Enhanced sampling for lipid-protein interactions during membrane dynamics

Introduction

The biological membrane is an effective mechanism to selectively isolate the cell from its environment (Sackmann, 1995; Chernomordik and Kozlov, 2008; Alberts et al., 2015). Along evolution, a modular design progressively facilitated specialized transport mechanisms through the membranes (Honigmann and Pralle, 2016). With self-organization being a prevailing characteristic across cellular structures (Karsenti, 2008), protein homeostasis is guaranteed by complex cellular processes that determine the function, conformational states, abundance, and location of the approximately 25,000 proteins found in a human cell (Klaips et al., 2018). Remarkably, still far away from thermodynamic equilibrium (Mayorga et al., 2012), cellular homeostasis ultimately depends on an intricate network of mechanisms as yet waiting to be fully unveiled. As stated by Macklem in a 2008 viewpoint, survival requires adaptations, and during adaptation, homeostasis must preserve order (Macklem, 2008).

In the 70 s, the fluid mosaic model, originally proposed by Singer and Nicolson, was used to explain the gross organization and structure of proteins and lipids in biological membranes (Singer and Nicolson, 1972). In this simple model, the lipid bilayer is assumed as a two-dimensional permeability barrier that presents different faces to the cytoplasm and the extracellular environment. Within the model, amphipathic proteins appear dissolved in a fluid lipid bilayer solvent (Brown, 2017). This first approximation provided a useful framework for membrane analysis at the nanometer scale (Nicolson and Ferreira de Mattos, 2021) and served, for example, as a reference to Rothman and Lenard in 1977 to first discuss lipid asymmetries in biomembranes (Rothman and Lenard, 1977).

This review focuses on the current state of knowledge of enhanced molecular dynamics simulations applied to lipid-protein interactions in specific cellular problems, namely: membrane deformations, membrane fusion, and the fusion pore. Relevant recent computational approaches and advances are described herein. When appropriate, the experimental data that support these approaches are commented upon. The lipid bilayer is presented here as an extraordinarily heterogeneous many-body structure, emphasizing the dynamic interactions with proteins that may contain intrinsically disordered regions. Along the text, the reader is pointed to the most relevant literature on each specific topic.

Enhanced Sampling and Collective Variables

Computational methods are indisputably one of the common choices for studying biological problems at the molecular level. Among them, molecular dynamics is an excellent technique to describe protein and membrane dynamics within a wide range of scenarios. Moreover, in silico methods have been shown to produce useful biological information that, when combined with experimental data, benefit biomedical research. Remarkably, in terms of their historical trend, biomolecular simulations have already exceeded Moore’s law (Schlick and Portillo-Ledesma, 2021). In computer science, Moore’s law shows that the performance of integrated circuits has increased exponentially over the last half-century by doubling approximately every two years (Vendruscolo and Dobson, 2011), suggesting an interesting future of experimental and computational cooperation to address greater scientific challenges.

However, for most biological events, a detailed description at atomistic resolution is still unreachable by classic molecular dynamics. Although, since the first simulation of a protein in 1977 by McCammon et al. (1977) intelligent solutions have been found to speed up atomistic simulations (Ryckaert et al., 1977; Andersen, 1983; Hess et al., 1997; Miyamoto and Kollman, 1992; Feenstra et al., 1999; Olesen et al., 2018), the problem is inherent to the algorithm itself. Atomistic molecular dynamics require an integration step in the order of the femtoseconds (10−15 s) to correctly describe the fastest degrees of freedom, namely, the vibration of bonds and angles involving hydrogen atoms. With most biological processes (e.g., large conformational changes) happening in the order of the micro or even milliseconds (10−6 s–10−3 s), the overwhelming difference of 12 orders of magnitude makes the problem clear.

