Traditionally, folding experiments have been directed at determining equilibrium and relaxation rate constants of proteins that fold with two-state-like kinetics. More recently, the combination of free energy surface approaches inspired by theory with the discovery of proteins that fold in the downhill regime has greatly widened the battlefield for experimentalists. Downhill folding proteins cross very small or no free energy barrier at all so that all relevant partially folded conformations become experimentally accessible. From these combined efforts we now have tools to estimate the height of thermodynamic and kinetic folding barriers. Procedures to measure with atomic resolution the structural heterogeneity of conformational ensembles at varying unfolding degrees are also available. Moreover, determining the dynamic modes driving folding and how they change as folding proceeds is finally at our fingertips. These developments allow us to address via experiment fundamental questions such as the origin of folding cooperativity, the relationship between structure and stability, or how to engineer folding barriers. Moreover, the level of detail attained in this new breed of experiments should provide powerful benchmarks for computer simulations of folding and force-field refinement.
Over 100 amino acid replacements in human Cu, Zn superoxide dismutase (SOD) are known to cause amyotrophic lateral sclerosis, a gain-of-function neurodegenerative disease that destroys motor neurons. Supposing that aggregates of partially-folded states are primarily responsible for toxicity, the role of the structurally-important zinc ion in defining the folding free energy surface of dimeric SOD was determined by comparing the thermodynamic and kinetic folding properties of the zinc-free and zinc-bound forms of the protein. The presence of zinc was found to decrease the free energies of a peptide model of the unfolded monomer, a stable variant of the folded monomeric intermediate and the folded dimeric species. The unfolded state binds zinc weakly with a micromolar dissociation constant, and the folded monomeric intermediate and the native dimeric form both bind zinc tightly, with sub-nanomolar dissociation constants. Coupled with the strong driving force for the subunit association reaction, the shift in the populations towards more well-folded states in the presence of zinc decreases the steady-state populations of higher-energy states in SOD under expected in vivo zinc concentrations (∼nanomolar). The significant decrease in the population of partially-folded states is expected to diminish their potential for aggregation and account for the known protective effect of zinc. The ∼100-fold increase in the rate of folding of SOD in the presence of micromolar concentrations of zinc demonstrates a significant role for a pre-organized zinc-binding loop in the transition state ensemble for the rate-limiting monomer folding reaction in this β-barrel protein.
ALS; beta-barrel dimer; metal binding; protein folding; thermodynamics and kinetics
Two fundamentally different views of how proteins fold are now being debated. Do proteins fold through multiple unpredictable routes directed only by the energetically downhill nature of the folding landscape or do they fold through specific intermediates in a defined pathway that systematically puts predetermined pieces of the target native protein into place? It has now become possible to determine the structure of protein folding intermediates, evaluate their equilibrium and kinetic parameters, and establish their pathway relationships. Results obtained for many proteins have serendipitously revealed a new dimension of protein structure. Cooperative structural units of the native protein, called foldons, unfold and refold repeatedly even under native conditions. Much evidence obtained by hydrogen exchange and other methods now indicates that cooperative foldon units and not individual amino acids account for the unit steps in protein folding pathways. The formation of foldons and their ordered pathway assembly systematically puts native-like foldon building blocks into place, guided by a sequential stabilization mechanism in which prior native-like structure templates the formation of incoming foldons with complementary structure. Thus the same propensities and interactions that specify the final native state, encoded in the amino-acid sequence of every protein, determine the pathway for getting there. Experimental observations that have been interpreted differently, in terms of multiple independent pathways, appear to be due to chance misfolding errors that cause different population fractions to block at different pathway points, populate different pathway intermediates, and fold at different rates. This paper summarizes the experimental basis for these three determining principles and their consequences. Cooperative native-like foldon units and the sequential stabilization process together generate predetermined stepwise pathways. Optional misfolding errors are responsible for 3-state and heterogeneous kinetic folding.
