Chain-Length Dependence of Peptide-Lipid Bilayer Interaction Strength and Binding Kinetics: A Combined Theoretical and Experimental Approach.

Physical interactions between polypeptide chains and lipid membranes underlie critical cellular processes. Yet, despite fundamental importance, key mechanistic aspects of these interactions remain elusive. Bulk experiments have revealed a linear relationship between free energy and peptide chain length in a model system, but does this linearity extend to the interaction strength and to the kinetics of lipid binding? To address these questions, we utilized a combination of coarse-grained molecular dynamics (CG MD) simulations, analytical modeling, and atomic force microscopy (AFM)-based single molecule force spectroscopy. Following previous bulk experiments, we focused on interactions between short hydrophobic peptides (WLn, n = 1, ..., 5) with 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine (POPC) bilayers, a simple system that probes peptide primary structure effects. Potentials of mean force extracted from CG MD recapitulated the linearity of free energy with the chain length. Simulation results were quantitatively connected to bulk biochemical experiments via a single scaling factor of order unity, corroborating the methodology. Additionally, CG MD revealed an increase in the distance to the transition state, a result that weakens the dependence of the dissociation force on the peptide chain length. AFM experiments elucidated rupture force distributions and, through modeling, intrinsic dissociation rates. Taken together, the analysis indicates a rupture force plateau in the WLn-POPC system, suggesting that the final rupture event involves the last 2 or 3 residues. In contrast, the linear dependence on chain length was preserved in the intrinsic dissociation rate. This study advances the understanding of peptide-lipid interactions and provides potentially useful insights for the design of peptides with tailored membrane-interacting properties.

Towards a Quantitative Understanding of Protein-Lipid Bilayer Interactions at the Single Molecule Level: Opportunities and Challenges.

Protein-lipid interfaces are among the most fundamental in biology. Yet applying conventional techniques to study the biophysical attributes of these systems is challenging and has left many unknowns. For example, what is the kinetic pathway and energy landscape experienced by a polypeptide chain when in close proximity to a fluid lipid bilayer? Here we review the experimental and theoretical progress we have made in addressing this question from a single molecule perspective. Some remaining impediments are also discussed.

Characterizing the Locus of a Peripheral Membrane Protein-Lipid Bilayer Interaction Underlying Protein Export Activity in E. coli.

Quantitative characterization of the strength of peripheral membrane protein-lipid bilayer interactions is fundamental in the understanding of many protein targeting pathways. SecA is a peripheral membrane protein that plays a central role in translocating precursor proteins across the inner membrane of E. coli. The membrane binding activity of the extreme N-terminus of SecA is critical for translocase function. Yet, the mechanical strength of the interaction and the kinetic pathways that this segment of SecA experiences when in proximity of an E. coli polar lipid bilayer has not been characterized. We directly measured the N-terminal SecA-lipid bilayer interaction using precision single molecule atomic force microscope (AFM)-based dynamic force spectroscopy. To provide conformational data inaccessible to AFM, we also performed all-atom molecular dynamics simulations and circular dichroism measurements. The N-terminal 10 amino acids of SecA have little secondary structure when bound to zwitterionic lipid head groups, but secondary structure, which rigidifies the lipid-bound protein segment, emerges when negatively charged lipids are present. Analysis of the single molecule protein-lipid dissociation data converged to a well-defined lipid-bound-state lifetime in the absence of force, τ0lipid = 0.9 s, which is well separated from and longer than the fundamental time scale of the secretion process, defined as the time required to translocate a single amino acid residue (∼50 ms). This value of τ0lipid is likely to represent a lower limit of the in vivo membrane-bound lifetime due to factors including the minimal system employed here.

Multiple stochastic pathways in forced peptide-lipid membrane detachment.

