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Algebraic Geometric Approaches to Biological Complexity
Molecular networks are subject to many interactions between components, while the components themselves can exist in multiple states. Researchers need sophisticated mathematical methods to understand how such complex networks process information, as Dr Jeremy Gunawardena, Associate Professor at Harvard Medical School explains
Making sense of molecular networks
The complexity of molecular networks is a challenge for biology researchers, who need sophisticated new mathematical methods to track how these networks process information and make decisions. This is an area of long-standing interest to Dr Jeremy Gunawardena, coordinator of the Algebraic Geometric Approaches to Biological Complexity project. “This project is trying to exploit some methods from pure mathematics which have not been used in biology at the molecular level before. We think these methods have some very powerful features that allow us to rise above molecular complexity,” he says. Based at Harvard Medical School in the US, Dr Gunawardena and his colleagues are now using these ideas, which have their roots in a discipline called algebraic geometry, to get a sense of the capabilities of very complicated networks. “We’re really trying to get a functional understanding of the network of molecular interactions. The underlying complexity has two forms,” he outlines. “One is that there are a lot of interactions between the components. The other issue is that the components themselves can exist in multiple states. So you have the complexity of the components themselves, as well as the complexity of the interactions through which the components talk to each other.”
Chemical signals
The molecular networks within cells can be stimulated by external chemical signals, such as growth factors or hormones that are typically conveyed around the body in blood or within tissues. These signals impinge on molecules in the membrane of the cell, the receptor molecules. “These receptor molecules become activated, and they instigate a process of signal transduction inside the cell. They recruit various molecular components, and they undertake various forms of processing on that signal until the cell decides what to do as a result of seeing that signal. Signal transduction networks are typical of the systems we look at,” explains Dr Gunawardena. The signal might be a cue for the cell to begin to divide and proliferate, or to go down a differentiation pathway and become a particular type of cell. “These signal transduction networks could participate in decision-making in early development,” continues Dr Gunawardena. “Once the organism has actually been constructed and reached adulthood then evolution is very good at re-using these mechanims, so that the same signal transduction networks can implement the organism’s normal physiological responses. They can also become deranged when the organism falls ill, which is why understanding their functionality can help us develop more effective therapies.”
There are multiple layers of complexity within these networks, with various signals, mechanisms and events affecting the way they are structured. The project is mainly focusing on the protein level, at which there is a particularly high level of complexity. “Once a gene has been turned on, once a protein has been expressed and is present in the cell, evolution has found ways to actually modify the structure of the protein,” explains Dr Gunawardena. These modifications can occur with different chemical groups. “Pretty much any protein in any cell in your body is continuously being subjected to this post-
translational modification, as it’s called. So, even though that protein came from a single gene, and one might think; ‘ok we’ve got a single gene, we’ve got a single protein’ – in practice that protein could be in millions of modification states,” points out Dr Gunawardena. “We’re talking about just one protein here, and we have this huge network of proteins, all of which are interacting and different modification states of one protein may behave differently to other modification states of the protein. We’re particularly interested in these kinds of protein-level complexities that come from post-translational modification.”
Mathematical methods
Researchers are using mathematical methods to distil some of the underlying principles behind this complexity. These methods are potentially very powerful, because of the way in which chemistry works. “Once you describe biochemistry in mathematical terms and try to explain how biochemical reactions work, they give rise to polynomial equations. These equations are sums of many terms, each of which looks like a product of the key variables,” explains Dr Gunawardena. From a mathematical point of view algebraic geometry can be thought of as the mathematical study of polynomial systems; Dr Gunawardena believes that combining these methods with biochemical understanding could yield important results. “There’s often a lot of accumulated knowledge about some aspects of the complexity that we see, and a lot of experimental evidence for instance about the number of modification states that a particular protein would have, as well as knowledge about the reactions through which other proteins control and regulate those modifications,” he says. “We often start from knowledge of the network of reactions that is outlined in the literature, that’s typically our starting point. We try to use mathematics to distil predictions from that, which we can then test experimentally.”
The systems inside cells tend to have a lot of moving parts but only certain things can be measured experimentally. Researchers have discovered that it is possible to focus on a small number of components, and by doing so gain wider insights. “We could say; ‘we’re particularly interested in these components, because we think these are the key regulators,’”
Full Project Title
Algebraic Geometric Approaches to Biological Complexity
Project Objectives
My research group studies information processing in mammalian cells using a combination of experimental, mathematical and computational approaches. We are particularly interested in exploiting new methods from pure mathematics to distill biological principles from the new molecular understanding that has emerged from the Human Genome and other genome projects.
Contact Details
Project Coordinator, Jeremy Gunawardena Associate Professor, Virtual Cell Program Department of Systems Biology Harvard Medical School 200 Longwood Avenue Boston, MA 02115, USA T: +1 617 432 4839 E: jeremy@hms.harvard.edu W: http://sysbio.med.harvard.edu/ faculty/gunawardena/
Jeremy Gunawardena
explains Dr Gunawardena. The question here is whether it’s possible to eliminate all the background complexity, and just focus on the key components of interest; Dr Gunawardena says algebraic geometry provides methods for doing this in a systematic way. “It may be that there isn’t an equation between the components that we’ve selected, because there’s more complexity that we didn’t appreciate,” he
says. “But what we can do is try to work out the equations, and if we fail then that gives us a hint as to what other things we might want to include, until finally we’ve got a small set of things that include the components we’re interested in, as well as those we possibly hadn’t appreciated previously. We’ve got an equation on just those things, and now we can go and test that. We don’t have to measure everything in the network, we just have to look at those particular components.”
These methods could in principle be applied to virtually any system, but in practice they only work efficiently for relatively small systems because the current algorithms are slow and computationally expensive. However, Dr Gunawardena says it’s often the case that researchers can still get by with restricting attention to a simpler class of equations. “We’re interested in developing more powerful computational tools, computational algorithms which are much faster, but which only tell us about certain
kinds of equations, which are good enough for the problem at hand” he outlines. “Everyone who tries to study biology these days comes up against the problem of molecular complexity. We believe that algebraic geometry offers us a mathematical language which can help us rise above that complexity and thereby complement the insights which come from experimental studies. It can help us to look at very complicated molecular and cellular machines and identify the principles on which they work.”
Project Coordinator
Jeremy Gunawardena is a pure mathematician by training. He held academic appointments at the University of Chicago and Trinity College, Cambridge before joining Hewlett-Packard (HP) Research. He became HP’s Director of Basic Research in Europe before returning to academic life as Associate Professor at Harvard Medical School’s Department of Systems Biology.