Amyloid diseases are caused by the aberrant assembly of a protein in the extracellular space. Folded proteins are not amyloidogenic, however the native state is generally in equilibrium with a minor population of unfolded or partially folded aggregation-competent conformers outside of the cell. Understanding how the partially unfolded conformers kinetically partition between the competing refolding and aggregation pathways provides insight into how misfolding, which occurs continuously, becomes pathogenic. Towards this end we have previously studied the amyloidogenicity of transthyretin (TTR), a human β-sheet rich homotetrameric protein that must undergo rate-limiting tetramer dissociation and partial monomer unfolding to misassemble into amyloid and other aggregates. We demonstrate herein that TTR homotetramers reassemble by an unusual monomer-dimer-trimer-tetramer (MDRT) pathway. Therefore, the rate of every step in the reassembly pathway is dependent on the concentration of folded TTR monomer. Partitioning soluble TTR monomers between the reassembly pathway and the aggregation pathway should therefore depend on the relative concentrations of aggregates and assembly intermediates. Aggregate clearance is envisioned to play an important role in the partitioning of protein in vivo, where partitioning to the aggregation pathway becomes increasingly favorable under conditions where the concentration of aggregates is increased because aggregate clearance is slow relative to the rate of aggregation. This shift from efficient to inefficient aggregate clearance could occur with aging, offering an explanation for the age-associated nature of these neurodegenerative diseases.
Proteins can sample a variety of partially folded conformations during the transition between the unfolded and native states. Some proteins never significantly populate these high-energy states and fold by an apparently two-state process. Many proteins, however, populate detectable, partially folded forms during the folding process. The role of such intermediates is a matter of considerable debate. A single amino acid change can convert E. coli ribonuclease H from a three-state folder that populates a kinetic intermediate to one that folds in an apparent two-state fashion. We have compared the folding trajectories of the three-state and two-state RNases H, proteins with the same native state topology but altered regional stability, using a protein engineering approach. Our data suggest that that both versions of RNase H fold through a similar trajectory with similar high-energy conformations. Mutations in the core and the periphery of the protein affect similar aspects of folding for both variants, suggesting a common trajectory with folding of the core region followed by the folding of the periphery. Our results suggest that formation of specific partially folded conformations may be a general feature of protein folding that can promote, rather than hinder, efficient folding.
Apomyolgobin (apoMb) is an important model for understanding the folding mechanism of helical proteins. This study focuses on a partially structured state of sperm whale apoMb populated at pH 4.2 (M-state), which structurally resembles a late kinetic intermediate in the formation of the native state (N) at higher pH. The thermodynamics and cooperativity of apoMb folding at pH 4.2 and 6.2 were studied by global analysis of the urea-induced unfolding transitions monitored by tryptophan fluorescence and circular dichroism. The kinetics of folding and unfolding of apoMb at pH 4.2 was measured over a time window from 40 to 850 μs, using fluorescence-detected continuous-flow measurements. Our observation of biphasic kinetics provides clear evidence for rapid (<100 μs) accumulation of previously unresolved intermediate states in both refolding and unfolding experiments. Quantitative kinetic modeling of the results, using a four-state mechanism with two intermediates on a direct route between the unfolded and folded states (U↔I↔L↔M), gave new insight into the conformational states and barriers that precede the rate-limiting step in the formation of the N-state of apoMb.
protein folding; myoglobin; rapid mixing; continuous flow; fluorescence; circular dichroism
Correcting aberrant folds that develop during protein folding disease states is now an active research endeavor that is attracting increasing attention from both academic and industrial circles. One particular approach focuses on developing or identifying small molecule correctors or pharmacological chaperones that specifically stabilize the native fold. Unfortunately, the limited screening platforms available to rapidly identify or validate potential drug candidates are usually inadequate or slow because the folding disease proteins in question are often transiently folded and/or aggregation-prone, complicating and/or interfering with the assay outcomes. In this review, we outline and discuss the numerous platform options currently being employed to identify small molecule therapeutics for folding diseases. Finally, we describe a new stability screening approach that is broad based and is easily applicable toward a very large number of both common and rare protein folding diseases. The label free screening method described herein couples the promiscuity of the GroEL binding to transient aggregation-prone hydrophobic folds with surface plasmon resonance enabling one to rapidly identify potential small molecule pharmacological chaperones.
Protein misfolding; missense mutations; pharmacological chaperones; GroEL chaperonin; Surface Plasmon Resonance
Protein aggregation has now become recognised as an important and generic aspect of protein energy landscapes. Since the discovery that numerous human diseases are caused by protein aggregation, the biophysical characterisation of misfolded states and their aggregation mechanisms has received increased attention. Utilising experimental techniques and computational approaches established for the analysis of protein folding reactions has ensured rapid advances in the study of pathways leading to amyloid fibrils and amyloid-related aggregates. Here we describe recent experimental and theoretical advances in the elucidation of the conformational properties of dynamic, heterogeneous and/or insoluble protein ensembles populated on complex, multidimensional protein energy landscapes. We discuss current understanding of aggregation mechanisms in this context and describe how the synergy between biochemical, biophysical and cell-biological experiments are beginning to provide detailed insights into the partitioning of non-native species between protein folding and aggregation pathways.
