Poster session and reception
Tuesday, June 5, 2018 - 4:30pm - 6:00pm
- Diffusion Dynamics on the Coexistence Subspace in a Stochastic Evolutionary Game
Lea Popovic (Concordia University)
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics which fluctuate due to random drift. Dependence of species selection advantages on the environment introduces additional possibilities for the evolutionary dynamics. We analyse a simple model in which a random environment allows competing species to coexist for a long time before a fixation of a single species happens. In our analysis we use stability in a linear combination of competing species to approximate the stochastic dynamics of the system by a diffusion on a one dimensional co-existence region. Our method significantly simplifies calculating the probability of first extinction and its expected time, and demonstrates a rigorous model reduction technique for evaluating quasistationary properties of a stochastic evolutionary model.
- Network inference of circadian clock
Seokjoo Chae (Korea Advanced Institute of Science and Technology (KAIST))
The Mammalian circadian rhythm is governed by the principal clock which is located in the suprachiasmatic nucleus (SCN). This clock is composed of ten thousands of neurons and their connection to one another is essential to important roles of SCN: synchronization, entrainment to light, etc. Previous studies about the SCN network used the maximal information coefficient (MIC) statistic to oscillating time course data during resynchronization after desynchronization by TTX. This method requires desynchronization and resynchronization because MIC detects too many false connections without using TTX. It has some critical drawbacks: experiments take a long time and the recovered structure may not be similar to the normal SCN network. We develop our own method, which can detect causality. This method does not require resynchronization by TTX, so it takes shorter time and one can obtain the normal network structure of the SCN. Moreover, it is able to obtain main results of previous studies: small-world network, exponential distribution of node degree.
- Modeling Axonal Cytoskeleton Segregation: Stochastic and PDE Approaches
Xige Yang (The Ohio State University)
Since the discovery of double-helix sturcture of DNA, molecular and cell level biology is evolving extremely fast in the recent few decades, attracting exclusive interdisciplinary works. From mathematical point of view, both stochastic and PDE modeling approaches have been used and compared in various context in microscopic biology. Roughly speaking, stochastic models are easier to integrate underlying biological phenomena, but hard to analyze mathematically and usually computationally expensive. PDE models, on the other hand, have well-developed mathematical and numerical analytical tools, but are sometimes not as good in capturing biological details. It is therefore important to compare these two different approaches, and to draw conclusion on which method shall be applied under which condition. Probably French physicist Paul Langevin was the first one who addressed the difference between stochastic dynamics and the deterministic conterpart. Later on in 1950s, Kiyoshi Ito and Ruslan Stratonovich rigorously introduced stochastic calculas, which quickly became famous within the community of mathematical finance, and interested physicists again especiallyin the field of statistical mechanics since 1970s. In my presentation, I will start with a new study area in neuroscience – axonal chemical
trasportation and its relation to neural diseases. and will therefore have connections with both stochastic models and the deterministic nonlocal model. Numerical simulations based on both approaches will be carried out, results will be compared. Besides, a preliminary stochastic hybrid model will be highlighted to illustrate some underline connections between these two approaches.
- Landscape-level Interactions between Pests and Biological Control Agents
Amanda Laubmeier (North Carolina State University)
Landscape composition affects insect diversity and abundance, which can have important implications for pest control. In particular, natural vegetation can provide a stable habitat for insects, which permits the growth of beneficial insect communities in nearby agricultural fields. We are interested in the biological control of a pest by its natural predators, and so we study the effect that different landscapes will have on the control of this pest. We motivate a simple partial differential equation model for the interactions between a crop, a pest, and a single group of predators. We investigate the impact of natural borders on field dynamics, which is dependent on field size. For both large- and small-scale agriculture, we are eventually interested in land-use strategies which effectively control the pest population.
- Population dynamics in random environments
Alexandru Hening (Tufts University)
Real populations do not evolve in isolation and as a result much of ecology is concerned with understanding the characteristics that allow two species to coexist, or one species to take over the habitat of another. Sometimes biotic effects can result in species going extinct. However, if one adds the effects of a random environment extinction might be reversed into coexistence. In other instances deterministic systems that coexist become extinct once one takes into account environmental fluctuations. One way of adding noise to the system, is by studying Piecewise Deterministic Markov Processes (PDMPs). These are processes that follow ordinary differential equations for random exponential times after which they switch to other ordinary differential equations, follow those for a random exponential time etc. The process is then repeated in this fashion. I will present general results regarding the persistence and extinction of populations modeled by PDMPs. As applications, I will showcase some unexpected results for two dimensional competition or predator-prey Lotka-Volterra systems. This is based on joint work with Dang Nguyen (Wayne State) and Edouard Strickler (Neuchatel).
