Dynamic interactions between a membrane binding protein and lipids induce fluctuating diffusivity

Single-Lipid Diffusion Behaviors in Cell Membranes Modulated by Cholesterol-Based Heterogeneity

Over a century after the proposal of Fluid Mosaic Model, the relationship between functionally related multiple-scale spatial heterogeneity of the cell membrane and mobility of component molecules, both inherent features of cell membrane, remains elusive. Single-lipid tracking enables the analysis of structural heterogeneity at different spatial scales within the cell membrane from a lipid diffusion perspective. Herein, specifically designed cholesterol (Chol)-based membrane systems were utilized to investigate the distinct impacts of molecular-level interactions between diverse membrane components and micrometer-scale spatial confinement on lipid diffusion. The results demonstrate that the incorporation of Chol into 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) membranes decelerates lipid diffusion, with a positive correlation observed between the degree of deceleration and the mole ratio of Chol molecules. Across all these systems, lipid diffusion consistently adheres to the continuous time random walk (CTRW) model, indicating lipid entrapment resulting from specific molecular interactions. Conversely, micrometer-scale spatial confinement induced by phase separation not only reduces the diffusion rate of DOPC molecules but also triggers a transition from CTRW to fractional Brownian motion (fBM) or random walk on a fractal (RWF) mode within a confinement width range of 6.3-5.4 μm, suggesting a crowded microenvironment. In living cell membranes, this transformation in lipid diffusion is observed following Chol depletion, implying that lipid raft disruption leads to increased crowding within the lipid microenvironment. This study enhances our understanding of the relationship between lipid diffusion and membrane microenvironment across different spatial scales while providing insights into characterizing spatially heterogeneous structures within cell membranes from the perspective of lipid diffusion.

Computing Nonequilibrium Responses with Score-Shifted Stochastic Differential Equations

Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic dynamics. For nonequilibrium systems, perturbations cannot be interpreted simply by monitoring fluctuations in a conjugate observable and general response results rely on path ensemble averaging. These techniques do not apply to perturbations that affect the diffusion tensor in a stochastic system. Here, we introduce an "effective" physical process that represents the diffusion perturbed dynamics and enables accurate calculations of responses to a change in the diffusion. Interestingly, the effective dynamics contain an additional drift involving the instantaneous "score" of the system, and we leverage score matching algorithms to carry out nonequilibrium response calculations on systems for which the exact stationary distribution is unknown.

A Membrane-Assisted Mechanism for the Release of Ceramide from the CERT START Domain

Ceramide transfer protein CERT is the mediator of nonvesicular transfer of ceramide from the ER to Golgi. In CERT, START is the domain responsible for the binding and transport of ceramide. A wealth of structural data has revealed a helix-grip fold surrounding a large hydrophobic cavity holding the ceramide. Yet, little is known about the mechanisms by which START releases the ceramide through the polar region and into the packed environment of cellular membranes. As such events do not lend themselves easily to experimental investigations, we used multiple unbiased microsecond-long molecular simulations. We propose a membrane-assisted mechanism in which the membrane acts as an allosteric effector initiating the release of ceramide and where the passage of the ceramide acyl chains is facilitated by the intercalation of a single phosphatidylcholine lipid in the cavity, practically greasing the ceramide way out. We verify using free energy calculation and experimental lipidomics data that CERT forms stable complexes with phosphatidylcholine lipids, in addition to ceramide, thus providing validation for the proposed mechanism.

Being Heterogeneous Is Advantageous: Extreme Brownian Non-Gaussian Searches

Redundancy in biology may be explained by the need to optimize extreme searching processes, where one or few among many particles are requested to reach the target like in human fertilization. We show that non-Gaussian rare fluctuations in Brownian diffusion dominates such searches, introducing drastic corrections to the known Gaussian behavior. Our demonstration entails different physical systems and pinpoints the relevance of diversity within redundancy to boost fast targeting. We sketch an experimental context to test our results: polydisperse systems.

Being heterogeneous is disadvantageous: Brownian non-Gaussian searches

Diffusing diffusivity models, polymers in the grand canonical ensemble and polydisperse, and continuous-time random walks all exhibit stages of non-Gaussian diffusion. Is non-Gaussian targeting more efficient than Gaussian? We address this question, central to, e.g., diffusion-limited reactions and some biological processes, through a general approach that makes use of Jensen's inequality and that encompasses all these systems. In terms of customary mean first-passage time, we show that Gaussian searches are more effective than non-Gaussian ones. A companion paper argues that non-Gaussianity becomes instead highly more efficient in applications where only a small fraction of tracers is required to reach the target.

Triggering Gaussian-to-Exponential Transition of Displacement Distribution in Polymer Nanocomposites via Adsorption-Induced Trapping

In many disordered systems, the diffusion of classical particles is described by a displacement distribution P(x, t) that displays exponential tails instead of Gaussian statistics expected for Brownian motion. However, the experimental demonstration of control of this behavior by increasing the disorder strength has remained challenging. In this work, we explore the Gaussian-to-exponential transition by using diffusion of poly(ethylene glycol) (PEG) in attractive nanoparticle-polymer mixtures and controlling the volume fraction of the nanoparticles. In this work, we find "knobs", namely nanoparticle concentration and interaction, which enable the change in the shape of P(x,t) in a well-defined way. The Gaussian-to-exponential transition is consistent with a modified large deviation approach for a continuous time random walk and also with Monte Carlo simulations involving a microscopic model of polymer trapping via reversible adsorption to the nanoparticle surface. Our work bears significance in unraveling the fundamental physics behind the exponential decay of the displacement distribution at the tails, which is commonly observed in soft materials and nanomaterials.

