## MBI Publications

### MBI Publications for 2010 (40)

• K. Zhao
On the isothermal compressible Euler equations with frictional damping
Communications in Mathematical AnalysisVol. 9 (2010) pp. 77-97

#### Abstract

This paper aims at initial-boundary value problems(IBVP) for the isothermal compressible Euler equations with damping on bounded domains. We first prove global existence and uniqueness of classical solutions for smooth initial data. Time asymptotically, it is shown that the density converges to its average over the domain and the momentum vanishes as time tends to infinity. Due to diffusion and boundary effects, the convergence rate is shown to be exponential. Second, based on the entropy principle, it is shown that similar results hold for $L^infty$ entropy weak solutions.
• K. Zhao
2D inviscid heat conductive Boussinesq equations on a bounded domain
Michigan Mathematical JournalVol. 59 (2010) pp. 329-352

#### Abstract

• M. Leite and Y. Wang
Multistability, Oscillations and Bifurcations in Feedback Loops.
Math. Biosci. EngVol. 7 No. 1 (2010) pp. 83-97

#### Abstract

Feedback loops are found to be important network structures in

regulatory networks of biological signaling systems because they are responsi-

ble for maintaining normal cellular activity. Recently, the functions of feedback

loops have received extensive attention. The existing results in the literature

mainly focus on verifying that negative feedback loops are responsible for oscil-

lations, positive feedback loops for multistability, and coupled feedback loops

for the combined dynamics observed in their individual loops. In this work,

we develop a general framework for studying systematically functions of feed-

back loops networks. We investigate the general dynamics of all networks with

one to three nodes and one to two feedback loops. Interestingly, our results

are consistent with ThomasÃ¢â?¬â?¢ conjectures although we assume each node in the

network undergoes a decay, which corresponds to a negative loop in ThomasÃ¢â?¬â?¢

setting. Besides studying how network structures influence dynamics at the

linear level, we explore the possibility of network structures having impact on

the nonlinear dynamical behavior by using Lyapunov-Schmidt reduction and

singularity theory.
• D. Turner, P. Paszek, D. Woodcock, D. Nelso, C. Horton, Y. Wang, D. Spiller, D. Rand, M. White and C. Harper
Physiological levels of TNFalpha stimulation induce stochastic dynamics of NF-kappaB responses in single living cells.
Journal of Cell BiologyVol. 123 No. 16 (2010) pp. p.p 2834-2843

#### Abstract

Nuclear factor kappa B (NF-Ã?ÂºB) signalling is activated by cellular stress and inflammation and regulates cytokine expression. We applied single-cell imaging to investigate dynamic responses to different doses of tumour necrosis factor alpha (TNFÃ?Â±). Lower doses activated fewer cells and those responding showed an increasingly variable delay in the initial NF-Ã?ÂºB nuclear translocation and associated IÃ?ÂºBÃ?Â± degradation. Robust 100 minute nuclear:cytoplasmic NF-Ã?ÂºB oscillations were observed over a wide range of TNFÃ?Â± concentrations. The result is supported by computational analyses, which identified a limit cycle in the system with a stable 100 minute period over a range of stimuli, and indicated no co-operativity in the pathway activation. These results suggest that a stochastic threshold controls functional all-or-nothing responses in individual cells. Deterministic and stochastic models simulated the experimentally observed activation threshold and gave rise to new predictions about the structure of the system and open the way for better mechanistic understanding of physiological TNFÃ?Â± activation of inflammatory responses in cells and tissues.
• S. Cantrell, C. Cosner and Y. Lou
Evolution of dispersal and ideal free distribution
Math Bios. Eng.Vol. 7 (2010) pp. 17-36

#### Abstract

• W. Ding, H. Finotti, S. Lenhart, Y. Lou and Q. Ye
Optimal control of growth coefficient on a steady-state population model
Nonlinear Analysis: Real World ApplicationsVol. 11 (2010) pp. 688-704

