Multilevel Framework for Analysis of Protein Folding Involving Disulfide Bond Formation.

In this study, a three-layered multicenter ONIOM approach is implemented to characterize the naive folding pathway of bovine pancreatic trypsin inhibitor (BPTI). Each layer represents a distinct level of theory, where the initial layer, encompassing the entire protein, is modeled by a general all-atom force-field GFN-FF. An intermediate electronic structure layer consisting of three multicenter fragments is introduced with the state-of-the-art semiempirical tight-binding method GFN2-xTB. Higher accuracy, specifically addressing the breaking and formation of the three disulfide bonds, is achieved at the innermost layer using the composite DFT method r2SCAN-3c. Our analysis sheds light on the structural stability of BPTI, particularly the significance of interlinking disulfide bonds. The accuracy and efficiency of the multicenter QM/SQM/MM approach are benchmarked using the oxidative formation of cystine. For the folding pathway of BPTI, relative stabilities are investigated through the calculation of free energy contributions for selected intermediates, focusing on the impact of the disulfide bond. Our results highlight the intricate trade-off between accuracy and computational cost, demonstrating that the multicenter ONIOM approach provides a well-balanced and comprehensive solution to describe electronic structure effects in biomolecular systems. We conclude that multiscale energy landscape exploration provides a robust methodology for the study of intriguing biological targets.

Free-Energy Landscape and Rate Estimation of the Aromatic Ring Flips in Basic Pancreatic Trypsin Inhibitors Using Metadynamics.

Aromatic side chains (phenylalanine and tyrosine) of a protein flip by 180° around the Cß-Cγ axis (χ2 dihedral of the side chain), producing two symmetry-equivalent states. The study of ring flip dynamics with nuclear magnetic resonance (NMR) experiments helps to understand local conformational fluctuations. Ring flips are categorized as slow (milliseconds and onward) or fast (nanoseconds to near milliseconds) based on timescales accessible to NMR experiments. In this study, we investigated the ability of the infrequent metadynamics approach to estimate the flip rate and discriminate between slow and fast ring flips for eight individual aromatic side chains (F4, Y10, Y21, F22, Y23, F33, Y35, and F45) of the basic pancreatic trypsin inhibitor. Well-tempered metadynamics simulations were performed to estimate the ring-flipping free-energy surfaces for all eight aromatic residues. The results indicate that χ2 as a standalone collective variable (CV) is not sufficient to obtain computationally consistent results. Inclusion of a complementary CV, such as χ1(Cα-Cß), solved the problem for most residues and enabled us to classify fast and slow ring flips. This indicates the importance of librational motions in ring flips. Multiple pathways and mechanisms were observed for residues F4, Y10, and F22. Recrossing events were observed for residues F22 and F33, indicating a possible role of friction effects in ring flipping. The results demonstrate the successful application of infrequent metadynamics to estimate ring flip rates and identify certain limitations of the approach.

Correlation between protein conformations and water structure and thermodynamics at high pressure: A molecular dynamics study of the Bovine Pancreatic Trypsin Inhibitor (BPTI) protein.

Pressure-induced perturbation of a protein structure leading to its folding-unfolding mechanism is an important yet not fully understood phenomenon. The key point here is the role of water and its coupling with protein conformations as a function of pressure. In the current work, using extensive molecular dynamics simulation at 298 K, we systematically examine the coupling between protein conformations and water structures of pressures of 0.001, 5, 10, 15, 20 kbar, starting from (partially) unfolded structures of the protein Bovine Pancreatic Trypsin Inhibitor (BPTI). We also calculate localized thermodynamics at those pressures as a function of protein-water distance. Our findings show that both protein-specific and generic effects of pressure are operating. In particular, we found that (1) the amount of increase in water density near the protein depends on the protein structural heterogeneity; (2) the intra-protein hydrogen bond decreases with pressure, while the water-water hydrogen bond per water in the first solvation shell (FSS) increases; protein-water hydrogen bonds also found to increase with pressure, (3) with pressure hydrogen bonds of waters in the FSS getting twisted; and (4) water's tetrahedrality in the FSS decreases with pressure, but it is dependent on the local environment. Thermodynamically, at higher pressure, the structural perturbation of BPTI is due to the pressure-volume work, while the entropy decreases with the increase of pressure due to the higher translational and rotational rigidity of waters in the FSS. The local and subtle effects of pressure, found in this work, are likely to be typical of pressure-induced protein structure perturbation.

