Entropic tension in crowded membranes

Abstract

Unlike their model membrane counterparts, biological membranes are richly decorated with a heterogeneous assembly of membrane proteins. These proteins are so tightly packed that their excluded area interactions can alter the free energy landscape controlling the conformational transitions suffered by such proteins. For membrane channels, this effect can alter the critical membrane tension at which they undergo a transition from a closed to an open state, and therefore influence protein function in vivo. Despite their obvious importance, crowding phenomena in membranes are much less well studied than in the cytoplasm. Using statistical mechanics results for hard disk liquids, we show that crowding induces an entropic tension in the membrane, which influences transitions that alter the projected area and circumference of a membrane protein. As a specific case study in this effect, we consider the impact of crowding on the gating properties of bacterial mechanosensitive membrane channels, which are thought to confer osmoprotection when these cells are subjected to osmotic shock. We find that crowding can alter the gating energies by more than [Formula: see text] in physiological conditions, a substantial fraction of the total gating energies in some cases. Given the ubiquity of membrane crowding, the nonspecific nature of excluded volume interactions, and the fact that the function of many membrane proteins involve significant conformational changes, this specific case study highlights a general aspect in the function of membrane proteins.

Figure 1. Relative abundance of membrane protein subunits with different number of transmembrane (TM) helices.

The histograms are based on data for synaptic vesicles , and the outer membrane (OM) of the Gram-negative bacterium A. baumannii . Proteins with no predicted TM domains were excluded.

Figure 2. Excluded-area interactions and channel gating.

(A) Gating of a channel (red) crowded by a single crowder (gray) of radius in the constant area ensemble, where the total surface area is fixed by the outer walls (dashed). (B) In the constant tension ensemble with applied tension , the total area increases as the channel opens, so that the total lipid area is conserved. For disk-shaped particles of finite size, the free area available for each center of mass is limited by the minimum distance between two centers of mass. This effect can be illustrated by exclusion zones of width around each protein. In the constant tension ensemble, the reduced area for the crowders is due to larger exclusion zone in the open compare to the closed state. In the high density regime (C), the exclusion zones overlap, which complicates the analysis. We use scaled-particle theory to analyze this case.

Figure 3. The effect of crowding on the open probability as a function of applied tension

. The graphs illustrate the ideal gas () and scaled-particle theory (SPT, ) results of table 2, using the constant tension ensemble as is appropriate for MscL. All non-crowding contributions to the gating free energy are lumped together in the gating tension .

Figure 4. Mechanisms for different excluded area for proteins and lipids.

One difference between the hard disk model of membrane proteins (A), and more complex protein structures (B,C) might be thought of in terms of different effective radii and for steric exclusion of surrounding proteins and lipids respectively. A protein (red) with a large domain outside of the bilayer (B) might exclude surrounding proteins, but not lipids, from approaching the transmembrane domain (dark red). Similarly, proteins with different hydrophobic thickness than the surrounding bilayer (C) generate a local zone of deformed lipid bilayer (gray) that effectively excludes other well-matched proteins. Horizontal lines indicate the surrounding lipid bilayer.