#### Abstract

• R. Hovmoller, B. Alexandrov, J. Hardman and D. Janies
Tracking the Geographic Spread of Avian Influenza (H5N1) with Multiple Phylogenetic Trees
CladisticsVol. 26 No. 1 (2010) pp. 1-13

#### Abstract

• J. Tien and D. Earn
Multiple transmission pathways and disease dynamics in a waterborne pathogen model
Bulletin of Mathematical BiologyVol. 72 No. 6 (2010) pp. 1506-1533

#### Abstract

• N. Filipski and M. Golubitsky
The abelian Hopf H mod K theorem
SIAM J. Appl. Dynam. Sys.Vol. 9 No. 2 (2010) pp. 283-291

#### Abstract

• A. Fiebig, C. Castro Rojas, D. Siegal-Gaskins and S. Crosson
Interaction specificity and toxicity in a paralogous set of ParE/RelE-family toxin-antitoxin systems
Mol MicrobiolVol. 77 (2010) pp. 236-251

#### Abstract

• Y. Lou, W. Ni and L. Su
An indefinite nonlinear diffusion P problem in population genetics, II: Stability and multiplicity
Disc. Cont. Dynam. Sys. Series AVol. 27 (2010) pp. 643-655

#### Abstract

• A. Bezuglyy and Y. Lou
Reaction-diffusion models with large advection coefficients
Applicable AnalysisVol. 89 (2010) pp. 983-1004

#### Abstract

• W. Polonik and Z. Wang
PRIM Analysis
J. of Multivariate AnalysisVol. 101 (2010) pp. 525-540

#### Abstract

• H. Coskun and H. Coskun
Cell Physician: Reading Cell Motion. A Mathematical Diagnostic Technique Through Analysis of Single Cell Motion
Bulletin of Mathematical Biology (2010)

#### Abstract

• H. Coskun, T. Summerfield, D. Kniss and A. Friedman
Mathematical Modeling of Preadipocyte Fate Determination
Journal of Theoretical BiologyVol. 265 No. 1 (2010)

#### Abstract

• S. Dai and D. Schaeffer
Chaos for cardiac arrhythmias through a one-dimensional modulation equation for alternans
ChaosVol. 20 No. 023131 (2010)

#### Abstract

• Y. Kim and A. Friedman
Interaction of tumor with its microenvironment : A Mathematical Model
Bulletin of Mathematical BiologyVol. 72 No. 5 (2010) pp. 1029-1068

#### Abstract

• G. Enciso, M. Rempe, A. Dmitriev, K. Gavrikov, D. Terman and S. Mangel
A Model of Direction Selectivity in the Starburst Amacrine Cell Network
J Comput Neurosci.Vol. 28 No. 3 (2010) pp. 567-578

#### Abstract

• A. Nevai, K. Passino and P. Srinivasan
Stability of choice in the honey bee nest-site selection process.
Journal of Theoretical BiologyVol. 263 (2010) pp. 93-107

#### Abstract

• S. Dai and D. Schaeffer
Bifurcations in a modulation equation for alternans in a cardiac fiber
Math. Modeling and Num. AnalysisVol. 44 (2010) pp. 1225-1238

#### Abstract

• T. Hallam, A. Raghavan, H. Kolli, D. Dimitrov, P. Federico, H. Qi, G. McCracken, M. Betke, J. Westbrook, K. Kennard and T. Kunz
Dense and sparse aggregations in complex motion: video coupled with simulation modeling
Ecological ComplexityVol. 7 (2010) pp. 69-75

#### Abstract

• Y. Kim and A. Friedman
Interaction of tumor with its microenvironment: A Mathematical Model
Bulletin of Mathematical BiologyVol. 72 No. 5 (2010) pp. 1029-1068

