From €oedegrade and Fireâ€@bullet to €oeintegrate and Fireâ€@bullet Dynamics --335 West Hall

Mathematical Biology Monday, September 14, 2015, 12:00pm-1:00pm 335 West Hall Bard Ermentrout (University of Pittsburgh) Keeping the beat: Homeostatic frequency control in coupled oscillators When nonlinear oscillators are forced or coupled they will generally lock if the frequency is in a narrow enough range. However, humans and other animals such as fireflies and Snowball the dancing cockatoo are able to adjust the intrinsic frequency of their oscillators to widen the range of locking and zeroing the phase-lag. In this talk, I will start with some simple abstract circle maps and show that when the frequency is modulated by the coupling there are many possible final states and fractal basin boundaries between them. I will then turn to continuous time oscillators. Using averaging I will derive a new class of phase models and analyze their properties. I apply this to some neural models and show how the homeostatic control of the frequency greatly expands the ability to lock. Finally, I show that traveling periodic wave trains can be destabilized in the when there is frequency adjustment in rings of coupled oscillators. http://www.math.lsa.umich.edu/seminars_events/ Page 2/6 Seminar & Events Bulletin: Mathematical Biology 07-01-2015 to 06-30-2016 Mathematical Biology Monday, October 05, 2015, 12:00pm-1:00pm 335 West Hall Sara Solla (Northwestern University) Statistical Inference on Networks of Spiking Neurons Coupling large numbers of relatively simple elements often results in networks with complex computational abilities. Examples abound in biological systems from genetic to neural networks, from metabolic networks to immune systems, from networks of proteins to networks of economic and social agents. Recent and continuing increases in the experimental ability to simultaneously track the dynamics of many constituent elements within these networks present a challenge to theorists: to provide conceptual frameworks and develop mathematical and numerical tools for the analysis of such vast data. The subject poses great challenges, as the systems of interest are noisy and the available information is incomplete. For the specific case of neural activity, Generalized Linear Models provide a useful framework for a systematic description. The formulation of these models is based on the exponential family of probability distributions; the Bernoulli and Poisson distributions are relevant to the case of stochastic spiking. In this approach, the time-dependent activity of each individual neuron is modeled in terms of experimentally accessible correlates: preceding patterns of activity of this neuron and other monitored neurons in the network, inputs provided through various sensory modalities or by other brain areas, and outputs such as muscle activity or motor responses. Model parameters are fit to maximize the likelihood of the observed firing statistics; smoothness and sparseness constraints can be incorporated via regularization techniques. When applied to neural data, this modeling approach provides a powerful tool for mapping the spatiotemporal receptive fields of individual neurons, characterizing network connectivity through pairwise interactions, and monitoring synaptic plasticity. http://www.math.lsa.umich.edu/seminars_events/ Page 3/6 Seminar & Events Bulletin: Mathematical Biology 07-01-2015 to 06-30-2016 Mathematical Biology Monday, November 09, 2015, 12:00pm-1:00pm 335 West Hall Anthony Hudetz (University of Michigan) Consciousness and neuronal dynamics: lessons from anesthesia What is consciousness and how does it arise from brain activity? These questions have intrigued philosophers for centuries and neuroscientists for decades. Today consciousness is believed to be an emergent phenomenon linked to the complexity of neuronal interactions. Anesthesia is a unique tool to reversibly alter the state consciousness and study its mechanism. We investigate the effect of various anesthetics on neuronal interactions in local circuits and large-scale networks of the brain using electrophysiology and fMRI in animals and human volunteers. We find that selective changes in neuronal spike transmission, burst synchrony, interaction complexity, and spatiotemporal fluctuations occur during the transitions to or back from unconsciousness. In addition, computer simulations using an fMRI connectivity-based spin-glass model suggest that the conscious state may be associated with complex system behavior near criticality but the relevant data from anesthesia are conflicting and imply the need for further research. Mathematical Biology Monday, November 23, 2015, 12:00pm-1:00pm 335 West Hall Yaoyu Zhang (Shanghai Jiao Tong University) Validity and reliability of Granger causality analysis on neuronal network reconstruction Granger causality (GC) analysis is one of the major approaches to explore the dynamical causal connectivity among individual neurons or neuronal populations. In this talk, focusing on the connectivity reconstruction of the conductance-based integrate-and-fire neuronal networks, we address two issues: (i) how the causal connectivity obtained from GC analysis can be mapped to the underlying anatomical connectivity; and (ii) how we can sample discretely from the time continuous quantities, e.g., membrane potential, to