## 2014 Workshop for Young Researchers in Mathematical Biology

### (August 25,2014 - August 28,2014 )

**DEADLINE EXTENDED**
The workshop is intended to broaden the scientific perspective of young researchers (primarily junior faculty, postdocs, and senior graduate students) in mathematical biology and to encourage interactions with other scientists. Workshop activities include plenary talks and poster sessions, as well as group discussions on issues relevant to mathematical biologists. Several abstracts will be chosen for short talks as well as to be presented as a poster. We cordially invite young mathematical biologists to participate.
For full consideration, please apply by May 31, 2014.

### Accepted Speakers

David Anderson
Mathematics, University of Wisconsin
Ruth Baker
Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford
Amy Buchmann
Applied and Computational Mathematics and Statistics, University of Notre Dame
Andrey Dovzhenok
Mathematical Sciences, University of Cincinnati
Rebecca Everett
Applied Mathematics, Arizona State University
Kenneth Ho
Mathematics, Stanford University
Majid Jaberi-Douraki
Physiology, McGill University
Jaejik Kim
Biostatistics & Epidemiology, Georgia Regents University
Christopher Knowlton
Physics, University of California, San Diego
Peter Kramer
Mathematical Sciences, Rensselaer Polytechnic Institute
shruti marwaha
Department of Molecular and Cellular Physiology, University of Cincinnati
Calistus Ngonghala
Global Health and Social Medicine, Harvard Medical School
Qing Nie
Biomedical Engineering & Mathematics, University of California, Irvine
Linus Schumacher
Centre for Mathematical Biology, University of Oxford
Peter Thomas
Department of Mathematics, Applied Mathematics, and Statistics, Case Western Reserve University
Henry Tuckwell
Max Planck Institute For Mathematics In The Sciences, Leipzig and Electrical and Electronic Engineering, University of Adelaide
Ryan Waters
Mathematical Sciences, Montana State University
Monday, August 25, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
08:45 AM

Breakfast

08:45 AM
09:00 AM

Opening remarks

09:00 AM
10:00 AM
Henry Tuckwell - Modeling brainstem neurons and their interactions

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).

10:00 AM
10:30 AM

Break

10:30 AM
11:00 AM

Short Talk, TBA

11:00 AM
11:30 AM

Short Talk, TBA

11:30 AM
01:30 PM

Lunch Break

01:30 PM
02:30 PM
Qing Nie - Stem Cells: From Simple Model to Big Data

In developing and renewing tissues, terminally differentiated cell types are typically specified through the actions of multistage cell lineages. Such lineages commonly include a stem cell and multiple progenitor cell stages, which ultimately give rise to terminally differentiated cells. In this talk, I will present several modeling frameworks with different complexity on multistage cell lineages driven by stem cells, which account for diffusive signaling molecules, regulatory networks, individual cells, mechanics, and evolution. Questions of our interest include role of feedbacks in regeneration, stem cell niche for tissue spatial organization, crosstalk between epigenetic and genetic regulations. In addition, I will discuss our recent effort on connecting modeling and big data by integrating prior knowledge and heterogeneous spatial and temporal data for elucidating developing tissues.

02:30 PM
02:45 PM

Break

02:45 PM
03:15 PM

Short Talk, TBA

03:15 PM
03:45 PM

Short Talk, TBA

03:45 PM
04:45 PM

Poster Preview

05:00 PM
07:00 PM

Poster Session with Reception

07:00 PM

Shuttle pick-up from MBI

Tuesday, August 26, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
Peter Thomas
10:00 AM
10:30 AM

Break

10:30 AM
11:00 AM

Short Talk, TBA

11:00 AM
11:30 AM

Short Talk, TBA

11:30 AM
02:00 PM

Lunch Break

02:00 PM
03:00 PM
David Anderson - Chemical reaction network theory for stochastic and deterministic models of biochemical reaction systems

I will give a short tutorial on the two most common modeling regimes for biochemical reaction systems: ODE models and stochastic discrete jump models. I will show how the two models are connected through the law of large numbers and will then give basic results relating network topology to qualitative behavior of the underlying system in both modeling regimes. In particular, I will give one set of conditions which guarantees that the long-term behaviors of the ODE and stochastic model are stable, and another set under which the long-term behaviors are quite different. The flavor of results presented fall into the field of Chemical Reaction Network Theory.

