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Transport and Rate Phenomena in Biological Systems

Transport and Rate Phenomena in Biological Systems. Organism, organ, cellular and genomic dynamics. Edward F. Leonard, leonard@columbia.edu , AKH 4 .J6.02 AKH website: http://www.akh-wien.ac.at/cvd/. The principle of sufficient reason:

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Transport and Rate Phenomena in Biological Systems

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  1. Transport and Rate Phenomena in Biological Systems Organism, organ, cellular and genomic dynamics Edward F. Leonard, leonard@columbia.edu, AKH 4.J6.02 AKH website: http://www.akh-wien.ac.at/cvd/

  2. The principle of sufficient reason: We want to be told enough for whatever it is that requires explanation to be seen to follow. (A. Schopenhauer)

  3. Molecular species can do only two things: • They can move – treated as a continuum of possibilities. • They can react – treated as discrete transformations.

  4. Molecular behavior

  5. Rates and Fluxes • Concepts: mass conservation (definite proportions); entity measures (molecules, moles, mass,); entity conservation; rate. • The concept of (specific) flux • Reactive • Homogeneous reactions: entity/volume·time • Heterogeneous reactions: entity/area·time • Pseudo-homogeneous reactions • Transport • Entity/area·time

  6. Quantities • Independent Variables • Time (transients, steady states, equilibrium) • Spatial position (continua and compartments) • Dependent Variables • Total entity • Concentration (always entity/volume) • Parameters: to know and to predict; not to know and to estimate.

  7. Compartments • Volumetric space is divided into discrete compartments. Each is spatially homogeneous. Spatial effects are expressed only as differences among compartments. • Transport occurs only at the boundaries of compartments • Compartmentalized systems have only one continuous independent variable, time, and are described by ODE’s in time …

  8. The misunderstood steady state(compartmental and distributed systems) • No variable of interest is a function of time. • In compartmental systems, ODE’s become algebraic equations. • Steady-state is not equilibrium • Equilibrium is applicable to the non-steady state. (Quasistatic behavior.)

  9. A Basic Equation:(written on a volume enclosed by a surface)

  10. Limiting Processes • Flow limitation, equilibrium (normal blood oxygenation) • Transport limitation (estimating diffusion-limited receptor binding) • Reaction limitation (maximum rate enzyme reaction) The rate-limiting step:

  11. Examples(and the insidious effect of what can be measured) • Whole body: water shifts during hemodialysis via segmental bioimpedence measurement (SBIA) of extravascular water distribution • Organ: renal blood flow via sequential MRI imaging of label washout • Microvasculature: Krogh tissue cylinder model of tissue metabolism – microbead distributions • Cellular: Environmental triggering of gene activation.

  12. A little problem (1)(entshuldigung, WAM) • Cell-surface receptors have easily measured KD’s. It is harder to get the separate k’s, kon and koff. ( KD = koff / kon) • A ‘diffusion limited’ kon allows estimation of koff and thus the mean residence time of a ligand on a cell receptor.

  13. A little problem (2)

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