Funded Grants

Spatial patterns of yeast cell growth and division: Molecular mechanisms and mathematical models; Substance and Significance

While the sequencing of the human genome is a great triumph of the late 20th Century, it poses an even greater challenge for 21st Century Science. How do we determine the complex physiology of a living cell from the digital information (strings of A,C,T,G) encoded in its genome? In broad strokes, we know how this information is read out: genetic sequences are translated into polypeptide chains (strings of amino acids); these chains fold up into delicate three-dimensional structures (proteins) that carry out most of the jobs in a cell; proteins act not in isolation but in intricate networks of self-regulating functionality; from these functional subsystems arises the goal-directed behavior of the living cell. Each step in this read-out is a research area studied by hosts of experimentalists. Less evidently, each step entails challenging theoretical and computational problems, on whose solution future progress depends. For instance, no really reliable methods for predicting protein structure from sequence exist, and ab initio calculation of function from structure is still a primitive art. The most neglected aspect of the read-out problem is the "last step," from complex networks of interacting proteins to the regulated behavior of intact cells. How are complex patterns of gene expression laid down during the first hours of development of a fruit fly embryo? How do epithelial cells know when to start and stop proliferation to close a wound? How does a bread mold anticipate the rising of the sun? How do yeast cells modulate their shape?

In each of these cases, the behavior of the cell or tissue is intricately coordinated in time and space by an underlying molecular regulatory system, governed by physicochemical laws that are locally deterministic. In order to survive, compete, and reproduce in a hostile world, living organisms behave as if they possess "clocks and maps," which must be created from such seemingly chaotic, disorganized, purposeless processes as chemical reactions, molecular diffusion, convective transport, and the like.

For many years now, it has been known that large-scale spatiotemporal organization can arise spontaneously from sufficiently complex, nonlinear, reaction-diffusion-convection systems. The basic principles of biocomplexity theory were laid down in the "heroic age" (by Lotka, Volterra, Rashevsky, Turing, Hodgkin & Huxley, Prigogine, and others) and fruitfully applied to a wide variety of cell- and tissue-level problems in the 1960s and 70s (by Hess, Goldbeter, Segel, Winfree, Oster, Perelson, Goodwin, and others). In our opinion, the field of theoretical cell biology reached an impasse in the 1980s: the fundamental idea of order-from-chaos was firmly established, but the actual molecular machinery underlying most cellular responses were still shrouded in mystery. In principle, we knew how to derive the coordinated behavior of cells from underlying mechanisms, if only we knew what those mechanisms were.

The situation changed dramatically in the 1980s, with the development of modern methods of molecular genetics. With these tools, experimentalists could dissect the molecular machinery of almost any physiological response in "model" organisms with well-characterized genetic systems. Indeed, this program was so successful that its practitioners, taking delight in each new piece of the puzzle, lost sight of the original goal of reconstructing the integrated behavior of intact cells and organisms from the underlying molecular components. Only recently have leading molecular biologists issued a call for theoretical and computational tools to carry out this reconstruction .

Recent calls for a theory to connect network dynamics to cell physiology.

Fraser & Harland, Cell 100:41 (2000)"[R]esults to date show a dizzying array of signaling systems acting within and between cells . In such settings, intuition can be inadequate, often
giving incomplete or incorrect predictions . ... In the face of such complexity,
computational tools must be employed as a tool for understanding."

Nurse, Cell 100:71 (2000) "Perhaps a proper understanding of the complex regulatory networks making up cellular systems like the cell cycle will require a ... shift from
common sense thinking. We might need to move into a strange more
abstract world, more readily analyzable in terms of mathematics than our
present imaginings of cells operating as a microcosm of our everyday
world."

Brent, Cell 100:169 (2000) "For a few prokaryotes and subsystems within eukaryotic cells, we are at or near a level of description where we can enumerate key players ... Better
predictive ability may depend on representations [of the key players] that
incorporate kinetic information. The classical frameworks for this are, of
course, systems of differential equations that describe the rates at which
enumerated species change ..."

Aebersold, Hood & "As it generates data on scales of complexity and volume unprecedented in
Watts, Nature biological sciences, defying analysis by normal means of interpretation,
Biotechnology 18:359 presentation, and publication, discovery science depends on the integration of computational tools to store, model, and disseminate these exploding
cascades of information . ... Ultimately, systems biology aims to establish
computational models that are predictive of the behavior of the system or its
emergent properties in response to an given perturbation."

Hartwell, Hopfield, "The best test of our understanding of cells will be to make quantitative predictions about their behaviour and test them. This will require detailed simulations of the biochemical processes taking place within [cells] . We need to develop simplifying, higher-level models and find general principles that will allow us to grasp and manipulate the functions of [biochemical networks]."

Ventner, quoted in Nature "If we hope to understand biology, instead of looking at one little protein at a 402:C70 (1999) time, which is not how biology works, we will need to understand the integration of thousands of proteins in a dynamically changing environment.
A computer will be the biologist's number one tool."

What these molecular biologists don't realize is that the tools they desire are already available, developed and refined by two generations of biocomplexity theorists. The greatest challenge of the next decade, in our opinion, is to demonstrate that the fundamental principles of spatiotemporal organization in nonlinear dynamical systems can be applied advantageously to the messy world of contemporary molecular biology. The goal of this next phase is to build realistic, comprehensive, accurate, predictive, computational models of the molecular machinery underlying fundamental cellular processes, such as cell growth and division, movement, interand intracellular signaling, cell suicide, embryonic development, etc.

Models at this level of detail and complexity are new not only to molecular biologists, who are used to purely intuitive arguments about mechanisms, but also to mathematical biologists, who have favored simple, elegant, dynamical models unsullied by the messy realities of living organisms. In order to be taken seriously by molecular biologists, a new generation of theoreticians must come to terms with these realities. On the other hand, experimentalists must learn that computers will not solve all their problems, that to understand how cell physiology derives from molecular interactions they will need help from sophisticated techniques of nonlinear dynamics (bifurcation theory, pattern formation, robustness, distributed control, etc.).