Electrophoretic mobility of sarcoplasmic reticulum vesicles is determined by amino acids of A+P+N domains of Ca2+-ATPase.

Abstract

Establishing the origin of electrophoretic mobility of sarcoplasmic reticulum (SR) vesicles is the primary goal of this work. It was found that the electrophoretic mobility originates from ionizable amino acids of cytoplasmic domains of the Ca2+-ATPase, the calcium pump of SR. The mobility was measured at pH 4.0, 4.7, 5.0, 6.0, 7.5, and 9.0 in the region of ionic strength from 0.05 to 0.2 M. Mobility measurements were supplemented by studies of SR vesicles by photoelectron microscopy. The median diameter of SR vesicles was 260 nm. Ca2+-ATPases were not resolved. The mobility data were standardized by interpolation to a reference ionic strength of 0.1M. The mobility of the SR vesicles is determined by the charge of the Ca2+-ATPase. It is due to the ionizable amino acids selected from the amino acid sequence of SERCA1a Ca2+-ATPase. The pH dependence of charge residing in various domains of Ca2+-ATPase was computed using pKa values in free water. The charge correlated with measured mobility. It was shown that a linear relationship exists between the mobility of the SR vesicles, mu, and the total computed charge, Q, on three cytoplasmic domains of Ca2+-ATPase: A, P, and N. It is given by mu=alpha+betaQ where the fitted values beta=(0.043+/-0.002) x 10(-8) m(2) V(-1) s(-1) e(-1) and alpha=(0.16+/-0.02) x 10(-8) m(2) V(-1) s(-1). Since beta and alpha values do not change from pH 4 to pH 9, one concludes that the hydrodynamic friction of the cytoplasmic domains of SR is independent of their charge.

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Electrophoretic mobility of sarcoplasmic reticulum vesicles is determined by amino
acids of A+P+N domains of Ca2+–ATPase
Pavel Smejtek⁎, Laura E. Satterfield, Robert C. Word, Jonathan J. Abramson
Department of Physics and Molecular Biosciences Group, Portland State University, Portland, Oregon 97207-0751, USA
a b s t r a c t a r t i c l ei n f o
Article history:
Received 10 December 2009
Received in revised form 19 April 2010
Accepted 4 May 2010
Available online 12 May 2010
Keywords:
Electrophoretic mobility
Sarcoplasmic reticulum
Photoelectron microscopy
Size distribution
Ca2+–ATPase
Calcium pump
Zeta potential
pH dependence
Cytoplasmic domain
SR vesicle
Establishing the origin of electrophoretic mobility of sarcoplasmic reticulum (SR) vesicles is the primary
goal of this work. It was found that the electrophoretic mobility originates from ionizable amino acids of
cytoplasmic domains of the Ca2+–ATPase, the calcium pump of SR. The mobility was measured at pH 4.0,
4.7, 5.0, 6.0, 7.5, and 9.0 in the region of ionic strength from 0.05 to 0.2 M. Mobility measurements were
supplemented by studies of SR vesicles by photoelectron microscopy. The median diameter of SR vesicles
was 260 nm. Ca2+–ATPases were not resolved. The mobility data were standardized by interpolation to a
reference ionic strength of 0.1 M. The mobility of the SR vesicles is determined by the charge of the Ca2+–
ATPase. It is due to the ionizable amino acids selected from the amino acid sequence of SERCA1a Ca2+–
ATPase. The pH dependence of charge residing in various domains of Ca2+–ATPase was computed using
pKa values in free water. The charge correlated with measured mobility. It was shown that a linear
relationship exists between the mobility of the SR vesicles, μ, and the total computed charge, Q, on three
cytoplasmic domains of Ca2+–ATPase: A, P, and N. It is given by μ=α+βQ where the fitted values β=
(0.043±0.002)×10−8m2V−1s−1e−1and α=(0.16±0.02)×10−8m2V−1s−1. Since β and α values do
not change from pH 4 to pH 9, one concludes that the hydrodynamic friction of the cytoplasmic domains
of SR is independent of their charge.
© 2010 Elsevier B.V. All rights reserved.
1. Introduction and background
Particle electrophoresis is now an established experimental
method for the study of the electrostatic and hydrodynamic
properties of colloids, whose sizes range from tens of nanometers to
several micrometers. It has been a valuable tool to characterize the
surface of particles in science, medicine, andtechnology.Furthermore,
the dependence of electrophoretic mobility on pH makes it possible to
establish the pH dependence of surface charge and thus it provides
insight into its origin. Notable are studies of red blood cells that
established a three layer model of red blood cell surface [1]. The
authors found thatthe charge of the innermostlayer becomes positive
at low pH due to the protonation of amino acids of surface
glycoproteins. This charge compensates the negative charge of the
outer surface layer that is pH-independent. Another pioneering work
that was also based on measurements of pH dependence of mobility
[2] was the study of Escherichia coli, a bacterium covered with
lipopolysaccharide layer and of Staphylococcus aureus, another
bacterium covered with peptidoglycan layer. Interfacial properties
of bacteria play important, but not well understood, roles in the
mechanism of interaction with their environments. Recent studies [3]
examined the electrostatic properties of the charge-regulated bacte-
rial surface of E. coli and Bacillus brevis.