#### Abstract

This paper is concerned with early development of transformed epithelial cells (TECs) in the presence of fibroblasts in the tumor microenvironment. These two types of cells interact by means of cytokines such as transforming growth factor (TGF-beta) and epidermal growth factor (EGF) secreted, respectively, by the TECs and the fibroblasts. As this interaction proceeds, TGF-beta induces fibroblasts to differentiate into myofibroblasts which secrete EGF at a larger rate than fibroblasts. We monitor the entire process in silico, in a setup which mimics experiments in a Tumor Chamber Invasion Assay, where a semi-permeable membrane coated by extracellular matrix (ECM) is placed between two chambers, one containing TECs and another containing fibroblasts. We develop a mathematical model, based on a system of PDEs, that includes the interaction between TECs, fibroblasts, myofibroblasts, TGF-beta, and EGF, and we show how model parameters affect tumor progression. The model is used to generate several hypotheses on how to slow tumor growth and invasion. In an Appendix, it is proved that the mathematical model has a unique global in-time solution.
• Y. Kim, J. Wallace, F. Li, M. Ostrowski and A. Friedman
Transformed Epithelias cells (TEC) and fibroblasts/myofibroblasts interaction in Breast Tumor: A Mathematical Model and Experiments
Journal of Mathematical BiologyVol. 61 No. 3 (2010) pp. 401-421

#### Abstract

It is well known that tumor and its microenvironment, or stroma, interact with each other and that this interaction plays a critical role in tumor initiation, growth, and metastasis. This interaction consists of complex relations between tumor cells, stromal cells such as fibroblasts, epithelial cells and immunocytes, the vascular system, the extracellular matrix, and cytokines secreted by the cells. Understanding these relationships may lead to new therapeutic approaches to cancer. In the present paper, we consider tumor-stroma crosstalk in a simple in vitro situation which involves interaction between tumor epithelial cells from breast cancer and a microenvironment consisting of just fibroblasts. The two populations of cells are separated by a semi-permeable membrane that allows only cytokines to cross over. We develop a mathematical model that includes two critical growth factors: TGF-beta, produced by the tumor cells, and EGF, secreted by the fibroblasts. The TGF-beta modifies the microenvironment by transforming fibroblasts into myofibroblasts. Myofibroblasts secrete higher concentrations of EGF than fibroblasts, thereby, increasing the proliferation of tumor cells. Thus already in this simple setup one sees a mutual interaction between tumor cells and their microenvironment. We conducted experiments which show good agreement with the model's simulations, hence confirming the model's ability to predict aspects of tumor cell behavior in response to signaling from fibroblasts.
• Y. Kim and S. Lim
The role of the microenvironment in tumor invasion
2009 Proceedings of the Fourth SIAM Conference on Mathematics for Industry (2010) pp. 84-92

#### Abstract

Fibroblasts and myofibroblasts in the tumor microenvironment are important players in tumor growth and metastasis because of their unique ability to coordinate events which increase cell proliferation and invasion especially in breast cancer. It has been experimentally shown that fibroblasts play an important role in promoting tumor growth. Our study illustrates a model in which tumor cells are able to communicate with these fibroblasts/myofibroblasts through proteinases for active invasion toward stroma near breast ducts.
• X. Liu, P. Srinivasan, E. Collard, P. Grajdeanu, K. Lok, S. Boyle, A. Friedman and J. Zweier
Oxygen regulates the effective diffusion distance of nitric oxide in the aortic wall
Free Radic Biol MedVol. 48 No. 4 (2010) pp. 554-559

