# Break/Poster Session

Tuesday, November 17, 2015 - 3:30pm - 4:00pm

Keller 3-176

**Model-guided Investigations of Ras Signaling in Cancer**

Edward Stites (Washington University)

The Ras signaling network controls processes like cellular proliferation. Ras mutations that result in persistent signaling through the pathway are commonly found in cancer. The processes that regulate Ras have been well-studied and biochemically characterized. Previously, we have developed a mathematical model that accounts for these different processes. Modeling finds the network is generally robust, and that the different Ras mutants found in cancer typically take advantage of the same vulnerability. Modeling has led to multiple other insights, such as there is increased wild-type Ras signaling when a mutant is present, that processes believed to be inconsequential account for as much as half of the increased Ras pathway activation, and that combinations of Ras pathway mutations can be synergistic and appear to be enriched in cancer samples.The model has also been applied to problems in drug development and the role of Ras mutations in conferring resistance to anti-cancer agents.**Layering the Analysis and Design of Biomolecular Networks**

Thomas Prescott (University of Oxford)

An important goal of systems and synthetic biology is a framework that enables the analysis and design of biological systems as interconnections of simpler subsystems, each of which represents a well-defined systems-level functionality. Our recent work has presented a new framework for the

decomposition of biomolecular reaction network models that distinguishes between complementary modular and layered decomposition strategies. The layering framework can be used to quantify and analyse the nonlinear effects of composing multiple functionalities into a single system. We have also applied layered decomposition to the model reduction of timescale-separated systems; the resulting approximated model decomposes multi-scale dynamic behaviour into an imposition of state constraints and a slow adaptation, which enables the design of each independently in a synthetic biology context.**Permanence in Reaction Network Models**

James Brunner (University of Wisconsin, Madison)

Biological and biochemical networks are often modeled using power law differential equations which arise, for example, from the assumption of mass action kinetics on a reaction network. A permanent dynamical system is one that has a compact attracting set in real, positive phase space. In models of biological networks, this can be interpreted to mean that no extinction of any species occurs. The set of permanent power law dynamical systems has not been fully characterized, even for two dimensional systems. We use the geometric properties of power law systems to investigate permanence. Inspired by chemical reaction network models, we define a property of generalized two dimensional power law systems called tropically endotactic. We prove that, in two dimensions, this property is necessary for permanence. We further define strongly tropically endotactic in two dimensions, and prove that this is equivalent to a robust version of permanence, which we call reaction robust variable k-permanence. The conditions which define tropically endotactic are furthermore relatively easy to verify for an individual system, using a geometrically embedded graph. We also seek to extend this definition to higher dimensions.**A Multiple-model Based Estimation Algorithm for Neural Mass Models of Pathological Oscillations**

Michelle Chong (Lund University)

Neural mass models form an important mathematical and computational tool in capturing pathological oscillations seen in the electroencephalogram (EEG), which are known to be related to Epilepsy and Parkinson’s disease [1,2,3]. A common thread in neural mass models is that the types of oscillations are captured by the evolution of model parameters such as the synaptic gains of the excitatory and inhibitory neuronal populations. Therefore, detecting the occurrence of pathological oscillations may be achieved by tracking the model parameters.

We present a model-based estimation algorithm to track the evolution of the parameters (the synaptic gain of each neuronal population) and state variables (the mean firing rate of each neuronal population) for a general class of neural mass models described by nonlinear ordinary differential equations. Improving on the deterministic estimation method presented in [4], we drew inspiration from the multiple model architecture prevalent in the stochastic estimation literature and propose an estimation algorithm with rigorously proven convergence guarantees [5]. Contrary to stochastic estimators usually used in the neuroscience literature, such as the nonlinear Kalman filter (see Chapter 2 of [6]), we prove that the estimates converge to a neighbourhood of the true values under certain conditions. Our multiple-model method involves sampling the parameter space sufficiently densely and implementing a state-only estimator for each parameter sample. From this bank of state estimators, we choose one to provide the parameter and state estimates based on a criterion.

We present results showing the efficacy of our algorithm for the Jansen and Rit model [2], where we track the evolution of the synaptic gains (parameters) and the mean membrane potential (states) of the excitatory and inhibitory neuronal populations, respectively, from a simulated EEG time series. This work might pave the way for computational model-based seizure prediction and detection for Epilepsy based on parameter estimation, and for feedback and control strategies to abate epileptic seizures.