Liposomes continue to have a prominent role as models for a great
variety of biological membranes [4] and for improvements of theoretical
models of electrophoretic mobility [5]. Initially the theories of electro-
phoretic mobility were developed for a class of “hard particles,” rigid
spheres with smooth surfaces. These studies were based on Helmholtz–
Smoluchowski theory [6] and later expanded to the “standard electroki-
netic model” that accounts for the effect of particle size [7,8]. The other
classofparticlesisknownas“softparticles”.Softparticleshaverigidcores
covered bycharged or unchargedpolymerlayers. Ohshima [5] is credited
for his major contributions to theoretical and experimental advances in
studies of soft particles and for numerous analytical solutions of
electrophoretic mobility models. Kuo [9] worked out a number of
theoretical problems on mobility of particles with complex surface
properties. An excellent overview of electrokinetic methods, including
practical recommendations, was recently produced by the Physical and
Biophysical Chemistry Division of IUPAC [10].
It is recognized that a description of soft particles in terms of a
homogeneous surface layer of constant thickness may not be adequate. It
hasbeenshownthatpolyethyleneglycolchainsanchoredinalipidbilayer
exist in various conformations, from mushroom-like to brush-like,
depending on their surface density. These studies indicate the need to
introducestatisticalmechanicsintotheelectrophoreticmobilitytheoryof
particles with complex surfaces [11,12].
Biochimica et Biophysica Acta 1798 (2010) 1689–1697
⁎ Corresponding author.
E-mail address: smejtekp@pdx.edu (P. Smejtek).
0005-2736/$ – see front matter © 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.bbamem.2010.05.003
Contents lists available at ScienceDirect
Biochimica et Biophysica Acta
journal homepage: www.elsevier.com/locate/bbamem

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There are a number of proposals that further generalize the
standard electrokinetic model. The most recent one [13] is based on
the assumption that a very thin layer of mobile ions exists at the
particle surface whose density is not determined by the conventional
diffuse layer model but by other mechanisms. In contrast to the
standard model, in the new generalized model the fluid (water) is
allowed to flow along the particle surface. The major impact of this
proposal is that the magnitude of mobility can be higher than that
predicted from the standard electrokinetic model.
Another important recent development is that some biological
particles may not be rigid. In the presence of an external electric field
used in an electrophoretic experiment, particles can deform due to
fluid flow and become ellipsoidal. Furthermore, their surface charges
may redistribute. The change in shape of biological particles was
demonstrated by controlling liposome rigidity via cholesterol content.
Less rigid liposomes exhibited greater mobility because they became
more elongated along the direction of motion [14,15]. These effects
are not included in the standard model and require special treatment.
The present study is focused on the origin of electrophoretic
mobility of sarcoplasmic reticulum (SR) vesicles. These vesicles have
very different surface properties compared to bacteria. The lipopoly-
saccharide (Gram-negative bacteria) or the peptidoglycan (Gram-
positive bacteria) layers are absent on the sarcoplasmic reticulum
membrane. Instead the SR membrane has Ca2+–ATPases incorporated
into the bilayer. Ca2+–ATPase is an ATP-driven calcium pump.
Understandingtherelationshipbetweentheelectrokinetic properties
and the surface properties of sarcoplasmic reticulum requires bringing
together two fields of study. The first is the structure of the Ca2+–ATPase
proteinandtheotheristheelectrophoretic mobilityof colloidalparticles.
On one hand, the Ca2+–ATPase is one of the most extensively studied
membrane enzymes [16] but, on the other hand, the origin of
electrokinetic properties of the SR membrane remains unknown.
The amount of published research on electrokinetic properties of SR
membrane is rather small. The lack of progress is most likely caused by
the complex structure and, consequently, electrokinetic properties of
the SR surface that were not interpretable. In retrospect, the
electrophoretic mobility data obtained already in the 1980s suggested
that the electrokinetic properties of SR are complex [17]. The most
notable contributions are the works of Arrio et al. who measured the
mobility of vesicles prepared from native SR and compared the results
with the mobility of SR vesicles reconstituted with uncharged and
charged lipids [18]. The mobility results were later rationalized in a
computational study based on numerical solution of one-dimensional
Poisson–Boltzmann and Navier–Stokes equations [19]. However, all
these earlier studies were done at a single pH value, and thus do not
provide insight into the origin of surface charge of the SR membrane.
AschematicdiagramofCa2+–ATPasearchitectureisdepictedinFig.1.
Themolecule,withboundCa2+,canbeenclosedinaboxwithdimensions
of 10 nm×8 nm×14 nm [20]. The outer surface of SR vesicles is covered
by dense arrays of Ca2+–ATPases. From optical diffraction analysis
of electron micrographs of freeze-fractured SR vesicles it was found that
Ca2+pumpsareorganizedintoarraysresemblinghexagonalortetragonal
lattices [21]. For tetragonal arrays the dimensions of unit cell are 11.7±
0.7 nm in the a-direction and 10.5±0.5 nm in the b-direction with unit
cell area of 123±9 nm2. For hexagonal arrays the unit cell defined as
body-centered rectangular cell had a repeat distance of 13.12 nm, and
unit cell area perfreeze-fractured particle (Ca2+pump) of 130±10 nm2.
Thus the surface density of Ca pumps is about 8.15×1015m−2(8150
pumps per µm2) for tetragonal array and 7.71×1015m−2(7710 pumps
per µm2) for hexagonal array.