#### Abstract

Endothelium-derived nitric oxide (NO) is critical in maintaining vascular tone. Accumulating evidence shows that NO bioavailability is regulated by oxygen concentration. However, it is unclear to what extent the oxygen concentration regulates NO bioavailability in the vascular wall. In this study, a recently developed experimental setup was used to measure the NO diffusion flux across the aortic wall at various oxygen concentrations. It was observed that for a constant NO concentration at the endothelial surface, the measured NO diffusion flux out of the adventitial surface at [O2] = 0 Î¼M is around fivefold greater than at [O2] = 150 Î¼M, indicating that NO is consumed in the aortic wall in an oxygen-dependent manner. Analysis of experimental data shows that the rate of NO consumption in the aortic wall is first order with respect to [NO] and first order with respect to [O2], and the rate constant k1 was determined as (4.0 Â± 0.3) Ã— 103 Mâˆ’1 sâˆ’1. Computer simulations demonstrate that NO concentration distribution significantly changes with oxygen concentration and the effective NO diffusion distance at low oxygen level ([O2] â‰¤ 25 Î¼M) is significantly longer than that at high oxygen level ([O2] = 200 Î¼M). These results suggest that oxygen-dependent NO consumption may play an important role in dilating blood vessels during hypoxia by increasing the effective NO diffusion distance.
• P. Grajdeanu, R. Schugart, A. Friedman, D. Birmingham and B. Rovin
Mathematical framework for human SLE Nephritis: disease dynamics and urine biomarkers
Theoretical Biology and Medical ModellingVol. 7 No. 14 (2010)

#### Abstract

Although the prognosis for Lupus Nephritis (LN) has dramatically improved with aggressive immunosuppressive therapies, these drugs carry significant side effects. To improve the effectiveness of these drugs, biomarkers of renal flare cycle could be used to detect the onset, severity, and responsiveness of kidney relapses, and to modify therapy accordingly. However, LN is a complex disease and individual biomarkers have so far not been sufficient to accurately describe disease activity. It has been postulated that biomarkers would be more informative if integrated into a pathogenic-based model of LN.
This work is a first attempt to integrate human LN biomarkers data into a model of kidney inflammation. Our approach is based on a system of differential equations that capture, in a simplified way, the complexity of interactions underlying disease activity. Using this model, we have been able to fit clinical urine biomarkers data from individual patients and estimate patient-specific parameters to reproduce disease dynamics, and to better understand disease mechanisms. Furthermore, our simulations suggest that the model can be used to evaluate therapeutic strategies for individual patients, or a group of patients that share similar data patterns.
We show that effective combination of clinical data and physiologically based mathematical modeling may provide a basis for more comprehensive modeling and improved clinical care for LN patients.
• S. Lim and E. Jung
A three-dimensional model of a closed valveless pup system immersed in a viscous fluid
SIAM J. Appl. Math.Vol. 70 No. 6 (2010) pp. 1999-2010

#### Abstract

: We present a three-dimensional model of flow driven by pumping without valves (valveless pumping) in a closed loop system in which the closed loop of tubing is immersed in an incompressible viscous fluid. This closed tube consists of two parts, an open cylindrical soft tube and an open rigid tube, smoothly connected to one another. At an asymmetric location of the soft tube, a periodic compress-and-release action with a time delay between actions is taken to create a net flow. Numerical results show that the magnitude of average net flow and flow direction inside the tube depend on the pumping frequency, the amplitude of periodic forcing, the compression duration, the length of the soft tube, and the elastic properties of the tube. Fluid viscosity is also found to influence net flow. The immersed boundary method is used to investigate the interaction between the tube and the fluid and to study the valveless pumping mechanism. (A correction to the this article has been appended at the end of the pdf file.)
• J. Day, L. Schlesinger and A. Friedman
Tuberculosis research: Going forward with a powerful "Translation Systems Biology" approach
Tuberculosis (Edinb)Vol. 90 No. 1 (2010) pp. 7-8

#### Abstract

Due to the complexity of the immune response to a Mycobacterium tuberculosis infection, identifying new, effective therapies and vaccines to combat it has been a problematic issue. Although many advances have been made in understanding particular mechanisms involved, they have, to date, proved insufficient to provide real breakthroughs in this area of tuberculosis research. The term â€œTranslational Systems Biologyâ€? has been formally proposed to describe the use of experimental findings combined with mathematical modeling and/or engineering principles to understand complex biological processes in an integrative fashion for the purpose of enhancing clinical practice. This opinion piece discusses the importance of using a translational systems biology approach for tuberculosis research as a means by which to go forward with the potential for significant breakthroughs to occur.
• J. Day, J. Rubin and G. Clermont
Using nonlinear model predictive control to find optimal therapeutic strategies to modulate inflammation
Math. Biosci. Eng.Vol. 7 No. 4 (2010) pp. 739-763