Heterogeneous anomalous transport in cellular and molecular biology

It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalised diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field ofheterogeneous anomalous transport(HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and nuclear magnetic resonance), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction-diffusion systems is also considered since it plays an important role in morphogenesis and signalling. In addition, we present specific examples from cellular biology including embryonic cells, leucocytes, cancer cells, bacterial cells, bacterial biofilms, and eukaryotic microorganisms. Case studies from molecular biology include DNA, membranes, endosomal transport, endoplasmic reticula, mucins, globular proteins, and amyloids.

Effects of crowding on the diffusivity of membrane adhered particles

The lateral diffusion of cell membrane inclusions, such as integral membrane proteins and bound receptors, drives critical biological processes, including the formation of complexes, cell-cell signaling, and membrane trafficking. These diffusive processes are complicated by how concentrated, or "crowded", the inclusions are, which can occupy between 30-50% of the area fraction of the membrane. In this work, we elucidate the effects of increasing concentration of model membrane inclusions in a free-standing artificial cell membrane on inclusion diffusivity and the apparent viscosity of the membrane. By multiple particle tracking of fluorescent microparticles covalently tethered to the bilayer, we show the transition from expected Brownian dynamics, which accurately measure the membrane viscosity, to subdiffusive behavior with decreased diffusion coefficient as the particle area fraction increases from 1% to around 30%, approaching physiological levels of crowding. At high crowding, the onset of non-Gaussian behavior is observed. Using hydrodynamic models relating the 2D diffusion coefficient to the viscosity of a membrane, we determine the apparent viscosity of the bilayer from the particle diffusivity and show an increase in the apparent membrane viscosity with increasing particle area fraction. However, the scaling of this increase is in contrast with the behavior of monolayer inclusion diffusion and bulk suspension rheology. These results demonstrate that physiological levels of model membrane crowding nontrivially alter the dynamics and apparent viscosity of the system, which has implications for understanding membrane protein interactions and particle-membrane transport processes.

Transition between Different Diffusion Modes of Individual Lipids during the Membrane-Specific Action of As-CATH4 Peptides

The cell membrane permeabilization ability of immune defense antimicrobial peptides (AMPs) is widely applied in biomedicine. Although the mechanisms of peptide-membrane interactions have been widely investigated, analyses at the molecular level are still lacking. Herein, the membrane-specific action of a native AMP, As-CATH4, is investigated using a single-lipid tracking method in combination with live cell and model membrane assays conducted at different scales. The peptide-membrane interaction process is characterized by analyzing single-lipid diffusion behaviors. As-CATH4 exhibits potent antimicrobial activity through bacterial membrane permeabilization, with moderate cytotoxicity against mammalian cells. In-plane diffusion analyses of individual lipids show that the lipid molecules exhibit non-Gaussian and heterogeneous diffusion behaviors in both pristine and peptide-treated membranes, which can be decomposed into two Gaussian subgroups corresponding to normal- and slow-diffusive lipids. Assessment of the temporal evolution of these two diffusion modes of lipids reveal that the peptide action states of As-CATH4 include surface binding, transmembrane defect formation, and dynamic equilibrium. The action mechanisms of As-CATH4 at varying concentrations and against different membranes are distinguished. This work resolves the simultaneous mixed diffusion mechanisms of single lipids in biomimetic cell membranes, especially during dynamic membrane permeabilization by AMPs.

Heterogeneous biological membranes regulate protein partitioning via fluctuating diffusivity

Cell membranes phase separate into ordered L o and disordered L d domains depending on their compositions. This membrane compartmentalization is heterogeneous and regulates the localization of specific proteins related to cell signaling and trafficking. However, it is unclear how the heterogeneity of the membranes affects the diffusion and localization of proteins in L o and L d domains. Here, using Langevin dynamics simulations coupled with the phase-field (LDPF) method, we investigate several tens of milliseconds-scale diffusion and localization of proteins in heterogeneous biological membrane models showing phase separation into L o and L d domains. The diffusivity of proteins exhibits temporal fluctuations depending on the field composition. Increases in molecular concentrations and domain preference of the molecule induce subdiffusive behavior due to molecular collisions by crowding and confinement effects, respectively. Moreover, we quantitatively demonstrate that the protein partitioning into the L o domain is determined by the difference in molecular diffusivity between domains, molecular preference of domain, and molecular concentration. These results pave the way for understanding how biological reactions caused by molecular partitioning may be controlled in heterogeneous media. Moreover, the methodology proposed here is applicable not only to biological membrane systems but also to the study of diffusion and localization phenomena of molecules in various heterogeneous systems.

Non-Gaussian Diffusion of Individual Lipids Unveils the Unique Peptide-Membrane Interaction Dynamics

The dynamics of protein (or peptide)-membrane interactions plays a central role in cellular functions; however, the underlying mechanisms remain unclear. Herein, through analyzing the diffusion of individual lipids in a bilayer membrane during the membrane actions of typical peptides (e.g., pore-forming peptide melittin and cell-penetrating peptide TAT) at varying concentrations, the spatial heterogeneity as well as temporal dynamics of lipid motions were investigated which showed close correlation with the peptide action mechanism. Specifically, the spatial heterogeneity of lipid diffusion was characterized by the non-Gaussianity of lipid trajectories, which was further decomposed into two basic diffusion modes; moreover, the temporal evolution of the Gaussian fitting parameters provided quantitative information on the varying metastable interaction states between peptides and the membrane (e.g., peptide landing, membrane insertion, and equilibrium). Generally, this work gives an insight into the correlation between single-lipid diffusion and function-realization of membrane-active peptides.