In Fig. 1 the transmembrane domains are designated by the letter M,
and the large structures above the lipid membrane surface are the
cytoplasmic domains: A (actuator), P (phosphorylation), and N (nucle-
otide binding).
The origin of electrophoretic mobility of sarcoplasmic reticulum
vesicles is the primary goal of this project. We measured their
electrophoretic mobility as a function of ionic strength for a series of
pH values from pH 4 to pH 9. We show that the pH dependence of
mobility has a unique dependence on the electric charge carried by
three cytoplasmic domains of Ca2+–ATPase designated as A, P and N.
The total charge of A+P+N domains of the Ca2+–ATPase determines
the electrophoretic mobility of SR vesicles.
2. Materials and methods
2.1. Suspensions of sarcoplasmic reticulum vesicles
SR vesicles were isolated from rabbit fast twitch skeletal muscle by
the method of MacLennan [22]. Samples were stored in liquid
nitrogen. The vesicles were physiologically active, they pumped and
released calcium. SR vesicles stored in liquid N2were functionally
indistinguishable from freshly prepared samples. The protein con-
centration was determined by absorption spectroscopy [23]. To
prepare samples for mobility measurements SR vesicles were diluted
down to 0.08 g/L in salt solutions of different ionic strength and pH.
Electrophoretic mobilities of vesicles suspended in aqueous
solution were measured as a function of ionic strength at six different
pH values (4.0, 4.7, 5.0, 6.0, 7.5, and 9.0). For each pH value, a stock
solution was made with buffer concentration equal to 10 mM. Sodium
acetate was used for pH 4, 4.7, and 5. MES was used for pH 6, HEPES
sodium salt for pH 7.5, and CHES for pH 9. Buffer solutions were
titrated to the appropriate pH using HCl or KOH. Salt stock solutions
were made using NaCl crystals dissolved in the buffer solution. The pH
of the salt stocks was monitoredand adjusted as needed.Salt dilutions
were made by mixing buffer solutions and salt stocks.
2.2. Photoelectron microscopy
Photoelectron microscopy was used with two goals in mind: (a) to
image the surface layer consisting of Ca2+–ATPases, and (b) to
measure the size distribution of SR vesicles to be used in standard
electrokinetic model [8]. This study was done with Portland State
University's aberration-corrected photoelectron microscope (CPEM).
Images in this microscope are produced by photoelectrons emitted
from the surface of SR vesicles when illuminated with UV light
produced by a 244-nm argon laser. The SR suspension prepared at pH
7 had a protein concentration of 27.0 g/L. This preparation of SR
Fig. 1. Topology of calcium pump of SR membrane illustrating the A, P, N cytoplasmic
domains,andtransmembranehelicesM.Nottoscale(adaptedfromStokesandGreen[35]).
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vesicles was diluted by a factor 10,000:1 with distilled water at pH 7
and deposited on chromium oxide-coated glass to generate high
contrast images.The surface layer consisting of Ca2+–ATPaseswas not
observed. It was assumed that the flattened desiccated vesicles were
elliptical and that their original shapes were spheres. The surface
areas of desiccated and original vesicles were assumed to be equal.
The median diameter of SR vesicles was 260 nm (Fig. 2). This is in
good agreement with previous measurements made with freeze-
fracture electron microscopy [24].
2.3. Particle electrophoresis
Electrophoretic mobility of SR vesicles was measured at 25 °C using
an electrophoretic mobility analyzer DELSA 440 (Beckman-Coulter,
Fullerton, CA, USA). The mobilities were obtained from simultaneous
measurements of light scattered at angles 8.6°, 17.1°, 25.6°, and 34.2°
using instrument settings recommended by the manufacturer.
2.4. Experimental design and approach to data analysis: dependence of
mobility of SR vesicles on pH and ionic strength
The objective of the mobility experiments is to obtain data on the
dependence of mobility on the pH under standardized conditions so
that the mobility data obtained for different pH can be compared. To
that effect, we have measured the mobility within a region of
moderate to high ionic strength, from about 0.05 to 0.2 M, as a
function of pH. The pH values were 4.0, 4.7, 5.0, 6.0, 7.5, and 9.0 with
uncertainty of about 0.1 pH units. pH values of mobility samples were
checked after the mobility measurement. For some pH values it was
not possible to obtain accurate data in full range of ionic strengths
because of instrumental limitations at the high end of the ionic
strength range, when the mobility values are too close to zero. The
reason is that the mobility analyzerDELSA 440 employs the concept of
frequency shifts of light scattered from the vesicles moving in the
applied electric field. At high ionic strength the frequency shifts
become too small and erratic resulting in unreliable mobility data.
2.5. General features of mobility of SR vesicles
We have measured the dependence of mobility of SR vesicles on
ionic strength of monovalent salt solution as a function of pH of
vesicle suspension. It is useful to correlate the mobility data with the
methods used in their analysis using an example. Fig. 3 compares
three approaches to analysis of mobility vs. ionic strength at pH 4—an
empirical linear least square fit, a nonlinear least square fit of the
Helmholtz–Smoluchowski model (broken curve), and the Standard
Electrokinetic Model computed using analytical formulation by
Ohshima, Healy and White, Eq. (3.184) [5] (solid curve). The mobility
computed from the Standard Electrokinetic Model was obtained for
the same value of charge density as that for the Helmholtz–
Smoluchowski model (9.93×10−3C-m−2which is the least square
fit value for the Helmholtz–Smoluchowski model).
