Vaccines protect their recipients by inducing long-term structural changes in populations of immune cells. Part of that restructuring is exactly analogous to Darwinian Selection. New antibody molecules are created by somatic mutation of existing antibody genes. Subsequently, the immune cell populations that possess these mutated receptors overtake the "wild-type" immune cells due  to the selective advantage they have acquired. Thus the immune system is vastly better prepared to recognize and eliminate the eliciting pathogen the next time around.

New sequencing and biosynthesis technologies, together with mathematical and computational tools, now allow us to investigate this fascinating and important phenomenon more deeply than ever before. I will illustrate this development with examples from the immune response to HIV infection.

Biological oscillators such as the cell cycle, circadian clocks, and metabolic rhythms are ubiquitous across the domains of life. These biochemical oscillators co-exist in the same cells, often sharing and competing for resources. Are there mechanisms and regulatory principles that ensure harmony between these oscillators? Recent studies have shown that in addition to the transcriptional circadian clock, many organisms (including Arabidopsis) have a circadian redox rhythm driven by the organism's metabolic activities. It has been hypothesized that the redox rhythm is linked to the circadian clock, but the mechanism and the biological significance of this link have only begun to be investigated. In the first half of my talk, I will describe our work (in collaboration with the Dong lab at Duke) on the coupling of redox rhythms and the plant circadian clock. In the second half of my talk, I will discuss our work on the coupling of yeast metabolic cycle and the cell division cycle.

In this talk, I will discuss a new result in fluid flows through channels with permeable membranes with simple pumping dynamics. Fluid will be exchanged and metabolized in a simple reservoir and I will demonstrate the existence of optimal reservoir properties that may either maximize or minimized the amount of fluid being extracted across the channel walls. The biological relevance of this work may be seen by noting that all living organisms of a sufficient size rely on complex systems of tubular networks to efficiently collect, transport and distribute nutrients or waste. These networks exchange material with the interstitium via embedded channels leading to effective permeabilities across the wall separating the channel interior from the interstitium. In many invertebrates, for example, respiratory systems are made of complex tracheal systems that branch out through the entire body allowing for passive exchange of oxygen and carbon dioxide. In many of these systems, certain animals utilize various pumping mechanisms that alter the flow of the air or fluid being transported. Although the net effect of pumping of the averaged rates of fluid flow through the channel is typically well understood, it is still a largely open problem to understand how, and in what circumstances, pumping enables and enhances the exchange of material across channel walls. It has been demonstrated experimentally, for example, that when certain insects flap their wings, compression of the trachea allow for more efficient oxygen extraction, however it is unclear if this pumping is optimized for flight, oxygen uptake or neither, and understanding this problem quantitatively will shed insight on this biological process. Many of these interesting scenarios occur at low Reynolds number and this regime will be the focus of the presentation.