Therefore, from a numerical simulation point of view, most biological events of interest fall into the category of rare events, this is, events not easily observable within practical simulation times using classical molecular dynamics. From a thermodynamic point of view, large conformational changes in proteins or major lipid remodeling in biomembranes are events that require transitions along high-energy barriers that separate metastable states. From a statistical-mechanics point of view, relatively high-energy conformations have small probabilities of being visited during a molecular dynamics simulation (Laio and Parrinello, 2002; Fiorin et al., 2013; Masone and Grosdidier, 2014). Consequently, new approaches were needed to conveniently drive molecular dynamics to explore large-scale collective motions (Chen and Ferguson, 2018; Bernardi et al., 2015; Karplus and Petsko, 1990).

Enhanced sampling techniques have been shown to be a useful tool to overcome this problem. However, the reliability of these simulations depends critically on the choice of effective collective variables. The necessity to reduce the number of degrees of freedom in a numerical simulation into a few reaction coordinates led to the development of convenient collective variables that bias sampling and overcome high energy barriers (Laio and Parrinello, 2002; Fiorin et al., 2013; Hub and Awasthi, 2017; Masone et al., 2018). Collective variable-driven molecular dynamics then allow projecting the multidimensional space into one or two dimensions to intuitively plot a quantitative energy landscape (Fig. 1). Although higher dimensionality makes visual representations rather problematic (Lee and Verleysen, 2007); adequately enhanced samplings conveniently reduce the simulation time required to characterize a system. In spite of the curse of dimensionality (Fu and Pfaendtner, 2018; Bellman and Dreyfus, 2015), different approaches have been developed to take into account more variables that describe high-dimensional free energy surfaces (Hénin, 2021; Ming et al., 2015; Li et al., 2012).

Figure 1: Alternative projections of a complex multidimensional free energy hypersurface. (a) Projection of the free energy over two collective variables (CV1 and CV2). (b) Projection over a single collective variable (CV1). The arrow indicates the same local minimum for both representations.

More than 40 years ago, Brito and Sousa (1981) eloquently discussed a classical analogy of the collective variable concept. They analyzed the extent to which it is possible to describe the behavior of a complex system (exhibiting a large number of degrees of freedom) by means of a reduced number of parameters that suppress unnecessary or redundant degrees of freedom. The concept of a collective variable assumes that the intrinsic and collective motions of a many-body system are sufficiently decoupled. Remarkably, such approximation allows for a significant reduction in the number of degrees of freedom to those necessary for the study of a particular behavior of a many-particle system.

However, the collective variable strategy has limitations. First, the computational cost to calculate a collective variable at each molecular dynamics step must be kept small, otherwise, the approach would generate the same problem seeking to be solved. Second, the definition of a collective variable is not an intuitive task. The problem of correctly projecting a free energy hypersurface (or manifold) into a few dimensions, with variables that correctly capture a biological event, is difficult (Hashemian et al., 2013). Badly defined collective variables can introduce wrong biases regarding how an event requiring large conformational changes should occur (Abrams and Vanden-Eijnden, 2010). Poor convergence or hysteresis are also problems associated with inadequate collective variables (Awasthi and Hub, 2016). With the aim to find better collective variables, several dimensionality reduction techniques that project data from biomolecular trajectories have been proposed (Tribello and Gasparotto, 2019; Wehmeyer and Noé, 2018; Hashemian et al., 2016). Particularly interesting are some innovative tools using machine learning (Doerr et al., 2021; Sidky et al., 2020) and neural network approaches (Hooft et al., 2021; Trapl et al., 2019).

Finally, during the study of the large majority of biological phenomena, long-lasting metastable states make classical sampling difficult, computationally too expensive, or even prohibitive (Zhang et al., 2019). Mainly by the umbrella sampling (Torrie and Valleau, 1977; Roux, 1995) and metadynamics (Laio and Gervasio, 2008) techniques, the development and improvement of collective variables have undoubtedly helped to overcome this problem (Pratyush and Berne, 2016). Still, new and better collective variables are objects of intense investigations (Zhang et al., 2019).