Heterogeneous Nanostructures Cause Anomalous Diffusion in Lipid Monolayers

The diffusion and mobility in biomembranes are crucial for various cell functions; however, the mechanisms involved in such processes remain ambiguous due to the complex membrane structures. Herein, we investigate how the heterogeneous nanostructures cause anomalous diffusion in dipalmitoylphosphatidylcholine (DPPC) monolayers. By identifying the existence of condensed nanodomains and clarifying their impact, our findings renew the understanding of the hydrodynamic description and the statistical feature of the diffusion in the monolayers. We find a universal characteristic of the multistage mean square displacement (MSD) with an intermediate crossover, signifying two membrane viscosities at different scales: the short-time scale describes the local fluidity and is independent of the nominal DPPC density, and the long-time scale represents the global continuous phase taking into account nanodomains and increases with DPPC density. The constant short-time viscosity reflects a dynamic equilibrium between the continuous fluid phase and the condensed nanodomains in the molecular scale. Notably, we observe an "anomalous yet Brownian" phenomenon exhibiting an unusual double-peaked displacement probability distribution (DPD), which is attributed to the net dipolar repulsive force from the heterogeneous nanodomains around the microdomains. The findings provide physical insights into the transport of membrane inclusions that underpin various biological functions and drug deliveries.

Stochastically switching diffusion with partially reactive surfaces

In this paper we develop a hybrid version of the encounter-based approach to diffusion-mediated absorption at a reactive surface, which takes into account stochastic switching of a diffusing particle's conformational state. For simplicity, we consider a two-state model in which the probability of surface absorption depends on the current particle state and the amount of time the particle has spent in a neighborhood of the surface in each state. The latter is determined by a pair of local times ℓ_{n,t}, n=0,1, which are Brownian functionals that keep track of particle-surface encounters over the time interval [0,t]. We proceed by constructing a differential Chapman-Kolmogorov equation for a pair of generalized propagators P_{n}(x,ℓ_{0},ℓ_{1},t), where P_{n} is the joint probability density for the set (X_{t},ℓ_{0,t},ℓ_{1,t}) when N_{t}=n, where X_{t} denotes the particle position and N_{t} is the corresponding conformational state. Performing a double Laplace transform with respect to ℓ_{0},ℓ_{1} yields an effective system of equations describing diffusion in a bounded domain Ω, in which there is switching between two Robin boundary conditions on ∂Ω. The corresponding constant reactivities are κ_{j}=Dz_{j} and j=0,1, where z_{j} is the Laplace variable corresponding to ℓ_{j} and D is the diffusivity. Given the solution for the propagators in Laplace space, we construct a corresponding probabilistic model for partial absorption, which requires finding the inverse Laplace transform with respect to z_{0},z_{1}. We illustrate the theory by considering diffusion of a particle on the half-line with the boundary at x=0 effectively switching between a totally reflecting and a partially absorbing state. We calculate the flux due to absorption and use this to compute the resulting MFPT in the presence of a renewal-based stochastic resetting protocol. The latter resets the position and conformational state of the particle as well as the corresponding local times. Finally, we indicate how to extend the analysis to higher spatial dimensions using the spectral theory of Dirichlet-to-Neumann operators.

Topology mediates transport of nanoparticles in macromolecular networks

Diffusion transport of nanoparticles in confined environments of macromolecular networks is common in diverse physical systems and regulates many biological responses. Macromolecular networks possess various topologies, featured by different numbers of degrees and genera. Although the network topologies can be manipulated from a molecular level, how the topology impacts the transport of nanoparticles in macromolecular networks remains unexplored. Here, we develop theoretical approaches combined with simulations to study nanoparticle transport in a model system consisting of network cells with defined topologies. We find that the topology of network cells has a profound effect on the free energy landscape experienced by a nanoparticle in the network cells, exhibiting various scaling laws dictated by the topology. Furthermore, the examination of the impact of cell topology on the detailed behavior of nanoparticle dynamics leads to different dynamical regimes that go beyond the particulars regarding the local network loop. The results might alter the conventional picture of the physical origin of transport in networks.

Macromolecular networks relevant for biological processes and technological applications, are often characterized by complex architectures. The authors uncover the impact of topology on the properties of nanoparticle transport in macromolecular networks.

Systematic simulation of the interactions of pleckstrin homology domains with membranes

Pleckstrin homology (PH) domains can recruit proteins to membranes by recognition of phosphatidylinositol phosphate (PIP) lipids. Several family members are linked to diseases including cancer. We report the systematic simulation of the interactions of 100 mammalian PH domains with PIP-containing membranes. The observed PIP interaction hotspots recapitulate crystallographic binding sites and reveal a number of insights: (i) The β1 and β2 strands and their connecting loop constitute the primary PIP interaction site but are typically supplemented by interactions at the β3-β4 and β5-β6 loops; (ii) we reveal exceptional cases such as the Exoc8 PH domain; (iii) PH domains adopt different membrane-bound orientations and induce clustering of anionic lipids; and (iv) beyond family-level insights, our dataset sheds new light on individual PH domains, e.g., by providing molecular detail of secondary PIP binding sites. This work provides a global view of PH domain/membrane association involving multivalent association with anionic lipids.

Role of ergodicity, aging, and Gaussianity in resolving the origins of biomolecule subdiffusion

The internal motions of biomolecules are essential to their function. Although biological macromolecules conventionally show subdiffusive dynamics, only recently has subdiffusion been associated with non-ergodicity. These findings have stimulated new questions in biophysics and statistical mechanics. Is non-ergodic subdiffusion a general strategy shared by biomolecules? What underlying mechanisms are responsible for it? Here, we performed extensive molecular dynamics (MD) simulations to characterize the internal dynamics of six different biomolecules, ranging from single or double-stranded DNA, a single domain protein (KRAS), two globular proteins (PGK and SHP2), to an intrinsically disordered protein (SNAP-25). We found that the subdiffusive behavior of these biomolecules falls into two classes. The internal motion of the first three cases is ergodic subdiffusion and can be interpreted by fractional Brownian motion (FBM), while the latter three cases involve non-ergodic subdiffusion and can be modeled by mixed origins of continuous-time random walk (CTRW) and FBM.

