategy for addressing these difficulties, in which dissipation is reduced by adding non-physical terms to the equations of motion. When these terms are chosen appropriately, the efficiency of the free energy estimate can improve dramatically. After sketching the general features of this strategy, I will illustrate its application using specific examples, and will discuss its relation to other strategies that are similar in spirit.
Robert L. Jernigan (Iowa State University) Structural control of motions?
Abstract: Are protein motions limited because of a higher level of cooperativity than indicated by usual potentials? Recently derived four-body coarse-grained potentials show improved performance in threading over pairwise potentials. Their apparently increased extent of cooperativity is consistent with the high level of control of motions manifested in the elastic network model computations. The elastic network models are providing strong evidence that proteins control their functional motions through their most important slowest domain motions. A major strength of these models appears to be their ability to represent the structures as highly cohesive rubbery materials, and much evidence supporting them has now accumulated. Such models exhibit strong control over their motions, arising principally from the shape, sometimes even including control of the motions of surface loops by domain motions and the motion of reactive atoms at enzyme active sites. These highly coordinated atom motions may be relevant to enzyme mechanisms. There is accumulating evidence that the behavior of protein machines can be understood with these models, and the important large domain motions can be obtained readily. For the ribosome, the results clearly indicate that its motions relate strongly to many aspects of its function. Already we have seen that the large ribosomal ratchet motion simultaneously causes the t-RNAs and mRNA to translate in the processing direction. The control of the mRNA at the anti-codon binding site is extremely strong, to ensure fidelity of copying, with the mRNA being moved translationally as a fully rigid body, with no internal motions.
Robert L. Jernigan (Iowa State University) Analyzing the protein-protein interaction network
Abstract: The abundant data available for protein interaction networks have not yet been fully understood. New types of analyses are needed to reveal organizational principles of these networks to investigate the details of functional and regulatory clusters of proteins. In the present work, individual clusters identified by an eigenmode analysis of the connectivity matrix of the protein-protein interaction network in yeast are investigated for possible functional relationships among the members of the cluster. With our functional clustering we have successfully predicted several new protein-protein interactions that indeed have been reported recently. Eigenmode analysis of the entire connectivity matrix yields both a global and a detailed view of the network. We have shown that the eigenmode clustering not only is guided by the number of proteins with which each protein interacts, but also leads to functional clustering that can be applied to predict new protein interactions. Some other applications of this type of analysis for the identification of important variable in a simulation will be considered.
Yannis G. Kevrekidis (Princeton University) Computational experiments in coarse-graining atomistic simulations
Abstract: I will present and discuss a number of computational experiments associated with the coarse-graining of atomistic/agent-based simulations. In particular, I will discuss coarse reverse integration, as well as the use of diffusion maps (a manifold-learning technique) to suggest the selection of certain coarse-grained observables ("reduction coordinates") for the atomistic simulations. The illustrations will come from molecular dynamics, Monte Carlo as well as agent-based models.
Soojeong Kim (University of Iowa) Topological analysis of DNA-binding protein complexes
Abstract: Difference topology is a methodology to derive the number of DNA crossings trapped in an unknown protein complex. By this method, Pathania, Jayaram, and Harshey revealed the topological structure within the Mu protein complex which consisted of three DNA segments containing five nodes [1]. In their experiments, they used a member of the site-specific recombinases which is known as Cre. Cre mediates DNA exchange by rearranging target sites of the DNA segments. During this DNA recombination, there are no extra DNA crossings introduced. The initial DNA conformation is unknotted. After Cre recombination, the products are knots or catenanes. Recently, Darcy, Luecke, and Vazquez analyzed these experimental results and proved that the five-noded conformation is the only biologically reasonable structure of the Mu protein DNA complex [2]. We address the possibility of protein complexes that binds four DNA segments. By the useful property of Cre, we can make the assumption that after Cre recombination, the topology of a DNA-protein complex would be a knot or catenane. The latest results of the topological tangle model for this case and very basic biological and mathematical backgrounds will be discussed. Reference: [1] S. Pathania, M. Jayaram, and R. Harshey, Path of DNA within the Mu transpososome: Transposase interaction bridging two Mu ends and the enhancer trap five DNA supercoils, Cell 109 (2002), 425-436. [2] I. K. Darcy, J. Luecke, and M. Vazquez, A tangle analysis of the Mu transpososome protein complex which binds three DNA segments, Preprint.
Patrice Koehl (University of California) The geometry of biomolecular solvation. Part 1: Hydrophobicity
Abstract: The molecular basis of life rests on the activity of biological macro-molecules, mostly nucleic acids and proteins. A perhaps surprising finding that crystallized over the last handful of decades is that geometric reasoning plays a major role in our attempt to understand these activities. In my presentations, I will explore the connection between the biological activities of proteins and geometry, using a representation of molecules as a union of balls. I will cover three topics: (1) the geometry of biomolecular solvation, (2) understanding electrostatics using implicit solvent models, and (3), designing protein shape descriptors. Part 1: Hydrophobicity. The structure of a biomolecule is greatly influenced by its environment in the cell, which mainly consists of water. Explicit representation of the solvent that includes individual water molecules are costly and cumbersome. It is therefore highly desirable to develop implicit solvent models that are nevertheless accurate. In such models, hydrophobicity is expressed as a weighted sum of atomic accessible surface areas. I will show how these surface areas can be computed from the dual complex, a filtering of the weighted Delaunay triangulation of the centers of the atoms.
Patrice Koehl (University of California) Part 2: Electrostatics
Abstract: Electrostatics plays an important role in stabilizing a molecule. In an implicit solvent model, the electric field generated by a molecule is obtained as a solution of the Poisson-Boltzmann equation, a second order elliptic equation to be solved over the whole space within and around the molecule. Analytical solutions of this equation are not available for large molecules. Numerical solutions are usually obtained using finite element methods on regular meshes. These meshes however are not adequate to represent accurately the surface of the molecule that serves as interface between the interior of the molecule and the solvent. I will discuss the application of tetrahedral meshes for solving the Poisson-Boltzmann equation, based on the meshing of the skin surface of the molecule. The skin surface is a smooth, differentiable surface of the molecule.
Patrice Koehl (University of California) Part 3: Protein shape descriptors
Abstract: As the number of proteins for which a high resolution structure is known grow, it is important to classify them. A classification of protein structure would be useful for example to derive structural signatures for the protein functions. Classification requires a measure of protein structure similarity: while there are tools available to align and superpose protein structures, these tools are usually slow and not practical for large scale comparisons. In this talk, I will discuss the development of protein shape descriptors that allow fast detection of similarity between protein structures.
Samuel Kou (Harvard University) Exploring global energy landscape of lattice protein models via Monte Carlo methods
Abstract: Efficient exploration of the configuration space of a protein is essential for its structure prediction. In this talk we will consider two recent Monte Carlo developments for such a task: (i) equi-energy (EE) sampler and (ii) fragment regrowth via energy-guided sequential sampling (FRESS). The EE sampler provides accurate estimation of the density of states of the energy landscape, which then allows detailed study of the thermodynamics of lattice protein folding. The FRESS algorithm provides an efficient means to sequentially simulate a protein structure. As an illustration we will consider 2D and 3D HP models. For the benchmark sequences, we not only found new lower energies for all the 3D sequences longer than 80 residues with little computing effort, but also were able to accurately estimate the density of states that characterizes the global energy landscape.