The notable feature of mobility of SR vesicles is that (a) neither the
Helmholtz–Smoluchowski nor the Standard Electrokinetic Model are
fully consistent with the experimental dependence of mobility on ionic
strength,and(b)thatthesimpleHelmholtz–Smoluchowskitheoryisan
adequate approximation of the Standard Electrokinetic Model when
analyzingtheexperimentalresults.Thereisnomobilitymodelavailable
intheliteraturethatwouldbeapplicabletothesurfaceofSRmembrane.
Thequantityκa,knownastheproductofthereciprocalDebyelength
of diffuse space charge layer surrounding the vesicle, κ, and the vesicle
radius, a, plays an important role in condition of applicability of
Helmholtz–Smoluchowski theory and in applicability of analytical
formulation of Standard Electrokinetic Model [5,25]. The reciprocal
Debye length is equal to
κ =
2F21000c0
ð
εε0RT
Þ
!1=2
:
ð1Þ
The quantity c0is the molar concentration of the 1:1 electrolyte
used in the study. c0 also determines the ionic strength of the
suspension. Other quantities have their usual meaning.
Fig. 3. Illustration of three approaches to the analysis of mobility using data for pH 4:
(1) empirical linear approximation and (2) nonlinear approximation by Helmholtz–
Smoluchowski model (broken curve) and (3) the mobility predicted from the Standard
Electrokinetic Model (solid curve). According to method (1) the data are interpolated
by a linear function to obtain a representative value of mobility for ionic strength of
0.1 M (shown by filled square). This mobility value is then used to obtain the apparent
ζ-potential and the apparent surface charge density σLinat a given pH. According to
method (2) the apparent surface charge density σHS=9.93×10−3C-m−2is found from
the least squares fit of the mobility data to Helmholtz–Smoluchowski model. The
broken curve illustrates the dependence of mobility on ionic strength predicted from
the Helmholtz–Smoluchowski model. (3) The solid curve shows the mobility predicted
from the analytic form of Standard Electrokinetic Model, Eq. (3.184) in reference [5]. It
was calculated for σHS=9.93×10−3C-m−2and for vesicle radius a=105 nm
(corresponding to the maximum in vesicle size distribution shown in Fig. 2).
Fig. 2. Size distribution of SR vesicles. The dashed curve represents a best-fit of the log-
normal distribution.
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The range of κa corresponding to ionic strengths of data shown in
Fig. 3 is 77bκab158. It was computed for vesicle radius a=105 nm.
This value of vesicle radius corresponds to the peak in SR vesicle size
distribution shown in Fig. 2.
It was concluded from the close agreement between the mobility
predicted from the Standard Electrokinetic Model and the Helmholtz–
Smoluchowski model (Fig. 3) that considering the scatter of
experimental mobility data it is valid to use the mobility obtained
from the Smoluchowski equation (Eq. (2)) for further analysis of
experimental data. In the Smoluchowski equation
μ =εε0
η
ζ
ð2Þ
μ represents the mobility, and ζ the apparent electrokinetic potential
or apparent ζ-potential.
For hard and smooth particles, the ζ-potential is the electrostatic
potential at the surface of shear, which is inside the diffuse layer. At
this surface water begins to move freely relative to the surface of the
particle. The shear surface loses its physical meaning for particles
whose surface is covered by water permeable surface layer, like the
layer of Ca2+–ATPases embedded in the bilayer. This layer is expected
to exert hydrodynamic drag on the SR vesicle and to reduce mobility.
In contrast to hard particles there is no sharp boundary in the velocity
of flow of water relative to the surface of the particle, rather a fuzzy
region inside the surface layer where the velocity markedly increases.
Cohen and Khorosheva [26] presented physically meaningful defini-
tion of the apparent ζ-potential and apparent shear surface for large
vesicles (κaNN1) covered with uncharged polymer layer.
In the present work the ζ-potential obtained from Eq. (2) is also
referred to as apparent ζ-potential even though the surface layer of SR
vesicles is different from the uncharged polymer layer used for the
definition of apparent electrokinetic quantities. Furthermore, no
distinction is made between the surface potential and the ζ-potential.
This is necessary since there is no adequate model for electrostatics
and hydrodynamics of SR.
2.6. Surface charge density and the ζ-potential
The apparent ζ-potential obtained from Eq. (2) is also used to
determine the apparent surface charge density σ. It follows from close
agreement of mobility obtained from the Standard Electrokinetic
Model and the Helmholtz–Smoluchowski model that in the range of
ionic strength used in the study, and particularly for ionic strength of
0.1 M, that a small segment of vesicle surface can be regarded as
planar. In this case the apparent surface charge density is related to
the apparent ζ-potential according to
σ = 8εε01000c0
½ðÞ?