Lipid-Protein Interactions in Plasma Membrane Organization and Function

Lipid-protein interactions in cells are involved in various biological processes, including metabolism, trafficking, signaling, host-pathogen interactions, and transmembrane transport. At the plasma membrane, lipid-protein interactions play major roles in membrane organization and function. Several membrane proteins have motifs for specific lipid binding, which modulate protein conformation and consequent function. In addition to such specific lipid-protein interactions, protein function can be regulated by the dynamic, collective behavior of lipids in membranes. Emerging analytical, biochemical, and computational technologies allow us to study the influence of specific lipid-protein interactions, as well as the collective behavior of membranes on protein function. In this article, we review the recent literature on lipid-protein interactions with a specific focus on the current state-of-the-art technologies that enable novel insights into these interactions.

Polymers critical point originates Brownian non-Gaussian diffusion

We demonstrate that size fluctuations close to polymers critical point originate the non-Gaussian diffusion of their center of mass. Static universal exponents γ and ν-depending on the polymer topology, on the dimension of the embedding space, and on equilibrium phase-concur to determine the potential divergency of a dynamic response, epitomized by the center-of-mass kurtosis. Prospects in experiments and stochastic modeling brought about by this result are briefly outlined.

PIP2-induced membrane binding of the vinculin tail competes with its other binding partners

Vinculin plays a key role during the first phase of focal adhesion formation and interacts with the plasma membrane through specific binding of its tail domain to the lipid phosphatidylinositol 4,5-bisphosphate (PIP₂). Our understanding of the PIP₂-vinculin interaction has been hampered by contradictory biochemical and structural data. Here, we used a multiscale molecular dynamics simulation approach, in which unbiased coarse-grained molecular dynamics were used to generate starting structures for subsequent microsecond-long all-atom simulations. This allowed us to map the interaction of the vinculin tail with PIP₂-enriched membranes in atomistic detail. In agreement with experimental data, we have shown that membrane binding is sterically incompatible with the intramolecular interaction between vinculin's head and tail domain. Our simulations further confirmed biochemical and structural results, which identified two positively charged surfaces, the basic collar and the basic ladder, as the main PIP₂ interaction sites. By introducing a valency-disaggregated binding network analysis, we were able to map the protein-lipid interactions in unprecedented detail. In contrast to the basic collar, in which PIP₂ is specifically recognized by an up to hexavalent binding pocket, the basic ladder forms a series of low-valency binding sites. Importantly, many of these PIP₂ binding residues are also involved in maintaining vinculin in a closed, autoinhibited conformation. These findings led us to propose a molecular mechanism for the coupling between vinculin activation and membrane binding. Finally, our refined binding site suggests an allosteric relationship between PIP₂ and F-actin binding that disfavors simultaneous interaction with both ligands, despite nonoverlapping binding sites.

Reversible Immunoaffinity Interface Enables Dynamic Manipulation of Trapping Force for Accumulated Capture and Efficient Release of Circulating Rare Cells

Controllable assembly and disassembly of recognition interface are vital for bioanalysis. Herein, a strategy of dynamic manipulation of trapping force by engineering a dynamic and reversible immunoaffinity microinterface (DynarFace) in a herringbone chip (DynarFace-Chip) for liquid biopsy is proposed. The DynarFace is assembled by magnetically attracting immunomagnetic beads (IMBs) on chip substrate, with merits of convenient operation and reversible assembly. The DynarFace allows accumulating attachment of IMBs on circulating rare cell (CRC) surfaces during hydrodynamically enhanced interface collision, where accumulatively enhanced magnetic trapping force improves capture efficiency toward CRCs with medium expression of biomarkers from blood samples by 134.81% compared with traditional non-dynamic interfaces. Moreover, magnet withdrawing-induced disappearance of trapping force affords DynarFace disassembly and CRC release with high efficiency (>98%) and high viability (≈98%), compatible with downstream in vitro culture and gene analysis of CRCs. This DynarFace strategy opens a new avenue to accumulated capture and reversible release of CRCs, holding great potential for liquid biopsy-based precision medicine.

Anomalous Diffusion of Peripheral Membrane Signaling Proteins from All-Atom Molecular Dynamics Simulations

Peripheral membrane proteins bind transiently to membrane surfaces as part of many signaling pathways. The bound proteins perform two-dimensional (2-D) diffusion on the membrane surface during the recruitment function. To better understand the interplay between the 2-D diffusion of these protein domains and their membrane binding modes, we performed multimicrosecond all-atom molecular dynamics simulations of two regulatory domains, a C2 domain and a pleckstrin homology (PH) domain, in their experimentally determined bound configuration to a lipid bilayer. The protein bound configurations are preserved throughout the simulation trajectories. Both protein domains exhibit anomalous diffusion with distinct features in their dynamics that reflect their different modes of binding. An analysis of their diffusive behavior reveals common features with the diffusion of lipid molecules in lipid bilayers, suggesting that the 2-D motion of protein domains bound to the membrane surface is modulated by the viscoelastic nature of the lipid bilayer.