- Dynamics and Implications of Models for Intermittent Androgen Suppression Therapy
Tin Phan (Arizona State University)
In this paper, we formulate a three-cell-population model of intermittent androgen suppression therapy for cancer patient to study the treatment resistance development. We compare it with other models that have different underlying cell population structure using patient prostate specific antigen (PSA) and androgen data sets. Our results show that in the absence of extensive data, a two-cell-population structure performs slightly better in replicating and forecasting the dynamics observed in clinical PSA data. We also observe that at least one absorbing state should be present in the cell population structure of a plausible model for it to produce treatment-resistance under continuous hormonal therapy. This suggests that the heterogeneity of prostate cancer cell population can be represented by two types of cells differentiated by their level of dependence on androgen, where the two types are linked via an irreversible transformation.
- Optimal control in HIV chemotherapy with termination viral load and latent reservoir
Damilola Olabode (Washington State University)
Although a number of cost-effective strategies have been proposed for the chemotherapy of HIV infection, the termination level of viral load and latent reservoir is barely considered. However, the viral load at the termination time is an important biomarker because suppressing viral load to below the detection limit is a major objective of current antiretroviral therapy. The pool size of latently infected cells at the termination time may also play a critical role in predicting a rapid viral rebound to the pre-treatment level or post-treatment control. In this work, we formulate an optimal control problem by incorporating the termination level in terms of viral load, latently and productively infected T cells into an existing HIV model. The necessary condition for this optimal system is derived using the Pontryagin's maximum principle. Numerical analysis is carried out using Runge-Kutta 4 method for the forward-backward sweep. Our results suggest that introducing the termination viral load into the control provides a better strategy in HIV chemotherapy.
- Heart Rhythm Control Using Novel Anti-Arrhythmic Pacing Protocol
Alena Talkachova (University of Minnesota, Twin Cities)
Introduction. Periodic pacing of the heart is incorporated in various medical devices and is clinically used to treat cardiovascular diseases. The widely accepted periodic pacing algorithm, however, suffers drawbacks and inherently has pro-arrhythmic properties. Cardiac alternans, a beat-to-beat alternation in action potential duration (APD), is a precursor to fatal arrhythmias. During periodic pacing, changes in diastolic interval (DI) depend on subsequent changes in APD, thus enhancing cardiac instabilities through ‘feedback’ mechanism. Recently, an anti-arrhythmic Constant DI pacing protocol was proposed and shown to be effective in suppressing alternans in 0D and 1D in-silico studies. However, experimental validation of Constant DI in the heart has been unsuccessful due to the spatio-temporal complexity of 2D cardiac tissue and the technical challenges in its real-time implementation.
Purpose. Here, we developed a novel closed loop system to detect T-waves from real-time ECG data, enabling successful implementation of Constant DI, and performed high-resolution optical mapping experiments on isolated whole rabbit hearts to validate its anti-arrhythmic effects. The results were compared with: (1) Periodic pacing and (2) pacing with heart rate variability (HRV) introduced by using either Gaussian or Physiological patterns.
Results. First, we successfully implemented an algorithm for real-time detection of T-waves and validated its efficacy in controlling the DI on a beat-to-beat basis in the heart. Second, Constant DI pacing prevented the occurrence of alternans in the heart, in comparison to traditional Periodic pacing (5% vs 100%, p less than 0.05) , thus providing an anti-arrhythmic effect. Constant DI pacing was associated with an increase in APD and decreases the maximum slope of APD restitution curve (Smax) while not affecting spatial heterogeneity of APD (µ) in comparison to Periodic pacing. On the other hand, feedback modulation using HRV pacing, which was modeled with either Gaussian or in-vivo Physiological patterns, promoted the formation of alternans and VF in the heart, thus enhancing arrhythmogenecity. HRV pacing was associated with both increased Smax and m, and earlier occurrence of alternans, in comparison to Periodic pacing, thus providing clear pro-arrhythmic effects.
Conclusion. We present a successful validation, using whole heart optical mapping experiments, of a novel anti-arrhythmic Constant DI pacing protocol that can be implemented in real time for the beat-to beat control of cardiac rhythm.