Changing the mechanical unfolding pathway of FnIII10 by tuning the pulling strength

Free Energy Landscape of Type III Fibronectin Domain with Identified Intermediate State and Hierarchical Symmetry

The tenth domain of type III fibronectin (FNIII_{10}) mediates cell adhesion to the extracellular matrix. Despite its structural similarity to immunoglobulin domains, FNIII_{10} exhibits unique unfolding behaviors. We employed magnetic tweezers to investigate the unfolding and folding dynamics of FNIII_{10} under physiological forces (4-50 pN). Our results showed that FNIII_{10} follows a consistent transition pathway with an intermediate state characterized by detached A and G β strands. We determined the folding free energies and all force-dependent transition rates of FNIII_{10} and found that both unfolding rates from the native state to the intermediate state and from the intermediate state to the unfolded state deviate from Bell's model. We constructed a quantitative free energy landscape with well-defined traps and barriers that exhibits a hierarchical symmetrical pattern. Our findings provide a comprehensive understanding of FNIII_{10} conformational dynamics and demonstrate how free energy landscape of multistate biomolecules can be precisely mapped, illuminating the relationship between thermal stability, intermediate states, and folding rates in protein folding.

Probing the Basis of α-Synuclein Aggregation by Comparing Simulations to Single-Molecule Experiments

Intrinsically disordered proteins often play an important role in protein aggregation. However, it is challenging to determine the structures and interactions that drive the early stages of aggregation because they are transient and obscured in a heterogeneous mixture of disordered states. Even computational methods are limited because the lack of ordered structure makes it difficult to ensure that the relevant conformations are sampled. We address these challenges by integrating atomistic simulations with high-resolution single-molecule measurements reported previously, using the measurements to help discern which parts of the disordered ensemble of structures in the simulations are most probable while using the simulations to identify residues and interactions that are important for oligomer stability. This approach was applied to α-synuclein, an intrinsically disordered protein that aggregates in the context of Parkinson's disease. We simulated single-molecule pulling experiments on dimers, the minimal oligomer, and compared them to force spectroscopy measurements. Force-extension curves were simulated starting from a set of 66 structures with substantial structured content selected from the ensemble of dimer structures generated at zero force via Monte Carlo simulations. The pattern of contour length changes as the structures unfolded through intermediate states was compared to the results from optical trapping measurements on the same dimer to discern likely structures occurring in the measurements. Simulated pulling curves were generally consistent with experimental data but with a larger number of transient intermediates. We identified an ensemble of β-rich dimer structures consistent with the experimental data from which dimer interfaces could be deduced. These results suggest specific druggable targets in the structural motifs of α-synuclein that may help prevent the earliest steps of oligomerization.

Stability and Local Unfolding of SOD1 in the Presence of Protein Crowders

Using NMR and Monte Carlo (MC) methods, we investigate the stability and dynamics of superoxide dismutase 1 (SOD1) in homogeneous crowding environments, where either bovine pancreatic trypsin inhibitor (BPTI) or the B1 domain of streptococcal protein G (PGB1) serves as a crowding agent. By NMR, we show that both crowders, and especially BPTI, cause a drastic loss in the overall stability of SOD1 in its apo monomeric form. Additionally, we determine chemical shift perturbations indicating that SOD1 interacts with the crowder proteins in a residue-specific manner that further depends on the identity of the crowding protein. Furthermore, the specificity of SOD1-crowder interactions is reciprocal: chemical shift perturbations on BPTI and PGB1 identify regions that interact preferentially with SOD1. By MC simulations, we investigate the local unfolding of SOD1 in the absence and presence of the crowders. We find that the crowders primarily interact with the long flexible loops of the folded SOD1 monomer. The basic mechanisms by which the SOD1 β-barrel core unfolds remain unchanged when adding the crowders. In particular, both with and without the crowders, the second β-sheet of the barrel is more dynamic and unfolding-prone than the first. Notably, the MC simulations (exploring the early stages of SOD1 unfolding) and the NMR experiments (under equilibrium conditions) identify largely the same set of PGB1 and BPTI residues as prone to form SOD1 contacts. Thus, contacts stabilizing the unfolded state of SOD1 in many cases appear to form early in the unfolding reaction.

Markov modeling of peptide folding in the presence of protein crowders

We use Markov state models (MSMs) to analyze the dynamics of a β-hairpin-forming peptide in Monte Carlo (MC) simulations with interacting protein crowders, for two different types of crowder proteins [bovine pancreatic trypsin inhibitor (BPTI) and GB1]. In these systems, at the temperature used, the peptide can be folded or unfolded and bound or unbound to crowder molecules. Four or five major free-energy minima can be identified. To estimate the dominant MC relaxation times of the peptide, we build MSMs using a range of different time resolutions or lag times. We show that stable relaxation-time estimates can be obtained from the MSM eigenfunctions through fits to autocorrelation data. The eigenfunctions remain sufficiently accurate to permit stable relaxation-time estimation down to small lag times, at which point simple estimates based on the corresponding eigenvalues have large systematic uncertainties. The presence of the crowders has a stabilizing effect on the peptide, especially with BPTI crowders, which can be attributed to a reduced unfolding rate ku, while the folding rate kf is left largely unchanged.