Energy landscape; Protein folding; Protein misfolding; Aggregation; Amyloid fibril formation; Intermediate states; Oligomers
The classification of protein folds is necessarily based on the structural elements that distinguish domains. Classification of protein domains consists of two problems: the partition of structures into domains and the classification of domains into sets of similar structures (or folds). Although similar topologies may arise by convergent evolution, the similarity of their respective folding pathways is unknown. The discovery and the characterization of the majority of protein folds will be followed by a similar enumeration of available protein folding pathways. Consequently, understanding the intricacies of structural domains is necessary to understanding their collective folding pathways. We review the current state of the art in the field of protein domain classification and discuss methods for the systematic and comprehensive study of protein folding across protein fold space via atomistic molecular dynamics simulation. Finally, we discuss our large-scale Dynameomics project, which includes simulations of representatives of all autonomous protein folds.
protein folds; protein folding; structural classification; molecular dynamics simulations
Aggregation and subsequent development of protein deposition diseases originate from conformational changes in corresponding amyloidogenic proteins. The accumulated data support the model where protein fibrillogenesis proceeds via the formation of a relatively unfolded amyloidogenic conformation, which shares many structural properties with the pre-molten globule state, a partially folded intermediate first found during the equilibrium and kinetic (un)folding studies of several globular proteins and later described as one of the structural forms of natively unfolded proteins. The flexibility of this structural form is essential for the conformational rearrangements driving the formation of the core cross-beta structure of the amyloid fibril. Obviously, molecular mechanisms describing amyloidogenesis of ordered and natively unfolded proteins are different. For ordered protein to fibrillate, its unique and rigid structure has to be destabilized and partially unfolded. On the other hand, fibrillogenesis of a natively unfolded protein involves the formation of partially folded conformation; i.e., partial folding rather than unfolding. In this review recent findings are surveyed to illustrate some unique features of the natively unfolded proteins amyloidogenesis.
Amyloid fibril; Fibrillation; Amyloidogenesis; Conformational disease; Partially folded conformation; Natively unfolded protein; Intrinsically disordered protein
Proteins are the most vital biological functional units in every living cell. Measurement
of protein stability is central to understanding their structure, function and role in
diseases. While proteins are also sought as therapeutic agents, they can cause diseases by
misfolding and aggregation in vivo. Here we demonstrate a novel method to measure protein
stability and denaturation kinetics, on unprecedented timescales, through optically-induced
heating of nanolitre samples in microfluidic capillaries. We obtain protein denaturation
kinetics as a function of temperature, and accurate thermodynamic stability data, from a
snapshot experiment on a single sample. We also report the first experimental
characterization of optical heating in controlled microcapillary flow, verified by
computational fluid dynamics modelling. Our results demonstrate that we now have the
engineering science in hand to design integrated all-optical microfluidic chips for a
diverse range of applications including in-vitro DNA amplification, healthcare diagnostics,
and flow chemistry.
Single molecule manipulation techniques combined with molecular dynamics simulations and protein engineering have enabled, during the last decade, the mechanical properties of proteins to be studied directly, thereby giving birth to the field of protein nanomechanics. Recent data obtained from such techniques have helped gain insight into the structural bases of protein resistance against forced unfolding, as well as revealing structural motifs involved in mechanical stability. Also, important technical developments have provided new perspectives into protein folding. Eventually, new and exciting data has shown that mechanical properties are key factors in cell signaling and pathologies, and has been used to rationally tune these properties in a variety of proteins.
