The Force Exerted by the Membrane Potential during Protein
Import into the Mitochondrial Matrix
Karim Shariff,* Sandip Ghosal,y and Andreas Matouschekz
*National Aeronautics and Space Administration, Ames Research Center, Moffett Field, California; and yDepartment of Mechanical
Engineering, zDepartment of Biochemistry, Molecular Biology and Cell Biology, Northwestern University, Evanston, Illinois
ABSTRACT The force exerted on a targeting sequence by the electrical potential across the inner mitochondrial membrane is
calculated on the basis of continuum electrostatics. The force is found to vary from 3.0 pN to 2.2 pN (per unit elementary charge)
as the radius of the inner membrane pore (assumed aqueous) is varied from 6.5 to 12 A˚, its measured range. In the present
model, the decrease in force with increasing pore width arises from the shielding effect of water. Since the pore is not very much
wider than the distance between water molecules, the full shielding effect of water may not be present; the extreme case
of a purely membranous pore without water gives a force of 3.2 pN per unit charge, which should represent an upper limit.
When applied to mitochondrial import experiments on the protein barnase, these results imply that forces between 11 6 2 pN
and 13.5 6 2.5 pN catalyze the unfolding of barnase in those experiments. A comparison of these results with unfolding forces
measured using atomic force microscopy is made.
INTRODUCTION
Most mitochondrial proteins are encoded in the cell’s nuclear
DNA, manufactured within the cytosol as precursors, and
translocated into mitochondria across the organelle’s inner
and outer membranes (henceforth IM and OM) through
points where the two membranes come into contact. For the
basic facts consult Alberts et al. (1994) and Pfanner and
Neupert (1990). After translocation, the precursors are sent
to the appropriate mitochondrial subcompartment where
they are assembled into protein complexes. Most precursors
that are targeted to the lumen of the mitochondria, called the
matrix, are synthesized with a targeting sequence (TS), also
called a presequence, attached at their amino terminus. This
TS marks the precursor for translocation. We are concerned
with precursors that are folded before import and where the
TS protrudes from the precursor. Targeting sequences of this
kind always have an abundant number of positively charged
residues with few negative ones. As previously suggested
(e.g., Martin et al., 1991) the positive charges allow the inner
membrane’s electric potential to exert a force that is directed
into the mitochondrion.
The translocation of protein precursors into mitochondria
involve a number of actors (Pfanner and Truscott, 2002)
besides the membrane potential; see Fig. 1. The TS first
interacts with protein receptors (Tom20 and Tom22) on the
surface of the outer membrane. These receptors may promote
insertion of the TS into the OM pore, which itself consists of
the protein Tom40. The pore of the inner membrane likewise
consists of transmembrane proteins (Tim17 and Tim23). A
portion of the Tim23 protein that lies exposed on the outer
face of the IM appears to facilitate insertion of the TS into the
IM pore; the membrane potential activates the insertion
(Bauer et al., 1996). The passage of the TS through the IM
pore may be driven by thermal motion, the electric field of
the membrane potential, interaction with the Tim proteins, or
a combination.
Once the TS has been threaded into both OM and IM
pores, the bulk of the protein lying on the outer
mitochondrial surface must then unfold. Huang et al.
(1999) concluded that the unfolding is initiated at the
targeting sequence and that precursor proteins are unraveled
sequentially from their N-termini. The unraveling occurs
when the targeting sequence engages the unfolding machin-
ery associated with the inner mitochondrial membrane
whereas the structured domain remains at the entrance to
the import channel. The simplest mechanism by which the
import machinery could unravel a protein at a distance would
be by pulling at the targeting sequence. Atomic force
microscopy (AFM) experiments show that the N-terminus of
a protein needs to be pulled only a short distance before the
protein denatures. This distance is an empirically defined
width of the potential well for unfolding and its values range
between 3 and 17 A˚ for different domains (Best et al., 2001;
Rief et al., 1997, 1998).
What pulls the targeting sequence through the required
distance? If the TS is long enough to span both membranes
and reach sufficiently far into the mitochondrial matrix, then
Tim44 in association with mtHsp70 is able to unfold the
protein by an ATP-driven action (e.g., Matouschek et al.,
2000). Many targeting sequences, however, are not long
enough to span both membranes; for instance the total
thickness of yeast mitochondrial membranes is at least 
140 A˚. This corresponds to 40 amino acids in the fully ex-
tended conformation, whereas the average length of yeast
Submitted January 30, 2004, and accepted for publication February 24,
2004.
Address reprint requests to Karim Shariff, NASA Ames Research Center,
Physics Simulation and Modeling Office, MS 19-44, Moffett Field, CA
94035. Tel.: 650-604-5361; E-mail: shariff@nas.nasa.gov.
 2004 by the Biophysical Society
0006-3495/04/06/3647/06 $2.00 doi: 10.1529/biophysj.104.040865
Biophysical Journal Volume 86 June 2004 3647–3652 3647

presequences is smaller, ;31 amino acids (Huang et al.,
2002). When targeting sequences are not long enough to in-
teract with mtHsp70, the rate of import of precursor pro-
teins depends upon the strength of the electrical potential and
the number of positively charged amino acids (Huang et al.,
2002). The simplest implication of this result is that for short
targeting sequences, the force exerted by the inner membrane
potential upon the charged residues of the targeting sequence
unfolds the passenger protein. In this work we investigate
this hypothesis by calculating the electrostatic force exerted
by the potential and make a preliminary attempt to determine
whether it is sufficient to unravel a protein.
