A precarious balance.

Many areas of modern science and engineering owe their strength and vitality to a rich interplay of experiment, theory and computation. For example, quantum chemistry, aerodynamics, meteorology and membrane electrophysiology are all firmly based on extensive quantitative observations, sound theoretical formalisms and accurate, predictive calculations. Molecular cell biology, on the other hand, is still, for the most part, proudly and precariously balanced on one leg – experimental observations – and its staunchest defenders believe that theoretical and computational approaches have little or nothing to contribute to our understanding of cell physiology (see Peter Lawrence's recent essay in these pages Theoretical embryology: a route to extinction?[1xTheoretical embryology: a route to extinction?. Lawrence, P. Curr. Biol. 2004; 14: R7–R8Abstract | Full Text | Full Text PDF | PubMedSee all References[1]).This view is surely wrong. A living cell is an intrinsically dynamical system, ceaselessly adapting in space, time and internal state to environmental challenges. Catalogs of genes and static diagrams of the structural and functional relationships of proteins, though necessary for full understanding, can never adequately account for the dynamism of organelles and cells. Take, for example, cilia: these beautiful tiny whips, attached to many cells, lash back and forth in wondrous synchrony, propelling cells through liquids or liquids past cells. Without cilia you wouldn't have been born (they transport eggs from ovary to uterus) and you couldn't breathe (they continually sweep mucus and debris from the lungs and airways). How do these elegant little machines accomplish their essential tasks?Open any modern textbook of cell biology and you will find an attempt to answer this fundamental question. What you will see is a parts list of a typical cilium – dynein, tubulin, nexin, and so on – and a pseudo-color, artist's rendition of how the parts seem to be connected. Then a few words about how dynein molecules can pull on microtubules, causing then to slide past each other. End of story.This explanation leaves me unsatisfied. How am I to understand the dynamic function of a cilium from this static textbook picture? The essence of a cilium is to move in space and time. What principles organize the tiny pulls of each dynein motor into the ‘power stroke’ that sweeps along the cilium from base to tip? What forces drive the recovery stroke along a trajectory so different from the power stroke? What invisible choreographer synchronizes the movements of vast fields of cilia to carry the egg to its destination?These sorts of questions cannot be answered by cataloging parts, defining their connections, and drawing schematic diagrams. The problem demands a movie. “Well then, if you want a movie, go to the electronic version of the textbook and click on the icon for the quick time movie of a beating cilium.” What you will see is either a living cilium observed through a microscope or an animated cartoon of how the author imagines a cilium to move. But animation is not scientific explanation; it is likely to be as entertaining and as fundamentally mistaken as a Road Runner cartoon.What we desire is a realistic computation of the coordinated motion of a field of cilia, based on solid principles of biochemistry and biophysics, including the forces exerted by motor proteins on the stiff and elastic components of the axoneme, and the forces exerted by cilia on the viscoelastic liquid in which they are immersed. Although much interesting work has been done on this problem [2.xAn integrative model of internal axoneme mechanics and external fluid dynamics in ciliary beating. Dillon, R.H. and Fauci, L.J. J. Theor. Biol. 2000; 207: 415–430Crossref | PubMed | Scopus (46)See all References, 3.xA three-dimensional model for ciliary motion based on the internal 9+2 structure. Gueron, S. and Levit-Gurevich, K. Proc. R. Soc. Lond. B. Biol. Sci. 2001; 268: 599–607Crossref | Scopus (30)See all References, 4.xComputer simulation of flagellar movement VIII: Coordination of dynein by local curvature control can generate helical bending waves. Brokaw, C.J. Cell Motil. Cytoskeleton. 2002; 53: 103–124Crossref | PubMed | Scopus (54)See all References, 5.xGeometric clutch model version 3: The role of the inner and outer arm dyneins in the ciliary beat. Lindemann, C.B. Cell Motil. Cytoskel. 2002; 52: 242–254Crossref | PubMed | Scopus (36)See all References, 6.xStructural-functional relationships of the dynein, spokes and central pair-projections predicted from an analysis of the forces acting within a flagellum. Lindemann, C.B. Biophys. J. 2003; 84: 4115–4126Abstract | Full Text | Full Text PDF | PubMedSee all References], a full and satisfying solution remains for the future.View Large Image | View Hi-Res Image | Download PowerPoint SlideEvery aspect of molecular cell biology faces the same challenge. How do cells move, feed, grow, divide, secrete, anticipate sunrise, find mates and avoid dangers? In the 1960s and 70s, some brave souls speculated about the dynamical systems underlying these behaviors before knowing anything about the molecular components inside the black box. For example, Rene Thom and Christopher Zeeman (much maligned by Lawrence) were basically correct in their contention that cells should be thought of as dynamical systems governed, in a deep sense, by the generic bifurcations of vector fields. Unfortunately, they picked the wrong sort of vector field: a gradient of potential, a good model in many areas of physics, but a bad assumption in biology. Nonetheless, in recent years it has been shown that the same sorts of bifurcations envisioned by Thom and Zeeman arise from realistic models of gene–protein networks and explain a great deal about the qualitative dynamical behavior of cells [7xComputational cell biology. Fall, C.P., Marland, E.S., Wagner, J.M., and Tyson, J.J. See all References[7].Another early practitioner of topological reasoning in biology was Arthur Winfree, whose stunning revelation of a ‘timeless’ point for the circadian oscillator was based on elegant theoretical ideas and unconventional experimental designs [8xThe geometry of biological time. Winfree, A.T. CrossrefSee all References[8]. Winfree later used high performance computing to uncover the timeless points in heart muscle that are the organizing centers of lethal cardiac arrythmias.Over the last ten years, an appreciation of dynamics has appeared in some areas of cell biology. People are tracing cell behavior back to elementary parts lists by means of realistic computational models based on sound equations of biophysics and biochemistry. My favorite examples include Bray et al.[9xComputer simulation of the phosphorylation cascade controlling bacterial chemotaxis. Bray, D., Bourret, R.B., and Simon, M.I. Mol. Biol. Cell. 1993; 4: 469–482Crossref | PubMedSee all References[9] on bacterial chemotaxis, Arkin et al.[10xStochastic kinetic analysis of developmental pathway bifurcation in phage λ-infected Escherichia coli cells. Arkin, A., Ross, J., and McAdams, H.H. Genetics. 1998; 149: 1633–1648PubMedSee all References[10] on lambda phage infections, and Teusink et al.[11xCan yeast glycolysis be understood in terms of in vitro kinetics of the constituent enzymes? Testing biochemistry. Teusink, B., Passarge, J., Reijenga, C.A., Esgalhado, E., van der Weijden, C.C., Schepper, M., Walsh, M.C., Bakker, B.M., van Dam, K., Westerhoff, H.V. et al. Eur. J. Biochem. 2000; 267: 5313–5329Crossref | PubMed | Scopus (400)See all References[11] on glycolysis. In all cases, the models provide accurate simulations – not just imaginative animations – of some aspect of cell physiology. From these models and simulations come insights and predictions that cannot be reached by intuition alone. It seems that a new generation of cell biologists is ready to stand on all three feet.