We have used high resolution AFM based dynamic force spectroscopy to investigate peptide-lipid membrane interactions by measuring the detachment (last-rupture) force distribution, P(F), and the corresponding force dependent rupture rate, k(F), for two different peptides and lipid bilayers. The measured quantities, which differed considerably for different peptides, lipid-membranes, AFM tips (prepared under identical conditions), and retraction speeds of the AFM cantilever, could not be described in terms of the standard theory, according to which detachment occurs along a single pathway, corresponding to a diffusive escape process across a free energy barrier. In particular, the prominent retraction speed dependence of k(F) was a clear indication that peptide-lipid membrane dissociation occurs stochastically along several detachment pathways. Thereby, we have formulated a general theoretical approach for describing P(F) and k(F), by assuming that peptide detachment from lipid membranes occurs, with certain probability, along a few dominant diffusive pathways. This new method was validated through a consistent interpretation of the experimental data. Furthermore, we have found that for moderate retraction speeds at intermediate force values, k(F) exhibits catch-bond behavior (i.e. decreasing detachment rate with increasing force). According to the proposed model this behavior is due to the stochastic mixing of individual detachment pathways which do not convert or cross during rupture. To our knowledge, such catch-bond mechanism has not been proposed and demonstrated before for a peptide-lipid interaction.

Single-Molecule Peptide-Lipid Affinity Assay Reveals Interplay between Solution Structure and Partitioning.

Interactions between short protein segments and phospholipid bilayers dictate fundamental aspects of cellular activity and have important applications in biotechnology. Yet, the lack of a suitable methodology for directly probing these interactions has hindered the mechanistic understanding. We developed a precision atomic force microscopy-based single-molecule force spectroscopy assay and probed partitioning into lipid bilayers by measuring the mechanical force experienced by a peptide. Protein segments were constructed from the peripheral membrane protein SecA, a key ATPase in bacterial secretion. We focused on the first 10 amino-terminal residues of SecA (SecA2-11) that are lipophilic. In addition to the core SecA2-11 sequence, constructs with nearly identical chemical composition but with differing geometry were used: two copies of SecA2-11 linked in series and two copies SecA2-11 linked in parallel. Lipid bilayer partitioning interactions of peptides with differing structures were distinguished. To model the energetic landscape, a theory of diffusive barrier crossing was extended to incorporate a superposition of potential barriers with variable weights. Analysis revealed two dissociation pathways for the core SecA2-11 sequence with well-separated intrinsic dissociation rates. Molecular dynamics simulations showed that the three peptides had significant conformational differences in solution that correlated well with the measured variations in the propensity to partition into the bilayer. The methodology is generalizable and can be applied to other peptide and lipid species.

Post-deposition bioink self-assembly: a quantitative study.

The outcome of a bioprinting process depends on both the deposition of the discrete bioink units and their ability to self-assemble into the desired structure following deposition. Post-printing structure formation is an autonomous process governed by fundamental biological organizing principles. As the quantitative formulation of such principles is notoriously difficult, bioprinting remains largely a trial and error approach. To address this problem, specifically in extrusion bioprinting, we have recently developed an effective computational method, the cellular particle dynamics (CPDs). We have demonstrated the predictive power of CPD in cases of simple printed constructs prepared with spherical multicellular bioink units. Here we generalize CPD to the important practical case of tubular grafts printed with cylindrical bioink units by taking into account the realistic experimental situation in which the length and the volume of the cylinders decrease post-printing. Based on our results, we provide a set of instructions for the use of CPD simulations to directly predict tubular graft formation without the need to carry out the corresponding complex and expensive control experiments. Using these instructions allows the efficient and timely biofabrication of tubular organ structures. A particularly instructive outcome of our analysis is that building tubular organ structures, such as vascular grafts by bioprinting can be done considerably faster by using cylindrical rather than spherical bionk units.

Selective refinement and selection of near-native models in protein structure prediction.

In recent years in silico protein structure prediction reached a level where fully automated servers can generate large pools of near-native structures. However, the identification and further refinement of the best structures from the pool of models remain problematic. To address these issues, we have developed (i) a target-specific selective refinement (SR) protocol; and (ii) molecular dynamics (MD) simulation based ranking (SMDR) method. In SR the all-atom refinement of structures is accomplished via the Rosetta Relax protocol, subject to specific constraints determined by the size and complexity of the target. The best-refined models are selected with SMDR by testing their relative stability against gradual heating through all-atom MD simulations. Through extensive testing we have found that Mufold-MD, our fully automated protein structure prediction server updated with the SR and SMDR modules consistently outperformed its previous versions.

Predictive modeling of post bioprinting structure formation.