Membrane Deformations

Curvature-related processes play a key role during protein-membrane interactions. Lipids are now recognized to significantly determine the structure and function of membrane-associated proteins (Brown, 2017). Concurrently, the shape of the biomembrane is conditioned by the proteins that interact with its lipids (McMahon et al., 2010; François et al., 2014; Duncan et al., 2017; Masone and Bustos, 2019). Interesting studies have been conducted to reveal coupled properties between the membrane and proteins. Using Helfrich–Canham elastic theory (Helfrich, 1973), Sansom and collaborators (Fowler et al., 2016) showed that membrane stiffness highly depends on the concentration of membrane proteins such as aquaporin or an inwardly-rectifying potassium channel. Schulten and collaborators (Arkhipov et al., 2008; Yin et al., 2009) used computational means to extensively study how the adsorption of Bin/Amphiphysin/Rvs (BAR) domains containing an N-terminal amphipathic helix, induces bending. Consequently, the search for more accurate descriptions of the reciprocal interactions between membranes and proteins has been an initial step to unveiling the behaviors of real cell membranes.

From a lipocentric perspective, spontaneous curvature depends on the collective properties of the lipid bilayer. These properties are ultimately dictated by the membrane’s lipid packing (Israelachvili et al., 1977) and lipid shapes (Cooke and Deserno, 2006). In realistic models of biological membranes, lipid composition is highly heterogeneous, and lipid species are distributed asymmetrically between the hemilayers (Ingólfsson et al., 2014). Such organization has a high propensity to exhibit spontaneous local bending (Koldsø et al., 2014). Membrane curvature generally forms part of even larger lipid reorganization events for a wide range of cellular phenomena and processes, e.g., membrane fusion (di Bartolo and Masone, 2022) and fission (Lipowsky, 2022), endo and exocytosis (Tomes, 2015), cytokinesis (Schiel and Prekeris, 2013), and autophagy (Gómez-Sánchez et al., 2021). As pointed out by Torres-Sánchez et al. (2019), local density asymmetries result in small but noticeable changes in shape that can be observed in the curvature energy. Thermodynamically, bending appears to be a mechanism to maximize molecular contacts while minimizing the free energy of the system (Stroh and Risselada, 2021).

A common strategy in computer simulations is to replicate a biological event so that it can be later studied under different conditions of interest. Consequently, the development of new methods that enhance molecular dynamics simulations to induce curvature has significantly increased in recent years (Yang et al., 2019). Masone et al. (2018) proposed Ψ, a collective variable that induces membrane bending inspired by a previous concept by den Otter and collaborators (Tolpekina et al., 2004; Wohlert et al., 2006), originally used to form hydrophilic pores in lipid bilayers. Ψ takes advantage of the curvature as a collective response of the bilayers to increased local density (de Jesus et al., 2013), that produce out-of-plane forces. Remarkably, Ψ does not anticipate the curved shape of the bilayer, which spontaneously emerges as saddle-like (Alimohamadi and Rangamani, 2018). This essential characteristic has made Ψ a convenient tool to study protein mechanisms that induce or sense curvature, such as α-synuclein (Caparotta et al., 2020a) or the N-BAR domain (Masone et al., 2018).

Alternatively, Bubnis et al. (2016) used permutation symmetry to calculate lipid remodeling free energies via umbrella sampling. Also, Fiorin et al. (2020) proposed a method to quantify the mismatch between the shape of the bilayer and a reference, using this mismatch to induce different membrane shapes. Stroh and Risselada (2021) proposed a method to calculate bending free energies as a direct function of membrane curvature. Durrant and Amaro (2014) developed LipidWrapper, a multi-scale utility to create curved membrane models with geometries derived from experimental and theoretical sources. Finally, Yesylevskyy and Khandelia (2021) developed EnCurv (Enforced Curvature), a practical tool ported into PLUMED (Tribello et al., 2014) that induces bending in lipid bilayers in a controlled manner.