Peter R. Kramer (Rensselaer Polytechnic Institute) Coarse-grained parameterizations of biomolecular systems
Abstract: I discuss two ongoing research programs concerning stochastic microphysical models in biology. First, in joint work with Grigorios Pavliotis (Imperial College) and Juan Latorre, we apply the methods of homogenization theory to compute transport properties for mathematical models (Brownian motors) of molecular motors in cells. The objective is to ascertain how the design properties of the motor affect its function. Secondly, in joint work with Shekhar Garde and Adnan Khan, we explore a simple stochastic model for the behavior of water molecules near a solute surface which has the potential for improving substantially upon Brownian dynamics models more conventionally used in engineering applications. We use exactly solvable mathematical models as a testbed for addressing some basic data-driven parameterization issues.
Krzysztof Kuczera (University of Kansas) Simulations of peptide folding and dynamics
Abstract: We report on replica-exchange simulations of the folding of a 21-residue alpha-helical peptide in explicit solvent. Using eight replicas over a 280-450 K temperature range, we were able to simulate both the folding equilibrium and the helix formation process. While the melting temperature was exaggerated by about 50 K, the folding enthalpy and entropy were in good agreement with experimental data. Simulations of the helix formation process showed a sequential mechanism, with helical structures formed within ca. 3 ns of simulation, and confirmed that the alpha-helical state was a global free energy minimum of the peptide at low temperatures. We also present long-term conventional MD simulations of several simple peptide model systems for which we compare simulation results to experimental data, in order to test current peptide and water models.
Satish Kumar (University of Minnesota) Brownian dynamics simulations of polymer behavior in nanofluidic and microfluidic systems
Abstract: Brownian Dynamics (BD) is a stochastic simulation method that can quantitatively describe the non-equilibrium behavior of long polymers (~1 micron contour length) over long time scales (~1 s). With the increasing use of nanofluidic and microfluidic devices for the handling of biopolymers such as DNA, BD has the potential to be a powerful design tool for the separation and transport processes carried out in these devices. As a coarse-grained simulation method, BD also serves as a natural bridge between atomistic and continuum modeling. In this talk, an introduction to the Brownian Dynamics simulation method will be given along with simulation results for some applications of current interest. The introduction will review basic molecular models for polymers (bead-rod, bead-spring) and the stochastic differential equations used to describe their dynamics. The applications will focus on polyelectrolyte adsorption and electrophoresis.
Christian E. Laing (New York University) Annotated tertiary interactions in RNA structures reveal new interactions, correlations in motifs and composite motifs
Abstract: RNA tertiary motifs play an important role in RNA folding. To understand the complex organization of RNA tertiary interactions, we compiled a dataset containing 54 high-resolution RNA crystal structures. Seven RNA tertiary motifs (coaxial helix, A-minor, ribose zipper, pseudoknot, kissing hairpin, tRNA D-loop:T-loop and tetraloop-tetraloop receptor) were searched by different computer programs. For the non-redundant RNA dataset, 601 RNA tertiary interactions were found. Most of these 3D interactions occur in the 16S and 23S rRNAs. Exhaustive search of these motifs revealed diversity of A-minor interactions, and other loop-loop receptor interactions similar to the tetraloop-tetraloop receptor. Correlation between motifs, such as pseudoknot or coaxial helix with A-minor, shows that they can form composite motifs. These findings may lead to tertiary structure constraints for RNA 3D prediction.
Christopher J. Lee (University of California) Mapping evolutionary pathways of HIV-1 drug resistance using conditional selection pressure
Abstract: Can genomics provide a new level of strategic intelligence about rapidly evolving pathogens? We have developed a new approach to measure the rates of all possible evolutionary pathways in a genome, using conditional Ka/Ks to estimate their “evolutionary velocity”, and have applied this to several datasets, including clinical sequencing of 50,000 HIV-1 samples. Conditional Ka/Ks predicts the preferred order and relative rates of competing evolutionary pathways. We recently tested this approach using independent data generously provided by Shafer and coworkers (Stanford HIV Database), in which multiple samples collected at different times from each patient make it possible to track which mutations occurred first during this time-course. Out of 35 such mutation pairs in protease and RT, conditional Ka/Ks correctly predicted the experimentally observed order in 28 cases (p=0.00025). Conditional Ka/Ks data reveal specific accessory mutations that greatly accelerate the evolution of multi-drug resistance. Our analysis was highly reproducible in four independent datasets, and can decipher a pathogen’s evolutionary pathways to multi-drug resistance even while such mutants are still rare. Analysis of samples from untreated patients shows that these rapid evolutionary pathways are specifically associated with drug treatment, and vanish in its absence.
Michael Levitt (Stanford University) Lecture 1: Fundamental forces and molecular architecture
Abstract: Over the last three decades computer simulation have been able to bring atomic motion to structural biology. Such motion is not seen in experimental structural studies but is relatively easily studied by applying law of motions to models of the proteins and nucleic acids. By bringing molecular to life in this way, simulation complements experimental work making it is much easily to understand how proteins biological macromolecules function. After introducing molecular structure and the fundamental forces that stabilize it, we consider molecular motion and protein folding. Lecture 1 will introduce fundamental forces between atoms and consider how these forces give rise to the stable protein structures.
Michael Levitt (Stanford University) Lecture 2: Simulating molecular motion
Abstract: Lecture 2 will describe the complementary methods of simulation: molecular dynamics and normal mode dynamic. We will show how they help understand the stability and the nature of protein motion.
Michael Levitt (Stanford University) Lecture 3: Simulating protein folding
Abstract: Lecture 3 will consider the protein folding both in terms of predicting the most stable structure and simulating the actual folding pathways.
Ronald M. Levy (Rutgers University) Simple models for simulating replica exchange simulations of protein folding and binding
Abstract: Replica exchange (RE) is a generalized ensemble simulation method for accelerating the exploration of free-energy landscapes which define many challenging problems in computational biophysics, including protein folding and binding. Although replica exchange is a parallel simulation technique whose implementation is relatively straightforward, kinetics and the approach to equilibrium in the replica exchange ensemble are complicated; there is much to learn about how to best employ RE to protein folding and binding problems. Protein folding rates often slow down as the temperature is raised above a critical value and this “anti-Arrhenius” behavior represents a challenge for RE. However, it is far from straightforward to systematically explore the impact of this on RE by brute force molecular simulations, since RE simulations of protein folding are very difficult to converge. In studies over the past two years using both atomistic and simplified models, we have clarified some of the obstacles to obtaining converged thermodynamic information from RE simulations. In my talk I will describe some simple continuous and discrete models we have constructed to explore the behavior of replica exchange sampling under a variety of conditions. References Andrec, M., A.K. Felts, E. Gallicchio, and R.M. Levy. Protein folding pathways from replica exchange simulations and a kinetic network model. Proceedings Natl. Acad. Sci. USA, 102, 6801-6806 (2005). K.P. Ravindranathan, E. Gallicchio, R.A. Friesner, A.E. McDermott, and R.M. Levy. Conformational equilibrium of a cytochrome P450 – substrate complex, a replica exchange MD study. J. Am. Chem. Soc., 128, 5786-5791 (2006) Zheng, W., M. Andrec, E. Gallicchio, and R.M. Levy. Simulating replica exchange simulations of protein folding with a kinetic network model. Proceedings Natl. Acad. Sci. USA, 104, 15340-15345 (2007). Zheng, W., M. Andrec, E. Gallicchio, and R.M. Levy. Simple continuous and discrete models for simulating replica exchange simulations of protein folding. J. Phys. Chem., in press.