Universal Relation between Instantaneous Diffusivity and Radius of Gyration of Proteins in Aqueous Solution

Protein conformational fluctuations are highly complex and exhibit long-term correlations. Here, molecular dynamics simulations of small proteins demonstrate that these conformational fluctuations directly affect the protein's instantaneous diffusivity D_{I}. We find that the radius of gyration R_{g} of the proteins exhibits 1/f fluctuations that are synchronous with the fluctuations of D_{I}. Our analysis demonstrates the validity of the local Stokes-Einstein-type relation D_{I}∝1/(R_{g}+R_{0}), where R_{0}∼0.3  nm is assumed to be a hydration layer around the protein. From the analysis of different protein types with both strong and weak conformational fluctuations, the validity of the Stokes-Einstein-type relation appears to be a general property.

Membrane Binding of Antimicrobial Peptides Is Modulated by Lipid Charge Modification

Peptide interactions with lipid bilayers play a key role in a range of biological processes and depend on electrostatic interactions between charged amino acids and lipid headgroups. Antimicrobial peptides (AMPs) initiate the killing of bacteria by binding to and destabilizing their membranes. The multiple peptide resistance factor (MprF) provides a defense mechanism for bacteria against a broad range of AMPs. MprF reduces the negative charge of bacterial membranes through enzymatic conversion of the anionic lipid phosphatidyl glycerol (PG) to either zwitterionic alanyl-phosphatidyl glycerol (Ala-PG) or cationic lysyl-phosphatidyl glycerol (Lys-PG). The resulting change in the membrane charge is suggested to reduce the binding of AMPs to membranes, thus impeding downstream AMP activity. Using coarse-grained molecular dynamics to investigate the effects of these modified lipids on AMP binding to model membranes, we show that AMPs have substantially reduced affinity for model membranes containing Ala-PG or Lys-PG. More than 5000 simulations in total are used to define the relationship between lipid bilayer composition, peptide sequence (using five different membrane-active peptides), and peptide binding to membranes. The degree of interaction of a peptide with a membrane correlates with the membrane surface charge density. Free energy profile (potential of mean force) calculations reveal that the lipid modifications due to MprF alter the energy barrier to peptide helix penetration of the bilayer. These results will offer a guide to the design of novel peptides, which addresses the issue of resistance via MprF-mediated membrane modification.

Fluorescence strategies for mapping cell membrane dynamics and structures

Fluorescence spectroscopy has been a cornerstone of research in membrane dynamics and organization. Technological advances in fluorescence spectroscopy went hand in hand with discovery of various physicochemical properties of membranes at nanometric spatial and microsecond timescales. In this perspective, we discuss the various challenges associated with quantification of physicochemical properties of membranes and how various modes of fluorescence spectroscopy have overcome these challenges to shed light on the structure and organization of membranes. Finally, we discuss newer measurement strategies and data analysis tools to investigate the structure, dynamics, and organization of membranes.

Diffusive transport of nanoscale objects through cell membranes: a computational perspective

Diffusion is an essential and fundamental means of transport of substances on cell membranes, and the dynamics of biomembranes plays a crucial role in the regulation of numerous cellular processes. The understanding of the complex mechanisms and the nature of particle diffusion have a bearing on establishing guidelines for the design of efficient transport materials and unique therapeutic approaches. Herein, this review article highlights the most recent advances in investigating diffusion dynamics of nanoscale objects on biological membranes, focusing on the approaches of tailored computer simulations and theoretical analysis. Due to the presence of the complicated and heterogeneous environment on native cell membranes, the diffusive transport behaviors of nanoparticles exhibit unique and variable characteristics. The general aspects and basic theories of normal diffusion and anomalous diffusion have been introduced. In addition, the influence of a series of external and internal factors on the diffusion behaviors is discussed, including particle size, membrane curvature, particle-membrane interactions or particle-inclusion, and the crowding degree of membranes. Finally, we seek to identify open problems in the existing experimental, simulation, and theoretical research studies, and to propose challenges for future development.

The energetics of protein-lipid interactions as viewed by molecular simulations

Membranes are formed from a bilayer containing diverse lipid species with which membrane proteins interact. Integral, membrane proteins are embedded in this bilayer, where they interact with lipids from their surroundings, whilst peripheral membrane proteins bind to lipids at the surface of membranes. Lipid interactions can influence the function of membrane proteins, either directly or allosterically. Both experimental (structural) and computational approaches can reveal lipid binding sites on membrane proteins. It is, therefore, important to understand the free energies of these interactions. This affords a more complete view of the engagement of a particular protein with the biological membrane surrounding it. Here, we describe many computational approaches currently in use for this purpose, including recent advances using both free energy and unbiased simulation methods. In particular, we focus on interactions of integral membrane proteins with cholesterol, and with anionic lipids such as phosphatidylinositol 4,5-bis-phosphate and cardiolipin. Peripheral membrane proteins are exemplified via interactions of PH domains with phosphoinositide-containing membranes. We summarise the current state of the field and provide an outlook on likely future directions of investigation.

