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ftNftLVSIS OF ELECTROPHORESIS PERFORMANCE
Final ReportRAI-84-E-3
Period Covered* 11/27/83 - 4/6/84Contract: NAS8-35912
Prepared fort
George C. Marshall Space Flight Center
flSFC, AL 35813
Prepared by*
Glyn 0. Roberts
Date: 4/6/84
Roberts Associates/ Incorporated1726 Pine Ualley Drive
Vienna* UA
https://ntrs.nasa.gov/search.jsp?R=19840016648 2018-08-12T06:07:53+00:00Z
ABSTRACT
Our computer code SAMPLE models electrophoresis separation
in a wide range of conditions. Applications include steady three-
dimensional continuous-flow electrophoresis (CFE), time-dependent
gel and acetate film experiments in one or two dimensions and
isoelectric focusing in one dimension. Sample results for all
these are included.
The code evolves N two-dimensional radical concentration
distributions in time, or distance down a CFE chamber. For each
time or distance increment, there are six stages,^successively
obtaining the pH distribution, the corresponding degrees of ion-
ization for each radical, the conductivity, the electric field
and current distribution, and the flux components in each direc-
tion for each separate radical. The final stage is to update the
radical concentrations.
The model formulation for ion motion in an electric field
ignores activity effects, and is valid only for low concentrations;
for larger concentrations the conductivity is therefore also in-
valid.
We have duplicated one-dimensional results obtained with
a similar model by Bier et al.
We have successfully modeled eight experiments done with
hemoglobin in a barbitol buffer on acetate film.
(i)
TABLE OF CONTENTS
Abstract (i)
Table of Contents (ii)
Section 1. Introduction 1-1
2. Description 2-1
3. Results 3-1
Appendix. Graphs 1-47 A-l
Section 1
INTRODUCTION
This report is brief, and references the numbered view graphs
in the Appendix.
Graphs 1-6 are an introduction to the presentation and to
electrophoretic separation processes, and are not further described.
Section 2 and graphs 7-22 are a description of the model
formulation, assumptions, and applications, and of the numerical
methods, coding and use.
Section 3 and graphs 23 - 46 present results of analytic
validations, acetate film experiment simulations, continuous flow
electrophoresis simulations, and simulations of electrophoresis
cases modeled by Bier et al.
This is a continuing program. Some plans for future work
are presented in graph 47.
1-1
Section 2
DESCRIPTION
Graph 7 is a code summary, listing the six stages in updating
N two-dimensional radical concentration distributions* and describing
some available applications of the code in its present form.
Graphs 8 and 9 describe the ionization model and assumptions.
All salts are fully ionized. The ionization equilibrium of each rad-
ical (or ampholyte, including proteins and cells) is a function only
of pH. Four distinct ionization models are used. The coefficients
are determined to fit titration measurements of the mean ionization.
Graph 10 presents the mean ionization for three hemoglobin types;
the root mean square difference from measurements is of order 0.1,
which,is excellent for magnitudes of order 20.
Graph 11 describes the calculation of the pH distribution
from local charge neutrality. Newtons iteration gives very high
efficiency and accuracy. .
Graph 12 describes the model for ion motion and radical flux,_
and for the resulting changes in radical concentration. The radical
flux is obtained by summing over the degrees of ionization, and has
terms representing transport by the mean flow, transport proportional
to the local electric field, and a diffusive flux.
The electric field distribution is calculated from charge
continuity, the computed total conductivity distribution, and the
computed ion diffusion current potential, as described in Graph 13.
Graph 14 discusses an improved model for ion motion, including
activity effects of varying concentration. This model has not yet
been finalised or implemented, but is a requirement for quantitative
agreement with measurements, except at the lowest concentrations.
Applications to continuous flow electrophoresis (CFE), moving-
wall CFE, and to time-dependent one and two-dimensional cases are
described in Graphs 15 through 19, with the corresponding requirements
for initial conditions, computational domain and boundary conditions.
2-1
Output options are listed in Graph 21.
Graph 22 show the input data, and demonstrates the code's
flexibility. This data file can be modified in a few moments to
make appropriate changes in the problem, the method or the-output.
This data is for a 3-radical computation with hemoglobin in a
barbitol buffer.
2-2
Section 3
RESULTS
Analytic code validations are discussed in Graph 23.
In certain simple cases and for some components of the problem,
analytic solutions and simple measurements are available. The
success of the code in duplicating these encourages us in app-
lying it to much more complicated situations. Graphs 24 and
25 are contour plots showing how a weak circular hemoglobin
sample preserves its shape after 40 seconds of advection in
a uniform barbitol buffer with pH 8.5, with a field of 100
V/cm. This is only one of the wide range of validations we
have performed.
Graphs 26 through 36 describe our successful simulations
of eight heraoglobin-barbitol experiments with.:a circular sample
in acetate film, performed in May i1983. Graph 27 is a poor
reproduction of.some of the original films, with the hemoglo-
bin "fixed" by standard processing. Graphs 28 through 36
(including some plots without graph numbers) are concerned
with one case, with sample 8.8% hemoglobin in a 2.5X MACDAC! • - - • • • • " .
barbitol solution, and with a 0.75X buffer. The mean field
is 12 V/cm to the left, and the computation went to 360 sec-
onds. Graphs 31 to 3 show successive center-line concentrations
of hemoglobin, barbiturate sodium; the hemoglobin spreads to
the right with a low constant concentration of approximately
circular shape, while the sodium arid >batbittrEate build up >on
the left and are depleted on the right. Graph 34 shows the
successive conductivity profiles on the center-line. The
ratio of maximum to minimum increases from 2 to 50; the max-
imum moves to the left and a minimum forms to the right.
3-1
The following plots show the successive pH profiles, the elec-
tric field along the film (varying from 2.8 to 25 compared
with a mean of 12 volts/cm), the current lines, and the trans-
verse electric field, with peak 6 V/cm, which spreads the
hemoglobin sample.
Graphs 35" through 39 are contour plots of continuous
flow electrophoresis (CFE) tests, with a weak circular hemoglo-
bin sample so that the conductivity and field remained effec-
tively uniform. The tests include a moving wall case where the
sample remains circular and CFE with electroosmosis respectively
zero, negative and positive. The distortions due to nonuni-
forra flow down the chamber and to positive electroosmosis approx-i
imately cancel in Graph 39, as predicted by theory.
Finally our successful duplication of the seven one-
dimensional computation of Bier et al. is described and demon-
strated in Graphs 40 through 46. ,
3-2
APPENDIX
Computer-generated viewgraphs numbered from 1 through 47 are
presented on the following pages.
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