Fast kinetics and mechanisms in protein folding

A Stochastic Landscape Approach for Protein Folding State Classification

Protein folding is a critical process that determines the functional state of proteins. Proper folding is essential for proteins to acquire their functional three-dimensional structures and execute their biological role, whereas misfolded proteins can lead to various diseases, including neurodegenerative disorders like Alzheimer's and Parkinson's. Therefore, a deeper understanding of protein folding is vital for understanding disease mechanisms and developing therapeutic strategies. This study introduces the Stochastic Landscape Classification (SLC), an innovative, automated, nonlearning algorithm that quantitatively analyzes protein folding dynamics. Focusing on collective variables (CVs) - low-dimensional representations of complex dynamical systems like molecular dynamics (MD) of macromolecules - the SLC approach segments the CVs into distinct macrostates, revealing the protein folding pathway explored by MD simulations. The segmentation is achieved by analyzing changes in CV trends and clustering these segments using a standard density-based spatial clustering of applications with noise (DBSCAN) scheme. Applied to the MD-based CV trajectories of Chignolin and Trp-Cage proteins, the SLC demonstrates apposite accuracy, validated by comparing standard classification metrics against ground-truth data. These metrics affirm the efficacy of the SLC in capturing intricate protein dynamics and offer a method to evaluate and select the most informative CVs. The practical application of this technique lies in its ability to provide a detailed, quantitative description of protein folding processes, with significant implications for understanding and manipulating protein behavior in industrial and pharmaceutical contexts.

Ca2+-Dependent and -Independent Calmodulin Binding to the Cytoplasmic Loop of Gap Junction Connexins

Ca²⁺/calmodulin (Ca²⁺/CaM) interaction with connexins (Cx) is well-established; however, the mechanistic basis of regulation of gap junction function by Ca²⁺/CaM is not fully understood. Ca²⁺/CaM is predicted to bind to a domain in the C-terminal portion of the intracellular loop (CL2) in the vast majority of Cx isoforms and for a number of Cx-s this prediction has proved correct. In this study, we investigate and characterise both Ca²⁺/CaM and apo-CaM binding to selected representatives of each of the α, β and γ connexin family to develop a better mechanistic understanding of CaM effects on gap junction function. The affinity and kinetics Ca²⁺/CaM and apo-CaM interactions of CL2 peptides of β-Cx32, γ-Cx35, α-Cx43, α-Cx45 and α-Cx57 were investigated. All five Cx CL2 peptides were found to have high affinity for Ca²⁺/CaM with dissociation constants (K_d(+Ca)) from 20 to 150 nM. The limiting rate of binding and the rates of dissociation covered a broad range. In addition, we obtained evidence for high affinity Ca²⁺-independent interaction of all five peptides with CaM, consistent with CaM remaining anchored to gap junctions in resting cells. However, for the α-Cx45 and α-Cx57 CL2 peptides, Ca²⁺-dependent association at resting [Ca²⁺] of 50-100 nM is indicated in these complexes as one of the CaM Ca²⁺ binding sites displays high affinity with K_d of 70 and 30 nM for Ca²⁺, respectively. Furthermore, complex conformational changes were observed in peptide-apo-CaM complexes with the structure of CaM compacted or stretched by the peptide in a concentration dependent manner suggesting that the CL2 domain may undergo helix-to-coil transition and/or forms bundles, which may be relevant in the hexameric gap junction. We demonstrate inhibition of gap junction permeability by Ca²⁺/CaM in a dose dependent manner, further cementing Ca²⁺/CaM as a regulator of gap junction function. The motion of a stretched CaM-CL2 complex compacting upon Ca²⁺ binding may bring about the Ca²⁺/CaM block of the gap junction pore by a push and pull action on the CL2 C-terminal hydrophobic residues of transmembrane domain 3 (TM3) in and out of the membrane.

Drug discovery by a basic research scientist

I was fortunate to do my military service during the Vietnam era as a medical officer at the National Institutes of Health (NIH) in Bethesda, Maryland. My first research at NIH was concerned with making a variety of optical measurements on nucleic acid bases and proteins, including single crystal spectra in linearly polarized light and near infrared circular dichroism, interpreting the spectra using molecular orbital and crystal field theories. What I do now is drug discovery, a field at the opposite end of the scientific spectrum. This article gives a brief account of my transition from spectroscopy to sickle cell hemoglobin polymerization to protein folding to drug discovery for treating sickle cell disease. My lab recently developed a high throughput assay to screen the 12,657 compounds of the California Institute of Biomedical Research ReFrame drug repurposing library. This is a precious library because the compounds have either been FDA approved or have been tested in clinical trials. Since the 1970s numerous agents have been reported in the literature to inhibit HbS polymerization and/or sickling with only one successful drug, hydroxyurea, and another of dubious value, voxelotor, even though it has been approved by the FDA. Our screen has discovered 106 anti-sickling agents in the ReFrame compound library. We estimate that as many as 21 of these compounds could become oral drugs for treating sickle cell disease because they inhibit at concentrations typical of the free concentrations of oral drugs in human serum.

A litmus test for classifying recognition mechanisms of transiently binding proteins

Partner recognition in protein binding is critical for all biological functions, and yet, delineating its mechanism is challenging, especially when recognition happens within microseconds. We present a theoretical and experimental framework based on straight-forward nuclear magnetic resonance relaxation dispersion measurements to investigate protein binding mechanisms on sub-millisecond timescales, which are beyond the reach of standard rapid-mixing experiments. This framework predicts that conformational selection prevails on ubiquitin’s paradigmatic interaction with an SH3 (Src-homology 3) domain. By contrast, the SH3 domain recognizes ubiquitin in a two-state binding process. Subsequent molecular dynamics simulations and Markov state modeling reveal that the ubiquitin conformation selected for binding exhibits a characteristically extended C-terminus. Our framework is robust and expandable for implementation in other binding scenarios with the potential to show that conformational selection might be the design principle of the hubs in protein interaction networks.