Florence J. Lin (University of Southern California) Overall rotation due to internal motions in the N-body dynamics of protein molecules
Abstract: For a protein molecule in vacuo, the net overall rotation due to flexibility is expressed in internal coordinates by using Eckart's decomposition of the total rotational angular momentum. Regardless of whether the total (rotational) angular momentum vanishes, the condition for zero overall rotation is zero orbital angular momentum. Previous approaches toward the elimination of overall rotation included (i) using normal modes, (ii) minimizing the root-mean-squared deviation (RMSD through finite rotations with respect to an initial configuration, and (iii) setting the total angular momentum to zero. These three approaches neglected the contribution of nonzero internal angular momentum. While this approach [1, 2] is motivated by results in geometric mechanics [3], the results agree with an experimental observation of a rotation of 20 degrees in triatomic photodissociation [4] and a computational observation of an overall rotation of 42 degrees in the dynamics of protein molecules [5]. References:
[1] F. J. Lin, Hamiltonian dynamics of atom-diatomic molecule complexes and collisions, Discrete and Continuous Dynamical Systems, Supplement 2007, 655 – 666 (2007).
[2] F. J. Lin, Separation of overall rotation and internal motion in the N-body dynamics of protein molecules, 2007a.
[3] J. E. Marsden, R. Montgomery, and T. Ratiu, Reduction, symmetry, and phases in mechanics, Memoirs of the American Mathematical Society, Vol. 88, No. 436, American Mathematical Society, Providence, RI, 1990.
[4] A. V. Demyanenko, V. Dribinski, H. Reisler, H. Meyer, and C. X. W. Qian, Quantum-product state-dependent anisotropies in photoinitiated unimolecular decomposition, Journal of Chemical Physics 111, 7383 – 7396 (1999).
[5] Y. Zhou, M. Cook and M. Karplus, Protein motions at zero-total angular momentum: The importance of long-range correlations, Biophysical Journal 79, 2902 – 2908 (2000).
Julie C. Mitchell (University of Wisconsin) Cluster optimization in protein docking
Abstract: Recent progress in obtaining docked protein complexes will be discussed. The combination of exhaustive search, clustering and localized global optimization can reliably find energy minima to highly nonconvex biomolecular energy functions. Using an energy function that adds desolvation and screened electrostatics to classical molecular mechanics potentials, the global minimum is found very near to the observed native state. This is demonstrated across a large number of benchmark examples.
Antonio Mucherino (Seconda Università di Napoli) Simulating protein conformations by a geometric model
Abstract: Protein molecules are usually studied through mathematical models which consider the physicochemical forces among the atoms forming the molecule. Recently, however, the interest on the geometric properties of protein conformations has been growing, and models mainly based on such properties have been developed. In this work, a global optimization problem is formulated for simulating protein conformations, that is based on the so-called "tube model", in which a protein is modeled as a thickened tube [1,2]. The optimization problem is solved by the meta-heuristic method Monkey Search [3], which is inspired by the behavior of a monkey climbing trees in its search for food. Computational experiences proved that conformations having the typical geometric properties of proteins can be generated and that some of them can be close to conformations that proteins in Nature actually have. [1] J.R. Banavar, A. Maritan, C. Micheletti and A. Trovato, "Geometry and Physics of Proteins", Proteins: Structure, Function, and Genetics 47 (3): 315–322, 2002 [2] G. Ceci, A. Mucherino, M. D’Apuzzo, D. di Serafino, S. Costantini, A. Facchiano, G. Colonna, "Computational Methods for Protein Fold Prediction: an Ab-Initio Topological Approach", Data Mining in Biomedicine, Springer Optimization and Its Applications, Panos Pardalos et al (Eds.), vol.7, 2007 [3] A. Mucherino and O. Seref, "Monkey Search: A Novel Meta-Heuristic Search for Global Optimization", AIP Conference Proceedings 953, Data Mining, System Analysis and Optimization in Biomedicine, 162–173, 2007
José Nelson Onuchic (University of California, San Diego) The energy landscape for folding and molecular motors
Abstract: Globally the energy landscape of a folding protein resembles a partially rough funnel. The local roughness of the funnel reflects transient trapping of the protein configurations in local free energy minima. The overall funnel shape of the landscape, superimposed on this roughness, arises because the interactions present in the native structure of natural proteins conflict with each other much less than expected if there were no constraints of evolutionary design to achieve reliable and relatively fast folding (minimal energetic frustration). A consequence of minimizing energetic frustration is that the topology of the native fold also plays a major role in the folding mechanism. Some folding motifs are easier to design than others suggesting the possibility that evolution not only selected sequences with sufficiently small energetic frustration but also selected more easily designable native structures. The overall structure of the on-route and off-route (traps) intermediates for the folding of more complex proteins is also strongly influenced by topology. In this context, folding of larger and more complex proteins will be discussed. Many cellular functions rely on interactions among proteins and between proteins and nucleic acids. The limited success of binding predictions may suggest that the physical and chemical principles of protein binding have to be revisited to correctly capture the essence of protein recognition. Going beyond folding, the power of reduced models to study the physics of protein assembly will be discussed. Since energetic frustration is sufficiently small, native topology-based models, which correspond to perfectly unfrustrated energy landscapes, have shown that binding mechanisms are robust and governed primarily by the protein’s native topology. These models impressively capture many of the binding characteristics found in experiments and highlight the fundamental role of flexibility in binding. Deciphering and quantifying the key ingredients for biological self-assembly is invaluable to reading out genomic sequences and understanding cellular interaction networks. Going even beyond binding, we will be discussing the energy landscape for the molecular motor kinesin.
Hans G. Othmer (University of Minnesota) Current issues in understanding complex biological networks
Abstract: Biological networks that arise in signal transduction, metabolism, gene control or other cellular functions frequently involve many steps and many levels of control, but are remarkably reliable in producing the desired output in response to inputs. In this talk we will discuss general characteristics such as sensitivity and adaptation of networks, give several examples that illustrate how robustness is achieved, and discuss the mathematical techniques that can contribute to understanding complex networks.
Sefika Banu Ozkan (Arizona State University) Protein folding by ZAM & FRODA
Abstract: Protein folding by ZAM & FRODA Protein folding problem’ stemming from Levinthal’s paradox (i.e. how proteins fold fast even though they have vast conformational space) has been answered by the zipping and assembly mechanism (ZA). According to ZA mechanism, an unfolded chain first explores locally favorable structures at multiple independent positions along the chain. Then, these local structures engage neighboring amino acids in the chain sequence to form additional contacts, growing individual local structures by zipping or assembling. Using ZA principle, an all-atom structure prediction method has been developed, called zipping and assembly method (ZAM). ZAM has successfully predicted protein structures of small single domain proteins. It uses replica exchange molecular dynamics for conformational sampling which creates a bottleneck in the assembly stage. We modify ZAM assembly stage by introducing FRODA which is a Monte Carlo based geometric simulation. Since FRODA can explore the large-amplitude motions of larger systems so much faster than molecular dynamics, we can speed up the assembly stage and generate the complete enumeration of all topologies quickly. The results show that the native structure of proteins can be sampled during the FRODA-assembly stage within a RMSD <3 Å.
