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/ / ftNftLVSIS OF ELECTROPHORESIS PERFORMANCE Final Report RAI-84-E-3 Period Covered* 11/27/83 - 4/6/84 Contract: NAS8-35912 Prepared fort George C. Marshall Space Flight Center flSFC, AL 35813 Prepared by* Glyn 0. Roberts Date: 4/6/84 Roberts Associates/ Incorporated 1726 Pine Ualley Drive Vienna* UA https://ntrs.nasa.gov/search.jsp?R=19840016648 2018-08-12T06:07:53+00:00Z

ftNftLVSIS OF ELECTROPHORESIS PERFORMANCE Final Report RAI ... · ftNftLVSIS OF ELECTROPHORESIS PERFORMANCE Final Report RAI-84-E-3 ... Analytic code validations are discussed in

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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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