Simultaneously, convenient post-processing tools were also developed to analyze complex membrane surfaces from molecular dynamics trajectories. Lukat et al. (2013) used Voronoi diagrams to develop APL@Voro, a tool to analyze GROMACS (van der Spoel et al., 2005) trajectories of lipid bilayer simulations. Also, Buchoux developed the software Fast Analysis Toolbox for Simulations of Lipid Membranes (FATSLiM) (Buchoux, 2017) to extract physical properties from molecular dynamics simulations of membranes. Allen et al. (2009) developed GridMAT-MD to aid in the analysis of lipid bilayers from molecular dynamics trajectories. Sejdiu and Tieleman (2021) developed ProLint, a web-based framework to analyze and visualize lipid-protein interactions. Membrainy, developed by Carr and MacPhee (2015) is a user-friendly membrane analysis tool to calculate a variety of properties of different bilayers. Lastly, using Delaunay triangulations, Bhatia et al. (2019) developed MemSurfer to assess the undulations in the membrane.

Membrane Fusion

Membrane fusion is a fundamental process in many cellular events (both in the intra and the extracellular spaces), such as exocytosis, endocytosis, membrane genesis, viral infection, and fertilization (Arnold, 1995). To merge, initially independent membranes (Fig. 2a) follow different stages historically classified in an event-oriented manner. First, bilayers bend during recognition upon binding (Fig. 2b), and then, the fusion stalk forms (Fig. 2c). From the stalk, two possible paths exist: (i) a traversing water channel forms through it (Fig. 2d), connecting initially isolated spaces and initiating the formation of a nascent fusion pore, or a hemifusion diaphragm (Fig. 2e) emerges before the water channel forms (Fig. 2f). Finally, the fusion pore expands in its well-known toroidal shape (di Bartolo et al., 2022) (Fig. 2g).

Figure 2: Possible pathways along membrane fusion and fusion pore formation. (a) Flat and parallel membranes. (b) Initial deformation and bending. (c) Fusion stalk. (d) Fusion pore nucleation from the stalk. (e) Hemifusion diaphragm. (f) Fusion pore nucleation from the diaphragm. (g) Fusion pore expansion (toroid-shaped).

As stated, the first stage in the membrane fusion process is the bending of the membrane (see Fig. 2b). However, to initiate effective membrane fusion, a substantial structural lipid reorganization is needed to either form the fusion stalk or the hemifusion diaphragm. In any case, lipid molecules forming the fusion stalk or surrounding the hemifusion diaphragm suffer from heavy tilting and splaying. Several studies have suggested that while membranes fuse, lipid acyl tails splay and protrude to the surface of the bilayers to initiate lipid mixing (Scheidt et al., 2020; Caparotta et al., 2020b; Pannuzzo et al., 2014; Smirnova et al., 2010; Smeijers et al., 2006).

Again, important efforts have been made to develop special-purpose computational methods to induce and study membrane fusion configurations. Kawamoto et al. (2014, 2015) used a continuum model to study the fusion stalk using coarse-grained molecular dynamics and to calculate its associated free energies of formation. Hub and collaborators (Hub and Awasthi, 2017; Poojari et al., 2021) proposed a novel collective variable to induce membrane fusion through the stalk mechanism. More than a decade ago, Chernomordik and Kozlov (2008) proposed that particular lipid geometries in proximal monolayers could facilitate or inhibit the formation of the hemifusion stalk. Nishizawa and Nishizawa (2013) studied pore propensity in hemifusion diaphragms using atomistic and coarse-grained molecular dynamics. Also, Risselada et al. (2012) used coarse-grained molecular dynamics to describe how the widening of the fusion stalk evolves into a single, bilayer H-shaped diaphragm. Gardner and Abrams (2017) studied the rate of expansion of large hemifusion diaphragms using solvent-free coarse-grained molecular dynamics.

The development of these tools allowed for further studies oriented to lipid-protein interactions. Caparotta et al. (2020b) studied membrane fusion and pore nucleation to describe synaptotagmin-1 C2B domain interactions with phosphatidylinositol 4, 5-bisphosphate lipids (PI (4,5) P2, or simply PIP2). di Bartolo and Masone (2022) described the effects on membrane fusion by a pair of synaptotagmin-1 C2B domains using a methodology by Hub and Awasthi for membrane fusion, 28 ported into PLUMED (Tribello et al., 2014) and freely available on GitHub: https://github.com/lautarodibartolo/MemFusion. Miyazaki et al. (2019) examined the free energy barrier for the creation of a pore in lipid membranes with and without multiple melittin peptides. Also, Hsiao et al. (2018) conducted a free energy study on cecropin B and its constituent domains to describe cooperative modes of action of antimicrobial peptides.