Cellular particle dynamics (CPD) is an effective computational method to describe the shape evolution and biomechanical relaxation processes in systems composed of micro tissues such as multicellular aggregates. Therefore, CPD is a useful tool to predict the outcome of postprinting structure formation in bioprinting. The predictive power of CPD has been demonstrated for multicellular systems composed of identical volume-conserving spherical and cylindrical bioink units. Experiments and computer simulations were related through an independently developed theoretical formalism based on continuum mechanics. Here we generalize the CPD formalism to (i) include non-identical bioink particles often used in specific bioprinting applications, (ii) describe the more realistic experimental situation in which during the post-printing structure formation via the fusion of spherical bioink units the volume of the system decreases, and (iii) directly connect CPD simulations to the corresponding experiments without the need of the intermediate continuum theory inherently based on simplifying assumptions.

Anomalous diffusion of water molecules in hydrated lipid bilayers.

We present a molecular dynamics (MD) study of the water molecules in a hydrated lipid bilayer. Due to the interactions at the surface of a solvated lipid membrane, the dynamics of the water and lipid molecules are to some degree correlated. In spite of previous efforts reported in the literature, little is known about the time and length scales of these correlations. Here, by employing a 0.1 µs long equilibrium MD simulation of a dimyristoylphosphatidylcholine (DMPC) lipid bilayer, we show that the waters in a hydrated lipid bilayer can be classified into four dynamically connected water layers, and provide a detailed analysis of the water dynamics within these four regions. We also show that there exists a cooperative molecular motion between the hydration waters and the DMPC lipid molecules, and determine the corresponding characteristic time and length scales.

Kinetic Monte Carlo and cellular particle dynamics simulations of multicellular systems.

Computer modeling of multicellular systems has been a valuable tool for interpreting and guiding in vitro experiments relevant to embryonic morphogenesis, tumor growth, angiogenesis and, lately, structure formation following the printing of cell aggregates as bioink particles. Here we formulate two computer simulation methods: (1) a kinetic Monte Carlo (KMC) and (2) a cellular particle dynamics (CPD) method, which are capable of describing and predicting the shape evolution in time of three-dimensional multicellular systems during their biomechanical relaxation. Our work is motivated by the need of developing quantitative methods for optimizing postprinting structure formation in bioprinting-assisted tissue engineering. The KMC and CPD model parameters are determined and calibrated by using an original computational-theoretical-experimental framework applied to the fusion of two spherical cell aggregates. The two methods are used to predict the (1) formation of a toroidal structure through fusion of spherical aggregates and (2) cell sorting within an aggregate formed by two types of cells with different adhesivities.

Prediction of protein tertiary structures using MUFOLD.

There have been steady improvements in protein structure prediction during the past two decades. However, current methods are still far from consistently predicting structural models accurately with computing power accessible to common users. To address this challenge, we developed MUFOLD, a hybrid method of using whole and partial template information along with new computational techniques for protein tertiary structure prediction. MUFOLD covers both template-based and ab initio predictions using the same framework and aims to achieve high accuracy and fast computing. Two major novel contributions of MUFOLD are graph-based model generation and molecular dynamics ranking (MDR). By formulating a prediction as a graph realization problem, we apply an efficient optimization approach of Multidimensional Scaling (MDS) to speed up the prediction dramatically. In addition, under this framework, we enhance the predictions consistently by iteratively using the information from generated models. MDR, in contrast to widely used static scoring functions, exploits dynamics properties of structures to evaluate their qualities, which can often identify best structures from a pool more effectively.

A multilayer evaluation approach for protein structure prediction and model quality assessment.

Protein tertiary structures are essential for studying functions of proteins at molecular level. An indispensable approach for protein structure solution is computational prediction. Most protein structure prediction methods generate candidate models first and select the best candidates by model quality assessment (QA). In many cases, good models can be produced, but the QA tools fail to select the best ones from the candidate model pool. Because of incomplete understanding of protein folding, each QA method only reflects partial facets of a structure model and thus has limited discerning power with no one consistently outperforming others. In this article, we developed a set of new QA methods, including two QA methods for evaluating target/template alignments, a molecular dynamics (MD)-based QA method, and three consensus QA methods with selected references to reveal new facets of protein structures complementary to the existing methods. Moreover, the underlying relationship among different QA methods were analyzed and then integrated into a multilayer evaluation approach to guide the model generation and model selection in prediction. All methods are integrated and implemented into an innovative and improved prediction system hereafter referred to as MUFOLD. In CASP8 and CASP9, MUFOLD has demonstrated the proof of the principles in terms of both QA discerning power and structure prediction accuracy.