Viscoelastic interactions of Myxococcus xanthus cells in a low-density domain close to the edge of a swarm have been recently studied in [1] using a combination of a cell-based three-dimensional Subcellular Element (SCE) model [1,2] and cell-tracking experiments. The model takes into account the flexible nature of M. xanthus as well as the effects of adhesion between cells arising from the interaction of the capsular polysaccharide covering two cells in contact with each other. New image and dynamic cell curvature analysis algorithms were used to track and measure the change in cell shapes that occur as flexible cells undergo significant bending during collisions resulting in direct calibration of the model parameters. It will be shown in this talk that flexibility of cells and the adhesive cell–cell and cell–substrate interactions of M. xanthus together with cell to aspect-ratio and directional reversals [3], play an important role in smooth cell gliding and more efficient swarming. In the second part of the talk results of the analysis of the three dimensional structures of fibrin networks, with and without cells, reconstructed from two-dimensional z-stacks of confocal microscopy sections using novel image analysis algorithms, will be presented. These images were used to establish microstructure-based models for studying the relationship between the structural features and the mechanical properties of the fibrin networks in blood clots. The change in the fibrin network alignment under applied strain and the elastic modulus values will be shown to agree well with the experimental data [4]. 1. C.W. Harvey, F. Morcos, C.R. Sweet, D. Kaiser, S. Chatterjee, X. Lu, D. Chen and M. Alber [2011], Study of elastic collisions of M. xanthus in swarms, Physical Biology 8, 026016. 2. C.R. Sweet, S. Chatterjee, Z. Xu, K. Bisordi, E.D. Rosen and M. Alber [2011], Modeling Platelet-Blood Flow Interaction Using Subcellular Element Langevin Method, J R Soc Interface, 2011 May 18. [Epub ahead of print], doi: 10.1098/rsif.2011.0180. 3. Y. Wu, Y. Jiang, D. Kaiser and M. Alber [2009], Periodic reversal of direction allows Myxobacteria to swarm, Proc. Natl. Acad. Sci. USA 106 4 1222-1227. 4. E. Kim, O.V. Kim, K.R. Machlus, X. Liu, T. Kupaev, J. Lioi, A.S. Wolberg, D.Z. Chen, E.D. Rosen, Z. Xu and M. Alber [2011], Soft Matter 7, 4983-4992.

The ability of animals to self-organize into remarkable patterns of movement is seen throughout nature from herds of large mammals, to flocks of birds, schools of fish, and swarms of insects. Remarkably, patterns of collective movement can be seen even in the simplest forms of life such as bacteria. M. xanthus are common soil bacteria that are among the most “social" bacteria in nature. In this talk clustering mechanism of swarming M. xanthus will be described using combination of experimental movies and stochastic model simulations. Continuous limits of discrete stochastic dynamical systems simulating cell aggregation will be described in the form of reaction-diffusion and nonlinear diffusion equations. Surface motility such as swarming is thought to precede biofilm formation during infection. Population of bacteria P. aeruginosa, major infection in hospitals, will be shown to efficiently propagate as high density waves that move symmetrically as rings within swarms towards the extending tendrils. Multi-scale model simulations suggest a mechanism of wave propagation as well as branched tendril formation at the edge of the population that depend upon competition between the changing viscosity of the bacterial liquid suspension and the liquid film boundary expansion caused by Marangoni forces. This collective mechanism of cell- cell coordination was recently shown to moderate swarming direction of individual bacteria to avoid a toxic environment. In the last part of the talk a three-dimensional multiscale modeling approach will be described for studying fluid–viscoelastic cell interaction during blood clot formation.

It has long been accepted that type 1 diabetes results from a lack of insulin, as the insulin-secreting pancreatic beta cells are destroyed by an autoimmune process. In contrast, the cause of type 2 diabetes (T2D) is less clear. Most people with pre-diabetes or in the early stages of T2D have abnormally high plasma insulin concentrations, and insulin rises before glucose does. We show that these difficulties are resolved by a mathematical model in which the onset of T2D is represented by the crossing of a threshold. The threshold is atypical in some respects and requires consideration of the slow manifolds to avoid incorrect conclusions.

The segregation of chromosomes during cell division is accomplished by kinetochore machinery that uses depolymerizing microtubules to pull the chromosomes to opposite poles of the dividing cell. While much is known about molecular motors that pull by walking or push by polymerizing, the mechanism of how a pulling force can be achieved by depolymerization is still unresolved. In this talk, I will describe a new model for the depolymerization motor that is used by eukaryotic cells to segregate chromosomes during mitosis. In the process we will explore the use of Huxley-type models (population models) of protein binding and unbinding to study load-velocity curves of several different motor-like proteins.

Stimulus tuning in a reduced model for neural competition leads to mixed-mode oscillations (MMOs), a temporal pattern featuring alternating small- and large-amplitude oscillations. Key ingredients for the generation of MMOs are mutual inhibition, slow negative-feedback in the form of adaptation, and nonlinearity of the gain function. Exploiting a normal form calculation, we show that MMOs occur due to the interaction of canard and singular Hopf mechanisms as the stimulus strength approaches a critical regime. We show then that local excitation and lateral inhibition-type coupling combined with the underlying MMOs produces complex spatio-temporal patterns in larger networks.