Protein 3D Hydration: A Case of Bovine Pancreatic Trypsin Inhibitor.

Characterization of the hydrated state of a protein is crucial for understanding its structural stability and function. In the present study, we have investigated the 3D hydration structure of the protein BPTI (bovine pancreatic trypsin inhibitor) by molecular dynamics (MD) and the integral equation method in the three-dimensional reference interaction site model (3D-RISM) approach. Both methods have found a well-defined hydration layer around the protein and revealed the localization of BPTI buried water molecules corresponding to the X-ray crystallography data. Moreover, under 3D-RISM calculations, the obtained positions of waters bound firmly to the BPTI sites are in reasonable agreement with the experimental results mentioned above for the BPTI crystal form. The analysis of the 3D hydration structure (thickness of hydration shell and hydration numbers) was performed for the entire protein and its polar and non-polar parts using various cut-off distances taken from the literature as well as by a straightforward procedure proposed here for determining the thickness of the hydration layer. Using the thickness of the hydration shell from this procedure allows for calculating the total hydration number of biomolecules properly under both methods. Following this approach, we have obtained the thickness of the BPTI hydration layer of 3.6 Å with 369 water molecules in the case of MD simulation and 3.9 Å with 333 water molecules in the case of the 3D-RISM approach. The above procedure was also applied for a more detailed description of the BPTI hydration structure near the polar charged and uncharged radicals as well as non-polar radicals. The results presented for the BPTI as an example bring new knowledge to the understanding of protein hydration.

Rapid Rational Design of Cyclic Peptides Mimicking Protein-Protein Interfaces.

The cPEPmatch approach is a rapid computational methodology for the rational design of cyclic peptides to target desired regions of protein-protein interfaces. The method selects cyclic peptides that structurally match backbone structures of short segments at a protein-protein interface. In a second step, the cyclic peptides act as templates for designed binders by adapting the amino acid side chains to the side chains found in the target complex. A link to access the different tools that comprise the cPEPmatch method and a detailed step-by-step guide is provided. We outline the protocol by following the application to a trypsin protease in complex with the bovine inhibitor protein (BPTI). An extension of our original approach is also presented, where we give a detailed description of the usage of the cPEPmatch methodology focusing on identifying hot regions of protein-protein interfaces prior to the matching. This extension allows one to reduce the amount of evaluated putative cyclic peptides and to specifically design only those that compete with the strongest protein-protein binding regions. It is illustrated by an application to an MHC class I protein complex.

Modulation of Gold Nanorod Growth via the Proteolysis of Dithiol Peptides for Enzymatic Biomarker Detection.

Gold nanorods possess optical properties that are tunable and highly sensitive to variations in their aspect ratio (length/width). Therefore, the development of a sensing platform where the gold nanorod morphology (i.e., aspect ratio) is modulated in response to an analyte holds promise in achieving ultralow detection limits. Here, we use a dithiol peptide as an enzyme substrate during nanorod growth. The sensing mechanism is enabled by the substrate design, where the dithiol peptide contains an enzyme cleavage site in-between cysteine amino acids. When cleaved, the peptide dramatically impacts gold nanorod growth and the resulting optical properties. We demonstrate that the optical response can be correlated with enzyme concentration and achieve a 45 pM limit of detection. Furthermore, we extend this sensing platform to colorimetrically detect tumor-associated inhibitors in a biologically relevant medium. Overall, these results present a subnanomolar method to detect proteases that are critical biomarkers found in cancers, infectious diseases, and inflammatory disorders.

Microscopic insights into dynamic disorder in the isomerization dynamics of the protein BPTI.