03:00 PM
03:15 PM

Break

03:15 PM
03:30 PM

Group photo in front of Jennings Hall

03:30 PM
04:45 PM

Panel Discussion

05:00 PM

Shuttle pick-up from MBI

Wednesday, August 27, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
Peter Kramer - Stochastic Modeling in Microbiological Systems

I will illustrate, via several examples, how concepts and techniques from the mathematical theory of stochastic processes can be used to help understand the effective behavior of a system of interacting microbiological agents.'' By an agent,'' I refer to a biological entity such as a molecular motor, a neuron, or a swimming bacterium. Each of these have been sufficiently studied that its operating principles at an individual level are by now relatively well understood, at least in a general sense. But several phenomena pertaining to systems of these agents remain difficult to explain in terms of the dynamical rules of the individual agents. What is challenging about these systems is they are fundamentally non-equilibrium, and only involve a moderately large number of agents, so that stochastic fluctuations remain important even on the collective (mesoscopic) level, and mean-field treatments are restricted in their validity. I will describe some remarkable phenomena regarding the tug-of-war dynamics of molecular motors, switching dynamics of sleep and wake states, and pattern formation by suspensions of swimming bacteria, and indicate how ideas from asymptotic analysis, metastability theory, and stochastic partial differential equations can be deployed to obtain some understanding of how these collective phenomena are quantitatively connected to the dynamics of the individual agents.

10:00 AM
10:30 AM

Break

10:30 AM
11:00 AM

Short Talk, TBA

11:00 AM
11:30 AM

Short Talk, TBA

11:30 AM
02:00 PM

Lunch Break

02:00 PM
03:00 PM
Ruth Baker - Experimental and modelling investigation of monolayer development with clustering

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.

03:00 PM
03:30 PM

Break

03:30 PM
04:00 PM

Short Talk, TBA

04:00 PM
04:30 PM

Short Talk, TBA

05:00 PM

Shuttle pick-up from MBI

Thursday, August 28, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:30 AM

Short Talk, TBA

09:30 AM
10:00 AM

Break

10:00 AM
10:30 AM

Short Talk, TBA

11:00 AM

Shuttle pick-up from MBI

Name Affiliation
Anderson, David anderson@math.wisc.edu Mathematics, University of Wisconsin
Baker, Ruth ruth.baker@maths.ox.ac.uk Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford
Kramer, Peter kramep@rpi.edu Mathematical Sciences, Rensselaer Polytechnic Institute
Nie, Qing qnie@math.uci.edu Biomedical Engineering & Mathematics, University of California, Irvine
Thomas, Peter pjthomas@case.edu Department of Mathematics, Applied Mathematics, and Statistics, Case Western Reserve University
Tuckwell, Henry tuckwell@mis.mpg.de Max Planck Institute For Mathematics In The Sciences, Leipzig and Electrical and Electronic Engineering, University of Adelaide
Chemical reaction network theory for stochastic and deterministic models of biochemical reaction systems

I will give a short tutorial on the two most common modeling regimes for biochemical reaction systems: ODE models and stochastic discrete jump models. I will show how the two models are connected through the law of large numbers and will then give basic results relating network topology to qualitative behavior of the underlying system in both modeling regimes. In particular, I will give one set of conditions which guarantees that the long-term behaviors of the ODE and stochastic model are stable, and another set under which the long-term behaviors are quite different. The flavor of results presented fall into the field of Chemical Reaction Network Theory.

Experimental and modelling investigation of monolayer development with clustering

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.

Modeling Pseudomonas aeruginosa Adhesion to Epithelial Cells

Pseudomonas aeruginosa is a common bacterium known to cause infections in humans as well as other animals. A better understanding of the bacterial swimming and attachment to epithelial cells could motivate new methods for treatment and prevention of infection. In this work, we have done an experimental analysis of two different strains of P. aeruginosa to study how they attach to both healthy epithelial cells as well as wounded epithelial cells. To better understand the dynamics of attachment, mathematical modeling is used. The subcellular element model is implemented to model the different strains and explain the dynamics of cell attachment and detachment to the epithelium.

Predictive modeling and validation of glucose and temperature compensation of the Neurospora circadian clock

Circadian rhythms play a vital role in an organism’s functions anticipating daily changes in its environment. The period of circadian oscillator is relatively insensitive to changes in physiological temperature and nutrients (e.g. glucose), which are referred to as temperature and glucose compensation, respectively. In this study, we constructed a mathematical model of the Neurospora circadian clock, and investigated molecular mechanisms of glucose and temperature compensation. Our model shows that the glucose compensation is achieved by balancing the expression rates of csp-1 and wc-1. More importantly, we experimentally validated loss of glucose compensation in wc-1 overexpression mutant and maintenance of nuclear abundance of FRQ as predicted in the model. Our work highlights predictive modeling of circadian clock machinery and experimental validations employing the model fungus, Neurospora crassa.

How Might Mathematical Models Help Improve Personalized Treatment of Prostate Cancer?

