Computational Biology

Our computational biology activities are focused on modeling the cell cycle regulatory network in yeast. They are a collaborative effort with John Tyson and T. M. Murali at Virginia Tech.

Computational Biology

Developing mathematical models of the phenotype encoded in DNA sequences in one of the fundamental problems of biology. Historically, geneticists have used statistical models. Now that we better understand the molecular mechanisms of the cellular physiology, it becomes possible to develop mathematical models that capture the dynamics of cellular processes. We are particularly focusing on stochastic models that take into account the randomness of the interactions among small populations of molecules enclosed in individual cells. Genes are present in one or two copies per cell. mRNAs are also present at low copy numbers ranging from a few copies per cell to tens of copies per cell (see figure below). Proteins tend to be more abundant. Even a few hundreds or a few thousands of copies in a cell are extremely small compared to the size of molecular populations in conventional chemistry.

We are particularly focusing on stochastic models that take into account the randomness of the interactions among small populations of molecules enclosed in individual cells. Genes are present in one or two copies per cell. mRNAs are also present at low copy numbers ranging from a few copies per cell to tens of copies per cell (see figure below). Proteins tend to be more abundant. Even a few hundreds or a few thousands of copies in a cell are extremely small compared to the size of molecular populations in conventional chemistry.

single-cell-data-cell-cycle-regulation

In this picture of yeast cells, the transcripts of a gene controlling the cell cycle are labeled with a green fluorescent probe. Each dot corresponds to a single mRNA molecule.

Our work aims at understanding how cellular phenotypes are fairly predictable despite the noise affecting the biomolecular networks that determine the cell phenotype.We are particularly interested in understanding the effect of molecular noise on the control of cell division.

The cell cycle is the process by which a growing cell replicates its genome and partitions the two copies of each chromosome to two daughter cells at division. It is of utmost importance to the perpetuation of life that these processes of replication (DNA synthesis) and partitioning (mitosis) be carried out with great fidelity. In eukaryotic cells, DNA synthesis (S phase) and mitosis (M phase) are separated in time by two gaps (G1 and G2). Proper alternation of S phase and M phase is enforced by `checkpoints’ that block progression through the cell cycle if the genomic integrity of the cell is compromised in any way. For example, if DNA is damaged in G1 phase a checkpoint blocks progression into S phase until the damage can be repaired. If replicated chromosomes are not properly aligned on the mitotic spindle, a different checkpoint blocks progression into anaphase (the phase of sister chromatid separation) until all sister chromatids are properly attached to opposite poles of the spindle. Checkpoints are able to block cell cycle progression by sending a STOP signal to the molecular mechanisms that govern specific cell-cycle transitions (G1-S, G2-M, and M-G1).

Stochastic model of cellular noise

The molecular mechanisms that govern each of these transitions have a peculiar property called `bistability.’ Under physiological conditions, the control mechanism can persist indefinitely in either of two characteristic states: the OFF state, which corresponds to holding the cell cycle in the pre-transition phase; and the ON state, which corresponds to pushing the cell cycle into the post-transition phase. Checkpoint STOP signals seem to act by stabilizing the appropriate bistable switches in its OFF state. Because these checkpoints are crucial to maintaining the integrity of an organism’s genome from one generation of cells to the next, it is vital that they function reliably even in the face of random molecular fluctuations that are inevitable in a cell a small as a yeast cell (30 fL). Calculations based on stochastic models of the molecular mechanisms governing cell cycle progression suggest that checkpoint functions are indeed robust in wild-type budding yeast cells, but they may be compromised in strains carrying mutations of specific checkpoint genes.

Our goal is to develop the mathematical models and collect experimental data needed to understand how cell cycle checkpoints operate reliably in wild-type yeast cells and how they fail in mutant cells. To reach this goal will require new advances in stochastic modeling and in the technology of measuring mRNA and protein molecules in single yeast cells. To test the models we construct new cell cycle mutants and characterize their phenotypes.

Because all eukaryotic organisms seem to employ the same fundamental molecular machinery that governs progression through the cell division cycle, the understanding of checkpoint operations in yeast cells will translate into a better understanding of checkpoint functions and failures in other types of cells, most notably human cells.

Computational Biology Publications