Unassisted Ion Transport Across Membranes

Protocellular walls must have been permeable ions. Ions were needed for such cellular functions as bioenergetics based on charge separation across cell walls, stabilization and self-assembly of a variety of molecular structures, and chemical catalysis. Also, ion transport stabilized the protocell against osmotic pressure.

Transport of ions requires that a charged species be moved from a polar, aqueous environment into the nonpolar interior of the membrane. This process is associated with a large activation barrier. In contemporary cells, ion transport is aided by specialized, complex molecules (ion channels and ion carriers) which help to lower this barrier. However, these molecules are usually too complex to have been present in protocells, at least at the earliest stage of their evolution. Therefore, less complicated mechanisms of ion transport must be examined, among which unassisted transport is the simplest.

The activation barrier and, subsequently, ionic permeability can be readily estimated from the dielectric continuum model in which both the water and the membrane are described as continuous media characterized by their dielectric constants and , respectively. The bilayer is represented as a rigid layer of a fixed width, d. Then, the free energy, of moving a spherical ion of radius a and charge q from bulk water into the center of the bilayer is [18]:

 

For = 77.4, = 2 [19, 20], q² = 1, a = 1.68 Å (the radius of Na⁺) and d = 35 Å, = 45 kcal/mol. This yields a permeability of 10^-27 cm sec^-1. These results are insensitive to the width of the bilayer; varies from 42 to 47 kcal/mol for d between 20 and 80 Å.

The permeability predicted by the simple dielectric continuum model is extremely low, approximately 13-15 orders of magnitude lower than the values measured for small ions permeating model phospholipid bilayers [21] This large difference cannot be eliminated by reasonable adjustments of the parameters in Eq. 2. Instead, it appears that the mechanism of ion transport is incorrectly described in the model. Several alternative mechanisms have been proposed focusing on ion hydration [21], defects in the membrane [22, 23, 24] and ordering of hydrocarbon tails [25].

Computer simulations of the transfer of Na⁺ and Cl^- through the GMO bilayer [] reveal the actual mechanism of unassisted ion transport. As the ion moves into the membrane, polar head groups on the incoming side of the GMO bilayer follow by tilting inwards, thereby creating a thinning defect in the membrane filled with water. Once the ion crosses the mid-plane of the bilayer, the defect on the incoming side of the membrane disappears and, instead, a similar deformation is formed on the outgoing side. This is illustrated in Fig. 1.

 
Figure 1: Instantaneous position of the water surface as Na⁺ crosses the membrane (left) as the ion enters the membrane from above, creating a downward bulge in the water surface and (right) as the ion leaves the membrane from below where an upward bulge has formed in the lower surface.

The ion inside the membrane looses some of its hydration shell but this loss is compensated by near-neighbor interactions with oxygen atoms from GMO head groups. As a result, the total solvation number, defined as the average number of oxygen atoms from water molecules and GMO head groups around the ion, remains constant throughout the whole transport process. Both the formation of local, asymmetric defects in the bilayer and partially solvation of the ion reduce the activation barrier to charge transfer. These features are not captured in the simple dielectric model. For Na⁺, the calculated decreases to to 26 kcal/mol yielding the permeability of approximately 10^-13 cm sec^-1. This agrees well with the experimental value [21]. For Cl^-, the calculated permeability is 1-2 orders of magnitude higher than for Na⁺, also in agreement with experiment [21].

The mechanism of unassisted ion transport focuses attention on an important property of lipid bilayers, namely their ability to deform, even in the absence of ions, from a rigid planar structure, such that the local width of the membrane fluctuates in time and space. This property was studied in detail in computer simulations of the pure water-GMO system [16]. It was shown that the probability of forming thinning defects decreases exponentially with their depth. This implies that the permeability of thin membranes to ions should be considerably more sensitive to the membrane width than predicted from Eq. 2. This conclusion is consistent with recent measurements of the ionic permeabilities of phosphatidylcholines with varying hydrocarbon chain lengths [26] The observed sensitivity might lead to establishing limits on the width of protocellular walls; membranes that were too thin would not provide an effective barrier to ions while membranes that were too wide would be practically impervious to charges.