Protein nanomechanics; Mechanical Stability; Single-Molecule Force Spectroscopy; Molecular Dynamics; Protein folding
To understand the physical and evolutionary determinants of protein folding, we map out the complete organization of thermodynamic and kinetic properties for protein sequences that share the same fold. The exhaustive nature of our study necessitates using simplified models of protein folding. We obtain a stability map and a folding rate map in sequence space. Comparison of the two maps reveals a common organizational principle: optimality decreases more or less uniformly with distance from the optimal sequence in the sequence space. This gives a funnel-shaped optimality surface. Evolutionary dynamics of a sequence population on these two maps reveal how the simple organization of sequence space affects the distributions of stability and folding rate preferred by evolution.
protein folding; protein sequence structure relationships; lattice model; hydrophobic polar; protein evolution
Several protein misfolding diseases are associated with the conversion of native proteins into ordered protein aggregates known as amyloid. Studies of amyloid assemblies have indicated that non-native proteins are responsible for initiating aggregation in vitro and in vivo. Despite the importance of these species for understanding amyloid disease, the structural and dynamic features of amyloidogenic intermediates and the molecular details of how they aggregate remain elusive. This review focuses on recent advances in developing a molecular description of the folding and aggregation mechanisms of the human amyloidogenic protein β2-microglobulin under physiologically relevant conditions. In particular, the structural and dynamic properties of the non-native folding intermediate IT and its role in the initiation of fibrillation and the development of dialysis-related amyloidosis are discussed.
amyloid; conformational conversion; dialysis-related amyloidosis; dynamics; NMR; prion
Numerous experimental techniques and computational studies, proposed in recent times, have revolutionized the understanding of protein-folding paradigm. The complete understanding of protein folding and intermediates are of medical relevance, as the aggregation of misfolding proteins underlies various diseases, including some neurodegenerative disorders. Here, we describe the unfolding of M-crystallin, a βγ-crystallin homologue protein from archaea, from its native state to its denatured state using multidimensional NMR and other biophysical techniques. The protein, which was earlier characterized to be a predominantly β-sheet protein in its native state, shows different structural propensities (α and β), under different denaturing conditions. In 2 M GdmCl, the protein starts showing two distinct sets of peaks, with one arising from a partially unfolded state and the other from a completely folded state. The native secondary structural elements start disappearing as the denaturant concentration approaches 4 M. Subsequently, the protein is completely unfolded when the denaturant concentration is 6 M. The 15N relaxation data (T1/T2), heteronuclear 1H-15N Overhauser effects (nOes), NOESY data, and other biophysical data taken together indicate that the protein shows a consistent, gradual change in its structural and motional preferences with increasing GdmCl concentration.
Understanding the interconversion between thermodynamically distinguishable states present in a protein folding pathway provides not only the kinetics and energetics of protein folding but also insights into the functional roles of these states in biological systems. The protein component of bacterial RNase P holoenzyme from Bacillus subtilis (P protein) was previously shown to be unfolded in the absence of its cognate RNA or other anionic ligands. P protein was used in the present study as a model system to explore general features of intrinsically disordered protein (IDP) folding mechanisms. The use of trimethylamine-N-oxide (TMAO), an osmolyte that stabilizes the unliganded folded form of the protein, enabled us to study the folding process of P protein in the absence of ligand. Transient stopped-flow kinetic traces at various final TMAO concentrations showed multiphasic kinetics. Equilibrium “cotitration” experiments were performed using both TMAO and urea during the titration to obtain a TMAO-urea titration surface of P protein. Both kinetic and equilibrium studies show evidence of a previously undetected intermediate state in the P protein folding process. The intermediate state is significantly populated and the folding rate constants involved in the reaction are relatively slow compared to intrinsically folded proteins of similar size and topology. The experiments and analysis described serve as a useful example for mechanistic folding studies of other IDPs.
Protein folding; Osmolyte; Intrinsically disordered; RNase P protein
A crucial challenge in present biomedical research is the elucidation of how fundamental processes like protein folding and aggregation occur in the complex environment of the cell. Many new physico-chemical factors like crowding and confinement must be considered, and immense technical hurdles must be overcome in order to explore these processes in vivo. Understanding protein misfolding and aggregation diseases and developing therapeutic strategies to these diseases demand that we gain mechanistic insight into behaviors and misbehaviors of proteins as they fold in vivo. We have developed a fluorescence approach using FlAsH labeling to study the thermodynamics of folding of a model β-rich protein, cellular retinoic acid binding protein (CRABP) in Escherichia coli cells. The labeling approach has also enabled us to follow aggregation of a modified version of CRABP and chimeras between CRABP and huntingtin exon 1 with its glutamine repeat tract. In this article, we review our recent results using FlAsH labeling to study in-vivo folding and present new observations that hint at fundamental differences between the thermodynamics and kinetics of protein folding in vivo and in vitro.