The authors provide a litmus test for the recognition mechanism of transiently binding proteins based on nuclear magnetic resonance and find a conformational selection binding mechanism through concentration-dependent kinetics of ubiquitin and SH3.

The mechanism for thermal-enhanced chaperone-like activity of α-crystallin against UV irradiation-induced aggregation of γD-crystallin

Exposure to solar UV irradiation damages γ-crystallin, leading to cataract formation via aggregation. α-Crystallin, as a small heat-shock protein (sHsps), efficiently suppresses this irreversible aggregation by selectively binding the denatured γ-crystallin monomer. In this study, liquid chromatography tandem mass spectrometry (LC-MS) was used to evaluate UV-325 nm irradiation-induced photodamage of human γD-crystallin in the presence of bovine α-crystallin, atomic force microscope (AFM) and dynamic light scattering (DLS) techniques were used to detect the quaternary structure changes of α-crystallin oligomer, and Fourier transform infrared (FTIR) spectroscopy and temperature-jump (T-jump) nanosecond time-resolved IR absorbance difference spectroscopy were used to probe the secondary structure changes of bovine α-crystallin. We find that the thermal-induced subunit dissociation of α-crystallin oligomer involves the breaking of hydrogen bonds at the dimeric interface, leading to three different spectral components at varied temperature regions as resolved from temperature-dependent IR spectra. Under UV-325 nm irradiation, unfolded γD-crystallin binds to the dissociated α-crystallin subunit to form αγ-complex, then follows the reassociation of αγ-complex to the partially dissociated α-crystallin oligomer. This prevents the aggregation of denatured γD-crystallin. The formation of the γD-bound α-crystallin oligomer is further confirmed by AFM and DLS analysis, which reveals an obvious size expansion in the reassociated αγ-oligomers. In addition, UV-325 nm irradiation causes a peptide bond cleavage of γD-crystallin at Ala158 in presence of α-crystallin. Our results suggest a very effective protection mechanism for subunits dissociated from α-crystallin oligomers against UV irradiation-induced aggregation of γD-crystallin, at an expense of a loss of a short C-terminal peptide in γD-crystallin.

Slowest-first protein translation scheme: Structural asymmetry and co-translational folding

Proteins are translated from the N to the C terminus, raising the basic question of how this innate directionality affects their evolution. To explore this question, we analyze 16,200 structures from the Protein Data Bank (PDB). We find remarkable enrichment of α helices at the C terminus and β strands at the N terminus. Furthermore, this α-β asymmetry correlates with sequence length and contact order, both determinants of folding rate, hinting at possible links to co-translational folding (CTF). Hence, we propose the "slowest-first" scheme, whereby protein sequences evolved structural asymmetry to accelerate CTF: the slowest of the cooperatively folding segments are positioned near the N terminus so they have more time to fold during translation. A phenomenological model predicts that CTF can be accelerated by asymmetry in folding rate, up to double the rate, when folding time is commensurate with translation time; analysis of the PDB predicts that structural asymmetry is indeed maximal in this regime. This correspondence is greater in prokaryotes, which generally require faster protein production. Altogether, this indicates that accelerating CTF is a substantial evolutionary force whose interplay with stability and functionality is encoded in secondary structure asymmetry.

Multiscale Model for Quantitative Prediction of Insulin Aggregation Nucleation Kinetics

We combined kinetic, thermodynamic, and structural information from single-molecule (protein folding) and two-molecule (association) explicit-solvent simulations for determination of kinetic parameters in protein aggregation nucleation with insulin as the model protein. A structural bioinformatics approach was developed to account for heterogeneity of aggregation-prone species, with the transition complex theory found applicable in modeling association kinetics involving non-native species. Specifically, the kinetic pathway for formation of aggregation-prone oligomeric species was found to contain a structurally specific dominant binding mode, making the kinetic process similar to native protein association. The kinetic parameters thus obtained were used in a population balance model, and accurate predictions for aggregation nucleation time varying over 2 orders of magnitude with changes in either insulin concentration or an aggregation-inhibitor ligand concentration were obtained, while an empirical parameter set was not found to be transferable for prediction of ligand effects. Further, this physically determined kinetic parameter set provided several mechanistic insights, such as identification of the rate-limiting step in aggregation nucleation and a quantitative explanation for the switch from Arrhenius to non-Arrhenius aggregation kinetics around the melting temperature of insulin.

Polymer looping kinetics in active heterogeneous environments

A typical biological environment is usually featured by crowding and heterogeneity, leading to complex reaction kinetics of the immersed macromolecules. In the present work, we adopt Langevin dynamics simulations to systematically investigate polymer looping kinetics in active heterogeneous media crowded with a mixture of mobile active particles and immobile obstacles. For comparison, a parallel study is also performed in the passive heterogeneous media. We explicitly analyze the change of looping time and looping probability with the variation of obstacle ratio, volume fraction and crowder size. We reveal the novel phenomena of inhibition-facilitation transition of the looping rate induced by heterogeneity, crowdedness and activity. In addition, our results demonstrate a very non-trivial crowder size effect on the looping kinetics. The underlying mechanism is rationalized by the interplay of polymer diffusion, conformational change and looping free-energy barrier. The competing effect arising from active particles and obstacles on structural and dynamical properties of the polymer yields a consistent scenario for our observations. Lastly, the non-exponential kinetics of the looping process is also analyzed. We find that both activity and crowding can strengthen the heterogeneity degree of the looping kinetics.