1
2sinh Fζ=2RT
ðÞ:
ð3Þ
This equation is known as the Gouy equation. It is applicable to
symmetric 1:1 electrolytes as used in our experiments. The quantity c0is
the molar concentration of the 1:1 electrolyte. For low potentials, Fζ/
2RT≪1,aconditionapplicabletoourexperimentaldata,Eq.(3)becomes
σ = εε0κζ:
ð3aÞ
3. Results and discussion
3.1. Electrophoretic mobility of SR vesicles, apparent ζ-potential and
apparent surface charge densities
BeforeanalyzingthepHdependenceofmobility,themobilitydataat
the high end of the ionic strength range were omitted since very small
mobilities are exceedingly difficult to measure and are therefore highly
unreliable. Mobility data at each pH were analyzed two ways: (1) for
each pH value, the measured mobilities were interpolated to ionic
strength of 0.1 M using an empirically selected linear interpolation
function. This interpolation uses a larger number of measured mobility
points within theionic strengthrange that reduces theerrorofmobility
at the reference ionic strength of 0.1 M and reduces the effect of
nonrandom errors. (2) For each pH value, the mobilities, measured as a
function of ionic strength, were fit using the Helmholtz–Smoluchowski
model. Using this approach we obtained a least squares fit value of an
apparent surface charge density at each pH.
Using the above two approaches we obtained two sets of apparent
surface charge densities: (1) σLinfrom the linear interpolation to ionic
strength 0.1 M, and (2) σHSfrom the least squares fit of mobility data
to Helmholtz–Smoluchowski model.
The experimental results of mobility measurements as a function
of ionic strength for pH 4.0, 4.7, 5.0, 6.0, 7.5 and 9.0 are presented in
Fig. 4A. Also shown are the results of data treatment by linear
interpolation and by the least squares fit of mobility data to
Helmholtz–Smoluchowski model.
The dependence of apparent charge densities obtained from the
linear interpolation of mobilities and the least squares fit of
Helmholtz–Smoluchowski model to all mobility data at a given pH
are shown in Fig. 4B. The plot shows that the results of both analytical
approaches produce very similar charge densities of SR vesicles.
In order to objectively establish whether the linear or nonlinear
treatment of the experimental data is more appropriate we estimated
the goodness of fits by calculating the variance of the fit, s2[27].
The values of variances of the fit, s2, were calculated for all
individual pH data sets for the linear fit and nonlinear Helmholtz–
Smoluchowski models, and the individual s2were added. It was found
that overall the dependence of mobility of SR vesicles on ionic
strength is represented better by the linear approximation than by the
Helmholtz–Smoluchowski model. The values of variances were s2
(total)Lin=0.018 whereas s2(total)HS=0.033.
In view of the absence of a mobility model suitable to describe the
dependence of mobility of SR vesicles on ionic strength we used a
referenceionicstrengthof0.1 Mintheanalysisofexperimentaldata.The
apparentζ-potentialandapparentsurfacechargedensityatthereference
ionic strength were obtained from the Helmholtz–Smoluchowski model.
The apparent charge density of SR vesicles depends on bulk pH as
illustrated by data in Fig. 4B. Since the protonation/deprotonation is
takingplaceatthechargedsurfaceofSRwetakeintotheaccountthatthe
interfacial concentration [H+]ifis different from that in the bulk aqueous
phase [H+],
Hþ
hi
if= Hþ
hi
exp −Fζ=RT
ðÞ:
ð4Þ
The bulk pH and the interfacial pH, the measured mobility μ, the
apparent ζ-potential and the apparent surface charge density σ are
summarized in Table 1.
At physiological pH the mobility, the apparent ζ-potential and the
apparent surface charge density σ are negative due to the prevailing
negative charge below the diffuse layer. We found the sign reversal of
mobility at bulk pH 5.6. At low pH (pHb5.6) the quantities μ, ζ, and σ
are positive indicating the dominance of the positive surface charge of
the SR membrane. Qualitatively similar properties were found for
human erythrocytes [1]. The dependence of experimental mobility on
interfacial pH is illustrated in Fig. 5.
3.2. Electric charge of SR membrane and its dependence on pH
The electric charge of the SR vesicle is the primary quantity
determiningitselectrophoreticmobility.Threemajorchargecontributors
areCa2+–ATPase—thedominantSRprotein,chargedlipids,andsialicacid
residues.ItwillbeshowninSection3.4thattheelectrophoreticmobilityis
determined by charges residing on the Ca2+–ATPase.
Charge of Ca+2-ATPase is due to ionizable amino acids. Since the
architecture of Ca2+–ATPase is complex, as shown in Fig. 1, it is not a
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priori known what portion of Ca2+–ATPase is electrophoretically
active. Therefore we compute the pH dependence of charges from
amino acid sequences for different structural units of Ca2+–ATPase.
These are A, P, and N domains, the transmembrane helices M, and the
entire Ca2+–ATPase. Of special interest are the charges residing in the
cytoplasmic domains A, P, and N. These domains protrude from the
outer surface of the SR vesicle and should therefore have a prominent
effect on vesicle mobility. This expectation follows from Eq. (5). It is
applicable to “large particles” having a charged plane at distance d
above the surface of the bilayer [28]. For such a particle the mobility in
Debye–Hückel approximation is
μ =
σ
ηκκd + exp −κd
ðÞ½?:
ð5Þ
It is important to recognize that the mobility of such particles is
greater than that predicted by the conventional electrokinetic model
assuming smeared charge at the physical surface. In case of SR, Eq. (5)
can be used as a theoretical guide that indicates that charges extended
from the surface have a greater influence on mobility than those
directly on the surface.
