Joint Reaction Coordinate for Computing the Free-Energy Landscape of Pore Nucleation and Pore Expansion in Lipid Membranes

AbstractTopological transitions of membranes, such as pore formation or membrane fusion, play key roles in biology, biotechnology, and in medical applications. Calculating the related free energy landscapes has been complicated by the fact that such processes involve a sequence of transitions along highly distinct directions in conformational space, making it difficult to define good reaction coordinates (RCs) for the overall process. In this study, we present a new RC capable of driving both pore nucleation and pore expansion in lipid membranes. The potential of mean force (PMF) along the RC computed with molecular dynamics (MD) simulations provides a comprehensive view on the free-energy landscape of pore formation, including a barrier for pore nucleation, the size, free energy, and metastability of the open pore, and the energetic cost for further pore expansion against the line tension of the pore rim. We illustrate the RC by quantifying the effects (i) of simulation system size and (ii) of the addition of dimethyl sulfoxide (DMSO) on the free energy landscape of pore formation. PMF calculations along the RC provide mechanistic and energetic understanding of pore formation, hence they will be useful to rationalize the effects of membrane-active peptides, electric fields, and membrane composition on transmembrane pores.

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Free Energy Landscape of Rim-Pore Expansion in Membrane Fusion

Biophysical Journal ◽

10.1016/j.bpj.2014.08.022 ◽

2014 ◽

Vol 107 (10) ◽

pp. 2287-2295 ◽

Cited By ~ 16

Author(s):

Herre Jelger Risselada ◽

Yuliya Smirnova ◽

Helmut Grubmüller

Keyword(s):

Free Energy ◽

Membrane Fusion ◽

Energy Landscape ◽

Free Energy Landscape ◽

Pore Expansion

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Free-energy landscape of ion-channel voltage-sensor–domain activation

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1416959112 ◽

2014 ◽

Vol 112 (1) ◽

pp. 124-129 ◽

Cited By ~ 40

Author(s):

Lucie Delemotte ◽

Marina A. Kasimova ◽

Michael L. Klein ◽

Mounir Tarek ◽

Vincenzo Carnevale

Keyword(s):

Free Energy ◽

Energy Landscape ◽

State Theory ◽

Voltage Sensor ◽

Reaction Coordinate ◽

Coarse Grained ◽

Free Energy Landscape ◽

Activation Process ◽

Discrete State ◽

Gating Charge

Voltage sensor domains (VSDs) are membrane-bound protein modules that confer voltage sensitivity to membrane proteins. VSDs sense changes in the transmembrane voltage and convert the electrical signal into a conformational change called activation. Activation involves a reorganization of the membrane protein charges that is detected experimentally as transient currents. These so-called gating currents have been investigated extensively within the theoretical framework of so-called discrete-state Markov models (DMMs), whereby activation is conceptualized as a series of transitions across a discrete set of states. Historically, the interpretation of DMM transition rates in terms of transition state theory has been instrumental in shaping our view of the activation process, whose free-energy profile is currently envisioned as composed of a few local minima separated by steep barriers. Here we use atomistic level modeling and well-tempered metadynamics to calculate the configurational free energy along a single transition from first principles. We show that this transition is intrinsically multidimensional and described by a rough free-energy landscape. Remarkably, a coarse-grained description of the system, based on the use of the gating charge as reaction coordinate, reveals a smooth profile with a single barrier, consistent with phenomenological models. Our results bridge the gap between microscopic and macroscopic descriptions of activation dynamics and show that choosing the gating charge as reaction coordinate masks the topological complexity of the network of microstates participating in the transition. Importantly, full characterization of the latter is a prerequisite to rationalize modulation of this process by lipids, toxins, drugs, and genetic mutations.

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Amyloid Formation on Lipid Membrane Surfaces

The Open Biology Journal ◽

10.2174/1874196700902010163 ◽

2009 ◽

Vol 2 (1) ◽

pp. 163-175 ◽

Cited By ~ 8

Author(s):

Paavo K.J. Kinnunen

Keyword(s):