Comparative study of polymer looping kinetics in passive and active environments

Intra-chain looping in complex environments is significant in advancing our understanding of biological processes in life. We adopt Langevin dynamics simulations to perform a comparative study of polymer looping kinetics in passive and active environments. From the analysis of looping quantities, including looping-unlooping times and looping probabilities, we unraveled the intriguing effects of active crowder size, activity and crowding. Firstly, we figured out the phase diagram involving a novel facilitation-inhibition transition in the parameter space of active crowder size and active force, and the two-fold roles of activity are clarified. In particular, we find that active particles of a size comparable to the polymer monomer are most favorable for facilitated looping, while those with a similar size to the polymer gyration radius impede the looping most seriously. Secondly, the underlying looping mechanisms in different active crowder size regimes are rationalized by the interplay among diffusion, polymer conformational change and the free-energy barrier. For small active crowders, activity significantly promotes end-to-end distance diffusion, which dominantly facilitates both looping and unlooping processes. In the case of moderate active crowders, the polymer chain suffers from prominent swelling, and thus inevitable inhibited looping will occur. For large active crowders, activity induces a counterintuitive non-cage effect on the looping kinetics, through yielding a higher effective temperature and larger unlooping free-energy barrier. This is in sharp contrast to the caging phenomena observed in passive media. Lastly, the volume-fraction dependence of the looping quantities in an active bath demonstrates dramatic discrepancies from that in a passive bath, which highlights the contrasting effects of activity and crowding.

Fundamentals to function: Quantitative and scalable approaches for measuring protein stability

Folding a linear chain of amino acids into a three-dimensional protein is a complex physical process that ultimately confers an impressive range of diverse functions. Although recent advances have driven significant progress in predicting three-dimensional protein structures from sequence, proteins are not static molecules. Rather, they exist as complex conformational ensembles defined by energy landscapes spanning the space of sequence and conditions. Quantitatively mapping the physical parameters that dictate these landscapes and protein stability is therefore critical to develop models that are capable of predicting how mutations alter function of proteins in disease and informing the design of proteins with desired functions. Here, we review the approaches that are used to quantify protein stability at a variety of scales, from returning multiple thermodynamic and kinetic measurements for a single protein sequence to yielding indirect insights into folding across a vast sequence space. The physical parameters derived from these approaches will provide a foundation for models that extend beyond the structural prediction to capture the complexity of conformational ensembles and, ultimately, their function.

Length Dependent Folding Kinetics of Alanine-Based Helical Peptides from Optimal Dimensionality Reduction

We present a computer simulation study of helix folding in alanine homopeptides (ALA)n of length n = 5, 8, 15, and 21 residues. Based on multi-microsecond molecular dynamics simulations at room temperature, we found helix populations and relaxation times increasing from about 6% and ~2 ns for ALA5 to about 60% and ~500 ns for ALA21, and folding free energies decreasing linearly with the increasing number of residues. The helix folding was analyzed with the Optimal Dimensionality Reduction method, yielding coarse-grained kinetic models that provided a detailed representation of the folding process. The shorter peptides, ALA5 and ALA8, tended to convert directly from coil to helix, while ALA15 and ALA21 traveled through several intermediates. Coarse-grained aggregate states representing the helix, coil, and intermediates were heterogeneous, encompassing multiple peptide conformations. The folding involved multiple pathways and interesting intermediate states were present on the folding paths, with partially formed helices, turns, and compact coils. Statistically, helix initiation was favored at both termini, and the helix was most stable in the central region. Importantly, we found the presence of underlying universal local dynamics in helical peptides with correlated transitions for neighboring hydrogen bonds. Overall, the structural and dynamical parameters extracted from the trajectories are in good agreement with experimental observables, providing microscopic insights into the complex helix folding kinetics.

Investigating the folding mechanism of the N-terminal domain of ribosomal protein L9

Protein folding is a popular topic in the life science. However, due to the limited sampling ability of experiments and simulations, the general folding mechanism is not yet clear to us. In this work, we study the folding of the N-terminal domain of ribosomal protein L9 (NTL9) in detail by a mixing replica exchange molecular dynamics method. The simulation results are close to previous experimental observations. According to the Markov state model, the folding of the protein follows a nucleation-condensation path. Moreover, after the comparison to its 39-residue β-α-β motif, we find that the helix at the C-terminal has a great influence on the folding process of the intact protein, including the nucleation of the key residues in the transition state ensemble and the packing of the hydrophobic residues in the native state.

The road less traveled in protein folding: evidence for multiple pathways

Free Energy Landscape theory of Protein Folding, introduced over 20 years ago, implies that a protein has many paths to the folded conformation with the lowest free energy. Despite the knowledge in principle, it has been remarkably hard to detect such pathways. The lack of such observations is primarily due to the fact that no one experimental technique can detect many parts of the protein simultaneously with the time resolution necessary to see such differences in paths. However, recent technical developments and employment of multiple experimental probes and folding prompts have illuminated multiple folding pathways in a number of proteins that had all previously been described with a single path.

Downhill, Ultrafast and Fast Folding Proteins Revised

Research on the protein folding problem differentiates the protein folding process with respect to the duration of this process. The current structure encoded in sequence dogma seems to be clearly justified, especially in the case of proteins referred to as fast-folding, ultra-fast-folding or downhill. In the present work, an attempt to determine the characteristics of this group of proteins using fuzzy oil drop model is undertaken. According to the fuzzy oil drop model, a protein is a specific micelle composed of bi-polar molecules such as amino acids. Protein folding is regarded as a spherical micelle formation process. The presence of covalent peptide bonds between amino acids eliminates the possibility of free mutual arrangement of neighbors. An example would be the construction of co-micelles composed of more than one type of bipolar molecules. In the case of fast folding proteins, the amino acid sequence represents the optimal bipolarity system to generate a spherical micelle. In order to achieve the native form, it is enough to have an external force field provided by the water environment which directs the folding process towards the generation of a centric hydrophobic core. The influence of the external field can be expressed using the 3D Gaussian function which is a mathematical model of the folding process orientation towards the concentration of hydrophobic residues in the center with polar residues exposed on the surface. The set of proteins under study reveals a hydrophobicity distribution compatible with a 3D Gaussian distribution, taken as representing an idealized micelle-like distribution. The structure of the present hydrophobic core is also discussed in relation to the distribution of hydrophobic residues in a partially unfolded form.

