DMMC COURSES & WORKSHOPS

THERMODYNAMICS OF MEMBRANE TRANSPORT PHYSIOLOGY
Lectures with hands-on computer modelling of membrane transport, pharmacokinetics, and pharmacodynamics
21 - 25 Feb 2005; 0930-1730 each day
Venue: Interactive Teaching Lab, RCSI Education & Research Centre, Beaumont Hospital, Dublin 9
location (from the hospital front entrance, turn left at the first roundabout, then right at the second roundabout)

This course is open to researchers throughout Ireland, and is limited to 40 participants

Course Coordinators:
S. Randall Thomas, PhD. DR2 CNRS
Laboratory of Computer Methods (LaMI), Genopole
Universite d'Evry Val d'Essonne, France.
Prof Brian Harvey, RCSI.

No programming experience required, but participants should have some affinity for a quantitative approach to science:
Be comfortable with calculus, simple differential equations, basic algebra, and logarithms. Have a basic knowledge of physical chemistry (have met the concepts of ionic strength, membrane potential, osmolality, activity coefficients), and principles of biochemistry (mass action kinetics, Michaelis-Menten).

LECTURES: Thermodynamics of Transport Physiology (days 1-3, mornings)

Basic thermodynamics: flow-force relations
a) Properties of state
b) 1st and 2nd Laws of thermodynamics
c) Gibbs free energy and "useful work"
d) The electrochemical potential
e) Equilibrium conditions
f) Irreversible thermodynamics

Isothermal diffusion
a) Nernst-Planck equation
b)"Constant field" -- Goldman-Hodgkin-Katz (GHK)
c) Implications of GHK-flux equation
d) Discontinuous diffusion

Diffusion potentials
a) Potential difference between two solutions of the same salt
b) GHK equation for membrane potential

Water transport
a) Osmosis, van't Hoff's law, and Staverman's reflection coefficient
b) Solute-solvent coupling: the Kedem-Katchalsky equations

Active transport
a) Definition of active transport
b) Experimental criteria for categorising transport processes

Coupled transport
a) General derivation of net driving force (and reversal potentials) for coupled transport
b) Facilitated transport
c) Competitive interactions and counter-transport
d) Cotransport
e) Primary active transport
f) Rheogenic transporters

HANDS-ON WORKSHOP: Introduction to the use of Berkeley Madonna for modelling in Physiology and Chemistry (days 1-3, afternoons)

Introduction

Network thermodynamics and compartmental models

Basic steps for development of a mathematical model in transport physiology or metabolic networks
a) Define the problem
b) Design the flow diagram
c) Program the network (on a text editor)
d) Run the simulation (we'll use the ODE solver Berkeley Madonna)
e) Explore parameter sensitivity
f) Compare with experimental data
g) If applicable, fit selected parameters to data

Basic building blocks
a) One-compartment input & output: inulin accumulation & excretion
b) Two-Compartment Model pump-leak: parallel diffusion and active transport
c) Chemical reactions
Mass balance & flow conservation in chemical reaction networks
Enzyme Kinetics (Michaelis-Menten derivation; detailed model of Michaelis-Menten reactions)
Chemical oscillations: Higgins-Selkov glycolytic model
Arbitrary stoichiometry
Nonlinear pharmacokinetics: salicylic acid

d) Coupled flows of solute and solvent: biphasic volume changes
The Kedem-Katchalsky equations
Glycerol transport and red blood cells
Fitting cell permeabilities to experimental data

e) Transmembrane ion flows
Bi-ionic potentials, GHK equation: NaCl across a membrane

f) Acid-base and buffers

Presentation of some integrated models
a) Multi-compartment reaction & diffusion: epithelial transport
b) Chemical networks: full model of glycolysis

Other useful programs: Mathematica, Matlab/Scilab, ...

Introduction to PK/PD modelling with Berkeley Madonna (days 4 & 5)

The examples in this section are drawn from a course given at UC Berkeley (not by SR Thomas). We will cover the following topics in as much depth as time permits, and students will be able to follow up on their own using the detailed course handout provided.

One compartment pharmacokinetics (inulin infusion)
Parameter estimation
Exponential responses
Dosage regimens

Two compartments in the body (salicylic acid - I)
Fitting parameters to data
Aspirin (salicylic acid - II)
Bonus: non-linear PK of SA degradation into multiple derivatives (salicylic acid - III)

PBPK - Physiologically-based pharmacokinetics (benzene distribution)

Pharmacodynamics
Receptors
Sigmoidal response

Combining pharmacokinetics and dynamics
Steroid regulation of cell trafficking: a direct response
Steroid regulation of enzyme synthesis: a gene mediated delayed response with down-regulation

Objectives of the lecture course

1. Understand well the following equations, their uses and their limitations:

- the electrochemical potentiel
- Nernst-Planck
- Fick's First Law
- GHK-flux
- Ussing Flux-Ratio
- GHK-PD
- Henderson
- Kedem-Katchalsky

2. Understand the difference between Intensive and Extensive Properties.

3. Understand the principles for analysing coupled membrane
transporters, for both charged and electroneutral substrates.

4. Understand the notion of a reference potential (electrical, chemical, ...), especially for the case of 'passage' from the interior of a membrane to the exterior medium.

5. Be able to explain the principle of coupling between two fluxes across a membrane, e.g., cotransport (or symport) and countertransport (or antiport), both of which may provide 'secondary active' transport.

6. Be able to characterise the differences among facilitated transport, active transport, secondary active transport, ....

7. Know how to use the electrochemical potential to calculate the transmembrane driving forces for solutes or for coupled transport with arbitrary stoichiometry.

Know how to answer the following sorts of questions

1. What condition is satisfied if a solute is at equilibrium across a membrane?

2. Under what conditions is the Gibbs Free Energy most useful?

3. In the GHK-PD equation, can one ignore terms for which the difference of electrochemical potential is near zero?

4. If a nonelectrolyte is at equilibrium across an interface, is it necessarily at the same concentration on both sides of the interface? Justify your answer.

5. Explain the origin of a transmembrane electrical potential difference, Vm.

6. Does the presence of a non-zero Vm imply a non-zero net current across the membrane, as it would across a resistor in an electrical circuit?

7. If we accept the inevitability of the constraint of macroscopic electroneutrality, how can we explain the existence of a transmembrane electrical potential difference, since an electric potential difference is necessarily due to a separation of charge?