The Fusion Pores

The fusion stalk and the hemifusion diaphragm are intermediate metastable configurations that await the formation of a fusion pore. As widely accepted, the energetics along the membrane fusion paths towards the fusion pore (Fig. 2) highly depends on the lipid composition of the interacting bilayers (di Bartolo et al., 2022; Kawamoto and Shinoda, 2014; Fuertes et al., 2011; Aeffner et al., 2012; Cunill-Semanat and Salgado, 2019) as well as their hydration level for different inter-membrane distances (di Bartolo and Masone, 2022; Caparotta et al., 2020b; Poojari et al., 2021; Smirnova et al., 2015; Smirnova et al., 2019; Wu et al., 2021).

The exocytosis mechanism allows eukaryotic cells to release biological cargo and effectively transport molecules across the plasma membrane (Tomes, 2015; Rizo, 2022). The complexity of the fusion pore as a mechanism to connect intra-cellular organelles and release the contents of vesicles during exocytosis, has made it an interesting object of study both experimentally (Wu et al., 2021; Chang, Chiang and Jackson, 2017; Gucek et al., 2016; Bai et al., 2004) and computationally (Risselada and Grubmüller, 2021; Risselada and Mayer, 2020; Risselada et al., 2014). Fig. 3a shows a 3D time-averaged density of a fusion pore from an enhanced molecular dynamics trajectory. The fusion pore for this figure was induced with the collective variable ξe (di Bartolo et al., 2022; Hub, 2021) (freely available on GitHub: https://github.com/lautarodibartolo/FusionPore), and the trajectory density was generated using GROmaps (Briones et al., 2019). Fig. 3b is a representation of the possible free energy landscape along the different stages during the life of the fusion pore. Starting from membrane bending and ending with the expansion of the fusion pore, this schematic curve follows the path of pore nucleation through the fusion stalk. The shape of the estimated free energy profile is based on results by Caparotta et al. (2020b), di Bartolo and Masone (2022), di Bartolo et al. (2022) and is in good agreement with previous studies on the energetics of the fusion pore (Lipowsky, 2022; Kawamoto et al., 2015; Smirnova et al., 2015; Gorai et al., 2021; Dhara et al., 2020; François-Martin et al., 2017; Markvoort and Marrink, 2011).

Figure 3: The fusion pore. (a) Time-averaged density of a fusion pore induced between two bilayers using enhanced molecular dynamics. For clarity, water molecules are not shown. (b) Schematics of the free energy landscape along membrane bending (green), the fusion stalk (light blue), fusion pore nucleation (pink), fusion pore expansion (orange), and possible further expansion (lilac).

The fusion pore is an excellent case of study to unveil complicated lipid-protein interactions. Recently, Caparotta et al. (2020b) showed that a single C2B domain of synaptotagmin-1 has negligible effects on the free energy during membrane fusion and fusion pore nucleation. Also, di Bartolo and Masone (2022) revealed a cooperative mechanism between a pair of C2B domains that significantly decrease the energy costs for the formation of the fusion stalk and the first traversing water channel. In another study, di Bartolo et al. (2022) demonstrated that C2B domains reduce the energy cost for fusion pore expansion and the probability of kiss-and-run events.

The Lipid-Protein Interplay

Lipid bilayers are composed of self-organizing molecules that form very stable structures. Hence, membrane fusion is thought to be mediated by protein fusogens that perturb their organization and dynamics (Pattnaik, Meher and Chakraborty, 2018; Joardar, Pattnaik and Chakraborty, 2022). Key proteins for evoked neurotransmitter release such as the synaptotagmin-1 C2B domains (Gruget et al., 2020) collaborate to overcome the energetic barriers for the fusion stalk (Di Bartolo and Masone, 2022) and fusion pore expansion (Di Bartolo et al., 2022; Nyenhuis et al., 2021; Das et al., 2020), possibly inducing PIP2 clusters (Caparotta et al., 2020b). Another significant example is myoblast fusion, where Myomaker and Myomerger promote the hemifusion diaphragm (Golani et al., 2021; Whitlock and Chernomordik, 2021). Also, local membrane deformations have been indicated to potentially affect the overall organization of signaling proteins and their biochemical functions (Orbach and Su, 2020).

