Transport and Rate Phenomena in Biological Systems Organism, organ, cellular and genomic dynamics Edward F. Leonard, AKH AKH website:

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)

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

Molecular behavior

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

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.

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 …

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.)

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

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 :

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.

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

A little problem (2)