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Transport and Rate Phenomena in Biological Systems
Redux
Molecules
They can only do two things:They reactThey move
They are the most important elements in biological systems. Atoms acquire meaning only in molecules. All larger-scale entities acquire their ultimate
meaning and explanation in molecules.
Molecules deliver:
MessagesMaterial – mass, energy
Molecular delivery is particularized by packaging what is to be delivered (message or material) so that only intended recipients are reached. Compare with path-particularized systems.
Molecular Motion
Convection
Diffusion
Convective diffusion
Compartments
dcvdz
2
2
d c
dzD
2
2
dc d cvdz dz
D
In + Reaction - Out = Accumulation = dc
Vdt
Compartment Representations
Input and output via convection, permeation – passive, permease-driven, active and coupled transport
Accumulation with and without volume change
Reaction: equilibrium, power-law, enzymatic.
( ),
d VC dcV
dt dt
Reaction
A few reactions among many are rate limiting. Others equilibrate either with reactants or products of rate-limiting processes.
In processes involving both reaction and transport, rate-limiting step may be of either type.
Enzyme reactions
Linear in enzyme concentration. Regulatible ('allosteric effectors') Substrate dependencies:
First-order at low concentration Zero-order at high concentration
Enzyme reactions are usually irreversible. Enzymes are catalysts – they never
change an equilibrium– only the rate.
Permeases
Can be regarded as enzymes that facilitate transport rather than reactions.
Unlike enzymes, permeases do show reversible behavior.
Models exist for both facilitated (not active) and active transport.
Ionic equilibria and membranes
Not considered in these lectures. May be important – especially in neural
cells.
Cooperativity
Desirable biological function that supports homeostasis.
Generated by multiple mechanisms. Expressed in terms of "Hill Functions":
n+ -
n n
Θ 1F (x) = where Θ = x/x * ; F (x) =
1 + Θ 1 + Θ
Steady State
All variables of interest have the same value at all moments of observation
Steady state is a property of the system and the frame of reference.
Steady state means, at the most fundamental level, no change in accumulation.
Cyclic and "practical" steady states.
Cells
A cellCohorts of cells
normally asynchronous synchronization cyclic and sequential behavior is
concealed in cohort-scale measurements.
When is a cell not one compartment?
When it is a nerve cellWhen its "organelles" must be considered:
NucleusMitochondriaProcessing elements
When related chemical species are considered: finite-rate chemical transformations define compartments, too.
Macroscopic Problems: Cell Aggregates, Organs
All basic representations are useful if properly reinterpreted:What goes in, plus what is made, minus what
goes out, is always what accumulates. But one must measure what is defined, or define what is measured!
The art (kunst) that must be added to the science (wissenschaft) of macroscopic analysis is picking the right compartments and the right "entities" to follow.
Genomics
The concept of the genome and the cells.
Regulation of homeostasisControl of Development
Reversibility of the normally unidirectional development pathway.
The Goodwin Equations
Gene transcription mRNA translation Product synthesis. Feedback to the genome.
Gene transcription
one or two genes are transcribed to mRNA by RNAP's controlled by transcription factors. (Constituitive genes)Inducing and repressing transcription
factorsAttenuation"Cross-talk" among genes.
mRNA translationmRNA's are generated by transcription,
destroyed by a first-order reaction, exist at a steady-state level. Normal and abnormal destruction kinetics – apoptosis.
Ribosomes copy instructions in mRNA into proteins. Some of these are final products. Many are catalysts (enzymes, permeases, signal molecules) that control the formation of a 'final' product.
Product Synthesis Some synthesized products are
molecules that feed back information to regulate the geneome: transcription factors. Transcription factors are frequently in "apo" form (incomplete, inactive) and must combine with small molecules to become active.
All products are candidates for destructive processes that may be 'smart' or 'dumb'.
Goodwin Equations as a feedback system
Equations thus constitute a genome-cell feedback system.
Positive feedback is not seen as destructive in biological systems because of saturation phenomena and developmental requirement.
Intercellular feedback – to synchronize clones and inter-relate different cell lines.
"Tissue Engineering"
"Ultimate*" solutions in the repair of deformed, damaged, or prematurely aged tissue.
Redirect the natural system.Timing issuesNew cells, old cells, transitional states.
* If you are going to predict the future, do it often. J.K. Galbraith