obtain a reliable GC network reconstruction. We numerically demonstrate that the anatomical connectivity can be successfully reconstructed from the GC analysis and theoretically establish a quadratic relation between the GC and the coupling strength. We also analyze in detail the impact of sampling interval length on the GC analysis of uniformly sampled data and propose a strategy to circumvent the possible sampling hazards for a reliable network reconstruction. In addition, we establish a nonuniform sampling GC analysis framework to achieve a reliable network reconstruction. Finally, we note that our analysis on the validity and reliability of GC analysis can be extended to more general dynamics. http://www.math.lsa.umich.edu/seminars_events/ Page 4/6 Seminar & Events Bulletin: Mathematical Biology 07-01-2015 to 06-30-2016 Mathematical Biology Monday, February 08, 2016, 12:00pm-1:00pm 335 West Hall Wylie Stroberg (University of Michigan Physiology) Microtubule Stability in Blood Platelet Formation and Activation Terminal platelet production and platelet activation involve considerable cytoskeletal reorganization. The morphological changes brought about by this remodeling are essential for proper platelet function. Recent discoveries suggest that the marginal bands of microtubules found at the equator of platelets and platelet precursors undergo similar instabilities during platelet biogenesis and activation. This buckling instability serves, in one case, as the final differentiator of platelet production, and in the other, as an essential early step in the activation pathway. We aim to understand the mechanical principles governing these processes. To accomplish this, we construct a theoretical framework describing a growing, elastic ring confined within a flexible vesicle. With this method we construct two phase diagrams. The first corresponds to an instability due the curvature elasticity of the membrane, and the second to the same instability, but resulting from the strain energy of the membrane cortex. Next, we develop a coarse-grained Monte Carlo model of a growing marginal band within the platelet/preplatelet cytoskeleton. With this model we observe that the confining membrane suppresses the instability more readily for smaller marginal bands, thereby increasing the stability of platelets compared to their precursors. Our analysis, in combination with experimental observations, indicates that, although marginal band stability is highly sensitive to platelet diameter, this alone is not enough to explain the size of circulating platelets. Mathematical Biology Monday, March 07, 2016, 12:00pm-1:00pm 335 West Hall Madhav Mani (Northwestern University) A Physical View of Gene Regulation Genes are much more than nodes in a network. They are physical objects, whose state is under cellular and developmental control. This physicality makes itself manifest in the degree of stochasticity observed in mRNA and protein levels, as well as the requirement for the local genomic vicinity of the gene to be physically mobile to recruit transcriptional machinery. To this end, I will present ongoing experimental, data-analysis, and modeling work conducted in close collaborations with the Carthew (Northwestern) and Gregor (Princeton) labs. Relying on a secure understanding of the biophysics of gene regulation in the early Drosophila embryo and larval wing, we hope to understand a little more about the logic of how gene regulation is controlled over space and time in developing organisms. http://www.math.lsa.umich.edu/seminars_events/ Page 5/6 Seminar & Events Bulletin: Mathematical Biology 07-01-2015 to 06-30-2016 Mathematical Biology Monday, March 14, 2016, 12:00pm-1:00pm 335 West Hall Jeff Hasty (University of California San Diego) Engineered Genetic Clocks: From “degrade and fire― to “integrate and fire― dynamics A defi ning component of Synthetic Biology is the development of theoretical modeling that can serve as the foundation for a new type of cellular engineering. This talk will be anchored by my quest to build genetic oscillators in bacteria, with a particular focus on the utility of theory and computation. I'll start by describing how the coupling of transcriptional activators and repressors was originally modeled as a type of classical "predator-prey" system. Although this system led to the design of a robust intracellular clock (http://biodynamics.ucsd.edu/Intracellular.mov), I'll show how the experiments pointed to a di fferent type of "degrade and fi re" oscillator characterized by a coupled set of delayed diff erential equations. Interestingly, the biological constraints naturally lead to a system that can be solved approximately. In terms of engineering, the clock was not of the Swiss variety; the period and amplitude exhibited large intracellular variability. However, it provided a benchmark for the development of general synchronization strategies that can restore determinism. I'll conclude with our e fforts to use cellular communication to couple clocks between cells (http://biodynamics.ucsd.edu/Intercellular.mov) and colonies (http://biodynamics.ucsd.edu/Intercolony.mov). Here, the threshold nature of the communication mechanism leads naturally to oscillators that are highly reminiscent of "integrate and fi re" systems in neuroscience. http://www.math.lsa.umich.edu/seminars_events/ Page 6/6