Physical approaches to the dynamics of genetic circuits: A tutorial

Physical approaches to the dynamics of genetic circuits: A tutorial Jordi Garcia-Ojalvo Departament de F´ısica i Enginyeria Nuclear Universitat Polit`ecnica de Catalunya Rambla de Sant Nebridi s/n, 08222 Terrassa, Spain Email: jordi.g.ojalvo@upc.edu May 22nd, 2011 Abstract Cellular behavior is governed by gene regulatory processes that are intrinsically dynamic and nonlinear, and are subject to non-negligible amounts of random fluctuations. Such conditions are ubiquitous in physical systems, where they have been studied for decades using the tools of statistical and nonlinear physics. The goal of this review is to show how approaches traditionally used in physics can help in reaching a systems-level understanding of living cells. To that end, we present an overview of the dynamical phenomena exhibited by genetic circuits and their functional significance. We also describe the theoretical and experimental approaches that are being used to unravel the relationship between circuit structure and function in dynamical cellular processes under the influence of noise, both at the single-cell level and in cellular populations, where intercellular coupling plays an impor- tant role. To be published in Contemporary Physics. 1 Introduction One of the main questions to be answered in the quest towards understanding life is how structure relates with function in living systems, in particular in cells. This question can be asked at many levels, from the microscopic scale of single proteins to the macroscopic level of complete organ- isms. A substantial amount of evidence has recently pointed to the relevance of a “mesoscopic” description, at the level of networks of interacting genes and proteins that coordinately govern most cellular processes [1]. This picture has relegated the notion of “one gene, one function” (and frequently “one disease”) that guided much of genetics and molecular biology in most of the 20th century. Within that framework, countless experimental evidence was gathered that revealed the identity of genes and proteins involved in diverse cellular functions. Using that in- valuable information, it is now time to rephrase the question posed above in terms of finding the relationship between cellular function and the architecture of the underlying genetic networks. Two main factors make the solution of this problem difficult. First, the number of proteins and genes involved in these gene regulatory networks is usually very large. This, together with the frequently nonlinear character of their interactions, gener- ates a highly complex behavior, riddled with multiple coexisting phenomena and impossible to 1 arXiv:1105.4335v1 [q-bio.MN] 22 May 2011 understand from the sum of the effects of the individual network elements. The situation is further complicated by the ubiquitous existence of heterogeneity and stochasticity inherent to the intrinsic randomness of biochemical interactions, which are forced to take place in a small and crowded bioreactor such as the cell. A tool frequently used to face this complexity is math- ematical modeling, which allows us to test what possible behaviors arise from a given molecular network. In the words of the computational cell biologist John Tyson, trying to understand living systems is “something like finding a jumble of jigsaw puzzle pieces in a paper bag”. We do not have the model of the picture that we should put together, we are not sure whether all the pieces are in the bag, and we do not even have a table to test if the pieces fit together. “Mathematical modeling provides the table” [2]. But the use of models highlights another problem that arises from the large size of typical gene regulatory networks: the number of parameters to be adjusted is frequently tremendously large, thus the problem of fitting the model to experimental data becomes seriously underdetermined. A second factor that prevents us from relating the architecture of gene regulatory networks with cellular function is the fact that cellular processes are strongly dynamic. Indeed, protein expression in cells varies in general with time, due either to temporal changes in the exter- nal conditions of the cells (such as circadian rhythms originated in the suprachiasmatic nuclei of mammals, which affect the rest of cells in the organism via the endocrine system), or to self-generated dynamical behavior (such as the cell cycle in dividing cells). Thus the complex networks of genes and proteins mentioned above, and the intricate pattern of interactions among them, are far from being static. It is therefore necessary to take into account that not all network connections are active at all times, and that it is the dynamical pattern of connectivity what has to be related with cellular function. Fortunately, the dynamic character of gene regulation alleviates the problems caused by the complexity of the underlying genetic networks. First, nonlinear physics tells us that dynamical behavior does not require a large numb

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