Prostate cancer is the most common non-skin cancer in men and second most fatal in the United States. It is often treated by a hormone therapy called androgen suppression therapy since both normal and cancerous prostate cells depend on androgens for growth and survival. Due to the side effects of this treatment, the quality of life decreases for the patients while on the therapy. Thus patients often choose intermittent androgen suppression therapy (IAS), in which the patients alternate between durations of on and off treatment. Using a mathematical model, we propose a novel computational method for predicting the main mechanism for resistance to treatment in individual patients. Using the same mathematical model, we also predict the future prostate specific antigen (PSA) levels, a biomarker for prostate cancer, in individual patients and compare the results to clinical data. Since biological processes take time, we also explore a delayed differential equations cancer model.

Unraveling the contribution of pancreatic beta-cell suicide in autoimmune type 1 diabetes

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.

Statistical Validation in Dynamic Molecular Systems for Gene Regulatory Networks

The description of network dynamics is an important and fundamental tool to understand gene regulation processes, along with the gene regulatory network. To describe the network dynamics, dynamic molecular systems consisting of a set of ordinary differential equations (ODEs) have been often used. However, since gene experiments cannot observe entire regulation processes and there might be multiple competing sets of ODEs generating similar dynamics, validation for dynamic systems are essential for more accurate inference and prediction for the processes. Moreover, since ODEs are deterministic while mRNA expression data typically have both measurement and instrument uncertainties with heteroscedasticity, they should be evaluated in terms of flexibility and model adequacy for given data. This study proposes statistical validation and selection methods for dynamic molecular systems based on a likelihood method and they are applied to the parotid de-differentiation network obtained from RT-PCR experiments. Although this study focuses on mRNA expression data, the proposed validation method can be extended into various biomedical studies.

Network Identification from Spike Timing Information

Networks of neurons perform functional control in complex organisms. In many systems, such as the HVC in song birds, a lot has been done in characterizing the behavior of individual cells and their synapses in response to external stimulus (1,2) and how the networks interact with each other (3) but little headway has been made into determining the actual neural circuits that comprise these networks (4). While HVC is just a familiar example, the inability to probe network behavior at the many cell level, as opposed to single cell or local mean field level, is a common problem in neural systems.

Network behavior is determined by the types of and distribution of the various types of neurons and the connection architecture of the synaptic connections between them. Determining the connection architecture would allow for a quantitative treatment of the network response to novel stimuli, the changes in network architecture over time due to plasticity, and to create better models of the behavior of the sub-network of interest for describing larger brain functions.

Characterizing the behavior of networks of neurons is complicated by the complexity of the individual elements and the difficulty of measuring their states. Estimating the full state of a network of spiking neurons requires sufficient information from measurement to be able to predict both current and future behavior. 'Sufficient' in this case refers to the amount of information required to both cause model and data to synchronize, and for sufficient resolution into any unmeasured time independent parameters – such as the connection strength.

For many neural systems, this information comes from voltage recordings of one or more cells in the network. While the voltage behavior of single cells can be measured using single electrode recordings, the invasiveness of these procedures prevent large numbers of simultaneous recordings. For large numbers of cells, extracellular recordings allow for a much broader, yet coarser measurement of activity. Whether these coarse measurements are sufficient to estimate both individual neuron and networks states depends heavily on the structure of the model and how it is stimulated.

I will present the use of a path integral method that can exploit some of the regularity in Hodgkin- Huxley type models to estimate the connectivity of small networks of neurons conditioned on extracellular spike time recordings in simulation. (5)

1: Toth BA, Kostuk M, Meliza CD, Margoliash D, Abarbanel HD. (2011) Dynamical estimation of neuron and network properties I: variational methods. Biol Cybern. 105(3-4):217-37

2: Gentner TQ, Margoliash D. (2003) Neuronal populations and single cells representing learned auditory objects. Nature 424: 669–674. 3: Nottebohm F (2005) The neural basis of birdsong. PLoS Biol 3(5): e164.

4: Mooney, R and J Prather (2005) The HVC microcircuit: the synaptic basis for interactions between song motor and vocal plasticity pathways. J Neurosci: 25 (8)

5: Christopher Knowlton, C. Daniel Meliza, Daniel Margoliash, and Henry D.I. Abarbanel, (2014) “Dynamic estimation of neuron and network properties III: Network Analysis Using Neuron Spike Times” Biological Cybernetics 1-13 (2014) link.springer.com/article/10.1007/s00422-014-0601-y

Stochastic Modeling in Microbiological Systems

I will illustrate, via several examples, how concepts and techniques from the mathematical theory of stochastic processes can be used to help understand the effective behavior of a system of interacting microbiological agents.'' By an agent,'' I refer to a biological entity such as a molecular motor, a neuron, or a swimming bacterium. Each of these have been sufficiently studied that its operating principles at an individual level are by now relatively well understood, at least in a general sense. But several phenomena pertaining to systems of these agents remain difficult to explain in terms of the dynamical rules of the individual agents. What is challenging about these systems is they are fundamentally non-equilibrium, and only involve a moderately large number of agents, so that stochastic fluctuations remain important even on the collective (mesoscopic) level, and mean-field treatments are restricted in their validity. I will describe some remarkable phenomena regarding the tug-of-war dynamics of molecular motors, switching dynamics of sleep and wake states, and pattern formation by suspensions of swimming bacteria, and indicate how ideas from asymptotic analysis, metastability theory, and stochastic partial differential equations can be deployed to obtain some understanding of how these collective phenomena are quantitatively connected to the dynamics of the individual agents.