Understanding the dynamic disorder behind a process, i.e., the dynamic effect of fluctuations that occur on a timescale slower or comparable with the timescale of the process, is essential for elucidating the dynamics and kinetics of complicated molecular processes in biomolecules and liquids. Despite numerous theoretical studies of single-molecule kinetics, our microscopic understanding of dynamic disorder remains limited. In the present study, we investigate the microscopic aspects of dynamic disorder in the isomerization dynamics of the Cys14-Cys38 disulfide bond in the protein bovine pancreatic trypsin inhibitor, which has been observed by nuclear magnetic resonance. We use a theoretical model with a stochastic transition rate coefficient, which is calculated from the 1-ms-long time molecular dynamics trajectory obtained by Shaw et al. [Science 330, 341-346 (2010)]. The isomerization dynamics are expressed by the transitions between coarse-grained states consisting of internal states, i.e., conformational sub-states. In this description, the rate for the transition from the coarse-grained states is stochastically modulated due to fluctuations between internal states. We examine the survival probability for the conformational transitions from a coarse-grained state using a theoretical model, which is a good approximation to the directly calculated survival probability. The dynamic disorder changes from a slow modulation limit to a fast modulation limit depending on the aspects of the coarse-grained states. Our analysis of the rate modulations behind the survival probability, in relation to the fluctuations between internal states, reveals the microscopic origin of dynamic disorder.

Quantifying and visualizing weak interactions between anions and proteins.

The molecular properties of proteins are influenced by various ions present in the same solution. While site-specific strong interactions between multivalent metal ions and proteins are well characterized, the behavior of other ions that are only weakly interacting with proteins remains elusive. In the current study, using NMR spectroscopy, we have investigated anion-protein interactions for three proteins that are similar in size but differ in overall charge. Using a unique NMR-based approach, we quantified anions accumulated around the proteins. The determined numbers of anions that are electrostatically attracted to the charged proteins were notably smaller than the overall charge valences and were consistent with predictions from the Poisson-Boltzmann theory. This NMR-based approach also allowed us to measure ionic diffusion and characterize the anions interacting with the positively charged proteins. Our data show that these anions rapidly diffuse while bound to the proteins. Using the same experimental approach, we observed the release of the anions from the protein surface upon the formation of the Antp homeodomain-DNA complex. Using paramagnetic relaxation enhancement (PRE), we visualized the spatial distribution of anions around the free proteins and the Antp homeodomain-DNA complex. The obtained PRE data revealed the localization of anions in the vicinity of the highly positively charged regions of the free Antp homeodomain and provided further evidence of the release of anions from the protein surface upon the protein-DNA association. This study sheds light on the dynamic behavior of anions that electrostatically interact with proteins.

Reversible Oligomerization and Reverse Hydrophobic Effect Induced by Isoleucine Tags Attached at the C-Terminus of a Simplified BPTI Variant.

Protein amorphous aggregation has become the focus of great attention, as it can impair the ability of cells to function properly. Here, we evaluated the effects of three peptide tags, consisting of one, three, and five consecutive isoleucines attached at the C-terminus end of a simplified bovine pancreatic trypsin inhibitor (BPTI) variant, BPTI-19A, on the thermal stability and oligomerization by circular dichroism spectrometry and differential scanning calorimetry in detail. All of the BPTI-19A variants exhibited a reversible and apparently two-state thermal transition like BPTI-19A at pH 4.7. The thermal transition of the five-isoleucine-tagged variant showed clear protein-concentration dependence, where the apparent denaturation temperature decreased as the protein concentration increased. Quantitative analysis indicated that this phenomenon originated from the presence of reversibly oligomerized (RO) states at high temperatures. The results also illustrated that the thermodynamic stability difference between the native and the monomeric denatured state in all the proteins was destabilized by the hydrophobic tags and was well explained by the reverse hydrophobic effect due to the tags. The existence of the RO states was confirmed by both analytical ultracentrifugation and dynamic light scattering. This indicated that the five-isoleucine hydrophobic tag is strong enough to induce intermolecular hydrophobic contact among the denatured molecules leading to oligomerization, and even one- or three-isoleucine tags are effective enough to generate intramolecular hydrophobic contact, thus provoking denaturation through the reverse hydrophobic effect.

Applications of WaterControl to TOCSY and COSY experiments.

