Numerous other modeling strategies have been or are being developed. Boolean networks are used for the qualitative analysis of complex gene regulatory networks containing large numbers of interacting components. In these models, each molecule is a node that can exist in either the active or inactive state, thereby affecting the state of the nodes it is linked to. Models of this sort provide insights into the flow of information through a network, and they were useful in helping us understand the complex gene regulatory network that controls the early development of the sea urchin (see Figure 7–43). Boolean networks therefore reduce complex networks to a highly simplified (and potentially inaccurate) form. At the other extreme are agent-based simulations, in which thousands of molecules (or “agents”) in a system are modeled individually, and their probable behaviors and interactions with each other over time are calculated on the basis of predicted physical and chemical behaviors, often while taking stochastic variation into account. Agent-based approaches are computationally demanding but have the potential to generate highly lifelike simulations of real biological systems.
Statistical Methods Are Critical For the Analysis of Biological Data
Dynamics, differential equations, and theoretical modeling are not the be-all and end-all of mathematics. Other branches of the subject are no less important for biologists. Statistics—the mathematics of probabilistic processes and noisy datasets—is an inescapable part of every biologist’s life.
This is true in two main ways. First, imperfect measurement devices and other errors generate experimental noise in our data. Second, all cell-biological processes depend on the stochastic behavior of individual molecules, as we just discussed, and this results in biological noise in our results. How, in the face of all this noise, do we come to conclusions about the truth of hypotheses? The answer is statistical analysis, which shows how to move from one level of description to
Figure 8–87 Different levels of gene expression in individual cells within a population of E. coli bacteria. For this experiment, two different reporter proteins (one fluorescing green, the other red), controlled by a copy of the same promoter, have been introduced into all of the bacteria. Some cells express only one gene copy, and so appear either red or green, while others express both gene copies, and so appear yellow. This experiment reveals variable levels of fluorescence, indicating variable levels of gene expression within an apparently uniform population of cells. (From M.B. Elowitz et al., Science 297:1183–1186, 2002. With permission from AAAS.) another: from a set of erratic individual data points to a simpler description of the WHAT WE DON’T KNOW key features of the data.
Statistics teaches us that the more times we repeat our measurements, the bet • Many of the tools that revolutionized ter and more refined the conclusions we can draw from them. Given many repeti-DNA technology were discovered by tions, it becomes possible to describe our data in terms of variables that summa-scientists studying basic biological rize the features that matter: the mean value of the measured variable, taken over problems that had no obvious the set of data points; the magnitude of the noise (the standard deviation of the applications. What are the best set of data points); the likely error in our estimate of the mean value (the standard strategies to ensure that such crucially important technologies will continue to error of the mean); and, for specialists, the details of the probability distribution be discovered?
describing the likelihood that an individual measurement will yield a given value. For all these things, statistics provides recipes and quantitative formulas that biol • As the cost of DNA sequencing ogists must understand if they are to make rigorous conclusions on the basis of decreases and the amount of variable results.
sequence data accumulates, how are we going to keep track of and Summary meaningfully analyze this vast amount of information? What new questions Quantitative mathematical analysis can provide a powerful extra dimension in our will this information allow us to answer? understanding of cell regulation and function. Cell regulatory systems often depend • Can we develop tools to analyze on macromolecular interactions, and mathematical analysis of the dynamics of each of the post-transcriptional these interactions can unveil important insights into the importance of binding modifications on the proteins in living affinities and protein stability in the generation of transcriptional or other signals.
cells, so as to follow all of their
Regulatory systems often employ network motifs that generate useful behaviors: changes in real time?