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