WaterControl is a solvent suppression method based on WATERGATE and PGSTE and is very efficient in selectively reducing the solvent signal in 1D pulse-acquire and 2D NOESY of protein solutions. In this study, the WaterControl technique was appended to two common 2D NMR methods used in resonance assignment of proteins, namely TOCSY and CLIP-COSY. Similar to that observed in regular 1D pulse-acquire and 2D NOESY, the incorporation of WaterControl in these 2D methods led to excellent solvent suppression superior to that obtained using W3- or W5-based WATERGATE sequences. The water signal was essentially eliminated in the TOCSY and CLIP-COSY with WaterControl while useful cross peaks around the water resonance at ω2 were preserved. This is in contrast to the 2D spectra obtained from the corresponding WATERGATE containing sequences, where these cross peaks in the ω2 region are usually suppressed together with the water resonance. These new WaterControl sequences provide significantly improved water suppression thereby facilitating protein NMR studies.

Nanometer-Sized Aggregates Generated Using Short Solubility Controlling Peptide Tags Do Increase the In Vivo Immunogenicity of a Nonimmunogenic Protein.

Subvisible aggregates of proteins are suspected to cause adverse immune response, and a recent FDA guideline has recommended the monitoring of micrometer-sized aggregates (2-10 µm) though recognizing that the underlying mechanism behind aggregation and immunogenicity remains unclear. Here, we report a correlation between the immunogenicity and the size of nanometer-scaled aggregates of a small 6.5 kDa model protein, bovine pancreatic trypsin inhibitor (BPTI) variant. BPTI-19A, a monomeric and nonimmunogenic protein, was oligomerized into subvisible aggregates with hydrodynamic radii (Rh) of 3-4 nm by attaching hydrophobic solubility controlling peptide (SCP) tags to its C-terminus. The results showed that the association of nonimmunogenic BPTI into nanometer-sized subvisible aggregates made it highly immunogenic, as assessed by the IgG antibody titers of the mice's sera. Overall, the study emphasizes that subvisible aggregates, as small as a few nanometers, which are presently ignored, are worth monitoring for deciphering the origin of undesired immunogenicity of therapeutic proteins.

Small protease inhibitors in tick saliva and salivary glands and their role in tick-host-pathogen interactions.

Ticks must durably suppress vertebrate host responses (hemostasis, inflammation, immunity) to avoid rejection and act as vectors of many pathogenic microorganisms that cause disease in humans and animals. Transcriptomics and proteomics studies have been used to study tick-host-pathogen interactions and have facilitated the systematic characterization of salivary composition and molecular dynamics throughout tick feeding. Tick saliva contains a complement of protease inhibitors that are differentially produced during feeding, many of which inhibit blood coagulation, platelet aggregation, vasodilation, and immunity. Here we focus on two major groups of protease inhibitors, the small molecular weight Kunitz inhibitors and cystatins. We discuss their role in tick-host-pathogen interactions, how they mediate the interaction between ticks and their hosts, and how they might be exploited both by pathogens to invade hosts and as candidates for the treatment of various human pathologies.

A nanometer-sized protease inhibitor for precise cancer diagnosis and treatment.

Inhibition of pro-cancer proteases is a potent anticancer strategy. However, protease inhibitors are mostly developed in the forms of small molecules or peptides, which normally suffer from insufficient metabolic stability. The fast clearance significantly impairs the antitumor effects of these inhibitors. In this study, we report a nanometer-sized inhibitor of a pro-cancer protease, suppressor of tumorigenicity 14 (st14), which has been reported as a potent prognostic marker for multiple cancers. This st14 inhibitor was fabricated by conjugating a recombinant st14 inhibitor (KD1) with carbon quantum dots (CQDs). CQD-KD1 not only demonstrated high potency of inhibiting st14 activity in biochemical experiments, but also remarkably suppressed the invasion of breast cancer cells. In contrast to the original recombinant KD1, CQD-KD1 demonstrated a prolonged retention time in plasma and at the tumor site because of the reduced renal clearance. Consistently, CQD-KD1 demonstrated enhanced efficacies of suppressing tumor growth and cancer metastases in vivo. In addition, CQD-KD1 precisely imaged tumor tissues in cancer-grafted mice by specifically targeting the over-expressed st14 on the tumor cell surface, which indicates CQD-KD1 as a potent probe for the fluorescence guided surgery of tumor resection. In conclusion, this study demonstrates that CQD-KD1 is a highly potent diagnostic and therapeutic agent for cancer treatments.