In silico predictions of LH2 ring sizes from the crystal structure of a single subunit using molecular dynamics simulations.

Most of the currently known light-harvesting complexes 2 (LH2) rings are formed by 8 or 9 subunits. As of now, questions like "what factors govern the LH2 ring size?" and "are there other ring sizes possible?" remain largely unanswered. Here, we investigate by means of molecular dynamics (MD) simulations and stochastic modeling the possibility of predicting the size of an LH2 ring from the sole knowledge of the high resolution crystal structure of a single subunit. Starting with single subunits of two LH2 rings with known size, that is, an 8-ring from Rs. moliscianum (MOLI) and a 9-ring from Rps. acidophila (ACI), and one with unknown size (referred to as X), we build atomic models of subunit dimers corresponding to assumed 8-, 9-, and 10-ring geometries. After inserting each of the dimers into a lipid-water environment, we determine the preferred angle between the corresponding subunits by three methods: (1) energy minimization, (2) free MD simulations, and (3) potential of mean force calculations. We find that the results from all three methods are consistent with each other, and when taken together, it allows one to predict with reasonable level of confidence the sizes of the corresponding ring structures. One finds that X and ACI very likely form a 9-ring, while MOLI is more likely to form an 8-ring than a 9-ring. Finally, we discuss both the merits and limitations of all three prediction methods.

MUFOLD: A new solution for protein 3D structure prediction.

There have been steady improvements in protein structure prediction during the past 2 decades. However, current methods are still far from consistently predicting structural models accurately with computing power accessible to common users. Toward achieving more accurate and efficient structure prediction, we developed a number of novel methods and integrated them into a software package, MUFOLD. First, a systematic protocol was developed to identify useful templates and fragments from Protein Data Bank for a given target protein. Then, an efficient process was applied for iterative coarse-grain model generation and evaluation at the Calpha or backbone level. In this process, we construct models using interresidue spatial restraints derived from alignments by multidimensional scaling, evaluate and select models through clustering and static scoring functions, and iteratively improve the selected models by integrating spatial restraints and previous models. Finally, the full-atom models were evaluated using molecular dynamics simulations based on structural changes under simulated heating. We have continuously improved the performance of MUFOLD by using a benchmark of 200 proteins from the Astral database, where no template with >25% sequence identity to any target protein is included. The average root-mean-square deviation of the best models from the native structures is 4.28 A, which shows significant and systematic improvement over our previous methods. The computing time of MUFOLD is much shorter than many other tools, such as Rosetta. MUFOLD demonstrated some success in the 2008 community-wide experiment for protein structure prediction CASP8.

Computational modeling of epithelial-mesenchymal transformations.

An epithelial-mesenchymal transformation (EMT) involves alterations in cell-cell and cell-matrix adhesion, the detachment of epithelial cells from their neighbors, the degradation of the basal lamina and acquisition of mesenchymal phenotype. Here we present Monte Carlo simulations for a specific EMT in early heart development: the formation of cardiac cushions. Cell rearrangements are described in accordance with Steinberg's differential adhesion hypothesis, which states that cells possess a type-dependent adhesion apparatus and are sufficiently motile to give rise to the tissue conformation with the largest number of strong bonds. We also implement epithelial and mesenchymal cell proliferation, cell type change and extracellular matrix production by mesenchymal cells. Our results show that an EMT is promoted more efficiently by an increase in cell-substrate adhesion than by a decrease in cell-cell adhesion. In addition to cushion tissue formation, the model also accounts for the phenomena of matrix invasion and mesenchymal condensation. We conclude that in order to maintain epithelial integrity during EMT the number of epithelial cells must increase at a controlled rate. Our model predictions are in qualitative agreement with available experimental data.

Using stochastic models calibrated from nanosecond nonequilibrium simulations to approximate mesoscale information.