Application of Monte Carlo simulation in addressing key issues of complex coacervation formed by polyelectrolytes and oppositely charged colloids

This paper reviews the recent advance of Monte Carlo (MC) simulation in addressing key issues of complex coacervation between polyelectrolytes and oppositely charged colloids. Readers were first supplied with a brief overview of current knowledge and experimental strategies in the study of complex coacervation. In the next section, the general MC simulation procedures as well as representative strategies applied in complex coacervation were summarized. The unique contributions of MC simulation in either capturing delicate features, easing the experimental trials or proving the concept were then elucidated through the following aspects: i) identify phase boundary and decouple interaction contributions; ii) clarify composition distribution and internal structure; iii) predict the influences of physicochemical conditions on complex coacervation; iv) delineate the mechanisms for "binding on the wrong side of the isoelectric point". Finally, current challenges as well as prospects of MC simulation in complex coacervation are also discussed. The ultimate goal of this review is to provide readers with basic guideline for synergistic design of experiments in combination with MC simulation, and deliver convincing interpretation and reliable prediction for the structure and behavior in polyelectrolyte-macroion complex coacervation.

The physics of pulling polyproteins: a review of single molecule force spectroscopy using the AFM to study protein unfolding

One of the most exciting developments in the field of biological physics in recent years is the ability to manipulate single molecules and probe their properties and function. Since its emergence over two decades ago, single molecule force spectroscopy has become a powerful tool to explore the response of biological molecules, including proteins, DNA, RNA and their complexes, to the application of an applied force. The force versus extension response of molecules can provide valuable insight into its mechanical stability, as well as details of the underlying energy landscape. In this review we will introduce the technique of single molecule force spectroscopy using the atomic force microscope (AFM), with particular focus on its application to study proteins. We will review the models which have been developed and employed to extract information from single molecule force spectroscopy experiments. Finally, we will end with a discussion of future directions in this field.

Mechanical stability analysis of the protein L immunoglobulin-binding domain by full alanine screening using molecular dynamics simulations

This article is the first to study the mechanical properties of the immunoglobulin-binding domain of protein L (referred to as protein L) and its mutants at the atomic level. In the structure of protein L, each amino acid residue (except for alanines and glycines) was replaced sequentially by alanine. Thus, 49 mutants of protein L were obtained. The proteins were stretched at their termini at constant velocity using molecular dynamics simulations in water, i.e. by forced unfolding. 19 out of 49 mutations resulted in a large decrease of mechanical protein stability. These amino acids were affecting either the secondary structure (11 mutations) or loop structures (8 mutations) of protein L. Analysis of mechanical unfolding of the generated protein that has the same topology as protein L but consists of only alanines and glycines allows us to suggest that the mechanical stability of proteins, and specifically protein L, is determined by interactions between certain amino acid residues, although the unfolding pathway depends on the protein topology. This insight can now be used to modulate the mechanical properties of proteins and their unfolding pathways in the desired direction for using them in various biochips, biosensors and biomaterials for medicine, industry, and household purposes.

A structure-based model fails to probe the mechanical unfolding pathways of the titin I27 domain

We discuss the use of a structure based Cα-Go model and Langevin dynamics to study in detail the mechanical properties and unfolding pathway of the titin I27 domain. We show that a simple Go-model does detect correctly the origin of the mechanical stability of this domain. The unfolding free energy landscape parameters x(u) and ΔG(‡), extracted from dependencies of unfolding forces on pulling speeds, are found to agree reasonably well with experiments. We predict that above v = 10(4) nm/s the additional force-induced intermediate state is populated at an end-to-end extension of about 75 Å. The force-induced switch in the unfolding pathway occurs at the critical pulling speed v(crit) ≈ 10(6)-10(7) nm/s. We argue that this critical pulling speed is an upper limit of the interval where Bell's theory works. However, our results suggest that the Go-model fails to reproduce the experimentally observed mechanical unfolding pathway properly, yielding an incomplete picture of the free energy landscape. Surprisingly, the experimentally observed intermediate state with the A strand detached is not populated in Go-model simulations over a wide range of pulling speeds. The discrepancy between simulation and experiment is clearly seen from the early stage of the unfolding process which shows the limitation of the Go model in reproducing unfolding pathways and deciphering the complete picture of the free energy landscape.