The ionizable amino acids of the Ca2+–ATPase of rabbit skeletal
muscle (known as SERCA1a) were determined from the amino acid
sequence given in Fig. 5 in reference [29]. To determine the types and
frequencies of occurrence of ionizable amino acids in the cytoplasmic
domains of SR vesicles we used the definitions of domains given by
Reuter, Hinsen, and Lacapere [30].
The types of ionizable amino acid side chains present in SERCA1a,
their number in the corresponding domains, and their pKa's are
summarized in Table 2. These data were used to calculate the pH
profiles of the charge of the individual segments of Ca2+–ATPase.
In addition to three individual domains: A, P, and N, two other
structures were considered. One is the combination domain desig-
nated as the APN domain and the other consists of the entire Ca2+–
ATPase. The charge of APN domain includes the sum of charges on the
A, P, and N domains. The APN domain was included because the A, P,
and N domains extend furthest from the surface of the bilayer and
constitutea large fraction of theouter surface of SR vesicles [16,20,30].
The entire Ca2+–ATPase was added for comparison.
The pH profiles of the net charge on individual A, P, and N domains
and on helices M1–M10 (H domain) are shown in Fig. 6A. It can be
seen that domain A is practically uncharged at high pH and becomes
positively charged at pH b7. Domain P carries a net negative charge at
pH N4.5. Domain N is positively charged at pH b5 and becomes
negatively charged at pH N7. Within 5bpHb7 domain N is
approximately neutral. In Fig. 6B the pH dependence of charge on
the combination APN domain and on the entire Ca2+–ATPase are
compared. It is notable that the pH profile of charge on the APN
domain and the N domain alone are similar to that of mobility (Fig. 5).
The N domain was not selected as the sole origin of mobility of SR
vesicles since there is no physically meaningful reason to assume that
A and P domains would be electrophoretically inactive. These
domains carry significant charge and their charges are also located
above the lipid bilayer for which they are expected to enhance the
vesicle mobility.
Helices were excluded as a candidate for electrophoretic activity
becauseoftheintra-bilayerlocation(d=0,seeEq.5),andbecauseofthe
absence of evidence that negatively charged lipids present in SR
membrane are electrophoretically active, as discussed below.
We also considered whole Ca2+–ATPase as the origin of mobility
(Fig. 6B). Total chargeofCa2+–ATPase is not a candidate because Ca2+–
ATPase acquires a high negative charge above pH 5 and the mobility
reversal would occur well below the observed pHrev=5.6.
3.3. The relationship between electrophoretic mobility of SR vesicles and
the electric charge of APN domains of Ca2+–ATPase
In this section existence of a direct correlation between the
measured electrophoreticmobilityofSRvesiclesandtheelectric charge
Table 1
Bulk pH, interfacial pH, mobility, apparent ζ-potential, and apparent surface charge
density of SR vesicles at reference ionic strength of 0.1 M.
pH pHif
μ, (10−8m2V−1s−1)
ζ, (V)
σ, (C-m−2)
4.0
4.7
5.0
6.0
7.5
9.0
4.25
4.8
5.1
5.9
7.4
8.9
1.14±0.07
0.51±0.06
0.30±0.03
−0.24±0.06
−0.46±0.05
−0.65±0.11
(15.0±0.9)×10−3
(6.5±0.7)×10−3
(3.9±0.4)×10−3
−(3.1±0.7)×10−3
−(5.8±0.7)×10−3
−(8.3±1.4)×10−3
(11.0±0.7)×10−3
(4.7±0.5)×10−3
(2.8±0.3)×10−3
−(2.2±0.5)×10−3
−(4.2±0.5)×10−3
−(6.0±1.0)×10−3
Fig. 4. A. Ionic strength dependence of mobility of SR vesicles at pH 4.0, 4.7, 5, 6.0, 7.5,
and 9.0. The solid lines show the linear regression used to obtain the representative
mobility values at ionic strength of 0.1 M. The broken curves illustrate the predictions of
the mobility from the least squares fit of the Helmholtz–Smoluchowski model.
B. Comparison of apparent surface charge density obtained by linear approximation of
mobility to 0.1 M (open circles by Method-1), and by the least squares fit of mobility
data to Helmholtz–Smoluchowski model (filled triangles by Method-2).
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QAPNof APN domain is demonstrated. The correlation is established in
Fig. 7 by the linear relationship between the mobility of SR vesicles and
the total charge of APN domain. Similar relationships exist between the
other electrokinetic quantities of SRvesicles ζ, σ and the chargeQAPN. In
Fig. 7 the mobility and interfacial pH were taken from Table 1 and the
charge of APN domain was computed from amino acid content and
interfacial pH using the pKa values given in Table 2.
The straight line Fig. 7 depicts the result of linear regression
between the mobility and the charge of APN domain. From the
regression equation
μ pH
ðÞ = α + βQAPNpH
ðÞð6Þ
follows that theoptimum slope βLSF=(0.043±0.002)×10−8m2V−1
s−1e−1and the offset αLSF=(0.16±0.02)×10−8m2V−1s−1. Thus
Eq. (6) and the data in Fig. 7 establish the correlation between the
mobility of SR vesicles and the charge of APN domain. The value of
slope β computed from Helmholtz–Smoluchowski model, βHS,
resulting from the combination of Eqs. (2) and (3), yielded a value
equal to 30% of the least square fit value βLSF. It indicates that the
hydrodynamic friction dominates over the mobility enhancement
predicted by Eq. (5).
