Download My research interests lie broadly in mathematical biology, though my

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R EGINALD L. M C G EE II
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I NTRODUCTION
My research interests lie broadly in mathematical biology, though my work to date has been centered on the analysis of models for physiological systems. My thesis focuses on deterministic
modeling of signal transduction pathways in B cells. Collaborations with experimentalists have
motivated and impacted the direction of much of my present work. Quantitatively investigating
biological problems has required me to utilize existing computational methods and mathematical
tools, but I also seek to make theoretical contributions. Future problems I will consider involve the
initiation of immune responses and intracellular signaling in other physiological systems.
I primarily use tools from dynamical systems and numerical analysis to investigate cellular
physiology questions of interest. A common challenge in modeling biological systems is the determination of parameters that reproduce biological data. This challenge can be exacerbated as
the number of model parameters increases, and also by nonlinearities and multiple time scales,
which are intrinsic properties of a dynamical system. Additionally, there is often limited data for
tuning model parameters, and conducting additional experiments can be difficult and possibly expensive. Overcoming such challenges has been a primary focus of my thesis work. The constraints
listed above highlight the utility of experimental design methods, where experiments can be systematically chosen to reduce dynamic uncertainty. Additionally, these design approaches can help
modelers fit biological data while avoiding the nonlinear, and sometimes intractable, optimization
problems that arise in conventional parameter estimation.
My thesis is centered around several objectives:
* Developing and using computational models for predicting molecular mechanisms for cellular behaviors that have yet to be completely characterized.
* Determining the relationship between dynamic stability properties for intracellular signaling
models and experimentally observed cellular responses, given that such a relationship would
provide a new perspective for understanding cell response.
* Generalizing convergence results for experimental design to encompass other design criteria
that are useful in practice but that are not backed by theoretical justification.
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T HESIS W ORK
My interest in cellular structure and physiology and collaborations with experimentalists who are
investigating the behavior and influence of the kinase Syk in B cells have motivated much of my
thesis work. My research experiences have generated a long term interest in understanding cell
response from a quantitative perspective.
2.1
M ODELING S IGNAL T RANSDUCTION PATHWAYS
Experimentalists have found that catalytically active Syk plays a central role in B cell receptor
(BCR) signaling, but questions still remain about the kinase’s behavior and the timing of its critical interactions. Analog-sensitive Syk (Syk-AQL), a mutated version of the kinase, has been
engineered to accept orthogonal inhibitors that cause the kinase to be rendered inactive almost immediately [8]. Syk-AQL provides experimentalists the ability to control the time that the kinase
remains active following receptor engagement, and has helped to confirm how BCR signaling is
modulated by the actions of Syk.
With a larger goal of understanding the full variety of B cell responses, we chose first to capture Syk-AQL behavior with a computational model of BCR signaling. Previous collaborations
between our group and experimentalists led to a mechanistic T cell receptor (TCR) model with
good predictive capabilities [11, 9]. Due to the similarities in signaling networks between T cells
and B cells, the TCR model provides a good starting point for model development. Thus, we
arrived at the following question:
Question 2.1 Can an existing TCR model be revised for BCR signaling and then be used to quantify behaviors of Syk and make further predictions?
I assumed primary responsibility for leading the revisions to the TCR model and formulating
dynamics for Syk-AQL and several other features unique to BCR signaling. The model is largely
biophysical, with individual variables representing each of the various forms of the species considered. After constructing the BCR model there was a need to tune the model parameters, which had
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been originally fit for T cell data. The T cell parameters placed within the revised signaling network led to issues with model stiffness, and thus unusually slow computation times. Additionally,
there were biologically infeasible oscillations during some simulations, arising from numerical error. Both issues required that we were deliberate in the choice of integrators used to to simulate
the model. Furthermore, the order of the numerical methods in all integrators tested was reduced
to two to ensure that the method was A-stable; the reduction of order removed the oscillations.
To further combat slow computation times, all scripts used were parallelized to run on twelve
cores on servers in the math department. Following the use of a sparse grid interpolation implementation of Sobol sensitivity analysis [3] to identify significant reaction parameters in the network,
we screened model simulations against cellular assay data that we collected. Each simulation corresponded to a vector in a 6000 point Latin hypercube sample of parameter space. Five parameter
vectors were determined that produced graded responses to BCR stimulation as is observed experimentally. In a recent paper [7], using the best of the five parameter vectors, we partially addressed
Question 2.1 by demonstrating qualitative agreement between our model and an independent set
of dose response data from literature for both mutant and wild-type kinases showing its validity
and predictive capacity.
2.2
S TABILITY ANALYSIS AND C ELL R ESPONSE
In addition to predictions about the signaling network components and interactions, I am currently
interested in understanding how cell responses are generated. Of the cell responses – activation
(proliferation), apoptosis (cell death), and anergy (chronic unresponsiveness) – anergy is the most
peculiar response. If there is insufficient stimulation collectively across the BCRs or from another
activated cell, B cells become anergic [1]. Once anergic, only a significant stimulation can force
cells from this state. This behavior is analogous to the behavior seen in stable steady states. Given
that stability is often of interest when considering dynamical systems, a question is:
Question 2.2 Can observed cell responses be put into correspondence with the results of stability
analysis for the BCR signaling model?
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Bistability has been found in some TCR receptor models [6], and a model for early BCR
signaling events was shown to exhibit different modes of stability after performing bifurcation
analysis [2], showing precedent for this type of study. Complications that could arise in the process
of addressing this question are a lack of variety of stability displayed by our model or continued
issues with model stiffness, which leads to subpar computation times. These issues may require
retuning parameters and slight model revisions. However, any future model development to our
BCR signaling model would also require more experimental data. This is one motivation for my
interest in experimental design.