Dramatic Shape Changes Occur as Cytochrome c Folds

Extensive experimental studies on the folding of cytochrome c (Cyt c) make this small protein an ideal target for atomic detailed simulations for the purposes of quantitatively characterizing the structural transitions and the associated time scales for folding to the native state from an ensemble of unfolded states. We use previously generated atomically detailed folding trajectories by the stochastic difference equation in length to calculate the time-dependent changes in the small-angle X-ray scattering (SAXS) profiles. Excellent agreement is obtained between experiments and simulations for the time-dependent SAXS spectra, allowing us to identify the structures of the folding intermediates, which shows that Cyt c reaches the native state by a sequential folding mechanism. Using the ensembles of structures along the folding pathways, we show that compaction and the sphericity of Cyt c change dramatically from the prolate ellipsoid shape in the unfolded state to the spherical native state. Our data, which are in unprecedented quantitative agreement with all aspects of time-resolved SAXS experiments, show that hydrophobic collapse and amide group protection coincide on the 100 microseconds time scale, which is in accordance with ultrafast hydrogen/deuterium exchange studies. Based on these results, we propose that compaction of polypeptide chains, accompanied by dramatic shape changes, is a universal characteristic of globular proteins, regardless of the underlying folding mechanism.

N-Terminal Decarboxylation as a Probe for Intramolecular Contact Formation in γ-Glu-(Pro)n-Met Peptides

The kinetics of intramolecular-contact formation between remote functional groups in peptides with restricted conformational flexibility were examined using designed peptides with variable-length proline bridges. As probes for this motion, free radicals were produced using the ^•OH-induced oxidation at the C-terminal methionine residue of γ-Glu-(Pro)_n-Met peptides (n = 0-3). The progress of the radicals' motion along the proline bridges was monitored as the radicals underwent reactions along the peptides' backbones. Of particular interest was the reaction between the sulfur atom located in the side chain of the oxidized Met residue and the unprotonated amino group of the glutamic acid moiety. Interactions between them were probed by the radiation-chemical yields (expressed as G values) of the formation of C-centered, α-aminoalkyl radicals (αN) on the Glu residue. These radicals were monitored directly or via their reaction with p-nitroacetophenone (PNAP) to generate the optically detected PNAP^•- radical anions. The yields of these αN radicals were found to be linearly dependent on the number of Pro residues. A constant decrease by 0.09 μM J^-1 per spacing Pro residue of the radiation-chemical yields of G(αN) was observed. Previous reports support the conclusion that the αN radicals in these cases would have to result from (S∴N)⁺-bonded cyclic radical cations that arose as a result from direct contact between the ends of the peptides. Furthermore, by analogy with the rate constants for the formation of intramolecularly (S∴S)⁺-bonded radical cations in Met-(Pro)_n-Met peptides ( J. Phys. Chem. B 2016, 120, 9732), the rate constants for the formation of intramolecularly (S∴N)⁺-bonded radical cations are activated to the same extent for all of the γ-Glu-(Pro)_n-Met peptides. Thus, the continuous decrease of G(αN) with the number of Pro residues (from 0 to 3) suggests that the formation of a contact between the S-atom in the C-terminal Met residue and the N-atom of a deprotonated N-terminal amino group of Glu is controlled in peptides with 0 to 3 Pro residues by the relative diffusion of the S^•+ and unoxidized N-atom. The overall rate constants of cyclization to form the (S∴N)-bonded radical cations were estimated to be 3.8 × 10⁶, 1.8 × 10⁶, and 8.1 × 10⁵ s^-1 for peptides with n = 0, 1, and 2 Pro residues, respectively. If activation is the same for all of the peptides, then these rate constants are a direct indication for the end-to-end dynamics along the chain.

The metastable states of proteins

The intriguing process of protein folding comprises discrete steps that stabilize the protein molecules in different conformations. The metastable state of protein is represented by specific conformational characteristics, which place the protein in a local free energy minimum state of the energy landscape. The native-to-metastable structural transitions are governed by transient or long-lived thermodynamic and kinetic fluctuations of the intrinsic interactions of the protein molecules. Depiction of the structural and functional properties of metastable proteins is not only required to understand the complexity of folding patterns but also to comprehend the mechanisms of anomalous aggregation of different proteins. In this article, we review the properties of metastable proteins in context of their stability and capability of undergoing atypical aggregation in physiological conditions.

Affinity versus specificity in coupled binding and folding reactions

Intrinsically disordered protein regions may fold upon binding to an interaction partner. It is often argued that such coupled binding and folding enables the combination of high specificity with low affinity. The basic tenet is that an unfavorable folding equilibrium will make the overall binding weaker while maintaining the interaction interface. While theoretically solid, we argue that this concept may be misleading for intrinsically disordered proteins. In fact, experimental evidence suggests that interactions of disordered regions usually involve extended conformations. In such cases, the disordered region is exceptionally unlikely to fold into a bound conformation in the absence of its binding partner. Instead, these disordered regions can bind to their partners in multiple different conformations and then fold into the native bound complex, thus, if anything, increasing the affinity through folding. We concede that (de)stabilization of native structural elements such as helices will modulate affinity, but this could work both ways, decreasing or increasing the stability of the complex. Moreover, experimental data show that intrinsically disordered binding regions display a range of affinities and specificities dictated by the particular side chains and length of the disordered region and not necessarily by the fact that they are disordered. We find it more likely that intrinsically disordered regions are common in protein-protein interactions because they increase the repertoire of binding partners, providing an accessible route to evolve interactions rather than providing a stability-affinity trade-off.