Sanghyun Park (Argonne National Laboratory) Computing conformational free energy by deactivated morphing
Abstract: "What is the free energy difference between two different conformations of a protein?" This simple question is apparently not so simple to answer. Despite the significant advances in free energy computations, there has been relatively little success in computing conformational free energies. To compute conformational free energy differences, we need a transformation path that connects different conformations. The free energy difference is the same no matter what path is taken, but not all paths are equally useful. Finding a path that allows an efficient computation of free energy is a crucial step. Tremendous recent efforts to find physical paths of conformational changes have motivated us to take a stab at using nonphysical paths. This poster introduces a method we call 'deactivated morphing' and presents applications to two test systems: alanine dipeptide (AlaD) and deca-alanine (Ala10), both in explicit water. In this method, the internal interaction of a protein is completely turned off before a transformation is carried out along a nonphysical path.
Bobby Philip (Los Alamos National Laboratory) An introduction to multigrid techniques
Abstract: The lecture will be a basic introduction to multigrid techniques. It will cover some background on stationary iterative methods. The two main components of linear multigrid algorithms: smoothing and coarse-grid correction will be introduced. A two grid algorithm will be introduced that then leads to the description of the multilevel Vand W-cycles. A brief description of algebraic multigrid methods will be followed by a description of the Full Approximation Scheme (FAS) for nonlinear problems. Time permitting, the generalization of these algorithms to handle grids with local refinement will also be outlined.
Jed W. Pitera (IBM Research Division) The limitations of temperature replica exchange (T-REMD) for protein folding
Abstract: The replica exchange/parallel tempering method and its variations offer the hope of improved sampling for many challenging problems in molecular simulation. Like all sampling methods, however, the effectiveness of replica exchange is highly dependent on the specific physical system being studied. We have carried out large scale temperature replica exchange (T-REMD) simulations of peptides and proteins in explicit solvent and encountered a number of issues that limit the effectiveness of the method in sampling biomolecular conformations. In particular, our results suggest the need to either replace or augment the temperature variable with an alternative extended variable, such as Hamiltonian scaling.
Hong Qian (University of Washington) From chemical reaction systems to cellular states: A computational approach
Abstract: The task of molecular biology is to identify and define cellular states and functions in terms of molecular structures, dynamics, and chemical reactions. At macromolecular level, functional states and dynamics of individual proteins and enzymes are determined by Newton's Law and/or statistical thermodynamics. Computational approach thus follows molecular dynamic simulations and statistical thermodynamics. At cellular level, "the structures" of biochemical reaction systems, i.e., metabolic networks, genetic regulatory modules and signaling pathways, have been the central focus of current reserch. We introduce the chemical master equation (CME) as the theoretical foundation of their dynamics. Dynamic models based on the CME represent open chemical systems that follow nonequilibrium statistical thermodynamics - a key ingredient for living cell but not in usual macromolecular models. The CME supersedes the traditional deterministic models based on the law of mass action; it provides reaction kinetics and concentration (or copy number) fluctuations; and it allows a rigorous definition of "cellular state(s)" in terms of the concentrations and copy numbers of biomolecules in a biochemical reaction system in open chemical environment. We discuss this computational approach to cellular biochemistry, its relation to open-system thermodynamics. In particular we outline its similarities to and distinctions from computational macromolecular dynamics.
Andrew J. Rader (Indiana University-Purdue University) Probing the diversity of unfolding pathways by simulated thermal denaturation
Abstract: In many cases the native structures of proteins encode information about their folding pathways. The degree to which this is true may be related to the similarity of various structural solutions, i.e. multiple NMR structures or independently solved X-ray structures. We explore both the robustness of the native state and its impact upon putative folding pathways for these structures by examining simulated thermal denaturation pathways for ensembles of “native” structures. Previous rigidity analysis of proteins using the FIRST software[1] has demonstrated that such simulated unfolding results correlate well with experimental hydrogen-deuterium exchange data[2] and mutational results[3]. We introduce an unfolding rigidity profile to characterize unfolding pathways and indicate which protein residues are most likely to adopt native-like conformations. This rigidity profile is also used to discriminate conformational sub-states of the protein native state which are the results of different folding pathways. [1] D. J. Jacobs, A.J. Rader, Leslie A. Kuhn, and M.F. Thorpe Protein Flexibility Prediction Using Graph Theory. Proteins, 44, 150-165, 2001. [2] B.M. Hespenheide, A.J. Rader, M.F. Thorpe, and L.K. Kuhn J. Molec. Graph. & Model., 21, 195-207, 2002. [3] A.J. Rader, G. Andersen, B. Isin, H.G. Khorana, I. Bahar and J. Klein-Seetharaman Identification of Core Amino Acids Stabilizing Rhodopsin. Proc. Natl. Acad. Sci., 101, 7246-7251, 2004.
Shantanu Roy (Universität Basel) Minima Hopping within an all-atom framework for biomolecular structure prediction
Abstract: We consider the protein folding problem as a global optimization problem on the free energy surface of the all-atom OPLS force field. Starting from amino acid sequences arranged in a linear chain configuration we use the Minima Hopping algorithm to find low energy configurations . The algorithm samples the potential energy surface following the Bell-Evans-Polanyi principle. In this way our moves are completely unbiased but have nevertheless a strong tendency to lead into other low energy configurations. Some small peptides like polyalanine were studied in vacuo. For an Ac(Ala)nLysH+ in vacuum we obtained a helical conformation while other (Ala)nH+ systems are found to be not helical.
Anchanee Sangcharoen (Mahidol University ) Investigation of the unfolding pathway of Cyt2Aa2 toxin
Abstract: The expressed 29-kDa Cyt2Aa2 protoxin is produced from Bacillus thuringiensis subsp. darmstadiensis during sporulation. This toxin is proteolytically processed into the 25-kDa active form which is lethal to Dipteran (Stegomyia and Culex) larvae. It has been proposed that the mechanism of action required a conformational change during the interaction with lipid membrane. We have demonstrated previously that the toxin can adopt a stable intermediate state between the transitions from native to unfolded state. In this study, we aim to investigate the conformational state of each secondary structure elements of the toxin in intermediate state. The Φ values analysis was employed as a tool to reveal the conformation state on various amino acid positions of toxin. Non-disruptive mutant toxins were designed and constructed as conformational probes using site-directed mutagenesis. The effect of mutation at different position is characterized in terms of protein expression level, solubility, mosquito-larvicidal toxicity and hemolytic activity compared to those of wild type. The results showed that an intermediate state of this toxin was found in the aggregation/oligomerization form. Transitional free energy and activation energy of these toxins were obtained and derived for the Φ values. The data revealed helices A, B and C of the intermediate are quite deviated from the native state while helix D is still maintained similar to native state conformation. The relocation of these helices was proposed to be related to the conformational changes and contributes to the functional mechanism of this toxin.