The fusion pore is particularly interesting from a driving protein point of view. Undoubtedly, SNAREs are among the most studied proteins in inducing membrane fusion reactions inside eukaryotic cells, both experimentally (Tomes et al., 2002; Fang and Lindau, 2014; Bao et al., 2018; Amos et al., 2022) and computationally (Smirnova et al., 2019; Risselada and Mayer, 2020; Risselada et al., 2011; Risselada and Grubmüller, 2012; Sharma and Lindau, 2018; D’Agostino et al., 2018). The key role of SNAREs during fusion pore formation makes them an ideal object of study to develop and test new methods that describe lipid-protein interactions during membrane remodeling that can be later integrated with experiments. Other proteins involved in the membrane fusion process, such as the synaptotagmin family (Fernandez et al., 2001; Seven et al., 2013; Rizo, 2018), have also received significant attention within the biomedical sciences, both computationally (di Bartolo and Masone, 2022; di Bartolo et al., 2022; Caparotta et al., 2020b) and experimentally (Wu et al., 2021; Bendahmane et al., 2018; Ying et al., 2013; Lynch et al., 2008).

Shape transformations along the membrane due to specialized curvature-sensing and curvature-inducing proteins are also interesting lines of research (Brown, 2017; Alimohamadi and Rangamani, 2018). For example, the relation of α-synuclein to vesicle trafficking, membrane fusion, and fission has been extensively studied (Auluck et al., 2010; Nemani et al., 2010; Thayanidhi et al., 2010; Cooper et al., 2006; Kamp and Beyer, 2006), due to its implications in Parkison’s disease (Jao et al., 2008; Bodner et al., 2009) and other pathologies, broadly known as synucleinopathies. In particular, Middleton and Rhoades (Middleton and Rhoades, 2010) showed how α-synuclein preferably binds to highly curved lipid vesicles. Also, Braun et al. (2012) described how a truncated version (1–100) of α-synuclein is able to induce negative and positive curvature. Recent results in α-synuclein implications along the membrane fusion process have renewed the attention toward this protein (Huang et al., 2019; Khounlo et al., 2021; Liu et al., 2021). Experimentally, using a single vesicle-to-supported bilayer fusion assay, Khounlo et al. (2021) examined the role of α-synuclein in membrane fusion. Following an in vitro approach with v-SNARE–reconstituted nanodiscs and t-SNARE–reconstituted black lipid membrane (Das et al., 2020; Bao et al., 2018), Nellikka et al. (2021) studied α-synuclein modes of action in different time-scales. Both experimental procedures could be applied to synaptotagmin.

The detailed characterization of the full network of interactions between human proteins is a major scientific ambition (Cusick et al., 2009). Protein folding and protein-protein binding are interdependent processes (Sugase et al., 2007), ultimately determining protein functions. Moreover, membrane deformations due to lipid influences have been established for protein folding in membranes (Moon and Fleming, 2011; Honerkamp-Smith et al., 2009; Curnow et al., 2004). Consequently, strategies to approach the problem of lipid-protein interactions from a coupled point of view would improve the overall understanding of complex biological events, ultimately allowing better and more accurate predictions.

Intrinsic Disorder in Lipid-Protein Interactions

Many proteins have no stable 3D structures under physiological conditions, and their functions are determined dynamically by coexisting binding partners. These proteins have been historically classified as intrinsically unstructured (Wright and Dyson, 1999) or intrinsically disordered (Dunker et al., 2001). Such is the case of α-synuclein, which folds into two anti-parallel α-helices (Jao et al., 2008; Drescher et al., 2008; Chandra et al., 2003) upon binding to the membrane (see UniProt ID: P37840). Recently, Bondos et al. (2021) have compiled thirteen relevant papers that highlight the importance of intrinsic disorder in current biochemistry and cell biology.