We demonstrate how the surrogate process approximation (SPA) method can be used to compute both the potential of mean force along a reaction coordinate and the associated diffusion coefficient using a relatively small number (10-20) of bidirectional nonequilibrium trajectories coming from a complex system. Our method provides confidence bands which take the variability of the initial configuration of the high-dimensional system, continuous nature of the work paths, and thermal fluctuations into account. Maximum-likelihood-type methods are used to estimate a stochastic differential equation (SDE) approximating the dynamics. For each observed time series, we estimate a new SDE resulting in a collection of SPA models. The physical significance of the collection of SPA models is discussed and methods for exploiting information in the population of estimated SPA models are demonstrated and suggested. Molecular dynamics simulations of potassium ion dynamics inside a gramicidin A channel are used to demonstrate the methodology, although SPA-type modeling has also proven useful in analyzing single-molecule experimental time series [J. Phys. Chem. B 113, 118 (2009)].

Subdiffusion and lateral diffusion coefficient of lipid atoms and molecules in phospholipid bilayers.

We use a long, all-atom molecular-dynamics (MD) simulation combined with theoretical modeling to investigate the dynamics of selected lipid atoms and lipid molecules in a hydrated diyristoyl-phosphatidylcholine lipid bilayer. From the analysis of a 0.1 micros MD trajectory, we find that the time evolution of the mean-square displacement, <[deltar(t)]2>, of lipid atoms and molecules exhibits three well-separated dynamical regions: (i) ballistic, with <[deltar(t)]2> approximately t2 for t approximately tbeta with beta<1 for 10 ps approximately t for t>or approximately 30 ns. We propose a memory-function approach for calculating <[deltar(t)]2> over the entire time range extending from the ballistic to the Fickian diffusion regimes. The results are in very good agreement with the ones from the MD simulations. We also examine the implications of the presence of the subdiffusive dynamics of lipids on the self-intermediate scattering function and the incoherent dynamic structure factor measured in neutron-scattering experiments.

Calculating free-energy profiles in biomolecular systems from fast nonequilibrium processes.

Often gaining insight into the functioning of biomolecular systems requires to follow their dynamics along a microscopic reaction coordinate (RC) on a macroscopic time scale, which is beyond the reach of current all atom molecular dynamics (MD) simulations. A practical approach to this inherently multiscale problem is to model the system as a fictitious overdamped Brownian particle that diffuses along the RC in the presence of an effective potential of mean force (PMF) due to the rest of the system. By employing the recently proposed FR method [I. Kosztin, J. Chem. Phys. 124, 064106 (2006)], which requires only a small number of fast nonequilibrium MD simulations of the system in both forward and time reversed directions along the RC, we reconstruct the PMF: (1) of deca-alanine as a function of its end-to-end distance, and (2) that guides the motion of potassium ions through the gramicidin A channel. In both cases the computed PMFs are found to be in good agreement with previous results obtained by different methods. Our approach appears to be about one order of magnitude faster than the other PMF calculation methods and, in addition, it also provides the position-dependent diffusion coefficient along the RC. Thus, the obtained PMF and diffusion coefficient can be used in an overdamped Brownian model to estimate important characteristics of the studied systems, e.g., the mean folding time of the stretched deca-alanine and the mean diffusion time of the potassium ion through gramicidin A.

Motional coherence in fluid phospholipid membranes.

We report a high energy-resolution neutron backscattering study, combined with in situ diffraction, to investigate slow molecular motions on nanosecond time scales in the fluid phase of phospholipid bilayers of 1,2-dimyristoyl-sn-glycero-3-phoshatidylcholine. A cooperative structural relaxation process was observed. From the in-plane scattering vector dependence of the relaxation rates in hydrogenated and deuterated samples, combined with results from a 0.1 micros long all-atom molecular dynamics simulation, it is concluded that correlated dynamics in lipid membranes occurs over several lipid distances, spanning a time interval from pico- to nanoseconds.

Relating cell and tissue mechanics: implications and applications.

The Differential Adhesion Hypothesis (DAH) posits that differences in adhesion provide the driving force for morphogenetic processes. A manifestation of differential adhesion is tissue liquidity and a measure for it is tissue surface tension. In terms of this property, DAH correctly predicts global developmental tissue patterns. However, it provides little information on how these patterns arise from the movement and shape changes of cells. We provide strong qualitative and quantitative support for tissue liquidity both in true developmental context and in vitro assays. We follow the movement and characteristic shape changes of individual cells in the course of specific tissue rearrangements leading to liquid-like configurations. Finally, we relate the measurable tissue-liquid properties to molecular entities, whose direct determination under realistic three-dimensional culture conditions is not possible. Our findings confirm the usefulness of tissue liquidity and provide the scientific underpinning for a novel tissue engineering technology.