The sequencing of the human genome has inspired many to anticipate a time when the most complicated biological phenomena will be understood in detail. But sceptics worry that a simple list of genes and proteins, no matter how complete, will be as useless to biologists as a list of a computer's transistors would be to an understanding of the software used to browse the online version of this article. At a recent meeting*, however, both sides found cause for optimism in computational and mathematical approaches to complement experiments in unravelling complex biological processes.
Computation is so prominent in genomics that the naive observer could be excused for mistaking this field for a branch of robotics or computer science. But the computational approaches discussed at the meeting were firmly focused on post-genomic issues — the dynamics and control of the networks of genes and proteins at work in cells. Here, increasingly sophisticated software packages, such as those at the web links listed at the end of this article, are proving vital. With them, biologists are finally gaining access to technology that has hitherto been restricted to the design of complex engineering systems, such as integrated circuits, aircraft, communication networks and chemical-processing plants. Many experimentalists are using mathematical modelling and computation to study biological systems that are just too complex to be understood by intuition and informal models. Meanwhile, those who are developing computational models fully appreciate that their models must be integrated with experimental data.
The control of the cell-division cycle is one area where complex molecular mechanisms, worked out by legions of molecular biologists, have been codified into a single mathematical model (J. Tyson, Virginia Polytechnic Inst.). Building such a model requires a long process of data collection and verification, but the efforts are well worth it. For example, models like this can be used to test theories about cellular processes by comparing the effects of virtual and real mutated genes.
The most popular mathematical models, in this and other studies, involve ordinary and partial differential equations to represent chemical kinetics. But models that systematically integrate several scales are also important. For example, stochastic chemical kinetics (D. Bray, Univ. Cambridge) can be used to model individual molecular interactions at various levels of detail. Such models capture fluctuations that tend to clump together in models based simply on differential equations. Also, the chemical dynamics of cells must be integrated with mechanical aspects (D. Ingber, Harvard Med. School), which — just as in complex engineering systems — become increasingly important at the network level. In another parallel to engineering principles, a model that integrates hypersensitivity and positive feedback in a signalling pathway known as the MAP kinase cascade predicts the occurrence of switch-like behaviour, where some internal chemical state of the pathway switches, as in a digital system (J. Ferrell, Stanford Univ.). Such behaviour is uncovered experimentally only when single cells are analysed (which is not common).
Widespread interest in sophisticated software is new. But the general approach of integrated modelling has a long and successful history. Computer modelling of individual ion channels and transporters in cardiac cells, at the level of differential equations, goes back 40 years. Since then, models of heart function have incorporated further details, such as pacemaker activity, the genetic defects underlying arrhythmic heart beats, mechanical–electrical feedback, and regional patterns of expression of ion transporters, to the point where high-fidelity simulations of the whole heart are possible (D. Noble, Oxford Univ.). Iterative interactions between experiment and simulation, and between molecular mechanisms and the physiology of the whole organ, were essential to this success.
Speaking from the experimentalist's point of view, T. Pollard (Salk Inst., San Diego) described how computation fits into a broad agenda for analysing cell-biological data. He detailed a model for cell motility, which involves actin filaments — a type of cytoskeletal structure. The model was constructed from a huge amount of experimental knowledge, including quantitative data on the identities, affinity constants and reaction rates of the interacting molecules. Such data are collected only rarely, but will become increasingly important.
Several other areas of biology have benefited from the interaction of experiment and modelling. For example, reaction–diffusion models (standard models of spatially dependent chemical kinetics) formed the basis for the first detailed picture of the transport of molecules into and out of the nucleus (A. Smith and I. Macara, Univ. Virginia). Likewise, the transport and sorting of proteins between the endoplasmic reticulum and the Golgi complex have been analysed by combining modelling with studies involving fluorescent markers (J. Lippincott-Schwartz, NIH, Bethesda). The transport of fluorescently labelled RNA granules to cellular sites of protein synthesis can be broken down into three characteristic patterns — vibrations, oscillations and movement. A stochastic model, integrating the rates at which motor proteins bind to these granules and are activated, can account for all of these behaviours (J. Carson, Univ. Connecticut Health Center).
Finally, the availability of electrophysiological and fluorescence methods to obtain quantitative data has made the dynamics of calcium ions one of the most popular subjects for modelling. A new model of calcium 'sparks' — the release of calcium ions from an organelle known as the sarcoplasmic reticulum — can account for the previously mysterious 'termination' phase of a spark (J. Lederer, Univ. Maryland). This model involves interactions within a cluster of calcium channels, and regulation of the channels by calcium within the sarcoplasmic reticulum. Sparks in skeletal muscle can be studied in preparations from frog muscle, and have been further analysed with a model that incorporates the characteristics of the microscope used to gather the data (D. Uttenweiler, Univ. Heidelberg). An image-based model of calcium waves in a neuron (L. Loew, Univ. Connecticut Health Center) emphasized the role of cell geometry, which can control the spatial and temporal patterns of calcium ions.
A prominent theme was that biology needs more theory, in addition to modelling and computation, to make sense of complex networks. Without underlying theories, software would be of limited use in engineering systems. Theory has a rather bad reputation among biologists, in part because the ideas so popular in physics — such as pattern formation, critical phase transitions and chaos — have proved largely irrelevant to molecular biology. So far, engineering theories of communication, control and computing have had little contact with biology, but perhaps that should change. If biologists are much like physicists in stretching the limits of experimental reductionism, they are also like engineers in revelling in the enormity, variety and sheer complexity of the systems they study. No interest in spherical cows here.
Web links
http://www.cds.caltech.edu/erato
http://websites.ntl.com/~igor.goryanin
http://members.tripod.co.uk/sauro/biotech.htm