Experimental and theoretical studies of mechanical unfolding of different proteins

Mechanical properties of proteins are important for a wide range of biological processes including cell adhesion, muscle contraction, and protein translocation across biological membranes. It is necessary to reveal how proteins achieve their required mechanical stability under natural conditions in order to understand the biological processes and also to use the knowledge for constructing new biomaterials for medical and industrial purposes. In this connection, it is important to know how a protein will behave in response to various impacts. Theoretical and experimental works on mechanical unfolding of globular proteins will be considered in detail in this review.

Mechanical resistance in unstructured proteins

Single-molecule pulling experiments on unstructured proteins linked to neurodegenerative diseases have measured rupture forces comparable to those for stable folded proteins. To investigate the structural mechanisms of this unexpected force resistance, we perform pulling simulations of the amyloid β-peptide (Aβ) and α-synuclein (αS), starting from simulated conformational ensembles for the free monomers. For both proteins, the simulations yield a set of rupture events that agree well with the experimental data. By analyzing the conformations occurring shortly before rupture in each event, we find that the mechanically resistant structures share a common architecture, with similarities to the folds adopted by Aβ and αS in amyloid fibrils. The disease-linked Arctic mutation of Aβ is found to increase the occurrence of highly force-resistant structures. Our study suggests that the high rupture forces observed in Aβ and αS pulling experiments are caused by structures that might have a key role in amyloid formation.

Right- and left-handed three-helix proteins. II. Similarity and differences in mechanical unfolding of proteins

Here, we study mechanical properties of eight 3-helix proteins (four right-handed and four left-handed ones), which are similar in size under stretching at a constant speed and at a constant force on the atomic level using molecular dynamics simulations. The analysis of 256 trajectories from molecular dynamics simulations with explicit water showed that the right-handed three-helix domains are more mechanically resistant than the left-handed domains. Such results are observed at different extension velocities studied (192 trajectories obtained at the following conditions: v = 0.1, 0.05, and 0.01 Å ps(-1) , T = 300 K) and under constant stretching force (64 trajectories, F = 800 pN, T = 300 K). We can explain this by the fact, at least in part, that the right-handed domains have a larger number of contacts per residue and the radius of cross section than the left-handed domains.

Local unfolding and aggregation mechanisms of SOD1: a Monte Carlo exploration

Copper, zinc superoxide dismutase 1 (SOD1) is a ubiquitous homodimeric enzyme, whose misfolding and aggregation play a potentially key role in the neurodegenerative disease amyotrophic lateral sclerosis (ALS). SOD1 aggregation is thought to be preceded by dimer dissociation and metal loss, but the mechanisms by which the metal-free monomer aggregates remain incompletely understood. Here we use implicit solvent all-atom Monte Carlo (MC) methods to investigate the local unfolding dynamics of the β-barrel-forming SOD1 monomer. Although event-to-event variations are large, on average, we find clear differences in dynamics among the eight strands forming the β-barrel. Most dynamic is the eighth strand, β8, which is located in the dimer interface of native SOD1. For the four strands in or near the dimer interface (β1, β2, β7, and β8), we perform aggregation simulations to assess the propensity of these chain segments to self-associate. We find that β1 and β2 readily self-associate to form intermolecular parallel β-sheets, whereas β8 shows a very low aggregation propensity.

Stochastic thermodynamics, fluctuation theorems and molecular machines

Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.

Protein unfolding under force: crack propagation in a network

The mechanical unfolding of a set of 12 proteins with diverse topologies is investigated using an all-atom constraint-based model. Proteins are represented as polypeptides cross-linked by hydrogen bonds, salt bridges, and hydrophobic contacts, each modeled as a harmonic inequality constraint capable of supporting a finite load before breaking. Stereochemically acceptable unfolding pathways are generated by minimally overloading the network in an iterative fashion, analogous to crack propagation in solids. By comparing the pathways to those from molecular dynamics simulations and intermediates identified from experiment, it is demonstrated that the dominant unfolding pathways for 9 of the 12 proteins studied are well described by crack propagation in a network.

Transient-state fluctuationlike relation for the driving force on a biomolecule

In experiments and simulations the force acting on a single biomolecular system has been observed as a fluctuating quantity if the system is driven under constant velocity. We ask the question that is analogous to transient state entropy production and work fluctuation relations whether the force fluctuations observed in the single biomolecular system satisfy a transient state fluctuationlike relation, and the answer is in the affirmative. Using a constant velocity pulling steered molecular dynamics simulation study for protein unfolding, we confirm that the force fluctuations of this single biomolecular system satisfy a transient-state fluctuationlike relation 1/γ(T,v) ln[P(v)(+f)/P(v)(-f)] = f. P(v)(±f) is the probability of positive and negative values of forces f = f · for a given unfolding velocity of magnitude v and the pulling direction n, nis the unit vector of n, and γ(T,v) is a factor that depends on initial equilibrium temperature T and the unfolding velocity. For different unfolding velocities we find that the system in the nonequilibrium pulling region displays substantial negative fluctuation in its unfolding force when velocity decreases. A negative value of force may indicate the emergence of refolding behavior during protein unfolding. We also find that γ(T,v) ~ T(-δ)v(α) and the system relaxation time τ(T,v) ~ T(δ)v(-(1+α), where α and δ are scaling exponents.

