Influence of Global and Local Membrane Curvature on Mechanosensitive Ion Channels: A Finite Element Approach

Abstract

Mechanosensitive (MS) channels are ubiquitous molecular force sensors that respond to a number of different mechanical stimuli including tensile, compressive and shear stress. MS channels are also proposed to be molecular curvature sensors gating in response to bending in their local environment. One of the main mechanisms to functionally study these channels is the patch clamp technique. However, the patch of membrane surveyed using this methodology is far from physiological. Here we use continuum mechanics to probe the question of how curvature, in a standard patch clamp experiment, at different length scales (global and local) affects a model MS channel. Firstly, to increase the accuracy of the Laplace’s equation in tension estimation in a patch membrane and to be able to more precisely describe the transient phenomena happening during patch clamping, we propose a modified Laplace’s equation. Most importantly, we unambiguously show that the global curvature of a patch, which is visible under the microscope during patch clamp experiments, is of negligible energetic consequence for activation of an MS channel in a model membrane. However, the local curvature (RL < 50) and the direction of bending are able to cause considerable changes in the stress distribution through the thickness of the membrane. Not only does local bending, in the order of physiologically relevant curvatures, cause a substantial change in the pressure profile but it also significantly modifies the stress distribution in response to force application. Understanding these stress variations in regions of high local bending is essential for a complete understanding of the effects of curvature on MS channels.

Biophysical and Structural Studies of Escherichia coli Mechanosensitive Channel of Large Conductance in Lipid Bilayers

“…In the first hypothesis, MscL mainly senses curvature-induced stress on the membrane, defined by the discrepancy between the cross-sectional areas of the phospholipid head groups and fatty acyl chains ( Fig. 1.11C) (Bavi, Cox, et al, 2016;Meyer et al, 2006;Powl et al, 2008b). This is supported by the lowered pressure threshold for MscL opening in liposomes containing "cone-shaped" phospholipids, which have larger head groups than the tail ends and consequently favour curvature formation (Powl et al, 2003).…”

“…The lowered channel gating threshold postulated for MscL in small liposomes might reflect an energetically less stable system, which has been confirmed in molecular dynamics studies (Bavi, Cox, et al, 2016;Bavi et al, 2014). In such small liposomes, aggregation of MscL may become energetically favourable.…”

“…The mass spectrometry result confirms that this relationship is primarily due to the membrane curvature rather than phospholipid composition. It was predicted with molecular dynamics simulations that curvature at global level such as that of small liposomes could affect MscL channel gating threshold (Meyer et al, 2006), followed by more in-depth discussion with mathematical analyses and further simulations recently (Bavi, Cox, et al, 2016;Bavi et al, 2014). However, due to the practical limitation of performing patch clamp experiments on small liposomes, it was difficult to experimentally confirm this.…”

“…Smaller liposomes are generally favoured for drug delivery because they tend to be more permeable to physiological barriers such as blood vessels (Garnier et al, 2012). There are conflicting hypotheses, both based on molecular dynamics studies, on the influence of global curvature in small liposomes on MscL function (Bavi, Cox, et al, 2016;Meyer et al, 2006), making an experimental confirmation of whether MscL is to be engineered for gating threshold (Iscla et al, 2013;Nakayama et al, 2015). Likewise, the relationship between MscL and lipids (including but not limited to phospholipids) needs to be better understood, since phospholipids used for liposome formulation can be dependent on the type of target tissues or objectives (H. I.…”

“…Moe & Blount, 2005), calling into question the validity of a number of studies. Other membrane environment factors are often not given serious consideration in experimental design or data analysis either: global curvature's influence on MscL function has not been explored beyond simulations (Bavi, Cox, et al, 2016;Meyer et al, 2006); the distribution pattern of MscL within membranes remains poorly understood apart from the observed clustering in DOPC (Grage et al, 2011;Nomura et al, 2012); and there have been few studies investigating protein-to-protein interaction, focusing on MscS (Andrew R. Battle et al, 2011;Nomura et al, 2012). However, there is increasing evidence that these have significant impact on MscL function as observed in both past publications (Grage et al, 2011;Nomura et al, 2012) and in this thesis (sections 3.3.2. and 3.3.3.…”