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Quantitative Cell Biology: Integrating Mathematics and Biology

Explore the integration of mathematics and biology in quantitative cell biology, making use of mathematical models and simulations to study complex cellular processes. Discover how computational methods can aid in hypothesis formulation, prediction, and experimentation, allowing for a deeper understanding of cellular structures and molecules.

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Quantitative Cell Biology: Integrating Mathematics and Biology

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  1. "Every attempt to employ mathematical methods in the study of biological questions must be considered profoundly irrational and contrary to the spirit of biology. “If mathematical analysis should ever hold a prominent place in biology - an aberration which is happily almost impossible - it would occasion a rapid and widespread degeneration of that science" -- Auguste Comte, Pilosophie Positive, 1830

  2. The Problem

  3. Hypothesis (Model) • What are the initial concentrations, diffusion coefficients and locations of all the implicated molecules? • What are the rate laws and rate constants for all the biochemical transformations? • How are the forces controlling cytoskeletal mechanics regulated? Quantitative Cell Biology Experiment Predictions Dynamics of Cellular Structures and Molecules Simulation Trends in Cell Biology 13:570-576 (2003)

  4. How Can Computation Help Cell Biologists? • Formulate a quantitative hypothesis (i.e. a model), make quantitative predictions (simulations), test them experimentally. • Analyze quantitative microscopy experiments • FRAP, uncaging, probe translocation • Visualize species that can’t be probed experimentally • Spatiotemporal patterns of post-translational modifications • Probe complex pathways and networks • Identify global or emergent network properties • Virtual knockouts; evaluate drug targets in silico • Facilitate the sharing of models and the collaborative construction of ‘supermodels’

  5. "I only claim that in any particular discipline you can meet only as much science as there is mathematics." Immanuel Kant

  6. "What are we to do with the enormous cornucopia of genes and molecules we have found in living cells? How can we see the wood for the trees and understand complex cellular processes? .... Although we poor mortals have difficulty manipulating seven things in our head at the same time, our silicon protégés do not suffer this limitation. ...The data are accumulating and the computers are humming. What we lack are the words, the grammar and the syntax of the new language." -- Dennis Bray, 1997

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