Plasma membrane asymmetry of lipid organization: fluorescence lifetime microscopy and correlation spectroscopy analysis

A fundamental feature of the eukaryotic cell membrane is the asymmetric arrangement of lipids in its two leaflets. A cell invests significant energy to maintain this asymmetry and uses it to regulate important biological processes, such as apoptosis and vesiculation. The dynamic coupling of the inner or cytoplasmic and outer or exofacial leaflets is a challenging open question in membrane biology. Here, we combined fluorescence lifetime imaging microscopy (FLIM) with imaging total internal reflection fluorescence correlation spectroscopy (ITIR-FCS) to differentiate the dynamics and organization of the two leaflets of live mammalian cells. We characterized the biophysical properties of fluorescent analogs of phosphatidylcholine, sphingomyelin, and phosphatidylserine in the plasma membrane of two mammalian cell lines (CHO-K1 and RBL-2H3). Because of their specific transverse membrane distribution, these probes allowed leaflet-specific investigation of the plasma membrane. We compared the results of the two methods having different temporal and spatial resolution. Fluorescence lifetimes of fluorescent lipid analogs were in ranges characteristic for the liquid ordered phase in the outer leaflet and for the liquid disordered phase in the inner leaflet. The observation of a more fluid inner leaflet was supported by free diffusion in the inner leaflet, with high average diffusion coefficients. The liquid ordered phase in the outer leaflet was accompanied by slower diffusion and diffusion with intermittent transient trapping. Our results show that the combination of FLIM and ITIR-FCS with specific fluorescent lipid analogs is a powerful tool for investigating lateral and transbilayer characteristics of plasma membrane in live cell lines.

Multiple lipid binding sites determine the affinity of PH domains for phosphoinositide-containing membranes

Association of peripheral proteins with lipid bilayers regulates membrane signaling and dynamics. Pleckstrin homology (PH) domains bind to phosphatidylinositol phosphate (PIP) molecules in membranes. The effects of local PIP enrichment on the interaction of PH domains with membranes is unclear. Molecular dynamics simulations allow estimation of the binding energy of GRP1 PH domain to PIP3-containing membranes. The free energy of interaction of the PH domain with more than two PIP3 molecules is comparable to experimental values, suggesting that PH domain binding involves local clustering of PIP molecules within membranes. We describe a mechanism of PH binding proceeding via an encounter state to two bound states which differ in the orientation of the protein relative to the membrane, these orientations depending on the local PIP concentration. These results suggest that nanoscale clustering of PIP molecules can control the strength and orientation of PH domain interaction in a concentration-dependent manner.

Understanding biochemical processes in the presence of sub-diffusive behavior of biomolecules in solution and living cells

In order to maintain cellular function, biomolecules like protein, DNA, and RNAs have to diffuse to the target spaces within the cell. Changes in the cytosolic microenvironment or in the nucleus during the fulfillment of these cellular processes affect their mobility, folding, and stability thereby impacting the transient or stable interactions with their adjacent neighbors in the organized and dynamic cellular interior. Using classical Brownian motion to elucidate the diffusion behavior of these biomolecules is hard considering their complex nature. The understanding of biomolecular diffusion inside cells still remains elusive due to the lack of a proper model that can be extrapolated to these cases. In this review, we have comprehensively addressed the progresses in this field, laying emphasis on the different aspects of anomalous diffusion in the different biochemical reactions in cell interior. These experiment-based models help to explain the diffusion behavior of biomolecules in the cytosolic and nuclear microenvironment. Moreover, since understanding of biochemical reactions within living cellular system is our main focus, we coupled the experimental observations with the concept of sub-diffusion from in vitro to in vivo condition. We believe that the pairing between the understanding of complex behavior and structure-function paradigm of biological molecules would take us forward by one step in order to solve the puzzle around diseases caused by cellular dysfunction.

Increased Confinement and Polydispersity of STIM1 and Orai1 after Ca2+ Store Depletion

STIM1 (a Ca²⁺ sensor in the endoplasmic reticulum (ER) membrane) and Orai1 (a pore-forming subunit of the Ca²⁺-release-activated calcium channel in the plasma membrane) diffuse in the ER membrane and plasma membrane, respectively. Upon depletion of Ca²⁺ stores in the ER, STIM1 translocates to the ER-plasma membrane junction and binds Orai1 to trigger store-operated Ca²⁺ entry. However, the motion of STIM1 and Orai1 during this process and its roles to Ca²⁺ entry is poorly understood. Here, we report real-time tracking of single STIM1 and Orai1 particles in the ER membrane and plasma membrane in living cells before and after Ca²⁺ store depletion. We found that the motion of single STIM1 and Orai1 particles exhibits anomalous diffusion both before and after store depletion, and their mobility-measured by the radius of gyration of the trajectories, mean-square displacement, and generalized diffusion coefficient-decreases drastically after store depletion. We also found that the measured displacement distribution is non-Gaussian, and the non-Gaussian parameter drastically increases after store depletion. Detailed analyses and simulations revealed that single STIM1 and Orai1 particles are confined in the compartmentalized membrane both before and after store depletion, and the changes in the motion after store depletion are explained by increased confinement and polydispersity of STIM1-Orai1 complexes formed at the ER-plasma membrane junctions. Further simulations showed that this increase in the confinement and polydispersity after store depletion localizes a rapid increase of Ca²⁺ influx, which can facilitate the rapid activation of local Ca²⁺ signaling pathways and the efficient replenishing of Ca²⁺ store in the ER in store-operated Ca²⁺ entry.

Tracking Single Molecules in Biomembranes: Is Seeing Always Believing?

The spatial organization of molecules in cell membranes and their dynamic interactions play a central role in regulating cell functions. Single-particle tracking (SPT), a technique in which single molecules are imaged and tracked in real time, has led to breakthrough discoveries regarding these spatiotemporal complexities of cell membranes. There are, however, emerging concerns about factors that might produce misleading interpretations of SPT results. Here, we briefly review the application of SPT to understanding the nanoscale heterogeneities of plasma membranes, with a focus on the unique challenges, pitfalls, and limitations that confront the use of nanoparticles as imaging probes for tracking the dynamics of single molecules in cell membranes.

