Transport and Rate Phenomena in Biological Systems

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Transport and Rate Phenomena in Biological Systems

• Organism, organ, cellular and genomic dynamics

Edward F. Leonard, leonard_at_columbia.edu, AKH
4.J6.02 AKH website http//www.akh-wien.ac.at/cv
d/
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• 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)

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Molecular species can do only two things

• They can move treated as a continuum of
  possibilities.
• They can react treated as discrete
  transformations.

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Molecular behavior
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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/volumetime
• Heterogeneous reactions entity/areatime
• Pseudo-homogeneous reactions
• Transport
• Entity/areatime

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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.

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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 ODEs in time

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The misunderstood steady state(compartmental and
distributed systems)

• No variable of interest is a function of time.
• In compartmental systems, ODEs become algebraic
  equations.
• Steady-state is not equilibrium
• Equilibrium is applicable to the non-steady
  state. (Quasistatic behavior.)

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

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A little problem (1)(entshuldigung, WAM)

• Cell-surface receptors have easily measured
  KDs. It is harder to get the separate ks, 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.

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A little problem (2)