On the competition between mixing rate and uniformity in a coaxial hydrodynamic focusing mixer

Fast microfluidic mixers for use with line-of-sight integrating detection schemes pose unique challenges. Such detectors typically cannot discriminate signal from slow moving (e.g. near internal walls) and fast-moving portions of the fluid stream. This convolves reaction rate dynamics with fluid flow residence time dynamics. Further, the small cross sections of typical three-dimensional hydrodynamic focusing devices lead to lower detection signals. The current study focuses on achieving both small time scales of mixing and homogenous residence times. This is achieved by injecting sample through a center capillary and hydrodynamically focusing using a sheath flow within a tapered second capillary. The current design also features a third, larger coaxial capillary. The mixed stream flows into the large cross-section of this third capillary to decelerate and expand the stream by up to 14-fold to improve line-of-sight signal strength of reaction products. Hydrodynamic focusing, mixing, and expansion are studied using analytical and numerical models and also studied experimentally using a fluorescein-iodide quenching reaction. The experimentally validated models are used to explore trade-offs between mixing rate and uniformity. For the first time, this work presents detailed analysis of the Lagrangian time history of species transport during mixing inside coaxial capillaries to measure mixing nonuniformity. The mixing region enables order 100 μs mixing times and residence time widths of the same order (140 μs).

A novel dual mode X-band EPR resonator for rapid in situ microwave heating

A unique dual mode X-band Continuous Wave (CW) EPR resonator designed for simultaneous EPR measurement and rapid microwave (MW) induced sample heating is described. Chemical reactions subjected to a flow of energy and matter can be perturbed away from the thermodynamic equilibrium by imposing a rapid shock or physical change to the system. Depending on the magnitude of the perturbation, these changes can dictate the subsequent evolution of the entire system, allowing for instance to populate non-equilibrium reactive intermediate states. Temperature jump (T-jump) experiments are a common method to achieve such perturbations. Most T-jump experiments are based on Joule Heating methods or IR lasers. Here we demonstrate the principle of rapid sample heating based on microwaves. The benefits of MW heating include (i) rapid and efficient heating (i.e. using a tuned resonant cavity, >99% efficient power transfer to the sample can be achieved), and (ii) volumetric heating (i.e. the entire sample volume rises in temperature at once, since heat is generated in the sample instead of being transferred to it). Accordingly, the key concept of the design is the use of a cavity resonator allowing EPR detection (at 9.5 GHz) and simultaneous sample heating (at 6.1 GHz). Temperature increments of 50 °C within a few seconds are possible. This is evidenced and illustrated here by probing the temperature-induced variation of the rotational dynamics of 16-doxyl stearic acid methyl ester (16-DSE) spin probe grafted on the surface of sodium dodecyl sulphate (SDS) micelles in water, as well as copper (II) acetylacetonate in chloroform. Rapid changes in the rotational dynamics of the paramagnetic centres provide direct evidence for the in situ and simultaneous EPR measurement-heating capabilities of the resonator. Improvements afforded by the use of pulsed MW sources will enable faster heating time scales to be achieved. In the longer term, this current study demonstrates the simple and direct possibilities for using MW heating as a means of performing T-jump experiments.

More than a Confinement: “Soft” and “Hard” Enzyme Entrapment Modulates Biological Catalyst Function

Catalysis makes chemical and biochemical reactions kinetically accessible. From a technological point of view, organic, inorganic, and biochemical catalysis is relevant for several applications, from industrial synthesis to biomedical, material, and food sciences. A heterogeneous catalyst, i.e., a catalyst confined in a different phase with respect to the reagents’ phase, requires either its physical confinement in an immobilization matrix or its physical adsorption on a surface. In this review, we will focus on the immobilization of biological catalysts, i.e., enzymes, by comparing hard and soft immobilization matrices and their effect on the modulation of the catalysts’ function. Indeed, unlike smaller molecules, the catalytic activity of protein catalysts depends on their structure, conformation, local environment, and dynamics, properties that can be strongly affected by the immobilization matrices, which, therefore, not only provide physical confinement, but also modulate catalysis.

How the dyes affect folding of small proteins in single-molecule FRET experiments: A simulation study

A key question in the application of the single-molecule Förster resonance energy transfer (smFRET) technique to study protein folding is how the dyes affect the protein behavior. Understanding of these effects is particularly important for small proteins, for which the dyes, along with their linkers, can be comparable in size (mass) with the protein. Using a coarse-grained model, we simulated folding of BBL protein and two of its FRET constructs. The obtained results suggest that even for small proteins, such as the 45-residue BBL, the appearance of the excluded volume in the protein conformation space due to the presence of dyes does not change the overall picture of folding. At the same time, some deviations from folding of the original protein are observed, in particular, the FRET constructs fold considerably slower than the original protein because the protein collapse in the initial state of folding is slowed down due to the protein loading with relatively massive dyes.

Application of millisecond time-resolved solid state NMR to the kinetics and mechanism of melittin self-assembly

Common experimental approaches for characterizing structural conversion processes such as protein folding and self-assembly do not report on all aspects of the evolution from an initial state to the final state. Here, we demonstrate an approach that is based on rapid mixing, freeze-trapping, and low-temperature solid-state NMR (ssNMR) with signal enhancements from dynamic nuclear polarization (DNP). Experiments on the folding and tetramerization of the 26-residue peptide melittin following a rapid pH jump show that multiple aspects of molecular structure can be followed with millisecond time resolution, including secondary structure at specific isotopically labeled sites, intramolecular and intermolecular contacts between specific pairs of labeled residues, and overall structural order. DNP-enhanced ssNMR data reveal that conversion of conformationally disordered melittin monomers at low pH to α-helical conformations at neutral pH occurs on nearly the same timescale as formation of antiparallel melittin dimers, about 6 to 9 ms for 0.3 mM melittin at 24 °C in aqueous solution containing 20% (vol/vol) glycerol and 75 mM sodium phosphate. Although stopped-flow fluorescence data suggest that melittin tetramers form quickly after dimerization, ssNMR spectra show that full structural order within melittin tetramers develops more slowly, in ∼60 ms. Time-resolved ssNMR is likely to find many applications to biomolecular structural conversion processes, including early stages of amyloid formation, viral capsid formation, and protein-protein recognition.

