Mathematical Biology Seminar - Fall 2018

In this talk, I will talk about new scalable, information theory-based variational methods for the efficient model reduction of high-dimensional reaction networks. The proposed methodology combines (a) information theoretic tools for sensitivity analysis that allow us to identify the proper coarse variables of the reaction network, with (b) variational approximate inference methods for training a best-fit reduced model. The overall approach takes advantage of both physicochemical modeling and data-based approaches and allows to construct optimal parameterized reduced dynamics in the number of species, reactions and parameters, while controlling the information loss due to the reduction.

Membrane hydrodynamics is intriguing due to an interplay of dimensionalities; momentum travels in the plane of the membrane at short distances, but moves through the outer fluid at larger ones, showing a crossover from 2D to 3D like behavior. Chemical reactions on the surface of a cell, therefore, require a special treatment. While it is possible to perform a simple Smoluchowski-like calculation in 2D to predict reaction rates in membranes, we will see that the expected rates are reduced by an order of magnitude when accounting for hydrodynamic interactions between reactants and targets. A biomembrane, however, is more than just a passive medium. ATP synthase and other proteins produce a great deal of hydrodynamic traffic. In the second part of the talk, we will explore the dynamics of active rotors embedded in a membrane. We will see a power law transition --- from Euler flows at small distances (1/r), to 1/r^2 at large distances. We will derive a Hamiltonian for a discrete system of rotors, find the conserved quantities, and describe a coarse-grained density field of rotors. We will present theory and simulations for the discrete and the continuous cases.

The striatal medium spiny neuron network controls the flow of information from cortex to motor control systems via the basal ganglia (BG). Since the striatum is purely inhibitory it has often been considered simply a static winner-take-all (WTA) network, whereby the `strongest' cortical input is selected for transmission downstream. However many in-vivo behavioural studies show that coherent bursting activity of MSN cell assemblies is important in the encoding and execution of motor programs and in sequence learning. Furthermore this essentially dynamical behaviour is disrupted in Parkinsons and Huntingtons Diseases. I show by computer simulation of a spiking network model that when MSNs are connected appropriately for the striatum cells display irregular spiking activity and form sequentially switching coherently burst ring assemblies. This activity is in strikingly close quantitative agreement with empirical studies but completely incompatible with a WTA role. Furthermore I find, quite remarkably, that the MSN network is poised precisely in a marginally stable critical state known as the `edge of chaos'. The next question addressed is why the MSN network needs these characteristics. I found that this state endows the striatum with optimal characteristics, for example facilitating the generation of strongly reproducible activation sequences for several seconds after variations in cortical excitation, and maximizing distinguishability of cortical stimuli. This complex activity may be relevant for central pattern generation of action sequences, or for the temporal credit assignment of stimuli and actions, or for switching between exploratory and exploitative behavioural modes, all functions hypothesized to rely on the striatum.

In more recent work I ask if such activity can be recovered in a larger network of more physiologically detailed MSN cells and compare network model generated spiking activity with recordings from mice. By estimating model parameters from multiple statistical quantities calculated from the spiking data we find the network provides an excellent fit, but only in the striatally relevant parameter regime. I next asked if modifications to the network can account for dysregulation of burst firing activity previously observed in mutant Huntington’s Disease (HD) mice. We find network parameter modifications which provide an excellent fit to HD data which are consistent across three types of HD mice (YAC128, Q175, R62). Amongst other results we find HD model networks display reduced excitatory drive compared to WT mice. Finally we show that WT networks are characterised by a fairly low dimensional dynamical regime supporting coherent bursting activity which is lost in HD networks. We discuss how this might relate to motor symptoms in HD mice.

Research in pharmacology has been undergoing radical changes in recent years. The central idea behind these transformations is to replace systemic drug delivery by local release strategies in order to minimize side effects and to avoid the physiological barriers that hinder the entry of drug molecules. The development of new medical platforms, that deliver drug directly into target tissues for extended periods of time, has gained centrality, constituting one of the pillars of a precision medicine.
To highlight how mathematical models can shape the current approaches to drug release, we will focus on two particular cases: drug delivery to the cardiovascular vessels and drug delivery to the retina. The models are described by coupled systems of partial differential equations that include parameters depending on patient-specific pharmacokinetic and pharmacodynamics properties. The characteristics of biodegradable release platforms will be also taken into account. A large number of numerical simulations will illustrate the results.

Imagine the following actions: walking, stair climbing, holding the armrests of a chair while standing up, and leaning on the wall while reaching for an object on the floor. These are all examples of everyday life activities that require the coordination between human body motion and the available contact interactions with the environment in order to maintain balance. While humans can instinctively plan and control their motion and contact interactions in time and space and use them as intentional support for agile and efficient movements, a mathematical framework for the generation and control of such coordinated actions in legged systems remains a challenge. In this talk, I will present two recent developments in the study of balance and locomotion through contacts: first, I will describe the formulation and application of a balance stability criterion for legged systems with multiple contact interactions; next, I will illustrate a method for the generation of optimal motion and control of general mechanisms during environment-aware tasks, while simultaneously predicting the optimal contacts. Integrating these two mathematical models could lead to a more unified approach to analyze, simulate, and control the coordinated motion of legged systems with contact-rich interactions, such as biped robots, the human body, and robotic exoskeletons.

One of the kidney functions is to maintain the body water and sodium within ranges compatible with life. In order to balance the blood volume and sodium content, hormones regulate certain permeability values in the membranes of the renal tubules. I will present a mathematical model of the kidney that includes the regulation of water and sodium excretion by varying two parameters, which represent the percentages of maximum concentrations of two hormones. Hence, depending on the activity of the hormones the model is able to produce different types of urine from dilute to concentrated. This model is suitable for studying regulation of body water and sodium by the kidney and it can be combined with models of other systems that can affect the renal flows.

Neural networks are required to meet significant metabolic demands associated with performing sophisticated computational tasks in the brain. The necessity for efficient transmission of information imposes stringent constraints on the metabolic pathways that can be used for energy generation at the synapse, and low availability of energetic substrate has been shown to reduce the efficacy of synaptic function. Here we study the effects of energetic substrate availability on global neural network behaviour and find that glucose alone can sustain excitatory neurotransmission required to generate high-frequency synchronous bursting that emerges in culture. In contrast, obligatory oxidative energetic substrates such as lactate and pyruvate are unable to substitute for glucose, indicating that processes involving glucose metabolism form the primary energy-generating pathways supporting coordinated network activity. Our experimental results are discussed in the context of the role that metabolism plays in supporting the performance of individual synapses, including the relative contributions from postsynaptic responses, astrocytes, and presynaptic vesicle cycling. We propose a simple computational model for our excitatory cultures that accurately captures the ability of compromised synaptic function to reduce the frequency of synchronous bursting in response to glucose depletion.

Larval zebrafish are young fish which swim using discrete units of activity, rather than continuously. Describing the kinematic parameters of these swim bouts and various maneuvers utilized by the fish to move around their environment gives us a solid foundation on which to ask questions about the neural control of locomotion. Using zebrafish we have unparalleled genetic and optical access to the vertebrate nervous system; we focus on the cell types and activation patterns in the brain and spinal cord which enable such locomotion. I will discuss my previous work understanding the neural control of these swim movements, and my future goals as I start my lab at NJIT. In this talk I hope to introduce myself, my research focus, and open discussion between myself and the Math-Bio group at NJIT about avenues of interest and potential points of collaboration.