The problem of intrinsically disordered regions in proteins that interact with lipid bilayers adds substantial complexity to the molecular description of the lipid-protein interplay. More two decades ago, Shoemaker et al. (2000) observed that a relatively unstructured protein could have a larger capture radius for a specific binding site with respect to the folded conformation. The fly-casting mechanism was then proposed (Shoemaker et al., 2000; Levy et al., 2007; Huang and Liu, 2009), where a disordered region of a protein binds weakly to its partner before folding. This hypothesis helped to highlight the importance of unstructured regions during protein binding and folding.

Accordingly, using enhanced molecular dynamics simulations, Caparotta et al. (2020a) showed that the intrinsically disordered region of α-synuclein is essential for the protein mechanism that induces bending in lipid bilayers. In agreement, Zeno et al. (2018) used Monte-Carlo simulations, in vitro, and live-cell measurements to show that proteins containing both structured and unstructured regions are significantly more sensitive to membrane curvature, with respect to fully-structured ones. Also, Busch et al. (2015) proposed that the large hydrodynamic radii of disordered domains generate a steric pressure that drives membrane bending.

Recently, new efforts have been made to improve computational modeling of intrinsically disordered proteins (Thomasen et al., 2022; Klein et al., 2021; Tran and Kitao, 2020). Several reviews have also been dedicated to the role of intrinsic disorder during lipid-protein interactions highlighting the effects on membrane curvature (Has, Sivadas and Das, 2022; Cornish et al., 2020; Fakhree, Blum and Claessens, 2019; Snead and Stachowiak, 2018). Intrinsic disorder presents itself as an additional complexity to the already difficult problem of lipid-protein interactions during biological events that require large configurational and conformational changes.

Lipid-protein interaction is a problem that could be addressed with an interdisciplinary approach, merging cell biology, chemistry, and physics. Such cross-disciplinary connections between different research fields, at experimental and computational levels, may help to find better descriptions with direct biomedical applications, e.g., to monitor disease development and to identify new targets for drug development.

Connecting Cell Biology and Physics

The idea of decomposing a biological problem into its fundamental building blocks in order to predict complex collective behaviors of the ensemble is an intelligent approach that for many years aimed to merge physics and cell biology (Alon, 2006; Hartwell et al., 1999; Gell-Mann, 1995). Among biological entities, each individual is characterized in part by its relations with other individuals (Nachtomy et al., 2002). Within the cell, the plasma membrane is a spatial boundary that actively isolates internal and external environments. A selective interchange of molecules takes place across the bilayers, and the properties of the bilayers are conditioned by their surrounding external and internal organizations.

In physics, the problem of reversibility is an elegant example that highlights collective behaviors. According to Fick’s first law, (Fick, 1995) a flux of particles evolves from regions of high concentrations to regions of low concentrations, with a magnitude proportional to the concentration gradient. From a microscopic point of view, each particle of the flux follows Newton’s laws, and its individual motion is fully reversible. However, when particles are taken together, they move collectively in a certain direction, following Fick’s first law (Dill et al., 2010). Reid and Latty (2016) recall that in a microbiological context, individual-level behaviors can lead to complex group-level patterns, which is well accepted. Richard Feynman observed that the behavior of a fluid depends very little on the nature of the individual particles in that fluid, for example, being the flow of sand very similar to the flow of water or a pile of ball bearings (Feynman et al., 2018). Communication seems to be the key between microbiological entities to transfer information and sense the environment to respond in ways that would be impossible for individuals to achieve on their own (Davies, 2004).

Almost twenty years ago, Davis (2004) commented on the problem of the minimum complexity needed by a system to exhibit emergent properties. As presented by Erwin Shcrödinger in 1944, life follows a spontaneous emergence of self-organized order (Schrödinger, 1944). Polanyi, already in 1968, commented on the irreducible structure of life, noting that although life obeys the laws of physics and chemistry, the design of living organisms is not ultimately determined by such laws (Polanyi, 1968). Although beyond the scope of this review, the philosophical discussion to distinguish between weak and strong emergent properties is of relevance and has been considered by others (O’Connor, 1994; Chalmers, 2006; Turkheimer et al., 2019).