Note that the regression line in Fig. 7 does not pass through the
origin, there is a residual mobility for QAPN=0. This residual mobility
determines the value of the offset, α, in the fitting function. The offset
originates from errors in the data, the effect of other charges in SR
membrane that are electrophoretically active, from incomplete
understanding of conditions of ionization of amino acids in APN
domain and the mechanism of mobility of SR vesicles.
Whereas Fig. 7 relates the measured mobility to the charge of
APN domain, Fig. 8 illustrates the pH dependence of the measured
mobility as well as the mobility predicted from Eq. (6). Even though
Figs. 7 and 8 are conceptually equivalent, the agreement between the
measured mobility and the mobility computed from Eq. (6) confirms
the notion that the electrophoretic mobility of SR vesicles originates
from charges on APN domains. The advantage of Fig. 8 is that the in-
terfacial pH is displayed on the horizontal axis of the plot as an inde-
pendent experimental variable, like experimental results in Fig. 5.
3.4. Why charged lipids of SR membrane do not significantly contribute
to mobility of SR
The lipid composition of SR obtained by Waku et al. [31] given in
terms of percentage of the total lipid content is as follows:
phosphatidylcholine (68.2%), phosphatidylethanolamine (16.8%),
phosphatidylinositol (7.6%), phosphatidylserine (2%), sphingomyelin
(3.7%) and unidentified lipids (1.7%). According to Narasimhan et al.
[32] SR contains 0.613 µg of sialic acid/mg SR protein, which yields
about 0.3 mol of sialic acid per mole of Ca2+–ATPase.
Within the pH range of interest, the charge of lipid matrix of SR is
dominated by phosphatidylinositol and phosphatidylserine. The
contribution of sialic acids is negligible, about −0.3e per unit cell.
Using the unit cell areas, 123 nm2for tetragonal and 130 nm2for
hexagonal [21], after subtracting 12.6 nm2for the stalk of the Ca2+–
ATPase, the lipid bilayer unit cell contains, respectively 3.2 molecules
of PS and 12.0 molecules of PI for the tetragonal cell and 3.4 molecules
of PS and 12.8 molecules of PI in the hexagonal cell. These estimates
were made for 0.7 nm2membrane surface area per lipid.
Phosphatidylserine has three protonation/deprotonation sites.
Their respective pKa's are 2.6 (R2-HPO4), 5.5 (R-COOH) and 11.55
(R-NH3+). Phosphatidylinositol has one protonation/deprotonation
site (R2-HPO4) with pKa=2.5. The pH dependence of mobility of a
vesicle containing the same amount of PS and PI per unit cell area as
present in SR membrane is depicted in Fig. 9. If the electrophoretic
mobility of SR originated from negatively charged lipids present in SR
Fig. 5. Experimental values of electrophoretic mobility, apparent ζ-potential, and apparent surface charge density σ as a function of pH at the surface of SR vesicles (pHif). The
interfacial pH includes the effect of electrostatic potential on [H+], Eq. (4). The connecting lines have no theoretical significance. The vertical line indicates the pH of polarity reversal
of electrophoretic mobility, pHrev=5.6.
Table 2
Amino acid composition of A, P, and N domains, M1–M10 helices, combination APN
domain, and total Ca2+–ATPase. The quantities in columns are the name of each amino
acida; pKa value, and their number in each domain.
Amino Acid pKaAPNM1–M10APNCa2+–ATPase
Arginine
Aspartic acid
Cysteine
Glutamic acid
Histidine
Lysine
Tyrosine
12.5
3.9
8.0
4.1
6.1
10.5
10.1
99 15
14
8
4
6
33
34
16
44
43
50
25
76
12
51
21
1010
7
13
0
7
2
18
121915
401
8
7
4
131737
1035
aThe amino acid composition of Ca2+–ATPase includes amino acids in links in
addition to A, P, N and M domains.
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membrane the pH dependence of mobility of SR vesicle would
resemble the mobility plot in Fig. 9. In contrast, the pH dependence of
mobility of SR vesicles predicted from the pH-dependent charge of
APN domain illustrated in Fig. 8 agrees with the data.
A contribution of charged lipids to mobility of SR vesicles has not
been observed. This phenomenon can be understood in terms of the
concept that charges above the surface of SR lipid bilayer, such as
chargesinAPNdomain,areelectrophoreticallymoreactivethancharges
at the surface of the bilayer. The mobility enhancement effect for
charges in APN domain follows from Eq. (5) where the expression in
square brackets can be defined as the mobility enhancement factor fd.
The existence ofmobility enhancementeffectwas confirmed bystudies
inMcLaughlin'slaboratory[28,33,34].ItalsofollowsfromEq.(5)thatfor
lipid vesicles fd(lipid)=1 since charged lipid headgroups are at the
surface of the bilayer, d=0, and that SR vesicles with charges displaced
above the surface of the bilayer have enhancement factor N1.
To evaluate the mobility enhancement effect consider that charges
on APN domains can be represented by an equivalent charged plane
passing through the center of mass of APN domains at distance dAPN.