Transport of a graphene nanosheet sandwiched inside cell membranes

The transport of nanoparticles at bio-nano interfaces is essential for many cellular responses and biomedical applications. How two-dimensional nanomaterials, such as graphene and transition-metal dichalcogenides, diffuse along the cell membrane is, however, unknown, posing an urgent and important issue to promote their applications in the biomedical area. Here, we show that the transport of graphene oxides (GOs) sandwiched inside cell membranes varies from Brownian to Lévy and even directional dynamics. Specifically, experiments evidence sandwiched graphene-cell membrane superstructures in different cells. Combined simulations and analysis identify a sandwiched GO-induced pore in cell membrane leaflets, spanning unstable, metastable, and stable states. An analytical model that rationalizes the regimes of these membrane-pore states fits simulations quantitatively, resulting in a mechanistic interpretation of the emergence of Lévy and directional dynamics. We finally demonstrate the applicability of sandwiched GOs in enhanced efficiency of membrane-specific drug delivery. Our findings inform approaches to programming intramembrane transport of two-dimensional nanomaterials toward advantageous biomedical applications.

Multiscale Simulations of Biological Membranes: The Challenge To Understand Biological Phenomena in a Living Substance

Biological membranes are tricky to investigate. They are complex in terms of molecular composition and structure, functional over a wide range of time scales, and characterized by nonequilibrium conditions. Because of all of these features, simulations are a great technique to study biomembrane behavior. A significant part of the functional processes in biological membranes takes place at the molecular level; thus computer simulations are the method of choice to explore how their properties emerge from specific molecular features and how the interplay among the numerous molecules gives rise to function over spatial and time scales larger than the molecular ones. In this review, we focus on this broad theme. We discuss the current state-of-the-art of biomembrane simulations that, until now, have largely focused on a rather narrow picture of the complexity of the membranes. Given this, we also discuss the challenges that we should unravel in the foreseeable future. Numerous features such as the actin-cytoskeleton network, the glycocalyx network, and nonequilibrium transport under ATP-driven conditions have so far received very little attention; however, the potential of simulations to solve them would be exceptionally high. A major milestone for this research would be that one day we could say that computer simulations genuinely research biological membranes, not just lipid bilayers.

Characterization of Lipid-Protein Interactions and Lipid-Mediated Modulation of Membrane Protein Function through Molecular Simulation

The cellular membrane constitutes one of the most fundamental compartments of a living cell, where key processes such as selective transport of material and exchange of information between the cell and its environment are mediated by proteins that are closely associated with the membrane. The heterogeneity of lipid composition of biological membranes and the effect of lipid molecules on the structure, dynamics, and function of membrane proteins are now widely recognized. Characterization of these functionally important lipid-protein interactions with experimental techniques is however still prohibitively challenging. Molecular dynamics (MD) simulations offer a powerful complementary approach with sufficient temporal and spatial resolutions to gain atomic-level structural information and energetics on lipid-protein interactions. In this review, we aim to provide a broad survey of MD simulations focusing on exploring lipid-protein interactions and characterizing lipid-modulated protein structure and dynamics that have been successful in providing novel insight into the mechanism of membrane protein function.

Non-Gaussian, non-ergodic, and non-Fickian diffusion of tracers in mucin hydrogels

Native mucus is polymer-based soft-matter material of paramount biological importance. How non-Gaussian and non-ergodic is the diffusive spreading of pathogens in mucus? We study the passive, thermally driven motion of micron-sized tracers in hydrogels of mucins, the main polymeric component of mucus. We report the results of the Bayesian analysis for ranking several diffusion models for a set of tracer trajectories [C. E. Wagner et al., Biomacromolecules, 2017, 18, 3654]. The models with "diffusing diffusivity", fractional and standard Brownian motion are used. The likelihood functions and evidences of each model are computed, ranking the significance of each model for individual traces. We find that viscoelastic anomalous diffusion is often most probable, followed by Brownian motion, while the model with a diffusing diffusion coefficient is only realised rarely. Our analysis also clarifies the distribution of time-averaged displacements, correlations of scaling exponents and diffusion coefficients, and the degree of non-Gaussianity of displacements at varying pH levels. Weak ergodicity breaking is also quantified. We conclude that-consistent with the original study-diffusion of tracers in the mucin gels is most non-Gaussian and non-ergodic at low pH that corresponds to the most heterogeneous networks. Using the Bayesian approach with the nested-sampling algorithm, together with the quantitative analysis of multiple statistical measures, we report new insights into possible physical mechanisms of diffusion in mucin gels.

Protein concentration gradients and switching diffusions

Morphogen gradients play a vital role in developmental biology by enabling embryonic cells to infer their spatial location and determine their developmental fate accordingly. The standard mechanism for generating a morphogen gradient involves a morphogen being produced from a localized source and subsequently degrading. While this mechanism is effective over the length and time scales of tissue development, it fails over typical subcellular length scales due to the rapid dissipation of spatial asymmetries. In a recent theoretical work, we found an alternative mechanism for generating concentration gradients of diffusing molecules, in which the molecules switch between spatially constant diffusivities at switching rates that depend on the spatial location of a molecule. Independently, an experimental and computational study later found that Caenorhabditis elegans zygotes rely on this mechanism for cell polarization. In this paper, we extend our analysis of switching diffusivities to determine its role in protein concentration gradient formation. In particular, we determine how switching diffusivities modifies the standard theory and show how space-dependent switching diffusivities can yield a gradient in the absence of a localized source. Our mathematical analysis yields explicit formulas for the intracellular concentration gradient which closely match the results of previous experiments and numerical simulations.