Jeffery G. Saven (University of Pennsylvania) Engineering protein structure and function with theoretical protein design
Abstract: Protein design opens new ways to probe the determinants of folding, to facilitate the study of proteins, and to arrive at novel molecules, materials and nanostructures. Recent theoretical methods for identifying the properties of amino acid sequences consistent with a desired structure and function will be discussed. Such methods address the structural complexity of proteins and their many possible amino acid sequences. Several computationally designed protein-based molecular systems will be presented that have been experimentally realized, including novel proteins tailored to accommodate nonbiological cofactors.
Brigitte Servatius (Worcester Polytechnic Institute) Combinatorial rigidity and the molecular conjecture
Abstract: Graph theory has successfully been used by several authors to predict protein flexibility, in particular, combinatorial rigidity is an important tool. The most important new result in combinatorial rigidity is the characterization of global rigidity while one of the most intriguing open problems is called "the molecular conjecture". We will explain the state of the art in the progress toward the conjecture and the implications of recent progress in rigidity theory, including the concept of combinatorial allostery, toward understanding the behavior of molecules.
Carlos L. Simmerling (SUNY) Challenges in generation of conformational ensembles for peptides and small proteins
Abstract: Useful insight into the folding behavior of proteins has been gained by studying the free energy landscapes of model peptides and very small proteins. These can be particularly useful in exploring the denatured state, which is difficult to characterize directly through experiments. Several key challenges remain in obtaining accurate and precise computational data for peptides in solution, including the accuracy of the biomolecular force field and solvent model along with difficulties in obtaining converged ensembles. In this talk these issues will be explored, including a comparison of the properties of several Amber parameter sets and the effects of simulation with different explicit and implicit water models. Methods that improve convergence will be discussed, such as modified replica exchange approaches that permit application to larger systems at reduced computational cost.
Robert D. Skeel (Purdue University) What is a transition path?
Abstract: Calculating transition paths of conformation change is not amenable to computer solution unless the problem is defined precisely. Inspired by the work of others, we offer a precise definition of the problem without invoking unmotivated stochastic forces. A weakness of this--and other--approaches is the need for the user to identify an appropriate set of collective variables. In principal at least, the quality of the result can be checked a posteriori by calculating committor values from dynamics trajectories. The approach we advocate leads to a nonstandard minimum free energy path that is more reasonable physically.
Ileana Streinu (Smith College) Geometric simulation of protein flexibility
Abstract: Solved protein structures from PDB depict a static picture, but proteins are flexible. We are interested in understanding how they move near the native conformation, or between two given conformations, without resorting to heavy-duty molecular dynamics techniques. Geometric simulations focus on motions of constrained structures behaving much like mechanical devices, without concern for certain forces (such as electrostatic or hydrophobic interactions). The idea is to isolate specific problems (pertaining to maintenance of geometric distance and angle constraints, or to collisions), and develop the mathematical and computational tools for addressing them efficiently. We will describe static flexibility analysis tools pioneered in the FIRST software, first-generation geometric simulation as done in FRODA, and recent methods aiming at speeding them up.
William Swope (IBM) Simulations on BlueGene of a fast folding mutant of lambda(6-85)
Abstract: Using the BlueGene computer at IBM Research we have performed extensive simulations on a mutant construct of lambda repressor. The protein consists of 80 amino acids stuctured as a five helix bundle in the folded state. The mutant was designed in the Gruebele lab at UIUC to exhibit sub-10 microsecond folding times in laser temperature jump experiments. Our simulations employed replica exchange and traditional molecular dynamics at a number of different temperatures. Although it is very difficult to thoroughly equilibrate and sample molecular systems of this size and complexity, our simulations clearly reveal very complex folding behavior. In particular, different structural elements exhibit different degrees of thermodynamic stability and melt at different temperatures. Some of the structural transitions appear to be relatively cooperative, whereas others are quite diffuse.
Sandor Vajda (Boston University) Multistage optimization for protein-protein docking
Abstract: We focus on the problem of determining the structure of complexes formed by the association of two proteins by searching for the global minimum of a function approximating the free energy of the complex. Solving this problem requires the combination of a number of different optimization methods. First we explore the conformational space by systematic global search based on the Fast Fourier Transform (FFT) correlation approach that evaluates the energies of billions of docked conformations on a grid. We show that the method can be efficiently used with pairwise interactions potentials that substantially improve the docking results. A new 5D FFT algorithm is also discussed. The 1000 best energy conformations are clustered, and the 30 largest clusters are retained for refinement. The conformations are refined by a new medium-range optimization method that has been developed to locate the global minima within well defined regions of the conformational space. In each cluster, the energy of the complex is a very noisy funnel-like function on the space of rigid body motions, the Euclidean group SE(3). The Semi-Definite programming based Underestimation (SDU) method constructs a convex quadratic under-estimator to the energy funnel based on a sample of the local mimima of the energy function, and uses the quadratic under-estimator to guide future sampling. We show that the parameterization of SE(3) has a significant impact on the effectiveness of SDU and introduce a parameterization that dramatically reduces the number of very costly energy function evaluations. We also discuss the application of the combined method to recent targets in CAPRI (Critical Assessment of Protein Interactions), the first community-wide docking experiment.
Jérôme Waldispühl (Massachusetts Institute of Technology) Modeling ensembles of transmembrane beta-barrel proteins
Abstract: Transmembrane beta-barrel (TMB) proteins are embedded in the outer membrane of Gram-negative bacteria, mitochondria, and chloroplasts. Despite their importance, very few nonhomologous TMB structures have been determined by X-ray diffraction because of the experimental difficulty encountered in crystallizing transmembrane proteins. We introduce the program partiFold to investigate the folding landscape of TMBs. By computing the Boltzmann partition function, partiFold estimates inter--strand residue interaction probabilities, predicts contacts and per-residue X-ray crystal structure B-values, and samples conformations from the Boltzmann low energy ensemble. This broad range of predictive capabilities is achieved using a single, parameterizable grammatical model to describe potential beta-barrel supersecondary structures, combined with a novel energy function of stacked amino acid pair statistical potentials. PartiFold outperforms existing programs for inter--strand residue contact prediction on TMB proteins, offering both higher average predictive accuracy as well as more consistent results. Moreover, the integration of these contact probabilities inside a stochastic contact map can be used to infer a more meaningful picture of the TMB folding landscape, which cannot be achieved with other methods. Partifold's predictions of B-values are competitive with recent methods specifically designed for this problem. Finally, we show that sampling TMBs from the Boltzmann ensemble matches the X-ray crystal structure better than single structure prediction methods. A webserver running partiFold is available at http://partiFold.csail.mit.edu/. Joint work with: Charles W. O'Donnell, Srini Devadas, Peter Clote and Bonnie Berger. References:
[1] J. Waldispühl*, C.W. O'Donnel*, S. Devadas, P. Clote and B. Berger, Modeling Ensembles of Transmembrane beta-barrel Proteins, PROTEINS: Structure, Function and Bioinformatics, published online 14 Nov. 2007. doi:10.1002/prot.21788
(* authors equally contributed)
[2]J. Waldispühl, B. Berger, P. Clote and J.-M. Steyaert, Predicting Transmembrane beta-barrels and Inter-strand Residue Interactions from Sequence, PROTEINS: Structure, Function and Bioinformatics, vol. 65, issue 1, p.61-74, 2006.
