Mathematics and 21st Century Biology (2005) / Chapter Skim
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4 Understanding Cells
4 Understanding Cells
Pages 51-79
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From page 51... ...
There is a long and successful history of mathematical modeling of cellular functions. The success stories come from systems that are rich in data and for which models can be validated or at least put in direct corre 51
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From page 52... ...
The result should be an increased ability to evaluate models, which is the limiting step in improving them. It is now possible to collect multivariable and spatiotemporally resolved data on cellular processes ranging from molecular trafficking and signal transduction to integrated responses such as the cell division cycle and cell migration.
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From page 53... ...
and ErbB2 proteins are shown for clarity, but the behaviors of ErbB3 and ErbB4 are similar to that of ErbB2. Activated EGFR and EGFR:ErbB2 heterodimers are internalized through a coated pit pathway, but other members of the ErbB family are probably internalized by a smooth pit pathway.
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From page 54... ...
By analyzing the ligand uptake data in cells that express mutant receptors and fitting these data to models, the functional roles of specific residues could be identified by changes in the rate constants of specific cellular processes (Wiley et al., 1991)
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From page 55... ...
The image shows an XlK2 cell during the process of cytokinesis stained for DNA, microtubules, and the auroraB protein kinase. Although the image demonstrates the relative localization of different cellular components and structures, quantitative analysis reveals specific characteristics that can be used to assay the effects of inhibitors on expressed proteins.
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From page 56... ...
More sophisticated models that use nonlinear partial differential equations based on the geometry derived from imaging have been used to describe the intracellular dynamics of calcium and metabolites (Slepchenko et al., 2003)
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From page 57... ...
Molecular simulations of these processes and population balance modeling of the evolution of primitive cellular compartments may provide the link between models at the molecular and cellular scales. DISCOVERY OF CELLULAR NETWORKS AND THEIR FUNCTIONS Since networks of interacting proteins control all cellular functions, understanding cellular functions requires quantitative analysis of the spatiotemporal dynamics of these networks in the cellular environment (Figure 4.3)
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From page 58... ...
(B) Examples of regulatory network motifs in hepatocytes.
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From page 59... ...
This situation is not surprising, given that even the most comprehensive models may be missing entire parts of a network, may neglect its spatial organization and temporal evolution, and may employ approximate functional forms for various cellular processes. While some tools for dealing with these issues can be borrowed from linear control systems (Csete and Doyle, 2002)
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From page 60... ...
This insight was enabled by the large size of the frog oocyte, which made it possible to carry out single-cell biochemical assays of cellular responses, once again underscoring the importance of examining cellular responses at a single-cell level. Other examples of quantitative analysis of network dynamics at the single-cell level are now available (Irish et al., 2004; Jones et al., 2004; Lahav et al., 2004; Nelson et al., 2004; Raser and O'Shea, 2004)
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From page 61... ...
UNDERSTANDING CELLS 61 FIGURE 4.4 Modular view of the chemoattractant-induced signaling pathway in Dictyostelium. Except for those in parentheses, the proteins depicted in this pathway have been shown to be involved in chemotactic signaling through analysis of cells in which the genes have been deleted.
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From page 62... ...
. Each of the biophysical and biochemical modules in cell migration, from signal transduction by integrins to the spatiotemporal dynamics of actin polymerization, is the subject of an extensive modeling effort (Grimm et al., 2003; Manahan et al., 2004)
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From page 63... ...
In the end, models of cellular responses that can be used in biotechnology and medicine are likely to be reasonably simple correlations, similar in form to but more realistic than the phenomenological models of cellular responses developed over the past two decades. The ultimate challenge in modeling cellular responses to signals is to track cause-and-effect relationships throughout the pathways leading from signal detection to cellular response.
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From page 64... ...
The evolution of the quantitative understanding of bacterial chemotaxis shows unequivocally that helpful quantitative models are impossible without experimental inno vations and are greatly enabled by the ease of genetic manipulation of the system. The phenomenon was originally described by Adler at the macro scopic level as a directed flux of bacteria in gradients of nutrients such as aspartate (see Berg (2000)
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From page 65... ...
. While we are still a long way from having an integrated model of bacterial chemotaxis that would integrate all the structural, genetic, and biochemical evidence, analysis of this system over the past decades sets an excellent example of the most productive integration of experiments, multiscale biophysical modeling, and mathematical analysis (Erban and Othmer, 2005)
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From page 66... ...
. Today, similar analyses can be complemented with increasingly detailed information about the coupling between intracellular processes, such as signal transduction or cytoskeletal dynamics, and cellular responses, such as proliferation and migration.
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From page 67... ...
dients are established by the combination of localized secretion of ligands, their extracellular transport, binding to cell surface receptors, and intracellular trafficking processes. Computational models can be used to identify the relevant spatial and temporal scales in the generation of the morphogen gradients and to evaluate the relative feasibility of competing
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From page 68... ...
. In all current biology textbooks, cell communication proceeds in a unidirectional way, where the signal is received by the cell and interpreted to direct cellular responses.
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From page 69... ...
. There is a need to develop a hypothesis representation language that can assist in integrating experimental information at the logical level, as well as approaches to aggregating validated hypotheses into increasingly quantitative models.
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From page 70... ...
Complex processes that exhibit nonlinear behavior, as biological systems do, are often more readily described by event-driven dynamics (Ho, 1989) than by differential equations.
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From page 71... ...
. Receptors at the cell surface and intracellular signaling proteins, signaling cascades (such as MAPK cascades)
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From page 72... ...
At this time, scientists are far from having an adequate quantitative description of cellular responses, even in well-studied systems such as bacterial chemotaxis. The field must make a concerted effort to improve the quantitative analysis of such model systems in order to achieve successes that can be used as templates for modeling and analysis in less well-established experimental systems.
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From page 73... ...
Quantitative experimental analyses of intracellular fluctuations and noise are critical for understanding cellular functions and the limits of applicability of conventional deterministic and continuum approaches. This type of analysis is also important for understanding the mechanisms and functional consequences of nongenetic individuality.
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From page 74... ...
2004. Mathematical modelling of thera pies targeted at bacterial quorum sensing.
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2005. From signal transduction to spatial pattern formation in E
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1996. Cell migration: A physically integrated mo lecular process.
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2004. Design in bacterial chemotaxis: A comparative study in Escherichia coli and Bacillus subtilis.
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From page 78... ...
2003. Signaling systems, guided cell migration, and organogenesis: Insights from genetic studies in Drosophila.
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From page 79... ...
2003. Early development and quorum sensing in bacterial biofilms.
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