Experiments on macaque monkeys show that spike-triggered stimulation performed by a Bidirectional Brain-Computer-Interfaces (BBCI) can artificially strengthen synaptic connections between distant neural sites in Motor Cortex (MC) and even between MC and spinal cord, with changes that last several days. Here, a neural implant records from some neurons in MC and electrically stimulates others after set delays. The working hypothesis is that this stimulation procedure, which interacts with the very fast spiking activity of cortical circuits (on the order of milliseconds), induces changes mediated by synaptic plasticity mechanisms on much longer timescales (hours and days). The field of online, closed-loop BBCI's is rapidly evolving, with applications ranging from a science-oriented tool to clinical treatments of motor injuries. However, with the enhanced capability of novel devices that can record and stimulate an ever-growing number of neural sites comes growing complexity. It is therefore crucial to develop a theoretical understanding of the effects of closed-loop artificial stimulation in the highly recurrent neural circuits found in cortex, and how such protocols affect functional cotex-to-muscle mappings across a range of timescales. In parallel with ongoing experiments, we are developing a mathematical model of recurrent MC networks with probabilistic spiking mechanisms and spike-time-dependent plastic synapses (STDP) capable of capturing both neural and synaptic activity statistics relevant to BBCI protocols. This model successfully reproduces key experimental results and we use analytical derivations to predict optimal operational regimes for BBCIs. We make experimental predictions concerning the efficacy of spike-triggered stimulation in different regimes of cortical activity such as awake behaving states or sleep. Importantly, this work provides a first step toward a theoretical framework aimed at the design and development of next-generations applications of BBCI's.

Visual processing begins in the outer plexiform layer of the retina, where
bipolar, horizontal, and photoreceptor cells interact. In vertebrates, the
onset of dim backgrounds can enhance small spot flicker responses of
retinal horizontal cells. This flicker response is called background-
induced flicker enhancement. The underlying mechanism for the feedback
is unclear but competing hypotheses have been proposed. One is the GABA
hypothesis, which states that the inhibitory neurotransmitter GABA,
released from horizontal cells, mediates the feedback by blocking calcium
channels. Another is the ephaptic hypothesis, which contends that calcium
entry is regulated by changes in the electrical potential within the
intersynaptic space between cones and horizontal cells. In this study, a
continuum spine model of cone-horizontal cell synaptic circuitry is
formulated. The model captures two spatial scales - the scale of an
individual synapse and the scale of the receptive field involving hundreds
to thousands of synapses. We show that the ephaptic mechanism produces
reasonable qualitative agreement with the temporal dynamics exhibited by
flicker enhancement experiments. We find that although GABA produces
enhancement, this mechanism alone is insufficient to reproduce the
experimental results. We view this multiscale continuum approach as a
first step in formulating a multi-layer mathematical model of retinal
circuitry, which would include the other ‘brain nuclei’ within the retina:
the inner plexiform layer where bipolar, amacrine, interplexiform, and
ganglion cells interact.

Birds, insects, and fish all exploit the fact that flexible wings or fins generally perform better than their rigid counterparts. Given the task of designing an optimal wing, though, it is not clear how to best distribute the flexibility: Should the wing be uniformly flexible along its length, or could some advantage be gained by making certain sections more rigid than others? I will discuss this question by using a 2D small-amplitude model for the fluid-structure interaction combined with an efficient Chebyshev PDE solver. Numerical optimization shows that concentrating flexibility near the leading edge of the wing maximizes thrust production, an arrangement that resembles the torsional-joint flexibility mechanism found in insect wings. I will discuss the possibility of extending into three dimensions to address the question of optimal wing architecture more generally.