protein folding; protein aggregation; fluorescence; in-cell folding; molecular crowding
Elucidation of the high-resolution structures of folding intermediates is a necessary but difficult step toward the ultimate understanding of the mechanism of protein folding. Here, using hydrogen exchange-directed protein engineering, we populated the folding intermediate of the T. thermophilus ribonuclease H, which forms before the rate-limiting transition state, by removing the unfolded regions of the intermediate, including an α-helix and two β-strands (51 folded residues). Using multi-dimensional NMR, we solved the structure of this intermediate mimic to an atomic resolution (backbone rmsd 0.51 Å). It has a native-like backbone topology and shows some local deviations from the native structure, revealing that the structure of the folded region of an early folding intermediate can be as well defined as the native structure. The topological parameters calculated from the structures of the intermediate mimic and the native state predict that the intermediate should fold on a millisecond time scale or less and form much faster than the native state. Other factors that may lead to the slow folding of the native state and the accumulation of the intermediate before the rate-limiting transition state are also discussed.
Recent discoveries of severe bone disorders in patients with deficiencies in several endoplasmic reticulum chaperones are reshaping the discussion of type I collagen folding and related diseases. Type I collagen is the most abundant protein in all vertebrates and a crucial structural molecule for bone and other connective tissues. Its misfolding causes bone fragility, skeletal deformities and other tissue failures. Studies of newly discovered bone disorders indicate that collagen folding, chaperones involved in the folding process, cellular responses to misfolding, and related bone pathologies may not follow conventional protein folding paradigms. In this review, we examine the features that distinguish collagen folding from that of other proteins and describe findings that are beginning to reveal how cells manage collagen folding and misfolding. We discuss implications of these studies on general protein folding paradigms, unfolded protein response in cells and protein folding diseases.
Evolutionary selective pressures have tuned the efficiency of the protein-folding reaction in the crowded complex environment in the cell. Nevertheless, the fidelity of folding is imperfect, leading to off-pathway intermolecular interactions that compete with proper folding and to consequent formation of thermodynamically stable aggregates. Such aggregates constitute the histopathological hallmarks of many neurodegenerative pathologies. Yet, most of the approaches to characterize protein folding and/or misfolding are limited to in vitro conditions. Here, we describe a strategy to directly monitor the behavior of a protein in prokaryotic and eukaryotic cells. The method is based on incorporation of structurally non-perturbing, specific binding motifs for a bis-arsenical fluoroscein dye, FlAsH, in sites that result in distinct dye fluorescence signals for the folded and unfolded states of the protein under study. Our approach has been developed using as a case study the predominantly β-sheet intracellular lipid-binding protein, cellular retinoic acid-binding protein, alone or as a chimera fused to the exon 1-encoded fragment of huntingtin, which harbors a polyglutamine repeat tract. We have designed protocols to label this protein in vivo and to monitor the resulting fluorescence signal, which reports on any misfolding transition and formation of aggregates, yielding quantitatively interpretable data.
Protein structure is highly diverse when considering a wide range of protein types, helping to give rise to the multitude of functions that proteins perform. In particular, certain proteins are known to adopt a knotted or slipknotted fold. How such proteins undergo mechanical unfolding was investigated utilizing a combination of single molecule atomic force microscopy (AFM), protein engineering and steered molecular dynamics (SMD) simulations to show the mechanical unfolding mechanism of the slipknotted protein AFV3-109. Our results reveal that the mechancial unfolding of AFV3-109 can proceed via multiple parallel unfolding pathways that all cause the protein slipknot to untie, and the polypeptide chain to completely extend. These distinct unfolding pathways proceed either via a two-state or three-state unfolding process involving the formation of a well-defined, stable intermediate state. SMD simulations predict the same contour length increments for different unfolding pathways as single molecule AFM results, thus provding a plausible molecular mechanism for the mechanical unfolding of AFV3-109. These SMD simulations also reveal that two-state unfolding is initiated from both the N- and C-termini, while three-state unfolding is initiated only from the C-terminus. In both pathways, the protein slipknot was untied during unfolding, and no tightened slipknot conformation observed. Detailed analysis revealed that interactions between key structural elements lock the knotting loop in place, preventing it from shrinking and the formation of a tightened slipknot conformation. Our results demonstrate the bifurcation of the mechancial unfolding pathway of AFV3-109, and point to the generality of a kinetic partitioning mechanism for protein folding/unfolding.