2.3
E XPERIMENTAL D ESIGN
Due to time and cost constraints, there is a limit to the number of experiments that can be realistically performed. Furthermore, certain experiments could be more useful for reducing dynamic
uncertainty, and this needs to be considered when choosing experiments. One approach to designing experiments are the Maximally Informative Next Experiment (MINE) criteria [5]. MINE
sequentially selects a single or multiple experiment to conduct depending on which of the three
criteria is being implemented.
The first criteria selects a single point in time to conduct an experiment based the point of
largest uncertainty (simulation variance). Recently, the first criteria of MINE was used to construct an estimator for system dynamics, and it was shown that the estimated dynamics converge
uniformly to the true biological dynamics [4]. The next natural question is:
Question 2.3 Can new estimators be constructed utilizing the other two MINE criteria and are
similar convergence results possible in these cases?
The later two criteria are primarily concerned with simultaneously reducing points with large uncertainty, but doing so in a manner that ensures the points are chosen as independently as possible.
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F UTURE R ESEARCH P LANS
I plan to broaden my current mathematical and scientific work to include:
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* Mathematical and computational investigation of intracellular signaling in other physiological systems
* Modeling the coordination of B cells and T cells using both intracellular and intercellular
interactions, and investigating the associated generation of immune responses.
Before beginning the B cell project and studying signal transduction, I spent eighteen months
learning tools for a project on cardiac modeling. The cardiac project did not come to fruition, but it
provided more exposure to the theory of dynamical systems and to object-oriented programming.
My experiences studying both immune cells and cardiac cells should prove invaluable in studying
other areas of cellular physiology in the future. For example, my background on intracellular
signaling will allow me to investigate molecular mechanisms for excitation-contraction dynamics
in cardiac and other muscle cells.
In future research I plan to consider the spatial and stochastic aspects of modeling signaling pathways. The size of the BCR model (37 dimensional) makes it less amenable to standard
dynamical systems tools like normal forms and phase plane analysis; applying model reduction
techniques to obtain models of a more tractable size will afford me the opportunity to implement
these techniques.
A longer term direction concerns agent-based modeling for biological processes. A recent
workshop and related paper [10] sparked an interest in how mean field theory can be used to
replace discrete agent-based simulations by continuum models. These experiences have inspired
the question:
Question 3.1 Can continuum modeling at the cellular level be melded with signal transduction
modeling at the molecular level and used to study how immune responses are initiated and how
they propagate?
The formulation in [10] leads to an advection-diffusion equation, while the addition of signaling dynamics corresponds in some sense to the addition of a reaction term. The main challenges
here are to specify the precise form of this PDE and show that it captures the dynamics seen with
agent-based models and physiologically.
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R EFERENCES
[1] S. F. A NDREWS AND P. C. W ILSON, The anergic b cell, Blood, 115 (2010), pp. 4976–4978.
[2] D. BARUA , W. S. H LAVACEK , AND T. L IPNIACKI, A computational model for early events
in b cell antigen receptor signaling: Analysis of the roles of lyn and fyn, Journal Immunology,
189 (2012), pp. 646–658.
[3] G. B UZZARD, Global sensitivity analysis using sparse grid interpolation and polynomial
chaos, Reliability Engineering & System Safety, 107 (2012), pp. 82–89.
[4] V. D INH , A. RUNDELL , AND G. B UZZARD, Experimental design for dynamics identification
of cellular processes, Bulletin of Mathematical Biology, 76 (2014), pp. 597–626.
[5] W. D ONG , X. TANG , Y. Y U , R. N ILSEN , R. K IM , J. G RIFFITH , J. A RNOLD , AND H.B. S CHTTLER, Systems biology of the clock in neurospora crassa, PLoS ONE, 3 (2008),
p. e3105.
[6] T. L IPNIACKI , B. H AT, J. R. FAEDER , AND W. S. H LAVACEK, Stochastic effects and bistability in t cell receptor signaling, Journal of Theoretical Biology, 254 (2008), pp. 110 – 122.
[7] R. L. M C G EE , M. O. K RISENKO , R. L. G EAHLEN , A. E. RUNDELL , AND G. T. B UZ ZARD , A computational study of the effects of syk activity on b cell receptor signaling dynamics, (approx. 17 pages). (Submitted).
[8] H. O H , E. O ZKIRIMLI , K. S HAH , M. L. H ARRISON , AND R. L. G EAHLEN, Generation
of an analog-sensitive syk tyrosine kinase for the study of signaling dynamics from the b cell
antigen receptor, Journal of Biological Chemistry, 282 (2007), pp. 33760–33768.
[9] J. P. P ERLEY, J. M IKOLAJCZAK , M. L. H ARRISON , G. T. B UZZARD , AND A. E. RUN DELL, Multiple model-informed open-loop control of uncertain intracellular signaling dynamics, PLOS Computational Biology, 10 (2014), pp. 1296–1310.
[10] M. J. S IMPSON , K. A. L ANDMAN , AND B. D. H UGHES, Multi-species simple exclusion
processes, Physica A: Statistical Mechanics and its Applications, 388 (2009), pp. 399 – 406.
[11] Y. Z HENG AND A. RUNDELL, Comparative study of parameter sensitivity analyses of the
tcr-activated erk-mapk signalling pathway, IEE Proceedings - Systems Biology, 153 (2006),
pp. 201–211.