doi:10.1002/prot.21046
Jin Wang (SUNY) Configuration-dependent diffusion can shift the kinetic transition state and barrier height of protein folding
Abstract: We show that diffusion can play an important role in proteinfolding kinetics. We explicitly calculate the diffusion coefficient of protein folding in a lattice model. We found that diffusion typically is configuration- or reaction coordinate-dependent. The diffusion coefficient is found to be decreasing with respect to the progression of folding toward the native state, which is caused by the collapse to a compact state constraining the configurational space for exploration. The configuration- or position-dependent diffusion coefficient has a significant contribution to the kinetics in addition to the thermodynamic free-energy barrier. It effectively changes (increases in this case) the kinetic barrier height as well as the position of the corresponding transition state and therefore modifies the folding kinetic rates as well as the kinetic routes. The resulting folding time, by considering both kinetic diffusion and the thermodynamic folding free-energy profile, thus is slower than the estimation from the thermodynamic free-energy barrier with constant diffusion but is consistent with the results from kinetic simulations. The configuration- or coordinate-dependent diffusion is especially important with respect to fast folding, when there is a small or no free-energy barrier and kinetics is controlled by diffusion. Including the configurational dependence will challenge the transition state theory of protein folding. The classical transition state theory will have to be modified to be consistent. The more detailed folding mechanistic studies involving phi value analysis based on the classical transition state theory also will have to be modified quantitatively.
Guowei Wei (Michigan State University) Mathematical methods for implicit solvent models
Abstract: Rigorous, quantitative, and atomic scale description of complex biological systems is a grand challenge. Explicit description of biomolecules and their aqueous environment, including solvent, co-solutes, and mobile ions, is prohibitively expensive although a variety of methods, including Ewald summations, Euler summations, periodic images and reaction field theory, have been developed in the past few decades. Therefore, multiscale analysis is an attractive and sometimes indispensable approach. Implicit solvent models which treat the solvent as a macroscopic continuum while admitting a microscopic atomic description for the biomolecule, are efficient multiscale approaches to complex, large scale biological systems. We summarize recent advances in mathematical methods for the Poisson-Boltzmann (PB) equation based implicit solvent theory. These include the rigorous mathematical treatments of molecular surface interfaces, surface geometric singularities, charge singularities and associated force evaluation for molecular dynamics.
Thomas Weikl (Max Planck Institute for Colloids and Interfaces) Transition states in protein folding
Abstract: Small single-domain proteins often exhibit only a single free-energy barrier, or transition state, between the denatured and the native state. The folding kinetics of these proteins is usually explored via mutational analysis. A central question is which structural information on the transition state can be derived from the mutational data. To interpret these data, we have developed models that are based (a) on the substructural cooperativity of helices and hairpins, and (b) on splitting up mutation-induced stability changes of a protein into components for its substructures. We obtain a consistent structural interpretation of mutational Phi-values by fitting few parameters that describe the degrees of structure formation of helices and hairpins in the transition state. Our models explain how mutations at a given site can lead to different Phi-values, and capture non-classical Phi-values smaller than 0 or larger than 1, which have been difficult to interpret. Non-classical Phi-values simply arise, e.g., if mutations stabilize a helix or hairpin, but destabilize its tertiary interactions. References:
[1] C. Merlo, K. A. Dill, and T. R. Weikl, PNAS 102, 10171 (2005).
[2] T. R. Weikl and K. A. Dill, J. Mol. Biol. 365, 1578 (2007).
[3] T. R. Weikl, Biophys. J., in press (2008).
Lauren Wickstrom (SUNY) The Dynamic Nature of the Folded and Unfolded States of the Villin Headpiece Helical Subdomain: An ultrafast folding protein
Abstract: In order to understand protein folding, we need to understand both folded and unfolded state structure. One of the key systems for these studies is the 36 residue villin headpiece helical subdomain (HP36) because of its simple topology, small size and fast folding properties. Structures of HP36 have been determined using X-ray crystallography and NMR spectroscopy, with the resulting structures exhibiting clear structural differences. We complement the existing data by using molecular dynamics simulations and experimental double mutant cycles to show that the x-ray structure is the better representation in solution at neutral conditions. Denatured state studies using fragment analysis coupled with relatively low resolution spectroscopic techniques show a small tendency to form locally stabilized structure. Using standard Replica Exchange Molecular Dynamics, our simulations show that the first helix contains the most native-like helical structure of all three helices. Overall, our analysis shows how theoretical and experimental collaborative efforts can help aid in the understanding of the dynamic nature of the folding pathway.
Zhijun Wu (Iowa State University) The solution of the distance geometry problem for protein modeling
Abstract: A well-known problem in protein modeling is the determination of the structure of a protein with a given set of inter-atomic or inter-residue distances obtained from either physical experiments or theoretical estimates. A general form of the problem is known as the distance geometry problem in mathematics, the graph embedding problem in computer science, and the multidimensional scaling problem in statistics. The problem has applications in many other scientific and engineering fields as well such as sensor network localization, image recognition, and protein classification. We describe the formulations and complexities of the problem in its various forms, and introduce a geometric buildup approach to the problem. Central to this approach is the idea that the coordinates of the atoms in a protein can be determined one atom at a time, with the distances from the determined atoms to the undetermined ones. The determination of each atom requires the solution of a small system of distance equations, which can usually be obtained in constant time. Therefore, in ideal cases, the coordinates of n atoms can be determined by a geometric buildup algorithm with O(n) distances in O(n) computing time instead of O(n2) distances in O(n2) computing time as required by a conventional singular-value decomposition algorithm. We present the general algorithm and discuss the methods for controlling the propagation of the numerical errors in the buildup process, for determining rigid vs. unique structures, and for handling problems with inexact distances (distances with errors). We show the results from applying the algorithm to a set of model protein problems with varying degrees of availability and accuracy of the distances and justify the potential use of the algorithm in protein modeling practice.
Jiaan Yang (MicrotechNano) A novel method for protein folding shape description
Abstract: A novel method has been developed to describe the protein folding shape structures. A set of 27 vectors is generated from an enclosed geometric space to describe the protein backbone folding shapes. This algorithm has mathematically reserved all possible folding shapes in space, and it is capable of making the complete assignment of folding shapes along the protein backbone without any gap. All possible types of folding can be uniquely described, including the regular protein secondary structures, irregular turn and loop structures and even rare possible folding structures. This method offers a simple one-dimensional description for the complicated three-dimensional folding structures which is able to align with the protein sequence for structural comparison. The results are compared with the protein data bank (PDB) and the structural assignments of other methods. This method has the ability to reveal the protein structural similarity and dissimilarity with the accurate and consistent meaning.
Sichun Yang (University of Chicago) Temperature dependence of Trp-cage folding kinetics from replica exchange simulations
Abstract: We examine the temperature dependence of the folding time in the Trp-cage mini-protein, using all-atom replica exchange molecular dynamics (REMD) simulations. This is done by using an "equation free" approach. The central idea is to use REMD simulations to generate appropriately initialized bursts of atomistic simulation trajectories to obtain the drift and diffusion coefficients of coarse variables of interest to capture quantitatively the coupling of fast with slow moving degrees of freedom. Then we employ a stochastic (Langevin) dynamic approach to follow the evolution of coarse variables and compute a distribution of folding times that is consistent with the drift and diffusion coefficients obtained from all-atom simulations. We use physically motivated order parameters as coarse variables. We describe the distribution of folding times as a function of temperature for the Trp-cage mini-protein.