Capillary electrophoretic reactor for estimation of spontaneous dissociation rate of Trypsin-Aprotinin complex.

A capillary electrophoretic reactor was used to analyze the dissociation kinetics of an enzyme-inhibitor complex in a homogeneous solution without immobilization. The complex consisting of trypsin (Try) and aprotinin (Apr) was used as the model. Capillary electrophoresis provided a reaction field for Try-Apr complex to dissociate through the steady removal of free Try and Apr from the Try-Apr zone. By analyzing the dependence of peak height of Try-Apr on separation time, the dissociation rate kdH was obtained as 2.73 × 10-4 s-1 (298 K) at pH 2.46. The dependence of kdH on the proton concentration (pH = 2.09-3.12) revealed a first-order dependence of kdH on [H+]; kdH = kd + k1[H+], where kd is the spontaneous dissociation rate and was 5.65 × 10-5 s-1, and k1 is the second-order rate constant and was 5.07 × 10-2 M-1 s-1. From the kd value, the half-life of the Try-Apr complex at physiological pH was determined as 3.4 h. The presence of the proton-assisted dissociation can be explained by the protonation of -COO- of the Asp residue in Try, which breaks the salt bridge with the -NH3+ group of Lys in Apr.

Hydrophobic surface residues can stabilize a protein through improved water-protein interactions.

Protein stabilization is difficult to rationalize, but the detailed thermodynamic and structural analysis of a series of carefully designed mutants may provide experimental insights into the mechanisms underlying stabilization. Here, we report a systematic structural and thermodynamic analysis of bovine pancreatic trypsin inhibitor (BPTI) variants that are significantly stabilized through a single amino acid substitution at residue 38, which is located in a loop mostly exposed on the protein surface. Differential scanning calorimetry indicated that the BPTI-[5,55]Gly14 variants with a single mutation at position 38 were stabilized in an enthalpy-driven manner and that the magnitude of the stabilization increased as the hydrophobicity of residue 38 increased. This increase in the thermal stability of BPTI was unexpected because a hydrophobic residue on a protein surface is usually destabilizing. To identify the structural determinants of this stabilization, we determined the crystal structures of six BPTI-[5,55]Gly14 variants (Gly14 Gly38 , Gly14 Ala38 , Gly14 Val38 , Gly14 Leu38 , Gly14 Ile38 , and Gly14 Lys38 ) at high resolutions and showed that they retain essentially the same structure as the wild-type BPTI. A more detailed examination of their structures indicated that the extent of thermal stabilization correlated with both improved local packing and increased hydration around the substitution sites. In particular, the number of water molecules near residue 38 increased upon mutation to a hydrophobic residue suggesting that improved hydration contributed to the enthalpy-driven stabilization. Increasing a protein's thermal stability by the placement of a hydrophobic amino acid on the protein surface is a novel and unexpected phenomenon, and its exact nature is worth further examination, as it may provide a generic method for stabilizing proteins in an enthalpy-driven manner. DATABASE: The coordinates and structure factors of Gly14 Gly38 , Gly14 Ile38 , Gly14 Leu38 , and Gly14 Lys38 variants of BPTI-[5,55] are deposited in the Protein Data Bank under the PDB entry codes 5XX3, 5XX5, 5XX2, and 5XX4, respectively. We previously reported the structures of Gly14 Ala38 (2ZJX) and Gly14 Val38 (2ZVX).

Disulfide engineering of human Kunitz-type serine protease inhibitors enhances proteolytic stability and target affinity toward mesotrypsin.