From a thermodynamic point of view, order is more improbable than disorder, and also transitions from disordered configurations to ordered ones require energy (Macklem, 2008). Ikegami et al. (2017) clearly distinguished that these emergent phenomena are an extension of self-organization, being self-organization a one-way formation of macroscopic order from microdynamics. On the contrary, emergent phenomena require the two-way circulation of recurrent information between macro- and micro-scales. Such emergent phenomena in life might as well characterize many diseases (Macklem, 2008). Computational modeling is, therefore, an excellent tool for predicting the global emergent properties of a tissue starting from local cellular rules (Pebay-Peyroula et al., 2016).

Mathematical models have helped to understand the underlying mechanisms and emergent properties of the cell (Mayorga et al., 2018). Important advances have been made in fibration symmetries and the functionality of biological networks (Leifer et al., 2020; Monteiro et al., 2022). In particular, a convenient graph representation of the information flow has been proposed by Morone et al. (2020). In their work, the authors introduce the use of symmetries in biological networks by analyzing the well-known transcriptional regulatory network of Escherichia coli. These studies contribute to the identification of the building blocks in biological networks and are a step forward in understanding life as an emergent property of physics.

Conclusions

Today it is well accepted that membrane deformations and associated protein functions are coupled mechanisms (Haylock et al., 2020; Song et al., 2019), with complex emergent properties derived in part from the highly heterogeneous nature of the bilayers (Nicolson, 2014; Mohammad et al., 2019), or as suggested by Lamparter and Galic (2020), a versatile, adaptive composite material. Membrane proteins may dynamically modify their curvature preference upon external stimuli (Stroh and Risselada, 2021), also making the coupled mechanism dynamic. Additionally, lipid dynamics have been shown to play an active part in the protein-mediated fusion machinery, for example, by SNAREs or synaptotagmins (Amos et al., 2022).

Already in 1945, Novikoff highlighted the necessity of understanding lower level phenomena to understand higher level ones, even if the knowledge at lower levels does not completely describe, nor fully predicts, what will occur at higher ones (Novikoff Alex, 1945). Such observation is aligned with modern views of life as an emergent property. Therefore, a proper understanding of the lipid-protein interactions during key biological events, such as membrane curvature, membrane fusion, and fusion pore formation, would provide crucial information to face more complex biomedical problems.

The predictive capabilities of computational simulations have reached an interesting stage in the biomedical sciences. Improved simulation packages (Brooks et al., 2021; Suh et al., 2022), better force-fields (Klein et al., 2021; Souza et al., 2021; Cruz-León et al., 2021; Yungerman et al., 2022), unprecedented supercomputer power (Yamazaki et al., 2021; Kutzner et al., 2022) and creative sampling techniques (Gilabert et al., 2019; Bonati et al., 2021) have boosted the study of exceptionally complex biological problems (Mosalaganti et al., 2022; Lotz and Dickson, 2018). More studies combining theoretical approaches, computer simulations, and experiments are currently envisioning new possibilities (Sica and Smulski, 2021; Bernetti and Bussi, 2021; Miguel et al., 2021; Quevedo et al., 2019; Saen-oon et al., 2015). Although computational models containing conceptual simplifications may, of course, exhibit inherent limitations (Alessandri et al., 2019; Jarin et al., 2021; Masone et al., 2012), the recent overall progress in the biomolecular simulations field at varied lengths and timescales has been outstanding (Schlick and Portillo-Ledesma, 2021; Pezeshkian et al., 2020).

Acknowledgement: The author thanks Prof. Luis Mayorga for his useful suggestions.

Author Contribution: The author confirms sole responsibility for the manuscript preparation.

Ethics Approval: Not applicable.

Funding Statement: Grants from CONICET (PIP-0409CO) and ANPCyT (PICT2020-1897) are gratefully acknowledged.

Conflicts of Interest: The authors declares that they have no conflicts of interest regarding the present study.

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