Most cells possess the ability to change morphology or migrate in response
to environmental cues. To understand the molecular mechanisms that drive
cell movement requires a systems-level approach that combines computational
approaches, including mathematical modeling and image analysis tools, with
high-resolution microscopy of living cells. Here we present several
examples for how such an integrated research strategy has been
successfully applied. First, we combine stochastic modeling with novel
biosensors for monitoring the spatiotemporal dynamics of Rho GTPase
activity to investigate the role of RhoG in cell polarization and
migration. Next, mathematical modeling and quantitative image analysis
methods are used to establish the role of cerebral cavernous malformation
(CCM) proteins in vascular tube formation. Finally, we present a novel
computational method for tracking and quantifying changes in cell shape.

Social contacts provide the backbone over which infectious diseases are transmitted. The dynamic networks that describe the contact patterns of social systems over time make predicting disease outbreaks difficult. In this talk, I'll discuss some computational experiments that show how disease patterns on static networks are observably different from those on dynamic networks. I'll then provide some intuition about how to prove boundary conditions about transmission on networks that explain why and under what circumstances we are likely to see those differences.

This talk will discuss previous work on quadrupedal gaits and recent work on a generalized model for binocular rivalry proposed by Hugh Wilson. Both applications show how rigid phase-shift synchrony in periodic solutions of coupled systems of differential equations can help understand high level collective behavior in the nervous system.

Clinical oncology generates patient data spanning from the molecular scale to the whole-body scale, which tend to be used in isolation when planning patient care. There is no current technique to quantitatively combine these with novel in vitro experimental data into comprehensive models that can illuminate complex, systems-level emergent phenomena and improve therapeutic and surgical planning. In this talk, we will discuss efforts by my lab, the USC Physical Sciences Oncology Center, and the Consortium for Integrative Computational Oncology to solve these issues. With a focus on patient pathology-calibrated breast cancer modeling and multidisciplinary modeling of liver metastases, we will explore agent-based and continuum model calibration to individual patient data, integration with novel experimental measurements, and emergent predictions of macroscopic and systems-level behavior. We will discuss the implications for making and quantitatively testing biological hypotheses, and the role of computational modeling in facilitating a deeper understanding of biology, pathology, and radiology. More information can be found at MathCancer.org.

Given the difficulty in finding a cure for HIV/AIDS, a promising prevention
strategy to reduce HIV transmission is to directly block infection at the
portal of entry. The recent Thai RV144 vaccine trial offered the first
evidence that a vaccine may provide location protection and block HIV
transmission in the vagina. Unfortunately, the underlying mechanisms for
protection remain unclear. In this talk, we examine theoretically a
hypothesis that builds on Sam Lai's recent laboratory observation that
virus-specific antibodies (Ab) may be capable of trapping individual
virions in genital mucus secretions. Ab are known to have a weak –
previously considered inconsequential – binding affinity with the mucin
fibers that constitute cervicovaginal mucus (CVM). However, several Ab
may be bound to a single virion at the same time, multiplying the Ab-mucin
binding effect, thereby creating an indirect virion-mucin affinity. Our
model takes into account biologically relevant length and time scales,
while incorporating known HIV-Ab affinity and the respective diffusivities
of viruses and Ab in semen and CVM. The model predicts that HIV-specific
Ab in CVM can effectively immobilize HIV in a shock-like front near the
semen-CVM interface, far from the vaginal epithelium. The robustness of
the result implies that even weak Ab-mucin affinity can markedly reduce the
flux of virions reaching target cells. Beyond this specific application,
the model developed here is adaptable to other pathogens, mucosal barriers,
geometries, kinetic and diffusional effects, providing a tool for hypothesis
testing and producing quantitative insights into dynamics of immune-
mediated protection.