Cu, Zn superoxide dismutase (SOD1) is a dimeric metal binding enzyme responsible for the dismutation of toxic superoxide to hydrogen peroxide and oxygen in cells. Mutations at dozens of sites in SOD1 induce amyotrophic lateral sclerosis (ALS), a fatal gain-of-function neurodegenerative disease whose molecular basis is unknown. To obtain insights into effects of the mutations on the folded and unfolded populations of immature monomeric forms whose aggregation or self-association may be responsible for ALS, the thermodynamic and kinetic folding properties of a set of disulfide-reduced and disulfide-oxidized Zn-free and Zn-bound stable monomeric SOD1 variants were compared to the wild-type (WT) protein. The most striking effect of the mutations on the monomer stability was observed for the disulfide-reduced metal-free variants. Whereas the WT and S134N monomers are >95% folded at neutral pH and 37 °C, A4V, L38V, G93A, and L106V ranged from 50% to ∼90% unfolded. The reduction of the disulfide-bond was also found to reduce the apparent Zn affinity of the WT monomer by 750-fold, into the nanomolar range where it may be unable to compete for free Zn in the cell. With the exception of the S134N metal-binding variant, the Zn affinity of disulfide-oxidized SOD1 monomers showed little sensitivity to amino acid replacements. These results suggest a model for SOD1 aggregation where the constant synthesis of ALS-variants of SOD1 on ribosomes provides a pool of species in which the increased population of the unfolded state may favor aggregation over productive folding to the stable native dimeric state.
Disulfide bond; Zn binding; protein folding; aggregation
Although our understanding of globular protein folding continues to advance, the irregular tertiary structures and high cooperativity of globular proteins complicates energetic dissection. Recently, proteins with regular, repetitive tertiary structures have been identified that sidestep limitations imposed by globular protein architecture. Here we review recent studies of repeat-protein folding. These studies uniquely advance our understanding of both the energetics and kinetics of protein folding. Equilibrium studies provide detailed maps of local stabilities, access to energy landscapes, insights into cooperativity, determination of nearest-neighbor interaction parameters using statistical thermodynamics, relationships between consensus sequences and repeat-protein stability. Kinetic studies provide insight into the influence of short-range topology on folding rates, the degree to which folding proceeds by parallel (versus localized) pathways, and the factors that select among multiple potential pathways. The recent application of force spectroscopy to repeat-protein unfolding is providing a unique route to test and extend many of these findings.
Repeat-protein; Ankyrin repeat; protein folding; energy landscape; atomic force microscopy
Discrete molecular dynamics (DMD) is a rapid sampling method used in protein folding and aggregation studies. Until now, DMD was used to perform simulations of simplified protein models in conjunction with structure-based force fields. Here, we develop an all-atom protein model and a transferable force field featuring packing, solvation, and environment-dependent hydrogen bond interactions. Using the replica exchange method, we perform folding simulations of six small proteins (20–60 residues) with distinct native structures. In all cases, native or near-native states are reached in simulations. For three small proteins, multiple folding transitions are observed and the computationally-characterized thermodynamics are in quantitative agreement with experiments. The predictive power of all-atom DMD highlights the importance of environment-dependent hydrogen bond interactions in modeling protein folding. The developed approach can be used for accurate and rapid sampling of conformational spaces of proteins and protein-protein complexes, and applied to protein engineering and design of protein-protein interactions.
ab initio protein folding; environment-dependent hydrogen bond; replica exchange; free energy landscape; conformational sampling
Single molecule methods are becoming routine biophysical techniques for studying biological macromolecules. In mechanical unfolding of proteins, an externally applied force is used to induce the unfolding of individual protein molecules. Such experiments have revealed novel information that has significantly enhanced our understanding of the function and folding mechanisms of several types of proteins. To obtain information on the unfolding kinetics and the free energy landscape of the protein molecule from mechanical unfolding data, a Monte Carlo simulation based on a simple two-state kinetic model is often used. In this paper, we provide a detailed description of the procedure to perform such simulations and discuss the approximations and assumptions involved. We show that the appearance of the force versus extension curves from mechanical unfolding of proteins is affected by a variety of experimental parameters, such as the length of the protein polymer and the force constant of the cantilever. We also analyze the errors associated with different methods of data pooling and present a quantitative measure of how well the simulation results fit experimental data. These findings will be helpful in experimental design, artifact identification, and data analysis for single molecule studies of various proteins using the mechanical unfolding method.
Atomic force microscopy; Mechanical unfolding; Monte Carlo simulation; Worm-like chain; Single molecule methods