2014 Workshop for Young Researchers in Mathematical Biology

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  Modeling brainstem neurons and their interactions
  Henry Tuckwell

  Brainstem and lower nuclei contain neurons which are the principal CNS sources of the neurotransmitters serotonin (dorsal and other raphe nuclei) and noradrenaline (locus coeruleus and associated centers). By means of vast ascending and descending tracts with extensive arborizations, these transmitters influence the physiological activity of practically every neuron (and some glia) in the CNS, including the cerebral cortex, hippocampus, cerebellum, spinal cord and the brainstem itself. The noradrenergic and serotonergic systems are intertwined, with reciprocal connections and common afferents so that their properties cannot really be studied independently of each other. Noradrenaline and serotonin are implicated in sleep and many affective and cognitive disorders, as indicated by genetic studies and the therapeutic efficacy of drugs which inhibit their transporters. The neuronal and endocrine circuits involving their actions are numerous and complex. Serotonergic neurons of the DRN, for example, are host to about 17 receptor types (Maejima et al., 2013, Frontiers Int. Neurosci. 7, #40) and there are about 15 neurotransmitters which are known to inhibit noradrenaline release (Kubista & Boehm, 2006, Pharmacology & Therapeutics 112, 213-242). Several groups, including researchers at OSU, have commenced quantitative research on these systems. We will examine some of these studies, including recently published mathematical modeling of spike generation in serotonergic neurons (HCT and NJ Penington, Progress in Neurobiology, 2014) and analysis of the interactions between the noradrenergic and serotonergic systems.

  
  

  
  

  Joint research with BP Guiard (Toulouse) and NJ Penington (New York).

  
  
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  Modeling Cell-Cell Communication and Information Transfer of Social Bacteria
  Amy Buchmann

  Many bacteria are able to communicate information by getting close to each other and signaling through direct contact between cells. This talk will focus on how information is spread between swarming Myxococcus xanthus cells. In particular, I will focus on how the physical cellular properties of individual cells and local behavioral rules influence and optimize information spread throughout the entire cell population. This study is done using both computational cell-based simulations and cell tracking in experiments.

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  Predictive Models of Type I Diabetes Progression
  Majid Jaberi-Douraki

  In type 1 diabetes, an autoimmune disease mediated by autoreactive T-cells that attack insulin-secreting pancreatic beta-cells, it has been suggested that disease progression may additionally require protective mechanisms in the target tissue to impede such auto-destructive mechanisms. We hypothesize that the autoimmune attack against beta-cells causes endoplasmic reticulum stress by forcing the remaining beta-cells to synthesize and secrete defective insulin. To rescue beta-cell from the endoplasmic reticulum stress, beta-cells activate the unfolded protein response to restore protein homeostasis and normal insulin synthesis. Here we investigate the compensatory role of unfolded protein response by developing a multi-state model of type 1 diabetes that takes into account beta-cell destruction caused by pathogenic autoreactive T-cells and apoptosis triggered by endoplasmic reticulum stress. We discuss the mechanism of unfolded protein response activation and how it counters beta-cell extinction caused by an autoimmune attack and/or irreversible damage by endoplasmic reticulum stress. Our results reveal important insights about the balance between beta-cell destruction by autoimmune attack (beta-cell homicide) and beta-cell apoptosis by endoplasmic reticulum stress (beta-cell suicide). It also provides an explanation as to why UPR may not be a successful therapeutic target to treat type 1 diabetes.

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  Analysis of CRISPR Distributions and Mechanisms for Acquisition
  Ryan Waters

  An adaptive immune system is important to ensure appropriate, precise, and rapid response to a foreign pathogen. While adaptive immune response has traditionally only be attributed to vertebrates, it has recently been discovered that some bacteria also demonstrate a form of dynamic immunity. The CRISPR (clustered regularly interspaced short palindromic repetitions) system is made up of short phage homologs which, with the help of Cas (CRISPR-associated) genes, work to recognize and silence exogenous genetic material. Additionally, when new foreign genetic material is recognized, the nucleic acid sequence can then be incorporated into the CRISPR gene. The mechanisms for acquisition and recognition are still not well understood. We are interested to look at ‘ideal’ CRISPR distributions and to explore how different acquisition strategies might lead to different CRISPR distributions. Additionally, we are interested in the role of stochastic effects in bacterial CRISPR acquisition and how this diversity may be important to community survival.

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  Estimating Residual Stresses in Arteries by an Inverse Spectral Technique
  Sunnie Joshi

  It is known that residual stresses play a significant role in determining the overall stress distribution in soft tissues. A mathematical model is studied to estimate residual stress field in the arterial wall by making use of intravascular ultrasound (IVUS) imaging techniques. The arterial wall is modeled as a nonlinear, isotropic, slightly compressible elastic body. A boundary value problem is formulated for the residually stressed arterial wall, the boundary of which is subjected to a quasi-static blood pressure, and then an idealized model for the IVUS interrogation is constructed by superimposing small amplitude time harmonic infinitesimal vibrations on large deformations. The analysis leads to a system of second order differential equations with homogeneous boundary conditions of Sturm-Liouville type. By making use of the classical theory of inverse Sturm-Liouville problems, and root finding and optimization techniques, an inverse spectral algorithm is developed to approximate the residual stress distribution in the arterial wall, given the first few eigenfrequencies of several induced blood pressures.

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  Experimental and modelling investigation of monolayer development with clustering
  Ruth Baker

  Standard differential equation models of collective cell behaviour, such as the logistic growth model, invoke a mean-field assumption which is equivalent to assuming that individuals within the population interact with each other in proportion to the average population density. Implementing such assumptions implies that the dynamics of the system are unaffected by spatial structure, such as the formation of patches or clusters within the population. Recent theoretical developments have introduced a class of models, known as moment dynamics models, that aim to account for the dynamics of individuals, pairs of individuals, triplets of individuals, and so on. Such models enable us to describe the dynamics of populations with clustering, however, little progress has been made with regard to applying moment dynamics models to experimental data. Here, we report new experimental results describing the formation of a monolayer of cells using two different cell types: 3T3 fibroblast cells and MDA MB 231 breast cancer cells. Our analysis indicates that the 3T3 fibroblast cells are relatively motile and we observe that the 3T3 fibroblast monolayer forms without clustering. Alternatively, the MDA MB 231 cells are less motile and we observe that the MDA MB 231 monolayer formation is associated with significant clustering. We calibrate a moment dynamics model and a standard mean-field model to both data sets. Our results indicate that the mean-field and moment dynamics models provide similar descriptions of the 3T3 fibroblast monolayer formation whereas these two models give very different predictions for the MDA MD 231 monolayer formation. These outcomes indicate that standard mean-field models of collective cell behaviour are not always appropriate and that care ought to be exercised when implementing such a model.