Free Energy ◽

Lipid Membranes ◽

Lipid Membrane ◽

Energy Landscape ◽

Amyloid Β ◽

Free Energy Landscape ◽

Amyloid Formation ◽

Β Cells ◽

Β Sheet

Several lines of research have concluded lipid membranes to efficiently induce the formation of amyloid-type fibers by a number of proteins. In brief, membranes, particularly when containing acidic, negatively charged lipids, concentrate cationic peptides/proteins onto their surfaces, into a local low pH milieu. The latter together with the anisotropic low dielectricity environment of the lipid membrane further forces polypeptides to align and adjust their conformation so as to enable a proper arrangement of the side chains according to their physicochemical characteristics, creating a hydrophobic surface contacting the lipid hydrocarbon region. Concomitantly, the low dielectricity also forces the polypeptides to maximize intramolecular hydrogen bonding by folding into amphipathic α-helices, which further aggregate, the latter adding cooperativity to the kinetics of membrane association. After the above, fast first events, several slower, cooperative conformational transitions of the oligomeric polypeptide chains take place in the membrane surface. Relaxation to the free energy minimum involves a complex free energy landscape of the above system comprised of a soft membrane interacting with, and accommodating peptide polymers. The overall free energy landscape thus involves a region of polypeptide aggregation associated with folding: polypeptide physicochemical properties and available conformation/oligomerization state spaces as determined by the amino acid sequence. In this respect, of major interest are those natively disordered proteins interacting with lipids, which in the absence of a ligand have no inherent structure and may adapt different functional states. Key sequence features for lipid and membrane interactions from the point of view of amyloid formation are i) conformational ambiguity, ii) adoption of amphipathic structures, iii) ion binding, and iv) propensity for aggregation and amyloid fibrillation. The pathways and states of the polypeptide conformational transitions further depend on the lipid composition, which thus couples the inherent properties of lipid membranes to the inherent properties of proteins. In other words, different lipids and their mixtures generate a very complex and rich scale of environments, involving also a number of cooperative transitions, sensitive to exogenous factors (temperature, ions, pH, small molecules), with small scale molecular properties and interactions translating into large scale 2- and 3-D organization. These lipid surface properties and topologies determine and couple to the transitions of the added polypeptide, the latter now undergoing oligomerization, with a sequence of specific and cooperative conformational changes. The above aggregation/folding pathways and transient intermediates of the polypeptide oligomers appear to have distinct biological functions. The latter involve i) the control of enzyme catalytic activity, ii) cell defence (e.g. antimicrobial and cancer killing peptides/proteins, as well as possibly also iii) control of cell shape and membrane traffic. On the other hand, these processes are also associated with the onset of major sporadic diseases, all involving protein misfolding, aggregation and amyloid formation, such as in Alzheimer’s and Parkinson’s diseases, prion disease, and type 2 diabetes. Exemplified by the latter, in an acidic phospholipid containing membrane human islet associated polypeptide (IAPP or amylin, secreted by pancreatic β-cells) efficiently transforms into amyloid β-sheet fibrils, the latter property being associated with established sequence features of IAPP, involved in aggregation and amyloid formation. IAPP sequence also harbors anion binding sites, such as those involving cationic side chains and N-terminal NH-groups of the α-helix. The association with acidic lipids neutralizes ‘gatekeeping’ cationic residues, abrogating electrostatic peptide-peptide repulsion. The subsequent aggregation of the α-helices involves further oligomerization and a sequence of slow transitions, driven by hydrogen bonding, and ending up as amyloid β-sheet fibrils. Importantly, the above processing of IAPP in its folding/aggregation free energy landscape under the influence of a lipid membrane involves also transient cytotoxic intermediates, which permeabilize membranes, allowing influx of Ca2+ and triggering of cell death, this process resulting in the loss of β-cells, seen in type 2 diabetes. Similar chains of events are believed to underlie the loss of tissue function in the other disorders mentioned above.

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Determination of Base Flipping Free Energy Landscapes from Nonequilibrium Stratification

10.26434/chemrxiv.7376081 ◽

2019 ◽

Author(s):

Xiaohui Wang ◽

Zhaoxi Sun

Keyword(s):

Free Energy ◽

Energy Landscape ◽

Sampling Technique ◽

Umbrella Sampling ◽

Energy Simulation ◽

Nonlinear Dependence ◽

Free Energy Landscape ◽

Convergence Criterion ◽

Base Flipping ◽

Convergence Behavior

<p>Correct calculation of the variation of free energy upon base flipping is crucial in understanding the dynamics of DNA systems. The free energy landscape along the flipping pathway gives the thermodynamic stability and the flexibility of base-paired states. Although numerous free energy simulations are performed in the base flipping cases, no theoretically rigorous nonequilibrium techniques are devised and employed to investigate the thermodynamics of base flipping. In the current work, we report a general nonequilibrium stratification scheme for efficient calculation of the free energy landscape of base flipping in DNA duplex. We carefully monitor the convergence behavior of the equilibrium sampling based free energy simulation and the nonequilibrium stratification and determine the empirical length of time blocks required for converged sampling. Comparison between the performances of equilibrium umbrella sampling and nonequilibrium stratification is given. The results show that nonequilibrium free energy simulation is able to give similar accuracy and efficiency compared with the equilibrium enhanced sampling technique in the base flipping cases. We further test a convergence criterion we previously proposed and it comes out that the convergence behavior determined by this criterion agrees with those given by the time-invariant behavior of PMF and the nonlinear dependence of standard deviation on the sample size. </p>

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