Unusual crowding-induced chain looping kinetics in hard-sphere fluids: a contrastive study with polymer solutions

A theoretical framework is developed to investigate the looping kinetics of a chain in hard-sphere (HS) fluids, based on a generalized Smoluchowski diffusion-reaction equation. A contrastive study with polymer solutions is performed. The crowding-associated effective viscosity and collapse effects are properly taken into account, which obey different scaling relations in HS and polymer fluids. We examine the dependence of the looping time on both concentration and size of crowders, demonstrating unusual and distinct discrepancies in the two crowded media. Firstly, in the solution of large polymers, the looping rate grows monotonically with polymer concentration. On the other hand, in the solution of large HSs, a caging regime can be observed, where the looping time tends to the value in the absence of crowders. Secondly, polymers in moderate size generally impede chain looping due to the enhanced viscosity. However, in HS fluids, the looping time exhibits a rather complicated variation with increasing HS size. We show a possible mechanism where in the case of small crowders with a relatively strong compaction in the probed chain, the looping kinetics can be facilitated. As the crowder size increases, the collapse effect is reduced and looping is dominated by viscosity-induced inhibition. Simultaneously, our theory rationalizes another possibility of the mechanism observed by recent simulation work. We conclude that the looping kinetics in specific systems actually should be governed by the critical competition between the two crowding factors. By giving reasonable measurements of effective viscosity and collapse, our theoretical framework can provide a unified strategy to analyze crowding effects on the looping rate in a systematic manner.

Nature's Shortcut to Protein Folding

This Feature Article presents a view of the protein folding transition based on the hypothesis that Nature has built features within the sequences that enable a Shortcut to efficient folding. Nature's Shortcut is proposed to be the early establishment of a set of nonlocal weak contacts, constituting protein loops that significantly constrain regions of the collapsed disordered protein into a native-like low-resolution fluctuating topology of major sections of the backbone. Nature's establishment of this scaffold of nonlocal contacts is claimed to bypass what would otherwise be a nearly hopeless unaided search for the final three-dimensional structure in proteins longer than ∼100 amino acids. To support this main contention of the Feature Article, the loop hypothesis (LH) description of early folding events is experimentally tested with time-resolved Förster resonance energy transfer techniques for adenylate kinase, and the data are shown to be consistent with theoretical predictions from the sequential collapse model (SCM). The experimentally based LH and the theoretically founded SCM are argued to provide a unified picture of the role of nonlocal contacts as constituting Nature's Shortcut to protein folding. Importantly, the SCM is shown to reliably predict key nonlocal contacts utilizing only primary sequence information. This view on Nature's Shortcut is open to the protein community for further detailed assessment, including its practical consequences, by suitable application of advanced experimental and computational techniques.

Alternation of phases of regular and irregular dynamics in protein folding

The regularity of the dynamics in different phases of protein folding is investigated for a set of proteins which undergo a cooperative, two-state folding transition. To determine the degree of regularity of the dynamics, the fractal dimension of probability fluxes is calculated on the basis of simulated folding trajectories. It has been found that the phases of regular and irregular dynamics alternate as follows. In the initial (collapse) phase of folding, the dynamics are essentially regular. Then, as the protein comes to the basin of semicompact states that precedes the transition state, the dynamics become irregular. At the transition state, the dynamics are regularized again but become less regular when the nativelike states are explored. Depending on the specific conditions at which the protein folding was considered, some phases of the dynamics could not be well resolved, but no significant deviation from this general picture has been observed. The regularization of the dynamics at the transition state is discussed in relation to the recent studies of the Hamiltonian dynamics of small clusters, where both regular and chaotic dynamics were observed depending on the flatness of the energy surface at the transition state.

Modeling of Multicolor Single-Molecule Förster Resonance Energy-Transfer Experiments on Protein Folding

Using a coarse-grained, C_α-model of BBL protein, a multicolor single-molecule Förster resonance energy transfer (FRET) experiment is modeled. Three fluorophores are introduced, which, for simplicity, are associated with C_α beads. Two fluorophores are placed at the ends of protein chain and the third one at the middle of the chain. The free-energy surfaces (FESs) depending on the interfluorophore distances and on the FRET efficiencies corresponding to these distances have been constructed and compared with the FESs depending on the conventional collective variables, such as the fraction of native contacts and radius of gyration. It has been found that multicolor experiments can successfully resolve all essential BBL states that are revealed by the conventional FESs. The resolution of these states with the FRET-efficiency histogram is found to be successful if the energy transfer is measured between the fluorophores at the BBL ends. We also show that, although the present model construct of BBL is very simple, it captures some characteristic features of the single-molecule FRET experiments, such as the pattern of the FRET-efficiency histograms and their evolution with the denaturant concentration.

How the Conformations of an Internal Junction Contribute to Fold an RNA Domain

Like proteins, some RNAs fold to compact structures. We can model functional RNAs as a series of short, rigid, base-paired elements, connected by non-base-paired nucleotides that serve as junctions. These connecting regions bend and twist, facilitating the formation of tertiary contacts that stabilize compact states. Here, we explore the roles of salt and junction sequence in determining the structures of a ubiquitous connector: an asymmetric internal loop. We focus on the J5/5a junction from the widely studied P4-P6 domain of the Tetrahymena ribozyme. Following the addition of magnesium ions to fold P4-P6, this junction bends dramatically, bringing the two halves of the RNA domain together for tertiary contact engagement. Using single-molecule fluorescence resonance energy transfer (smFRET), we examine the role of sequence and salt on model RNA constructs that contain these junction regions. We explore the wild-type J5/5a junction as well as two sequence variants. These junctions display distinct, salt-dependent conformations. Small-angle X-ray scattering (SAXS) measurements verify that these effects persist in the full-length P4-P6 domain. These measurements underscore the importance of junction sequence and interactions with ions in facilitating RNA folding.