#### Abstract

Modulation of the inflammatory response has become a key focal point in the treatment of critically ill patients. Much of the computational work in this emerging field has been carried out with the goal of unraveling the primary drivers, interconnections, and dynamics of systemic inflammation. To translate these theoretical efforts into clinical approaches, the proper biological targets and specific manipulations must be identified. In this work, we pursue this goal by implementing a nonlinear model predictive control (NMPC) algorithm in the context of a reduced computational model of the acute inflammatory response to severe infection. In our simulations, NMPC successfully identifies patient-specific therapeutic strategies, based on simulated observations of clinically accessible inflammatory mediators, which outperform standardized therapies, even when the latter are derived using a general optimization routine. These results imply that a combination of computational modeling and NMPC may be of practical use in suggesting novel immuno-modulatory strategies for the treatment of intensive care patients.
• D. Siegal-Gaskins, M. Mejia-Guerra, G. Smith and E. Grotewold
Emergence of switch-like behavior in a large family of simple biochemical networks
PLoS Computational BiologyVol. 7 No. 5 (2010)

#### Abstract

• A. Fiebig, C. Castro Rojas, D. Siegal-Gaskins and S. Crosson
Interaction specificity and toxicity in a paralogous set of ParE/RelE-family toxin-antitoxin systems
Mol MicrobiolVol. 77 (2010) pp. 236-251

#### Abstract

• A. Friedman, B. Hu and C. Xue
Analysis of a mathematical model of ischemic cutaneous wounds
SIAM J. Math. Anal.Vol. 42 No. 5 (2010) pp. 2013-2040

#### Abstract

• S. Arragain, S. Handelman, F. Forouhar, F. Wei, K. Tomizawa, J. Hunt, T. Douki, M. Fontecave, E. Mulliez and M. Atta
Identification of eukaryotic and prokaryotic methythiotransferases for biosynthesis of 2-methylthio-N6-threonylcarbamoyladenosine in tRNA
J Biol Chem. (2010)

#### Abstract

• P. Bressloff and A. Oster
A theory for the alignment of cortical feature maps during development
Phys Rev E Stat Nonlin Soft Matter PhysVol. 82 No. 2 Pt 1 (2010)

#### Abstract

• Y. Kim, A. Friedman, J. Wallace, F. Li and M. Ostrowski
Transformed Epithelial cells (TEC) and fibroblasts/myofibroblasts interaction in Breast Tumor: A Mathematical Model and Experiments
Journal of Mathematical BiologyVol. 61 No. 3 (2010)

#### Abstract

• S. Hsu, S. Hsu and Y. Lou
Single species growth with light and advection in a water column
SIAM J. Appl. Math.Vol. 70 (2010) pp. 2942-2974

#### Abstract

• M. Golubitsky, D. Romano and Y. Wang
Network periodic solutions: full oscillation and rigid synchrony
NonlinearityVol. 23 (2010) pp. 3227-3243

#### Abstract

• C. Kao, Y. Lou and W. Shen
Random dispersal vs non-local dispersal
Disc. Cont. Dynam. Sys. Series AVol. 26 (2010) pp. 551-596

#### Abstract

• R. Parshad and J. Gutierrez
On the Well Posedness and Refined Estimates for the Global Attractor for the TYC model
Boundary Value ProblemsVol. 2010 (2010)

#### Abstract

• M. Eisenberg, F. Santini, A. Marsili, A. Pinchera and J. Distefano
TSH Regulation Dynamics In Central & Extreme Primary Hypothyroidism
ThyroidVol. 22 No. 11 (2010) pp. 1215-1228