Mathematics and 21st Century Biology (2005) / Chapter Skim
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5 Understanding Organisms
5 Understanding Organisms
Pages 80-98
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From page 80... ...
However, the committee draws its main examples in this chapter from more traditional areas of mathematical modeling, such as physiological processes. In recent years the importance of mathematical models in the study of physiological processes has become widely accepted.
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From page 81... ...
. Missing is the ability to integrate how the various components of organs work together to achieve dynamic function, and how change of specific components or combinations thereof impact function.
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From page 82... ...
A substantial amount of ongoing research is aimed at understanding the dynamics of cardiac cells using mathematical and computational models. There is a long history to this direction of investigation, which has its origins with the Hodgkin-Huxley equations.
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From page 83... ...
Today, an established multidisciplinary community of mathematicians, bioengineers, biophysicists, and physiologists is working on the experimental, theoretical, and computational challenges associated with formulating, implementing, and validating predictive models that integrate functionally across interacting cellular processes such as electrical excitation, mechanical contraction, and energy metabolism, and structurally across scales of biological organization from molecule to organ and system (McCulloch et al., 1998)
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From page 84... ...
Continuum and multiphase models can be applied to study blood flow. Simulations of mass and heat transport also typically require solution of nonlinear partial differential equations.
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From page 85... ...
Past and even current experimental and modeling research focuses either on a specific level of lung structure -- for example, on a single airway, the airway wall, tissue rheology, airway smooth muscle, or even airway smooth muscle and alveolar cell -- or on function at a gross level -- for example, whole-lung mechanical properties and indices of ventilation distribution. What is missing is the capacity to integrate how all the components in the lung work together to achieve dynamic function and how degradation in specific components or combinations of components might impact function.
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From page 86... ...
. In a similar way, the human auditory system from the inner ear to the auditory cortex is a complex multilevel pathway of sound information processing (Dallos et al., 1990)
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From page 87... ...
Such equations are much less well understood than the more familiar partial differential equations of reaction diffusion systems. ENDOCRINE PHYSIOLOGY Mathematical modeling has led to an improved understanding of several important endocrine processes (Bertram and Sherman, 2004; Kukkonen et al., 2001; Mosekilde et al., 2001)
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From page 88... ...
These questions invite mathematical modeling and simulations, some of which are currently taking place. MORPHOGENESIS AND PATTERN FORMATION The combination of developmental genetics with rapidly advancing imaging and transcriptional profiling technologies promises a golden age for the modeling and computational analysis of developing systems.
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From page 89... ...
Gene expression patterns in developing tissues can be very finegrained, with the characteristic domains of gene expression spanning only a few cell diameters. Such patterns cannot be captured with the continuum models traditionally used to model developmental patterning (Murray, 1993)
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From page 90... ...
Instead, the committee simply cites examples that illustrate the breadth of important problems on which progress has been made. At the subcellular level, molecular motors based on actin and tubulin polymerization are of central importance in many basic cellular processes, including chromosome segregation during cell division, cell motility, muscle contraction, and intracellular transport of organelles (for a review, see Mogilner and Oster, 2003)
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From page 91... ...
Mathematical models depicting how these processes affect drug delivery to tumor cells could suggest the treat
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From page 92... ...
, and modeling the heterogeneity of tumor populations. The mathematical tools needed include partial differential equations with free boundary conditions, bifurcation in systems of many nonlinear ordinary differential equations, and branching processes with infinite-type space.
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From page 93... ...
Challenges for the field involve the development of more realistic models of drug action and cell proliferation and heterogeneity as well as new methods for parameter estimation. IN VIVO DYNAMICS OF THE HIV-1 INFECTION Mathematical models of HIV infection and treatment have provided quantitative insights into the main biological processes that underlie HIV pathogenesis and helped establish the treatment of patients with combination therapy.1 This in turn has changed HIV from a fatal disease to a treatable one.
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From page 94... ...
Detailed analysis showed that this viral decay was governed by two processes: the clearance of free virus particles and the loss of productively infected cells. From this rapid clearance of virus one could compute that at steady state, ~1010 virions are produced daily and, given the mutation rate of HIV, that each single and most double mutations of the HIV genome are produced daily.
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From page 95... ...
1998. Overestimation of minimal model glucose effectiveness in presence of insulin response is due to undermodeling.
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From page 96... ...
2004. Inferring cellular networks using probabilistic graphical models.
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From page 97... ...
2000. Integration of blood flow control to skeletal muscle: Key role of feed arteries.
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From page 98... ...
2004. Cell sorting by differential cell motility: A model for pattern formation in Dictyostelium.
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