For such particles the mobility enhancement factor fd(APN)=κdAPN+
exp(−κdAPN). For 0.1 M monovalent salt solution used in our studies
the Debye length, 1/κ, is about 0.96 nm. From Toyoshima's diagrams
of the conformations of A, P, and N domains during the Ca2+transport
cycle, (Fig. 1 in reference [16]) we estimate that the center of mass of
the cytoplasmic domains is about 7.5 nm above the bilayer. For a
hypothetical charged plane at distance dAPN=7.5 nm above the
surface of the bilayer the mobility enhancement factor is fd(APN)=
7.8, i.e. almost one order of magnitude greater than that for the
charged bilayer. The above values of fdare applicable to particles
without frictional surface layer.
In contrast to fdthat is applicable to smooth particle, we assign Fd
to be the mobility enhancement factor for a particle with hydrody-
namic friction layer. The effect of hydrodynamic friction is that, in
general, Fdbfd. Due to hydrodynamic friction within the surface layer
of SR the contribution of charged lipids to the mobility of SR vesicles is
smaller than that for a smooth particle. The magnitude of the mobility
enhancement factor originating from the charges displaced from the
bilayer (Eq. (5)) is also reduced due to the attenuation of velocity of
electroosmotic flow within the frictional layer. These conclusions
follow from the solution of Navier–Stokes equation for electroosmotic
Fig. 6. A. The dependence of the net charge of A, P, and N domains and of M1–M10
helices (H) of the Ca2+–ATPase on interfacial pH. The pH profile was calculated from
frequencies of occurrence and pKa values of amino acids given in Table 2. The vertical
line indicates the pH of polarity reversal of electrophoretic mobility, pHrev=5.6.
B. Comparison of pH dependence of charge on APN domain, QAPN, and that of the charge
of the total Ca2+–ATPase, QATPase. The vertical line indicates the pH of polarity reversal
of electrophoretic mobility, pHrev=5.6. The pH profile was calculated from frequencies
of occurrence and pKa values of amino acids given in Table 2. The pH dependencies of
charge, QAPNand QATPaseshould be compared with the pH dependence of mobility in
Fig. 5.
Fig. 7. Demonstration of existence of linear relationship between the mobility and
charge of APN domain. The experimental mobility was taken from Fig. 5 and the charge
of APN domain from Fig. 6B.
Fig. 8. Plot of mobility of SR vesicles (solid curve) predicted from the pH dependence of
the total charge QAPNaccording to Eq.(6). The squares denote the experimental values
of mobility of SR vesicles at ionic strength 0.1 M given in Table 1. The vertical line
indicates the pH of polarity reversal of electrophoretic mobility, pHrev=5.6.
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velocity of flow within frictional layers shown in references
[19,26,28]. In our opinion, the properties of frictional layers and
spatial distribution of charges are the main reasons why the mobility
contribution from charged lipids in SR bilayer is not observable in the
mobility data.
3.5. Implications of the linear relationship between the mobility of SR
vesicles and the charge of APN domain of SR
The charge of APN domain is pH-dependent. At pHbpHrevthe net
charge of APN domain is positive and it becomes negative at pHNpHrev.
Inspite ofthechange of charge polarity of thecytoplasmicdomainsand
possible changes in conformations in APN domain the slope of mobility
vs. charge shown in Fig. 7 is pH-independent. The value of slope β in
Eq.(6),βLSF=(0.043±0.002)×10−8m2V−1s−1e−1,isvalidforthefull
rangeofpHvalues,frompH4topH9.Sincetheslopeofthemobilityfor
the low and high pH data is the same there appears to be no significant
reorganizationofmembranesurfaceofSRwithpHthatwouldaffectthe
electrophoretic mobility of SR vesicles.
4. Conclusions
The significance of this work is that it demonstrated that the
electrophoretically active charge of Ca2+–ATPase are ionizable amino
acids of APN domain obtained from the amino acid sequence of
SERCA1a Ca2+–ATPase. The experimental pH dependence of mobility
was reproduced by the pH dependence of total charge of A, P, and N
domains computed using pKa values for their free state in water. The
agreement suggests that A, P, and N domains are not compact but
possess loose water-penetrable structure. This notion is consistent
with results of molecular dynamics simulations demonstrating that A,
P, and N domains undergo large conformational changes and
movement during the calcium pumping cycle and that the thermal
energy can drive these conformational changes. Apparently the
conformational barriers are lowest when the cytoplasmic domains
are loose and hydrated. Other features of the mobility of SR
vesicles are that (a) there is no traceable contribution to mobility of
SR vesicles from negatively charged lipids, and (2) the mobility is a
linear function of the calculated total charge of cytoplasmic domains
of Ca2+–ATPase. The pH-independent constant of proportionality
between the charge of APN domain and mobility indicates that the
expected hydrodynamic friction produced by the cytoplasmic
domains is independent of their charge.
Acknowledgements
We appreciate the support from the Physics Department of
Portland State University, and would like to thank Mr. Rod Cruse of
Beckman-Coulter and Mr. Leroy Laush of the Portland State University
electronic shop for the past and the present maintenance of the
electrophoretic mobility analyzer DELSA. We thank Professor P. T.
Leung for the discussion of theoretical issues of this project and
Professors Rolf Könenkamp and Gertrude Rempfer for the use of the
photoelectron microscope for characterization of SR vesicles. This
research was partially supported by DOE under grant number DE-
FG02-07ER46406 and NSF grant number DBI-0352224.
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