Visitors in Residence
Hoda Abdel-Aal Bettley University of Manchester 1/13/2008 - 1/18/2008
Nancy M. Amato Texas A & M University 1/13/2008 - 1/18/2008
David F Anderson University of Wisconsin 1/13/2008 - 1/18/2008
Douglas N. Arnold University of Minnesota 7/15/2001 - 6/30/2008
Donald G. Aronson University of Minnesota 9/1/2007 - 8/31/2009
Rolf Backofen Albert-Ludwigs-Universität Freiburg 1/13/2008 - 1/18/2008
Ivet Bahar University of Pittsburgh 1/13/2008 - 1/24/2008
Nathan A. Baker Washington University School of Medicine 1/13/2008 - 1/17/2008
Daniel J. Bates University of Minnesota 9/1/2006 - 8/31/2008
John Baxter University of Minnesota 8/1/2007 - 7/30/2009
Yermal Sujeet Bhat University of Minnesota 9/1/2006 - 8/31/2008
Victor Bloomfield University of Minnesota 1/15/2008 - 1/18/2008
Jamie Blundell University of Cambridge 1/9/2008 - 1/19/2008
Khalid Boushaba Iowa State University 1/16/2008 - 6/30/2008
Maria-Carme T. Calderer University of Minnesota 1/10/2008 - 1/18/2008
Hannah Callender University of Minnesota 9/1/2007 - 8/31/2009
Larry Carson 3M 1/10/2008 - 1/11/2008
Alessandro Cembran University of Minnesota 1/10/2008 - 1/18/2008
Hue-Sun Chan University of Toronto 1/13/2008 - 1/18/2008
Shi-Jie Chen University of Missouri 1/13/2008 - 1/18/2008
Alan C. Cheng Amgen Cambridge Research Center 1/13/2008 - 1/18/2008
Gregory S. Chirikjian Johns Hopkins University 1/11/2008 - 1/18/2008
Patrick L Coleman 3M 1/10/2008 - 1/11/2008
Ludovica Cecilia Cotta-Ramusino University of Minnesota 10/1/2007 - 8/30/2009
Evangelos A. Coutsias University of New Mexico 1/13/2008 - 1/18/2008
Lenore J. Cowen Tufts University 1/13/2008 - 1/19/2008
Isabel K. Darcy University of Iowa 9/1/2007 - 1/19/2008
Yuanan Diao University of North Carolina - Charlotte 1/9/2008 - 1/18/2008
Ken A. Dill University of San Francisco 1/13/2008 - 1/23/2008
Yang Ding Boston College 1/9/2008 - 1/19/2008
Olivier Dubois University of Minnesota 9/3/2007 - 8/31/2009
Oguz C. Durumeric University of Iowa 1/9/2008 - 1/12/2008
Ron Elber University of Texas 1/13/2008 - 1/18/2008
Claus Ernst Western Kentucky University 1/12/2008 - 1/18/2008
Elisenda Feliu University of Barcelona 1/13/2008 - 1/19/2008
Christodoulos A. Floudas Princeton University 1/8/2008 - 1/20/2008
Ece Cazibe Gaffarogullari University of Minnesota 1/10/2008 - 1/11/2008
Andrew Gillette University of Texas 1/9/2008 - 1/12/2008
Anant Godbole East Tennessee State University 1/13/2008 - 1/18/2008
Laura Rocio Gonzalez-Ramirez CINVESTAV 1/9/2008 - 1/18/2008
Jason E. Gower University of Minnesota 9/1/2006 - 8/31/2008
Sergei Grudinin INRIA Rhone-Alpes Research Unit 1/13/2008 - 1/18/2008
Esfandiar Haghverdi Indiana University 1/2/2008 - 6/30/2008
Omar Haq Rutgers University 1/9/2008 - 1/18/2008
Milena Hering University of Minnesota 9/1/2006 - 8/31/2008
Peter Hinow University of Minnesota 9/1/2007 - 8/31/2009
Kenneth Hinson University of North Carolina - Charlotte 1/13/2008 - 1/19/2008
Xia Hua Massachusetts Institute of Technology 1/13/2008 - 1/18/2008
Kimberly Jean Huerter University of Iowa 1/9/2008 - 1/11/2008
Gerhard Hummer National Institutes of Health (NIH) 1/15/2008 - 1/18/2008
Sorin Istrail Brown University 1/14/2008 - 1/18/2008
Filip Jagodzinski University of Massachusetts 1/9/2008 - 1/18/2008
Richard D. James University of Minnesota 9/4/2007 - 6/30/2008
Christopher Jarzynski University of Maryland 1/13/2008 - 1/18/2008
Robert L. Jernigan Iowa State University 1/13/2008 - 1/24/2008
Tiefeng Jiang University of Minnesota 9/1/2007 - 6/30/2008
Christopher Kauffman University of Minnesota 1/14/2008 - 1/18/2008
Yiannis Kaznessis University of Minnesota 1/15/2008 - 1/18/2008
Yannis G. Kevrekidis Princeton University 1/13/2008 - 1/18/2008
Abdul Khaliq Middle Tennessee State University 1/9/2008 - 1/19/2008
Soojeong Kim University of Iowa 8/30/2007 - 1/20/2008
Debra Knisley East Tennessee State University 8/17/2007 - 6/1/2008
Patrice Koehl University of California 1/9/2008 - 1/12/2008
Dmitry A. Kondrashov University of Chicago 1/13/2008 - 1/18/2008
Samuel Kou Harvard University 1/13/2008 - 1/18/2008
Dmytro Kozakov Boston University 1/13/2008 - 1/19/2008
Peter R. Kramer Rensselaer Polytechnic Institute 1/8/2008 - 6/30/2008
Krzysztof Kuczera University of Kansas 1/13/2008 - 1/18/2008
Satish Kumar University of Minnesota 1/22/2008 - 1/22/2008
Christian E. Laing New York University 1/9/2008 - 1/18/2008
Fumei Lam Brown University 1/13/2008 - 1/18/2008
Juan Latorre Rensselaer Polytechnic Institute 1/10/2008 - 6/30/2008
Audrey Lee University of Massachusetts 1/9/2008 - 1/18/2008
Chang Hyeong Lee Worcester Polytechnic Institute 10/14/2007 - 1/4/2008
Christopher J. Lee University of California 1/10/2008 - 3/10/2008
Michael Levitt Stanford University 1/9/2008 - 1/18/2008
Ronald M. Levy Rutgers University 1/13/2008 - 1/18/2008
Robert Michael Lewis College of William and Mary 1/9/2008 - 1/19/2008
Anton Leykin University of Minnesota 8/16/2006 - 8/15/2008
Timothy Lezon University of Pittsburgh 1/13/2008 - 1/18/2008
Florence J. Lin University of Southern California 1/14/2008 - 1/17/2008
Andy Lorenz Boston College 1/13/2008 - 1/19/2008
Roger Lui Worcester Polytechnic Institute 9/1/2007 - 6/30/2008
Laura Lurati University of Minnesota 9/1/2006 - 8/31/2008
Christopher Michael Maloney Brown University 1/14/2008 - 1/18/2008
Yi Mao Michigan State University 1/13/2008 - 1/18/2008
Ezra Miller University of Minnesota 9/1/2007 - 6/30/2008
Kenneth C. Millett University of California 1/10/2008 - 2/9/2008
Julie C. Mitchell University of Wisconsin 1/13/2008 - 1/18/2008