MODEL
Computational model
Fig. 2 shows the assumed geometry. Shading denotes membranous regions
where the dielectric constant e ¼ em ¼ 2. We took hi ¼ ho ¼ 65 A˚, a value
consistent with electron micrograph pictures (Perkins et al., 1997).
Lack of shading denotes regions of aqueous buffer (e ¼ ea ¼ 80). These
include the cytosol, mitochondrial matrix, and the intermembrane space
where the layer of 1 charge is located. The OM and IM pores are also
assumed to be aqueous based on their observed hydrophilic character (see
Hill et al., 1998; Truscott et al., 2001). The radius ro of the OM pore was
taken to be 12 A˚ based on reported measurements, namely, between 10 and
13 A˚ according to Schwartz and Matouschek (1999), 11 A˚ according to Hill
et al. (1998), and 10 A˚ according to Ku¨nkele et al. (1998). Less is known
about the radius ri of the IM pore. Schwartz and Matouschek (1999)
concluded that ri is at most 10 A˚. Here we will consider values in the wider
range 6.5, ri, 12 A˚, suggested by Truscott et al. (2001). Since the spacing
between water molecules is;3 A˚, only a few water molecules will be able to
occupy the pores. To qualitatively allow for such an effect, values of ri down
to 0 A˚, representative of a non-aqueous pore, will also be considered.
Proton pumping across the inner mitochondrial membrane leads to layers
of charge on its two sides. The buffer in the experiments of Huang et al.
(2002) has an ionic concentration of 0.17 M, which is in the physiological
range, and implies that the charge layers have a (Debye) thickness of 7 A˚
(Probstein, 1994). Since this thickness is small compared to the width of the
inner membrane, the electric field in the pore will be insensitive to the details
of charge distribution within these layers. In the present work we assume that
the layers have uniform charge density with thickness hc ¼ 10 A˚. The details
of the charge distribution can be obtained through solution of a Poisson-
Boltzmann equation (Probstein, 1994). The radius rc of the holes in the
charged layers was taken to be 10 A˚.
A distribution of charge density r(x) (per unit volume) in a medium with
dielectric constant e(x) produces an electric field E ¼ =C, where C is
obtained from the Poisson equation
=  ðe=CÞ ¼ 4pr: (1)
For the value of the mitochondrial membrane potential, DC, we used 150
mV corresponding to the protein import experiments of Huang et al. (2002).
The charge density s (per unit area) is then inferred to be
s ¼
emDC
4pð2dÞ
; (2)
where 2d ¼ hi 1 hc is the distance between the charged layers. The volume
charge density is then r ¼ s/hc.
Equation 1 was solved numerically using a B-spline Galerkin scheme
(Shariff andMoser, 1998) in cylindrical polar coordinates (x, r), where x is the
axial coordinate (measured from the entrance of the IM pore and positive into
the mitochondrion) and r is the radius. The discretization cells were designed
to be small at interfaces where jumps in dielectric constant and charge density
occur, and to become larger as the computational boundary is approached. In
most runs the smallest computational cell size was 1 A˚ 3 1 A˚ and the
computational domain was x 2 [200, 200] A˚, r 2 [0, 110] A˚. As a check on
accuracy, a computationwith half the cell sizes in each direction and twice the
radial domain size was also run. The boundary condition @C/@n ¼ 0 was
applied at the boundary of the computational domain which is large enough
for the boundary condition to be accurate. Here n is the coordinate normal to
the boundary. At the symmetry axis we required @C/@r ¼ 0, which is
precisely the condition required for an axisymmetric function to have
continuous radial derivatives at the axis. Since the Galerkin method is based
upon integrals, discontinuous distributions of e(x) and r(x), which occur in
the present model, can be treated. At an interface across which e suffers
a jump, En, the component of the electric field normal to the interface, also
jumps. Since the computed solution is a projection of the exact solution upon
the space of B-splines, this jump leads to some Gibbs oscillation in En. Such
oscillation may be witnessed in Fig. 5 and was generally found to be weak.
Analytical model
Since = 3 E ¼ 0, the tangential component of E is always continuous
across charge layers and across discontinuities in e; and since =  (eE) ¼
0 outside of charge layers, the normal component of E suffers a jump across
discontinuities in e (see e.g., Jackson, 1962). In particular, when e increases
FIGURE 2 Sketch for computational model. Subscripts: o, outer
membrane; i, inner membrane; c, charge layer.
FIGURE 1 Schematic of protein import.
3648 Shariff et al.
Biophysical Journal 86(6) 3647–3652