Polyphosphoinositide-Binding Domains: Insights from Peripheral Membrane and Lipid-Transfer Proteins

Within eukaryotic cells, biochemical reactions need to be organized on the surface of membrane compartments that use distinct lipid constituents to dynamically modulate the functions of integral proteins or influence the selective recruitment of peripheral membrane effectors. As a result of these complex interactions, a variety of human pathologies can be traced back to improper communication between proteins and membrane surfaces; either due to mutations that directly alter protein structure or as a result of changes in membrane lipid composition. Among the known structural lipids found in cellular membranes, phosphatidylinositol (PtdIns) is unique in that it also serves as the membrane-anchored precursor of low-abundance regulatory lipids, the polyphosphoinositides (PPIn), which have restricted distributions within specific subcellular compartments. The ability of PPIn lipids to function as signaling platforms relies on both non-specific electrostatic interactions and the selective stereospecific recognition of PPIn headgroups by specialized protein folds. In this chapter, we will attempt to summarize the structural diversity of modular PPIn-interacting domains that facilitate the reversible recruitment and conformational regulation of peripheral membrane proteins. Outside of protein folds capable of capturing PPIn headgroups at the membrane interface, recent studies detailing the selective binding and bilayer extraction of PPIn species by unique functional domains within specific families of lipid-transfer proteins will also be highlighted. Overall, this overview will help to outline the fundamental physiochemical mechanisms that facilitate localized interactions between PPIn lipids and the wide-variety of PPIn-binding proteins that are essential for the coordinate regulation of cellular metabolism and membrane dynamics.

Time averages and their statistical variation for the Ornstein-Uhlenbeck process: Role of initial particle distributions and relaxation to stationarity

How ergodic is diffusion under harmonic confinements? How strongly do ensemble- and time-averaged displacements differ for a thermally-agitated particle performing confined motion for different initial conditions? We here study these questions for the generic Ornstein-Uhlenbeck (OU) process and derive the analytical expressions for the second and fourth moment. These quantifiers are particularly relevant for the increasing number of single-particle tracking experiments using optical traps. For a fixed starting position, we discuss the definitions underlying the ensemble averages. We also quantify effects of equilibrium and nonequilibrium initial particle distributions onto the relaxation properties and emerging nonequivalence of the ensemble- and time-averaged displacements (even in the limit of long trajectories). We derive analytical expressions for the ergodicity breaking parameter quantifying the amplitude scatter of individual time-averaged trajectories, both for equilibrium and out-of-equilibrium initial particle positions, in the entire range of lag times. Our analytical predictions are in excellent agreement with results of computer simulations of the Langevin equation in a parabolic potential. We also examine the validity of the Einstein relation for the ensemble- and time-averaged moments of the OU-particle. Some physical systems, in which the relaxation and nonergodic features we unveiled may be observable, are discussed.

Transient subdiffusion from an Ising environment

We introduce a model in which a particle performs a continuous-time random walk (CTRW) coupled to an environment with Ising dynamics. The particle shows locally varying diffusivity determined by the geometrical properties of the underlying Ising environment, that is, the diffusivity depends on the size of the connected area of spins pointing in the same direction. The model shows anomalous diffusion when the Ising environment is at critical temperature. We show that any finite scale introduced by a temperature different from the critical one, or a finite size of the environment, cause subdiffusion only during a transient time. The characteristic time, at which the system returns to normal diffusion after the subdiffusive plateau depends on the limiting scale and on how close the temperature is to criticality. The system also displays apparent ergodicity breaking at intermediate time, while ergodicity breaking at longer time occurs only under the idealized infinite environment at the critical temperature.

Non-Gaussianity, population heterogeneity, and transient superdiffusion in the spreading dynamics of amoeboid cells

What is the underlying diffusion process governing the spreading dynamics and search strategies employed by amoeboid cells?

Detection of transition times from single-particle-tracking trajectories

In heterogeneous environments, the diffusivity is not constant but changes with time. It is important to detect changes in the diffusivity from single-particle-tracking trajectories in experiments. Here, we devise a novel method for detecting the transition times of the diffusivity from trajectory data. A key idea of this method is the introduction of a characteristic time scale of the diffusive states, which is obtained by a fluctuation analysis of the time-averaged mean square displacements. We test our method in silico by using the Langevin equation with a fluctuating diffusivity. We show that our method can successfully detect the transition times of diffusive states and obtain the diffusion coefficient as a function of time. This method will provide a quantitative description of the fluctuating diffusivity in heterogeneous environments and can be applied to time series with transitions of states.

Hybrid colored noise process with space-dependent switching rates

A fundamental issue in the theory of continuous stochastic process is the interpretation of multiplicative white noise, which is often referred to as the Itô-Stratonovich dilemma. From a physical perspective, this reflects the need to introduce additional constraints in order to specify the nature of the noise, whereas from a mathematical perspective it reflects an ambiguity in the formulation of stochastic differential equations (SDEs). Recently, we have identified a mechanism for obtaining an Itô SDE based on a form of temporal disorder. Motivated by switching processes in molecular biology, we considered a Brownian particle that randomly switches between two distinct conformational states with different diffusivities. In each state, the particle undergoes normal diffusion (additive noise) so there is no ambiguity in the interpretation of the noise. However, if the switching rates depend on position, then in the fast switching limit one obtains Brownian motion with a space-dependent diffusivity of the Itô form. In this paper, we extend our theory to include colored additive noise. We show that the nature of the effective multiplicative noise process obtained by taking both the white-noise limit (κ→0) and fast switching limit (ε→0) depends on the order the two limits are taken. If the white-noise limit is taken first, then we obtain Itô, and if the fast switching limit is taken first, then we obtain Stratonovich. Moreover, the form of the effective diffusion coefficient differs in the two cases. The latter result holds even in the case of space-independent transition rates, where one obtains additive noise processes with different diffusion coefficients. Finally, we show that yet another form of multiplicative noise is obtained in the simultaneous limit ε,κ→0 with ε/κ^{2} fixed.