Serine protease inhibitors of the Kunitz-bovine pancreatic trypsin inhibitor (BPTI) family are ubiquitous biological regulators of proteolysis. These small proteins are resistant to proteolysis, but can be slowly cleaved within the protease-binding loop by target proteases, thereby compromising their activity. For the human protease mesotrypsin, this cleavage is especially rapid. Here, we aimed to stabilize the Kunitz domain structure against proteolysis through disulfide engineering. Substitution within the Kunitz inhibitor domain of the amyloid precursor protein (APPI) that incorporated a new disulfide bond between residues 17 and 34 reduced proteolysis by mesotrypsin 74-fold. Similar disulfide engineering of tissue factor pathway inhibitor-1 Kunitz domain 1 (KD1TFPI1) and bikunin Kunitz domain 2 (KD2bikunin) likewise stabilized these inhibitors against mesotrypsin proteolysis 17- and 6.6-fold, respectively. Crystal structures of disulfide-engineered APPI and KD1TFPI1 variants in a complex with mesotrypsin at 1.5 and 2.0 Å resolution, respectively, confirmed the formation of well-ordered disulfide bonds positioned to stabilize the binding loop. Long all-atom molecular dynamics simulations of disulfide-engineered Kunitz domains and their complexes with mesotrypsin revealed conformational stabilization of the primed side of the inhibitor-binding loop by the engineered disulfide, along with global suppression of conformational dynamics in the Kunitz domain. Our findings suggest that the Cys-17-Cys-34 disulfide slows proteolysis by dampening conformational fluctuations in the binding loop and minimizing motion at the enzyme-inhibitor interface. The generalizable approach developed here for the stabilization against proteolysis of Kunitz domains, which can serve as important scaffolds for therapeutics, may thus find applications in drug development.

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 ß-barrel core unfolds remain unchanged when adding the crowders. In particular, both with and without the crowders, the second ß-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.

Aprotinin Encapsulated Gold Nanoclusters: A Fluorescent Bioprobe with Dynamic Nuclear Targeting and Selective Detection of Trypsin and Heavy Metal.

Fluorescence imaging has currently emerged as one of the most frequently used noninvasive imaging technologies to selectively monitor biological processes in living systems. In past decades, gold nanoclusters (Au NCs) has received increasing attraction because of their intrinsic fluorescence and their inherent biocompatibility. As a stabilizing and reducing agent, an abundant, sustainable, and widely used polypeptide derived drug molecule, aprotinin (Ap), is selected for the synthesis of Au nanoclusters (Ap-Au NCs) due to characteristic bioactivity, excellent biocompatibility, biodegradability, and non-allergenic character. Herein, Ap encapsulated Au NCs with desirable red fluorescence was facilely produced for the first time, which were subsequently used for cell imaging and detection of various analytes. Much interestingly, dynamically subcellular targeting  from the cytoplasm to the nucleus in HeLa cells was observed. Besides, it has shown that, the selective and quantitative detection of trypsin has been established by using Ap-Au NCs. Finally, Ap-Au NCs were readily used for quantitative detection of mercury and copper. The photoluminescence of the Ap-Au NCs was quenched with the addition of the aforementioned analytes. This study not only  discusses a multifunctional nanomaterial  for cell imaging, dynamically nuclear targeting and biosensing, but also opens crucial insights on the integration of funtional biomolecule with metal nanoclusters intended for extensively biomedical applications.

ANCA: Anharmonic Conformational Analysis of Biomolecular Simulations.

Anharmonicity in time-dependent conformational fluctuations is noted to be a key feature of functional dynamics of biomolecules. Although anharmonic events are rare, long-timescale (µs-ms and beyond) simulations facilitate probing of such events. We have previously developed quasi-anharmonic analysis to resolve higher-order spatial correlations and characterize anharmonicity in biomolecular simulations. In this article, we have extended this toolbox to resolve higher-order temporal correlations and built a scalable Python package called anharmonic conformational analysis (ANCA). ANCA has modules to: 1) measure anharmonicity in the form of higher-order statistics and its variation as a function of time, 2) output a storyboard representation of the simulations to identify key anharmonic conformational events, and 3) identify putative anharmonic conformational substates and visualization of transitions between these substates.

Markov modeling of peptide folding in the presence of protein crowders.

We use Markov state models (MSMs) to analyze the dynamics of a ß-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.