Coupled economic and ecological processes can generate poverty traps

Economic activity is coupled to ecological processes through an array of mechanisms across the spectrum of conceivable scales. In pursuit of general integrated frameworks, here we combine the dominant paradigmatic model of economic growth theory with standard models of disease ecology. Our calibrated model indicates that the structure of these systems can create bistable outcomes, and therefore poverty traps, in both income and disease that do not occur independently in the uncoupled models. The presence of poverty traps is dependent on various biologically-determined parameters, such as the background transmission rate of disease, and the number of pathogens in the system. In particular, our model indicates that the number of pathogens in the system increases the inten­sity of ecological-economic feedback, making poverty traps inevitable at suf.ciently high numbers of pathogens that prevent the acquisition of human capital. The framework provides a general ap­proach for modeling the dynamics of coupled ecological-economic systems, equally reliant on ex­isting paradigms in both the social and natural sciences. More speci.cally, it offers a model on the relationship between human health and economic growth.

Stem Cells: From Simple Model to Big Data

In developing and renewing tissues, terminally differentiated cell types are typically specified through the actions of multistage cell lineages. Such lineages commonly include a stem cell and multiple progenitor cell stages, which ultimately give rise to terminally differentiated cells. In this talk, I will present several modeling frameworks with different complexity on multistage cell lineages driven by stem cells, which account for diffusive signaling molecules, regulatory networks, individual cells, mechanics, and evolution. Questions of our interest include role of feedbacks in regeneration, stem cell niche for tissue spatial organization, crosstalk between epigenetic and genetic regulations. In addition, I will discuss our recent effort on connecting modeling and big data by integrating prior knowledge and heterogeneous spatial and temporal data for elucidating developing tissues.

Unravelling the rules of multicellular migration during development with models and experiments

We study the mechanisms underlying cell migration in the developing embryo, using a computational model developed in close collaboration with in vivo ex­periments in the chick cranial neural crest. Here, a stream of cells has to invade a target tissue and at the same time distribute along the migratory route. Cranial neural crest cells are known to seek out a chemoattractant (VEGF). However, the chemoattractant is uniformly produced. Our working hypothesis is that a chemotactic gradient is induced by the cells themselves through internalisation of chemoattractant. This is represented computationally within a hybrid model framework (discrete cells o.-lattice, continuous chemoattractant) on a growing domain.

Previous work has indicated the need for two subpopulations of cells with di.erent behaviours. The presence of these subpopulations was validated ex­perimentally, both by gene pro.ling and by con.rming model predictions for tissue transplantation experiments. Our focus is now to extend this modelling framework, incorporating realistic cell sensing and di.erences in cell cohesion recently observed experimentally. The goal is to identify critical cell behaviours that lead to robust multicellular neural crest migration. Together with our col­laborators we plan experiments and then conduct them in parallel in vivo, in vitro and computationally. Experimental results parameterise and inform the simulations, which in turn help to interpret existing results and suggest new ex­periments. We repeat this cycle of hypothesis generation and testing iteratively with the aim of providing a framework generalizable to multicellular migration in di.erent organisms.

Modeling brainstem neurons and their interactions

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).

Analysis of CRISPR Distributions and Mechanisms for Acquisition

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.

### Posters

Linearization of the Median Genome under DCJ

Reconstruction of the median genome consisting of linear chromosomes from three given genomes is known to be intractable. There exist efficient methods for solving a relaxed version of this problem, where the median genome is allowed to have circular chromosomes. We propose a method for construction of an approximate solution to the original problem from a solution to the relaxed problem and prove a bound on its approximation accuracy. Our method also provides insights into the combinatorial structure of genome transformations with respect to appearance of circular chromosomes.

Linearization of the Median Genome under DCJ

Reconstruction of the median genome consisting of linear chromosomes from three given genomes is known to be intractable. There exist efficient methods for solving a relaxed version of this problem, where the median genome is allowed to have circular chromosomes. We propose a method for construction of an approximate solution to the original problem from a solution to the relaxed problem and prove a bound on its approximation accuracy. Our method also provides insights into the combinatorial structure of genome transformations with respect to appearance of circular chromosomes.

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