Direction-dependent mechanical unfolding and green fluorescent protein as a force sensor

An Ising-like model of proteins is used to investigate the mechanical unfolding of the green fluorescent protein along different directions. When the protein is pulled from its ends, we recover the major and minor unfolding pathways observed in experiments. Upon varying the pulling direction, we find the correct order of magnitude and ranking of the unfolding forces. Exploiting the direction dependence of the unfolding force at equilibrium, we propose a force sensor whose luminescence depends on the applied force.

Nanomechanics of Ig-like domains of human contactin (BIG-2)

Contactins are modular extracellular cell matrix proteins that are present in the brain, and they are responsible for the proper development and functioning of neurons. They contain six immunoglobulin-like IgC2 domains and four fibronectin type III repeats. The interactions of contactin with other proteins are poorly understood. The mechanical properties of all IgC2 domains of human contactin 4 were studied using a steered molecular dynamics approach and CHARMM force field with an explicit TIP3P water environment on a 10-ns timescale. Force spectra of all domains were determined computationally and the nanomechanical unfolding process is described. The domains show different mechanical stabilities. The calculated maxima of the unfolding force are in the range of 900–1700 pN at a loading rate of 7 N/s. Our data indicate that critical regions of IgC2 domains 2 and 3, which are responsible for interactions with tyrosine phosphatases and are important in nervous system development, are affected by even weak mechanical stretching. Thus, tensions present in the cell may modulate cellular activities related to contactin function. The present data should facilitate the interpretation of atomic force microscope single-molecule spectra of numerous proteins with similar IgC2 motives.

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Unravelling the design principles for single protein mechanical strength

In recent years single molecule manipulation techniques have improved to the extent that measurements of the mechanical strength of single proteins can now be undertaken routinely. This powerful new tool, coupled with theoretical frameworks to characterise the unfolding process, has enabled significant progress to be made in understanding the physical mechanisms that underlie protein mechanical strength. These design concepts have allowed the search for proteins with novel, mechanically strong folds to be automated and for previously mechanically characterised proteins to be engineered rationally. Methods to achieve the latter are diverse and include re-engineering of specific hydrophobic core residues, changing solvent conditions and the 'cross-linking' of side-chains that are separated in the rate-limiting unfolding transition. Predicting the mechanical behaviour of larger proteins and those with more complex structures remains a significant challenge while on-going instrument development is beginning to allow the examination of mechanical strength of protein across a wide range of force loading rates. The integral role of force in biology and the potential for exploitation of catalytic and structural proteins as functional bio-materials makes this a particularly important area of research.

An effective all-atom potential for proteins

We describe and test an implicit solvent all-atom potential for simulations of protein folding and aggregation. The potential is developed through studies of structural and thermodynamic properties of 17 peptides with diverse secondary structure. Results obtained using the final form of the potential are presented for all these peptides. The same model, with unchanged parameters, is furthermore applied to a heterodimeric coiled-coil system, a mixed α/β protein and a three-helix-bundle protein, with very good results. The computational efficiency of the potential makes it possible to investigate the free-energy landscape of these 49–67-residue systems with high statistical accuracy, using only modest computational resources by today's standards.

PACS Codes: 87.14.E-, 87.15.A-, 87.15.Cc

Methods for Monte Carlo simulations of biomacromolecules

The state-of-the-art for Monte Carlo (MC) simulations of biomacromolecules is reviewed. Available methodologies for sampling conformational equilibria and associations of biomacromolecules in the canonical ensemble, given a continuum description of the solvent environment, are reviewed. Detailed sections are provided dealing with the choice of degrees of freedom, the efficiencies of MC algorithms and algorithmic peculiarities, as well as the optimization of simple movesets. The issue of introducing correlations into elementary MC moves, and the applicability of such methods to simulations of biomacromolecules is discussed. A brief discussion of multicanonical methods and an overview of recent simulation work highlighting the potential of MC methods are also provided. It is argued that MC simulations, while underutilized biomacromolecular simulation community, hold promise for simulations of complex systems and phenomena that span multiple length scales, especially when used in conjunction with implicit solvation models or other coarse graining strategies.