Understanding chain looping kinetics in polymer solutions: crowding effects of microviscosity and collapse

A theoretical framework based on a generalized Langevin equation with fractional Gaussian noise is presented to describe the looping kinetics of chains in polymer solutions. Particular attention is paid to quantitatively revealing crowding effects on the loop formation rate in terms of microviscosity and collapse. By the aid of empirical relations for these two crowding associated physical quantities, we explicitly investigate the relationship between the looping rate and polymer concentration, the degree of polymerization, and system parameters. According to our analysis, the dependence of the looping rate on the crowder volume fraction exhibits three typical regimes: monotonic decreasing, a non-monotonic trend and monotonic increasing. We reveal that these non-trivial behaviors can be attributed to the competition between the two opposing factors of viscosity-associated inhibition and collapse-induced facilitation of loop formation. We apply our theory to analyze the kinetics of single-stranded DNA hairpin base pairing in polyethylene glycol solutions. The theoretical results can reproduce the experimental data on the closing rate of hairpins quantitatively to a certain degree with reasonable fitting parameters. The unexpected increase of the closing rate upon the addition of increasing amounts of polymer is well rationalised. Such good agreements clearly demonstrate the validity of our theory, appropriately addressing the very role of crowding effects in the relevant kinetics.

Mapping an Equilibrium Folding Intermediate of the Cytolytic Pore Toxin ClyA with Single-Molecule FRET

The 303-residue cytolytic toxin ClyA forms a stable α-helical monomer. In the presence of detergents or membranes, however, the protein makes a large conformational transition to the protomer state, which is competent for assembly into a dodecameric cytolytic pore. In this study, we map the structure of the ClyA monomer during denaturant-induced unfolding with single-molecule Förster resonance energy transfer (FRET) spectroscopy. To this end, we probe intramolecular distances of six different segments of ClyA by placing donor and acceptor fluorophores at corresponding positions along the chain. We identify an intermediate state that contains the folded core consisting of three of the α-helices that make up the helical bundle present in the structure of both the monomer and the protomer, but with the C- and N-terminal helices unfolded, in accord with the secondary structure content estimated from circular dichroism (CD) spectroscopy. The existence of this intermediate is likely to be a consequence of the structural bistability underlying the biological function of ClyA: The terminal helices are part of the largest rearrangements during protomer formation, and the local differences in stability we detect may prime the protein for the required conformational transition.

Temperature-induced collapse of a disordered peptide observed by three sampling methods in molecular dynamics simulations

The conformational ensembles of a disordered peptide, polyglutamine Q15, over a wide temperature range were sampled using multiple replicates of conventional molecular dynamics (cMD) simulations as well as two enhanced sampling methods, temperature replica exchange (TREMD) and replica exchange with solute tempering (REST). The radius of gyration, asphericity, secondary structure, and hydrogen bonding patterns were used for the comparison of the sampling methods. Overall, the three sampling methods generated similar conformational ensembles, with progressive collapse at higher temperatures. Although accumulating the longest simulation time (90 μs), cMD at room temperature missed a small subspace that was sampled by both TREMD and REST. This subspace was high in α-helical content and separated from the main conformational space by an energy barrier. REST used less simulation time than TREMD (36 μs versus 42 μs), and this gap is expected to widen significantly for larger disordered proteins. We conclude that REST is the method of choice for conformational sampling of intrinsically disordered proteins.

A proline switch explains kinetic heterogeneity in a coupled folding and binding reaction

The interactions of intrinsically disordered proteins (IDPs) with their molecular targets are essential for the regulation of many cellular processes. IDPs can perform their functions while disordered, and they may fold to structured conformations on binding. Here we show that the cis/trans isomerization of peptidyl−prolyl bonds can have a pronounced effect on the interactions of IDPs. By single-molecule spectroscopy, we identify a conserved proline residue in NCBD (the nuclear-coactivator binding domain of CBP) whose cis/trans isomerization in the unbound state modulates the association and dissociation rates with its binding partner, ACTR. As a result, NCBD switches on a time scale of tens of seconds between two populations that differ in their affinities to ACTR by about an order of magnitude. Molecular dynamics simulations indicate as a cause reduced packing of the complex for the cis isomer. Peptidyl-prolyl cis/trans isomerization may be an important previously unidentified mechanism for regulating IDP interactions.

How intrinsically disordered proteins (IDPs) undergo a coupled folding and binding reaction with their molecular targets remains to be understood. Here authors use single-molecule FRET to assess the contribution of cis/trans isomerization of peptidyl-prolyl bonds in regulating IDP interactions.

Global Protein Stabilization Does Not Suffice to Prevent Amyloid Fibril Formation

Mutations or cellular conditions that destabilize the native protein conformation promote the population of partially unfolded conformations, which in many cases assemble into insoluble amyloid fibrils, a process associated with multiple human pathologies. Therefore, stabilization of protein structures is seen as an efficient way to prevent misfolding and subsequent aggregation. This has been suggested to be the underlying reason why proteins living in harsh environments, such as the extracellular space, have evolved disulfide bonds. The effect of protein disulfides on the thermodynamics and kinetics of folding has been extensively studied, but much less is known on its effect on aggregation reactions. Here, we designed a single point mutation that introduces a disulfide bond in the all-α FF domain, a protein that, despite being devoid of preformed β-sheets, forms β-sheet-rich amyloid fibrils. The novel and unique covalent bond in the FF domain dramatically increases its thermodynamic stability and folding speed. Nevertheless, these optimized properties cannot counteract the inherent aggregation propensity of the protein, thus indicating that a high global protein stabilization does not suffice to prevent amyloid formation unless it contributes to hide from exposure the specific regions that nucleate the aggregation reaction.

