Research conducted in our group spans a broad range of topics related to the mathematical modeling of complex fluids and soft matter including multiscale modeling and simulation of viscoelastic fluid flows, viscoelastic and diffusive transport processes
in biopolymers, dynamic organization of chromosomes in yeast cells, and pituitary organogenesis.
The common thread in our research is the close collaboration between mathematicians and researchers from the biology, physics, chemistry and engineering fields. We have established the Complex Fluids Lab as part of the Math Department at UofSC. This lab is used both as a complement to our modeling and simulation approaches and as educational tool whose main objective is to show math majors how to apply experimental principles to formulate mathematical models and to interpret the data and to non-math majors how models provide rigorous information about a given process arising from experimental data and once formulated and solved, afford predictions beyond the experiments.
Critical chromosomal functions have been linked to the spatial conformation of chromosomes. Understanding the spatial dynamics of the genome is a crucial step in characterizing how DNA adopts and transitions between different functional states over
the course of the cell cycle, facilitating vital functions such as gene expression, DNA replication, recombination and repair.
Using mathematical models, we investigate the role that entropic forces play in the formation of domains of high chromosomal interactions. A persistent view is that this spatial organization is primarily established by enzymatic, biochemistry-guided cellular processes. We have shown that entropy and confinement dictate the leading order structure and dynamics of the genome, and the role of enzymes is to guide, stabilize, and sustain cycle-specific genome states. This work is in collaboration with Kerry Bloom’s lab and Greg Forest’s group at the University of North Carolina at Chapel Hill.
In mammalian organogenesis, progenitor cells carry out complex morphogenetic processes through the coordinated movement and rearrangement of individual cells. Such processes mediate the key developmental events responsible for the structural organization of organs and tissues. These cellular processes are difficult to assess through direct observation of embryos, especially for internal organs like the pituitary gland. Mathematical modeling provides an adaptable platform to simulate these dynamic processes and rigorously test assumptions generated from experimental observations. We combine pituitary experimental approaches and mathematical modeling to develop the first realistic model of pituitary organogenesis. This modeling platform will increase our understanding of and provide novel insight into the biological processes involved in pituitary organogenesis. This work is in collaboration with Shannon Davis’ group at the University of South Carolina.
Regions of highly repetitive DNA, such as those found in the nucleolus, show a self-organization that is marked by spatial segregation and frequent self-interaction. The mechanisms that underlie the sequestration of these sub-domains are largely
unknown. Using a stochastic, bead-spring representation of chromatin in budding yeast, we find enrichment of protein-mediated, dynamic chromosomal cross-links recapitulates the segregation, morphology and self-interaction of the nucleolus. Rates
and enrichment of dynamic crosslinking have profound consequences on domain morphology.
Our model demonstrates the nucleolus is phase separated from other chromatin in the nucleus and predicts that multiple rDNA loci will form a single nucleolus independent of their location within the genome. We propose that nuclear sub-domains, such as the nucleolus, result from phase separations within the nucleus, which are driven by the enrichment of protein-mediated, dynamic chromosomal crosslinks. This work is in collaboration with Kerry Bloom’s lab and Greg Forest’s group at the University of North Carolina at Chapel Hill.
Human airways diseases, such as cystic fibrosis (CF) and chronic obstructive pulmonary disease (COPD), compromise host defense, often resulting in airways inflammation and infection. Mucus clearance and trapping of inhaled pathogens constitute key elements of host defense. Clearance rates are governed by mucus viscous and elastic moduli at physiological driving frequencies, whereas transport of trapped pathogens in mucus layers is governed by diffusivity. There is a clear need for the formulation of constitutive models capable of predicting and correlating these properties. Human bronchial epithelial (HBE) cell cultures are a transformational assay for exploring the fundamental biological process of mucus transport in the lung. Our research focuses on the formulation of mucus constitutive modeling from micro- and macro-rheological experimental data and building numerical methods to solve the flow of mucus in the cell culture geometry and in physiologically-relevant conditions. This work is in collaboration with Greg Forest’s group and David Hill’s group at the University of North Carolina at Chapel Hill.
The mechanisms by which sister chromatids maintain biorientation on the metaphase spindle are critical to the fidelity of chromosome segregation. Active force interplay exists between predominantly extensional microtubule-based spindle forces and
restoring forces from chromatin. These forces regulate tension at the kinetochore that silences the spindle assembly checkpoint to ensure faithful chromosome segregation. Models of the spindle apparatus with linear chromatin springs that match
spindle dynamics fail to predict the behavior of pericentromeric chromatin in wild-type and mutant spindles.
We have demonstrated that a nonlinear spring with a threshold extension to switch between spring states predicts asymmetric chromatin stretching observed in vivo. The addition of cross-links between adjacent springs recapitulates coordination between pericentromeres of neighboring chromosomes. This work is in collaboration with Kerry Bloom’s lab and Greg Forest’s group at the University of North Carolina at Chapel Hill.
Chromatin exhibits increased mobility on DNA damage, but the biophysical basis for this behavior remains unknown. To explore the mechanisms that drive DNA damage–induced chromosome mobility, we use single-particle tracking of tagged chromosomal
loci during interphase in live yeast cells together with polymer models of chromatin chains. Polymer simulations predict altered centromere and telomere localizations on release of tethering.
This work is in collaboration with Kerry Bloom’s lab at the University of North Carolina at Chapel Hill.