Gerda De Vries

Biography

Gerda de Vries is an assistant professor belongs to the department of Mathematical & Statistical Sciences from the university of Alberta.

Research Interest

Determining kinetic parameters underlying protein dynamics We use mathematical models to interpret FRAP (Fluorescence Recovery After Photobleaching) data obtained in the nucleus. The experimental data contains information about the mobility of nuclear proteins. Conventional models assume that the dynamics of the proteins are governed by diffusion alone, and are used to determine estimates of an effective diffusion coefficient for the proteins. For many proteins, the effective diffusion coefficient is orders of magnitude smaller than the diffusion coefficient expected based on the molecular weight of the proteins. We have hypothesized that the mobility of the proteins is reduced because of their temporary association with immobile or slowly moving nuclear structures. Incorporating such hypothesis in a PDE model leads to systems of reaction-diffusion equations, solutions of which are non-trivial. We have proposed an alternate modelling approach, namely to use compartmental modelling, leading to a system of ODEs much easier to analyze, and simplifying the task of parameter estimation. Using perturbation analysis, we have characterized fluorescence recovery curves. The analysis has led to a clear explanation of two important limiting dynamical types of behaviour exhibited by experimental recovery curves, namely, (1) a reduced diffusive recovery, and (2) a biphasic recovery characterized by a fast phase and a slow phase. The perturbation analysis also led to a relationship of the results of the two different modelling approaches (reaction-diffusion equations versus compartmental modelling). We have applied our results in the analysis of FRAP data of both nuclear actin and histone H1. We showed that the FRAP data for actin is consistent with the hypothesis that nuclear actin exists in both monomeric and filamentous forms (this is a highly controversial topic in cell biology, and although many researchers believe this to be the case, there is not yet definitive proof), and obtained estimates of binding and unbinding rates (of monomeric actin to and from filamentous actin). The second application was in the context of histone H1 dynamics. Histone H1 molecules are either bound to a spatially homogeneously distributed chromatin structure, or unbound and free to diffuse. Fluorescence recovery data suggest that almost all of the histone H1 population is bound to the chromatin structure, and only a very small proportion of the histone H1 molecules are free to diffuse. This small proportion allows histone molecules to move randomly from one binding site to another, which we believe is crucial for the functional dynamics of histone (in particular, if histone H1 proteins were permanently associated with chromatin, it would be more difficult for chromatin remodelling factors to gain access to chromatin). This research answers questions about modelling methodology in interpreting experiments on protein dynamics. Correct determination of kinetic parameters underlying protein dynamics is essential for further modelling work, and contributes to the understanding of nuclear processes. Origin of nuclear compartments An interesting and open problem in cell biology concerns the dynamic nature of nuclear architecture. Under certain conditions, such as viral infection and transcriptional inhibition, the nuclear architecture undergoes profound changes, with compartments either being disassembled or enlarged. Furthermore, most nuclear compartments are observed to disassemble during the M-phase of the cell cycle, and reassemble in the daughter cells. The current focus in our research is to understand the dynamical organization of the eukaryotic cell nucleus. In particular, we are addressing the mechanism responsible for the formation, maintenance and disappearance of speckles, which are heterogeneously distributed nuclear compartments enriched with pre-mRNA splicing factors. It has been hypothesized that self-organization of dephosphorylated splicing factors, modulated by a phosphorylation-dephosphorylation cycle, is responsible for the origin and disappearance of speckles. Also, it is thought that the existence of an underlying nuclear structure plays a major role in the organization of splicing factors. Based on these hypotheses, we have derived a fourth-order aggregation-diffusion model that describes a possible mechanism underlying the organization of splicing factors in speckles. A linear stability analysis about homogeneous steady-state solutions has shown how the self-interaction among dephosphorylated splicing factors can result in the onset of spatial patterns. Also, a bifurcation analysis of the model can describe how the processes of phosphorylation and dephosphorylation modulate the onset of the compartmentalization of splicing factors. This research advances knowledge in the area of spatial pattern formation. Specifically, it addresses the origin of nuclear architecture, which ultimately affects nuclear function. Successful outcomes of this research puts us in a better position to predict outcomes of changes in nuclear architecture, such as seen with cancer. This research is in collaboration with PhD student Gustavo Carrero and Dr. Michael Hendzel from the Cross Cancer Institute, Department of Oncology, University of Alberta. Bursting oscillations In my earlier research, I have focussed attention on mathematical models of electrical activity in pancreatic beta-cells. These cells produce and secrete the hormone insulin, which is the principal hormone regulating the blood glucose level. In the presence of glucose, these cells exhibit a complex pattern of oscillations called bursting. Pancreatic beta-cells are organized in clusters, called islets of Langerhans, and bursting is synchronized within islets. The synchronization is due to coupling between neighbouring cells, through low-resistance electrical pathways called gap junctions. Modelling efforts related to the electrical activity of beta-cells can be divided broadly into two categories, single-cell models and coupled-cell models. Single-cell models typically include much biophysical detail, and are used to explain specific experimental observations. These models represent bursting as observed in an islet, and a single-cell model can be viewed as a model of the behaviour of an average cell within an islet. Coupled-cell models typically include less biophysical detail, so that attention can be focussed on the role of coupling in the generation of synchronized oscillations. During the last few years, my attention has been concentrated on coupled-cell models for pancreatic beta cells. Through mathematical and computational analyses of these models, I have obtained a broad and deep understanding of the role of coupling, and its interaction with system noise and parameter variability, in the generation of network behaviour. A recent discovery is bursting as an emergent phenomenon (bursting obtained in a network of cells, each of which is incapable of bursting individually). Research on bursting oscillations continues within a broadened context. In particular, attention is focussed on a comparison of coupling mechanisms, and their effect on different classes of bursting models, as well as on the behaviour of discrete-time models that generate bursting oscillations. Bursting oscillations are observed in many electrically excitable cells other than pancreatic beta cells, such as thalamic neurons and hippocampal pyramidal neurons. This research therefore has strong reciprocal connections with mathematical neurophysiology.