The MIFE^TM system 
for non-invasive measurement of specific fluxes in solution near living plant or animal tissue

Overview
Membrane Transport & fluxes
MIFE Key Features
MIFE applications
development
references

MIFE theory
 ion flux theory
multivalent ion mobility
ionic mobility values
neutral molecule flux
Methodological isues
H+ flux in buffered media

Hardware
amplifier
microscope
manipulator
System requirements

Software
analysis

Purchasing
Univ of Tas
Eppendorf NP2

Flux of neutral molecules – Theory

Basic Theory

Chemicals in solution move under the influence of chemical forces of diffusion directed towards lower concentration regions. Neutral molecules, with valence z = 0, do not have electric forces that are experienced by ions. Otherwise, the assumptions and general conditions are the same as for ions. See the review (Newman, 2001). The following treatment is also given in Pang et al (2006). 
For neutral molecules, the electrochemical potential µ (J mol^-1) is given by Newman (2001, Equ 1): -

            µ = µ₀ + RT ln(gc).                [Equ 1]

The molecular flux J (mol m^-2 s^-1) into the tissue is given by Newman (2001, Equ 2): -

            J = c u (dµ/dx).                       [Equ 2]

The concentration is c (mol m^-3), g is the activity coefficient, u is the mobility (m s^-1 per N mol^-1) and x is distance (m) from the tissue.

Mathematically (dµ/dx) = (dµ/dc)(dc/dx),
and, differentiating Equ 1,             (dµ/dc) = RT/c. Hence the flux can be written

            J = u R T (dc/dx).                [Equ 3]

This equation is known as Fick’s Law of diffusion, J = D (dc/dx), where the diffusion coefficient D = u R T. Thus for uncharged molecules, unlike the situation for ions, the treatment based on electrochemical potential is identical to diffusion theory based on Fick’s Law.

Calibration of electrodes

Electrodes used to measure the concentration of neutral molecules require calibration to obtain a graph of output voltage ~ concentration. If this graph is linear, as is the case for Clark-type oxygen electrodes for example ( e.g Armstrong et al. 2000), the equation is: -

            V = V₀ + a c.             [Equ 4]

The intercept is V₀ and the slope of the graph is a.

Thus, (dV/dc) = a, or dc = dV/a, so the flux Equ 3 becomes: -

            J = u R T (dV/dx)/a.                   [Equ 5]

This is the equation used in the MIFE software to calculate flux of oxygen or other uncharged molecules. The intercept and slope of the calibration graph are recorded and are transferred by the calibration average file to MIFEFLUX for analysis. For each manipulator cycle, MIFEFLUX uses Equ 4 to calculate the local concentration (mean for the two positions). Equ 5 is used to calculate the flux, using the measured dV and dx values, with the known parameters.

Geometrical considerations

When the diffusion is not from a source having a flat surface, for a cylindrical root or spherical protoplast with radius r for example, Equ 5 must be modified. By doing the appropriate integration, it can be shown that the dx in Equ 5 must be replaced as described by Newman (2001, Equs 8 & 9): -

for a sphere:             dx = r²[1/(r + x) – 1/(r + x + dx)];

for a cylinder:             dx = r ln[(r + x + dx)/(r + x)].

These are used in the MIFEFLUX analytical software.