Cell Cycle Dynamics and Clustering

Project Summary

Steady progress has been made in understanding how cells communicate in populations. Communication and quorum sensing are a dominant topic in biology. Surprisingly little work has been done to understand how communication and feedback influence the cell cycle coordination of growth and division. Working in yeast we have shown that population density and cell cycle dependent feedback of simple form appears to produce periodic population structure generically. The mathematical results, observed across a wide range of models, with and without randomness, suggest the phenomena is robust. Experimental evidence supports the mathematical modeling and the existence of pseudo-synchronized clusters of cells. The main observation is that feedback that results in cell cycle advances and or delays of a subpopulation of cells causes the population density to become multimodal and clustered. The particular form of the feedbacks are patterned on biological knowledge of the mechanisms of intercellular communication via metabolites and pheromones. Despite this natural underpinning and the prevalence of these mechanisms in biology, very little mathematical attention has been devoted to feedback dynamics of this form. Our recent work shows that the size and location of signaling and responsive regions within the cell cycle influences the number of emergent clusters. Yeast of different generations have different cell cycle lengths and these necessarily interact with the feedback mechanism in the formation of clusters. This suggests a bifurcation picture in which the geometry of the cell cycle is more influential than the explicit form and strength of the feedback. By focusing narrowly on phenomenological models of feedback that involve density dependence and the geometry of the cell cycle we will make progress toward understanding the phenomenon of clustered solutions and lay the foundations of a bifurcation theory in this setting. We have shown several ways in which periodic population structures can be exploited in biology and bioprocess. The mathematical models are essential for understanding the dynamical aspects of the population structure and its bifurcations because the experimental methods do not exist to observe them as yet. The goals of this project are to develop and analyze a wide range of mathematical models that robustly develop clustered population structures to understand the essential features of this phenomenon.

The principal investigator for the project is Erik Bozcko of Vanderbilt University School of Medicine. The mathematical part of this research will be coordinated by Todd Young and much of it will occur in the Department of Mathematics at Ohio University, a state university located in the Appalachian region of southeastern Ohio, with a renewed commitment to strengthening its research at all levels. The research group will include both undergraduate and graduate students, who will contribute to this project and develop valuable skills in computational mathematics. The students will also learn about the research process and develop their skills at communicating mathematics.

Acknowledgments

This work is supported by the National Science Foundation, National Institutes of Health, Joint DMS/NIGMS Initiative to Support Research in the Area of Mathematical Biology grant NIH-NIGMS 1R01GM090207-0109. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation or the National Institutes of Health.

Goals

Scientific Goal

The primary scientific goal is to deepen our understanding of the cell cycle in biological systems and how the cell cycle influences other biological process of cells and organisms. The role of the group at Ohio University is to develop mathematical tools for understanding the models that arise in the study of the cell cycle and other biological process that react with it. These mathematical goals are being pursued symbiotically with the biological goals. Biology has driven models and analysis of models has informed experiments.

Educational Goal

By participating in this research project, students will learn specific mathematical and computational skills, learn about specific biological systems and how they can be modelled and also develop an understanding of how science and mathematics research works. Since the students will range from advanced doctoral students to undergraduates, the desired outcome will vary with the individual. Students at all levels will develop the ability to express mathematical ideas, both in writing and orally.

Process Goal

Both science and education are imprecise, imperfect processes. By consciously monitoring the process we use when pursuing the scientific and educational goals, we will attempt to continually improve this process.

Opportunities to Participate

This project has many facets, from purely theoretical mathematical considerations, to very concrete programming tasks. The interests of individual students will be accommodated whenever possible. There are several levels at which you can participate, from exploratory to full-time research.

Exploratory Participation

Anyone who wishes to can join the project for one quarter. You will learn more about the project, as well as develop valuable skills in mathematical writing, searching the literature, reading a research paper, presenting a seminar talk, and programming. I will learn about your strengths and weaknesses, and we both will learn how well you would fit into the research effort.

Each week we will have a group meeting where we will discuss what was accomplished on the project so far and what the next steps should be. As exploratory participants you will have a small task to complete each week. A common task each week is to write a journal entry about what you did. A sample weekly plan of other tasks for the quarter is as follows:

Write your mathematical autobiography, using LaTeX.
Write up something mathematical (like a homework assignment for a class) using LaTeX.
Read the introduction to the latest research paper from this project. Write a short summary in your own words of the topic, and some questions you had.
Program something very simple in Matlab.
Create a design for a subroutine to compute something related to this project, and write about it.
Implement the subroutine you designed, and test it. (Re-implement the subroutine if needed.)
Locate and get copies of two papers referenced by this project.
Read the two papers and write a paragraph summary of the topic of each. Choose your favorite.
Present your paper.
Critique the presentations of others.

Research Assistants

For graduate students in the Mathematics department, a limited number of paid research assistantships are available. In general, a student must participate at the exploratory level for one quarter before being considered for a paid assistantship. For Ph.D. students, assistantships will generally support summer work on thesis research.

For undergraduate students, paid research assistantships are available for 5-10 hours per week, at an hourly rate of $10/hr. In the near future, credit for MATH 492 Undergraduate Research (Teir III equivalent) may be available instead.

Each participant's research project will be determined to meet their interests and level. To help keep them on track and progressing toward the overall project's three goals, there are the following specific expectations:

Meet weekly with the research group.
Each week submit a journal of what they did the previous week, questions or difficulties they encountered, and what they plan to do next.
Each week update a summary document of what they have learned so far that quarter. This document contains research results and other information that should be preserved. At the end of the quarter this becomes their final report.
Be prepared each week to informally present to the group what they have done. Give a formal presentation at least once per quarter.
Assist in the direction of more junior participants.
Give feedback and suggestions on how the group's research process could be improved.