[1] Deco, G.; Jirsa, V.; Robinson, P.; Breakspear, M. & Friston, K., The Dynamic Brain: From Spiking Neurons to Neural Masses and Cortical Fields, Cerebral Cortex, 2008, 4, 1-35.

[2] Jansen, B. & Rit, V., Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns, Biological Cybernetics, 1995, 73, 357-366

[3] Wendling, F.; Hernandez, A.; Bellanger, J.; Chauvel, P. & Bartolomei, F., Interictal to ictal transition in human temporal lobe epilepsy: insights from a computational model of intracerebral, EEG Journal of Clinical Neurophysiology, 2005, 22, 343.

[4] Freestone, D.; Kuhlmann, L.; Chong, M.; Nesic, D.; Grayden, D. B.; Aram, P.; Postoyan, R.; Cook, M. J., Patient-specific neural mass modelling: stochastic and deterministic methods, Recent Advances in Predicting and Preventing Epileptic Seizures, 2013, 63-82.

[5] Chong, M.; Nešić, D.; Postoyan, R. & Kuhlmann, L., Parameter and state estimation using a multi-observer under the supervisory framework, IEEE Transactions of Automatic Control, 2015, Vol. 60, No. 9, 2336-2349.

[6] Schiff, S., Neural Control Engineering: The Emerging Intersection Between Control Theory and Neuroscience, The MIT Press, 2011.**Towards a Modular Approach to Analyzing Bio-chemical Networks**

Hari Sivakumar (University of California)

An engineer’s approach to analyzing complex networks involves the conception of the network as a collection of functionally isolated interacting modules. By doing this, network properties like stability and robustness can be predicted just from properties of each individual module in the network and

knowledge of the interconnection structure. From a computational perspective, computing network parameters such as its equilibrium point(s) can be greatly simplified, since the computations can be done over a set of modules as opposed to over the entire network. We attempt to adopt such an approach to analyzing biological networks, by delimiting these networks into biological modules. We argue that to be useful, these modules need to admit two properties which we term dynamic modularity and parametric modularity. The former implies that the properties of each module do not change upon interconnection with other modules, and the latter implies that the network parameters within a module appear in no other module. We develop a systematic method to decompose an arbitrary network of biochemical reactions into modules that exhibit both dynamic and parametric modularity, which specifies how to partition species and reactions into modules and also how to define the signals that connect the modules. An important novelty of our approach towards a modular decomposition is the use of reaction rates as the communicating signals between modules (as opposed to species concentrations). Aside from permitting parametric modularity, this allows the use of summation junctions to combine alternative pathways that are used to produce or degrade particular species and hence further simplify the modules that result from the decomposition. To illustrate our results, we define and analyze a few key biological modules that arise in gene

regulation, enzymatic networks, and signaling pathways. We also provide a collection of examples that demonstrate how the behavior of a biological network can be deduced from the properties of its constituent modules, based on results from control systems theory.**Convex Design of Combination Drug Therapy**

Mihailo Jovanovic (University of Minnesota, Twin Cities)

With Neil Dhingra

We study the problem of designing doses of drugs to treat disease. The disease has many different mutagens which can mutate into one another and each drug affects different mutagens differently. To approach this problem, we consider a class of structured optimal control problems for positive systems in which the design variable modifies the main diagonal of the dynamic matrix. For this class of systems, we establish convexity of both the $\cH_2$ and $\cH_\infty$ optimal control formulations. In contrast to previous approaches, our formulation allows for arbitrary convex constraints and regularization of the design parameter. We apply our framework on an example with 35 HIV mutagens and 5 broadly neutralizing antibodies.**Biological Mathematical Models: A Survey of Recent Theorems**

Ricardo Sanchez (Art Institutes International Minnesota)**Stochastic Control Analysis for Biological Reaction System**

Herbert Sauro (University of Washington)**Displacement of Bacterial Plasmids by Engineered Unilateral Incompatibility**

Brian Ingalls (University of Waterloo)**Cell Shape Regulation through Mechanosensory Feedback Control**

Pablo Iglesias (Johns Hopkins University)