Alejandro Morales Valencia University of Guadalajara 1/9/2008 - 1/19/2008
Naoto Morikawa GENOCRIPT 1/8/2008 - 1/12/2008
Antonio Mucherino Seconda Università di Napoli 1/7/2008 - 1/21/2008
Chitra Narayanan Rutgers University 1/13/2008 - 1/18/2008
Junalyn Navarra-Madsen Texas Woman's University 1/9/2008 - 1/19/2008
Timothy Newman Arizona State University 9/1/2007 - 6/30/2008
Duane Nykamp University of Minnesota 9/1/2007 - 6/30/2008
David Odde University of Minnesota 1/9/2008 - 6/30/2008
Charles W. O'Donnell Massachusetts Institute of Technology 1/13/2008 - 1/19/2008
José Nelson Onuchic University of California, San Diego 1/15/2008 - 1/17/2008
Hans G. Othmer University of Minnesota 9/1/2007 - 6/30/2008
Sefika Banu Ozkan Arizona State University 1/13/2008 - 1/18/2008
Sanghyun Park Argonne National Laboratory 1/13/2008 - 1/18/2008
Ioannis Paschalidis Boston University 1/13/2008 - 1/18/2008
Bobby Philip Los Alamos National Laboratory 1/9/2008 - 1/18/2008
Jed W. Pitera IBM Research Division 1/16/2008 - 1/18/2008
Candice Price University of Iowa 1/9/2008 - 1/12/2008
Andrea Pugliese Università di Trento 1/14/2008 - 1/18/2008
Hong Qian University of Washington 1/13/2008 - 1/18/2008
Terrance Quinn Middle Tennessee State University 1/13/2008 - 1/18/2008
Andrew J. Rader Indiana University-Purdue University 1/14/2008 - 1/23/2008
Subramanian Ramamoorthy University of Edinburgh 1/13/2008 - 1/20/2008
Rahul Ravindrudu Iowa State University 1/9/2008 - 1/18/2008
Eric Rawdon University of St. Thomas 1/10/2008 - 6/30/2008
Stephane Redon INRIA Rhône-Alpes 1/12/2008 - 1/18/2008
Shantanu Roy Universität Basel 1/11/2008 - 1/20/2008
Anchanee Sangcharoen Mahidol University 1/12/2008 - 1/18/2008
Jeffery G. Saven University of Pennsylvania 1/13/2008 - 1/18/2008
Deena Schmidt University of Minnesota 9/1/2007 - 8/31/2009
Tamara Schmidt-Hegge University of Minnesota 1/10/2008 - 1/17/2008
Brigitte Servatius Worcester Polytechnic Institute 1/10/2008 - 2/8/2008
Chehrzad Shakiban University of Minnesota 9/1/2006 - 8/31/2008
Yang Shen Boston University 1/13/2008 - 1/19/2008
Carlos L. Simmerling SUNY 1/13/2008 - 1/18/2008
Zachariah Sinkala Middle Tennessee State University 1/12/2008 - 1/18/2008
Atilla Sit Iowa State University 1/11/2008 - 1/11/2008
Robert D. Skeel Purdue University 1/13/2008 - 1/18/2008
Daniel Smith University of Pittsburgh 1/9/2008 - 1/13/2008
Carlos Sosa University of Minnesota 1/14/2008 - 1/18/2008
Andrew Stein University of Minnesota 9/1/2007 - 8/31/2009
Benjamin Stottrup Augsburg College 1/8/2008 - 1/8/2008
Ileana Streinu Smith College 1/9/2008 - 1/18/2008
Kirk Sturtz US Air Force Research Laboratory 1/9/2008 - 1/9/2008
Vlad Sukhoy Iowa State University 1/11/2008 - 1/11/2008
Weitao Sun New Mexico State University 1/9/2008 - 1/19/2008
Vladimir Sverak University of Minnesota 9/1/2007 - 6/30/2008
William Swope IBM 1/13/2008 - 1/18/2008
Michael Tomasini Rutgers University 1/10/2008 - 1/18/2008
Alex Tropsha University of North Carolina 1/7/2008 - 1/13/2008
Erkan Tüzel University of Minnesota 9/1/2007 - 8/31/2009
George Vacek Hewlett Packard 1/13/2008 - 1/18/2008
Sandor Vajda Boston University 1/13/2008 - 1/19/2008
Jérôme Waldispühl Massachusetts Institute of Technology 1/13/2008 - 1/18/2008
Jin Wang SUNY 1/13/2008 - 1/18/2008
Zhian Wang University of Minnesota 9/1/2007 - 8/31/2009
Guowei Wei Michigan State University 1/13/2008 - 1/18/2008
Thomas Weikl Max Planck Institute for Colloids and Interfaces 1/13/2008 - 1/21/2008
Lauren Wickstrom SUNY 1/13/2008 - 1/18/2008
Sebastian Will Albert-Ludwigs-Universität Freiburg 1/13/2008 - 1/20/2008
Steven Wojtkiewicz University of Minnesota 1/10/2008 - 1/11/2008
Di Wu Western Kentucky University 1/9/2008 - 1/18/2008
Zhijun Wu Iowa State University 9/4/2007 - 6/1/2008
Chuan Xue University of Minnesota 1/10/2008 - 1/11/2008
Jiaan Yang MicrotechNano 1/13/2008 - 1/18/2008
Sichun Yang University of Chicago 1/13/2008 - 1/18/2008
Ya-xiang Yuan Chinese Academy of Sciences 1/9/2008 - 1/25/2008
Adam Zemla Lawrence Livermore National Laboratory 1/13/2008 - 1/19/2008
Hongchao Zhang University of Minnesota 9/1/2006 - 8/31/2008
Likun Zheng University of Minnesota 1/10/2008 - 1/11/2008
Carol L. Ecale Zhou Lawrence Livermore National Laboratory 1/13/2008 - 1/19/2008
Legend: Postdoc or Industrial Postdoc Long-term Visitor

IMA Affiliates:
3M, Arizona State University, Boeing, Carnegie Mellon University, Corning, ExxonMobil, Ford, General Electric, General Motors, Georgia Institute of Technology, Honeywell, IBM, Indiana University, Iowa State University, Johnson & Johnson, Kent State University, Lawrence Livermore National Laboratory, Lockheed Martin, Los Alamos National Laboratory, Medtronic, Michigan State University, Michigan Technological University, Microsoft Research, Mississippi State University, Motorola, Northern Illinois University, Ohio State University, Pennsylvania State University, Purdue University, Rice University, Rutgers University, Sandia National Laboratories, Schlumberger-Doll, Schlumberger-Doll Research, Seoul National University, Siemens, Telcordia, Texas A & M University, University of Central Florida, University of Chicago, University of Cincinnati, University of Delaware, University of Houston, University of Illinois at Urbana-Champaign, University of Iowa, University of Kentucky, University of Maryland, University of Michigan, University of Minnesota, University of Notre Dame, University of Pittsburgh, University of Tennessee, University of Texas, University of Wisconsin, University of Wyoming, US Air Force Research Laboratory, Wayne State University, Worcester Polytechnic Institute