This talk is about extending classical limit theorems of probability (law of large numbers, central limit theorem) to a non-Euclidean setting. I'll talk about new and interesting phenomena observed when sampling independent points from certain singular geometric spaces. The main result is a limit theorem -- the "sticky central limit theorem" -- which applies to the mean or barycenter of a family of independent samples as the number of samples grows. The theorem shows that the geometry of the underlying space may have an interesting effect on the asymptotic fluctuations of the sample means, in a way that does not occur with independent samples in Euclidean space. One motivation for thinking about statistics in singular geometric spaces comes from evolutionary biology; one can consider phylogenetic trees as points in a metric space of the sort discussed in this talk. Apart from this basic motivation, however, the talk will have little biological content and will be mainly about probability.

There are two generally accepted models for the cell biological positive feedback loops that allow yeast cells to break symmetry and establish an axis of polarity. Both have been subjects of published mathematical analyses. Here I will argue that the models used to support a vesicle trafficking model incorporated a simplifying assumption that seemed innocuous but in fact was critical to their success. The assumption is not physically plausible, and its removal means that the model fails. I will show how changing other assumptions can make the model work, but there is no experimental support for those changes. And without them, the vesicle trafficking model perturbs polarity, rather than establishing polarity

Traditional infectious disease epidemiology is built on the foundation of high quality and high accuracy data on disease and behavior. While these data are usually characterized by smallsize, they benefit from designed sampling schemes that make it possible to make population-level inferences. On the other hand, digital infectious disease epidemiology uses existing digital traces, re-purposing them to identify patterns in health-related processes. In this talk, I will discuss our work using data from small epidemiological studies as well as administrative “big data” to understand influenza transmission dynamics and inform disease surveillance and control.

In order to better understand wound contraction fibroblast populated collagen lattices have been studied for many years.  In this talk I will discuss mathematical models for lattice contraction.  The models are formulated with components at the cellular and sub cellular level with the goal of understanding the macroscopic behavior of the lattice.

The jellyfish has been the subject of numerous mathematical and physical studies ranging from the discovery of reentry phenomenon in electrophysiology to the development of axisymmetric methods for solving fluid-structure interaction problems. In this presentation, we develop and test mathematical models describing the pulsing dynamics and the resulting fluid flow generated by the upside down jellyfish, Cassiopea. The kinematics of contraction and distributions of pulse frequencies were obtained from videos and used as inputs into numerical simulations. Particle image velocimetry was used to obtain spatially and temporally resolved flow fields experimentally. The immersed boundary method was then used to solve the fluid-structure interaction problem and explore how changes in morphology and pulsing dynamics alter the resulting fluid flow. Unlike pelagic (swimming) jellyfish, there is no evidence of the formation of a train of vortex rings. Instead, significant mixing occurs around and directly above the oral arms and secondary mouths. We found good agreement between the numerical simulations and experiments, suggesting that the presence of porous oral arms induce net horizontal flow towards the bell and mixing.

John Hopfield pointed out, in his seminal paper on kinetic proofreading, that if a biochemical system operates at thermodynamic equilibrium there is a barrier to how well it can achieve high-fidelity in transcription and translation. Hopfield showed that the only way to bypass this barrier is to dissipate energy and maintain the system away from equilibrium. Eukaryotic gene regulation uses dissipative mechanisms, such as nucleosome remodelling, DNA methylation and post-translational modification of histones, which are known to play a critical regulatory role but have been largely ignored in quantitative treatments. I will describe joint work with my colleague Angela DePace in which we use the recently-developed, graph-theoretic “linear framework” to show that the sharpness with which a gene is turned “on” or “off” in response to an upstream transcription factor is limited if the regulatory system operates at equilibrium, even with arbitrary degrees of higher-order cooperativity. In contrast, if the regulatory system is maintained away from equilibrium, substantially higher degrees of sharpness can be achieved. We suggest that achieving sharpness in gene regulation exhibits a Hopfield Barrier, and uncover, along the way, a new interpretation for the ubiquitously used, but poorly justified, Hill function.