The Research Environment
This program is a partnership between the Virginia Bioinformatics Institute (VBI) and the Interdisciplinary Center for Applied Mathematics (ICAM).
The organizational principle of VBI is team science. The academic disciplines come
together as needed for a particular research project, rather than dissecting the project
into disciplinary components. Collaboration between computational and experimental
faculty is particularly encouraged. Space arrangements reflect the needs of projects.
Since its beginning in 2000, VBI researchers have
mentored many undergraduate students in a broad range of research projects. The program participants
will be assigned space within the research groups and will be exposed to the
daily operations of a large research enterprise.
The Interdisciplinary Center for Applied Mathematics (ICAM) is home to 10 core faculty
in mathematics and engineering and 4 affiliated faculty. Research areas range from
computational fluid dynamics and mathematical biology to control theory, numerical
analysis, and partial differential equations. It is housed in a small dedicated building with
high-performance computing resources, faculty and student offices, as well as a
conference room. The program participants will have access to ICAM resources and shared
space, and will meet with faculty mentors there.
Examples of Research Projects
Modeling and simulation of biological networks provides a scientific focus that is broad
enough to allow a variety of research projects but narrow enough so that all research
projects have common elements that unify the students’ research experience. Following
are four example projects.
1. Modeling and Simulation of Biochemical Networks.
The nematode Caenorhabditis elegans is one of the model organisms studied
extensively in molecular biology. Its genome has been sequenced and extensive
information is available about various aspects of its embryonal development. This project will focus on some aspects of the gene
regulatory network responsible for embryonal development of ectoderm and muscle
cells. Several genes have been identified as regulators of tissue development. What is largely unknown is the network
structure of the collection of genes responsible for tissue development.
have begun to address this problem by identifying the genes
regulated by PAL-1. They identified a regulatory cascade of genes by analyzing a time
course of DNA microarray data and the available literature.
The goal of the project is to make a dynamic model of a network of 14 muscle
development genes. This will be done in two steps.
The first step is to use a network inference algorithm, which provides a wiring diagram for the
network, that is, a directed graph with the genes as nodes and regulatory interactions as
edges. The next step will be to use the information from Step 1, together with
information from the literature, to build a Boolean network model of the regulatory
network.
2. Modeling and Control of Cancer with Drug Treatments
In this project we plan to extend previous models of the immune response to the growth
of breast cancer cells and investigate the impact of certain drug therapies on the cancer.
The models account for tumor cells during mitosis, interphase and quiescence and the
immune response cells. Also, in order to evaluate treatment strategies the models
include drug intervention terms. The resulting models are described by delay differential
equations and are typical in the existing literature.
Some models assume discrete delays and constant initial history functions.
It is much more realistic to assume that the number of cancer cells at the time of
detection (i.e. t = 0) was not constant for all previous time. This project addresses this
issue by allowing general initial histories and investigate the impact these initial
conditions have on the tumor growth and treatment. Also, we plan to allow distributed
delays in the model and recover the discrete delays as limits.
A second issue is concerned with developing long-term simulations of
models. It is possible to run a one or two
year simulation of a drug treatment case and produce a response that appears to predict
a successful ``cancer free state.'' However, if one continues that same run for five or ten
years longer, then it is possible to see a reemergence of the tumor. The issue is to
determine how to predict that the simulation is converging to a true steady state solution.
We propose to use sensitivity equation methods to analyze the sensitivity of the model
with respect to the initial data, parameters and drug treatments.
3. Sensitivity Analysis and a Dynamical Systems Study of an M. tuberculosis and HIV-1
Co-Infection Model
Tuberculosis (TB) has seen a resurgence in the past two decades. This is due to,
among other factors, an introduction of HIV. For this project, the students will study a
published model. This model describes the evolution of populations
of T cells, macrophages, HIV and M. tuberculosis resulting in four coupled nonlinear
ordinary differential equations (ODEs). The project will begin with a reading of the model
description and an identification of important model parameters. Sensitivity analysis
(quantifying the influence of model parameters on the outputs of the model) will then be
used to supplement the parameter identification. This model has four significant steady-
states: uninfected, HIV-only, TB-only, co-infected (nontrivial HIV and TB populations). In
addition, there are interesting model dynamics (Hopf and transcritical bifurcations, stable
improper nodes, etc.). The sensitivity analysis study will also be used to analyze the
effects of model parameters on bifurcation diagrams associated with this model. Upon
completion of this preliminary study, the students will investigate the inclusion of a
compartmental model that discriminates interactions occurring in the lymph cells and
periphery. This project will emphasize
modeling, numerical methods, sensitivity analysis, and dynamical systems theory for
ODEs. The students will be expected to have an undergraduate course on ODEs and
some exposure to numerical methods.
4. Dynamics of Infectious Diseases on Social Networks.
Classical models of epidemiological phenomena typically employ ordinary or partial
differential equations (ODEs, PDEs). Examples include SIR models where the fractions
of susceptible, infectious and recovered individuals are studied. A drawback of ODE and
PDE models is that it is difficult to study intervention strategies. For example, it is hard to
adapt these models to incorporate school closures and isolation of critical personnel.
Individual-based models are computationally demanding, but can be used for studies of
such interventions. In this case one considers the dynamics of the epidemiological
process over the actual social network representing individuals and their contacts.
Examples of such models and simulation systems are EpiSims and Simdemics.
In an individual-based model such as the EpiSims model, the study of interventions is
very natural and can be done directly on the level of the social contact network. As an
example, isolating a particular person corresponds to removing this person’s edges in
the social contact network. A goal in the study of these models is to understand how the
structure of the social contact graph governs the evolution of the dynamics.
In this project the students will learn about infectious diseases, how they are modeled as
dynamical systems over social networks (GDS), and how interventions affect
propagation. In the project the students will participate in ongoing research in the
Network Dynamics and Simulation Science Laboratory (NDSSL) at VBI. They will
conduct computer experiments and theoretical analyses relating the structure of the
social contact graph to phase space properties of the stochastic graph dynamical system
governing the epidemic. The dynamics will be analyzed through measures such as
epidemic curves, cumulative epidemic curves and vulnerability. The work will be done
as a cooperative effort with postdoctoral fellows and staff in NDSSL.