Protein Folding Cooperativity and Thermodynamic Barriers of the Simplest β-Sheet Fold: A Survey of WW Domains

Theory and experiments have shown that microsecond folding proteins exhibit characteristic thermodynamic properties that reflect the limited cooperativity of folding over marginal barriers (downhill folding). Those studies have mostly focused on proteins with large α-helical contents and small size, which tend to be the fastest folders. A key open question is whether such properties are also present in the fastest all-β proteins. We address this issue by investigating the unfolding thermodynamics of a collection of WW domains as representatives of the simplest β-sheet fold. WW domains are small microsecond folders, although they do not fold as fast as their α-helical counterparts. In previous work on the NEDD4-WW4 domain, we reported deviations from two-state thermodynamics that were less apparent and thus suggestive of an incipient downhill scenario. Here we investigate the unfolding thermodynamics of four other WW domains (NEDD4-WW3, YAP65-WW1(L30K), FBP11-WW1, and FBP11-WW2) by performing all of the thermodynamic tests for downhill folding that have been previously developed on α-helical proteins. This set of five WW domains shares low sequence identity and include examples from two specificity classes, thus providing a comprehensive survey. Thermodynamic analysis of the four new WW domains consistently reveals all of the properties of downhill folding equilibria, which are in all cases more marked than what we found before in NEDD4-WW4. Our results show that fast-folding all-β proteins do share limited cooperativity and gradual unfolding thermodynamics with fast α-helical proteins and suggest that the free energy barrier to folding of natural proteins is mostly determined by size and fold topology and much less by the specific amino acid sequence.

Pressure- and heat-induced protein unfolding in bacterial cells: crowding vs. sticking

In-cell protein stability is increased by crowding, but can be reduced by destabilizing surface interactions. Will different denaturation techniques yield similar trends? Here, we apply pressure and thermal denaturation to green fluorescent protein/ReAsH-labeled yeast phosphoglycerate kinase (PGK) in Escherichia coli cells. Pressure denaturation is more two state-like in E. coli than in vitro, stabilizing the native state. Thermal denaturation destabilizes PGK in E. coli, unlike in mammalian cells. Results in wild-type MG1655 strain are corroborated in pressure-resistant J1 strain, where PGK is less prone to aggregation. Thus, destabilizing surface interactions overcome stabilizing crowding in the E. coli cytoplasm under thermal denaturation, but not under pressure denaturation.

Estimating the mean first passage time of protein misfolding

Most theoretical and experimental studies confirm that proteins fold in the time scale of microseconds to milliseconds, but the kinetics of the protein misfolding remains largely unexplored. The kinetics of unfolding-folding-misfolding equilibrium in proteins is formulated in the analytical framework of the Master equation. The folded, unfolded and the misfolded state are characterized in terms of their respective contacts. The Mean First Passage Time (MFPT) to acquire the misfolded conformation from the native or folded state is derived from this equation with different boundary conditions. The MFPT is found to be practically independent of the length of the protein, the number of native contacts and the rate constant for the misfolded to the folded state. The results obtained from the survival probability are directly correlated to the age of onset and appearance of misfolding diseases in humans.

Roles of conformational disorder and downhill folding in modulating protein-DNA recognition

Transcription factors are thought to efficiently search for their target DNA site via a combination of conventional 3D diffusion and 1D diffusion along the DNA molecule mediated by non-specific electrostatic interactions. This process requires the DNA-binding protein to quickly exchange between a search competent and a target recognition mode, but little is known as to how these two binding modes are encoded in the conformational properties of the protein. Here, we investigate this issue on the engrailed homeodomain (EngHD), a DNA-binding domain that folds ultrafast and exhibits a complex conformational behavior consistent with the downhill folding scenario. We explore the interplay between folding and DNA recognition using a coarse-grained computational model that allows us to manipulate the folding properties of the protein and monitor its non-specific and specific binding to DNA. We find that conformational disorder increases the search efficiency of EngHD by promoting a fast gliding search mode in addition to sliding. When gliding, EngHD remains loosely bound to DNA moving linearly along its length. A partially disordered EngHD also binds more dynamically to the target site, reducing the half-life of the specific complex via a spring-loaded mechanism. These findings apply to all conditions leading to partial disorder. However, we also find that at physiologically relevant temperatures EngHD is well folded and can only obtain the conformational flexibility required to accelerate 1D diffusion when it folds/unfolds within the downhill scenario (crossing a marginal free energy barrier). In addition, the conformational flexibility of native downhill EngHD enables its fast reconfiguration to lock into the specific binding site upon arrival, thereby affording finer control of the on- and off-rates of the specific complex. Our results provide key mechanistic insights into how DNA-binding domains optimize specific DNA recognition through the control of their conformational dynamics and folding mechanism.

Turbulence in protein folding: Vorticity, scaling and diffusion of probability flows

Recently, when studying folding of a SH3 domain, we discovered that the flows of transitions between protein states can be surprisingly similar to turbulent fluid flows. This similarity was not restricted by a vortex pattern of the flow fields but extended to a spatial correlation of flow fluctuations, resulting, in particular, in the structure functions such as in the Kolmogorov theory of homogeneous and isotropic turbulence. Here, we undertake a detailed analysis of spatial distribution of folding flows and their similarity to turbulent fluid flows. Using molecular dynamics simulations, we study folding of another benchmark system—Trp-cage miniprotein, which has different content of secondary structure elements and mechanism of folding. Calculating the probability fluxes of transitions in a three-dimensional space of collective variables, we have found that similar to the SH3 domain, the structure functions of the second and third orders correspond to the Kolmogorov functions. The spatial distributions of the probability fluxes are self-similar with a fractal dimension, and the fractal index decreases toward the native state, indicating that the flow becomes more turbulent as the native state is approached. We also show that the process of folding can be viewed as Brownian diffusion in the space of probability fluxes. The diffusion coefficient plays a role of the key parameter that defines the structures functions, similar to the rate of dissipation of kinetic energy in hydrodynamic turbulence. The obtained results, first, show that the very complex dynamics of protein folding allows a simple characterization in terms of scaling and diffusion of probability fluxes, and, secondly, they suggest that the turbulence phenomena similar to hydrodynamic turbulence are not specific of folding of a particular protein but are common to protein folding.

Disulfide driven folding for a conditionally disordered protein

Conditionally disordered proteins are either ordered or disordered depending on the environmental context. The substrates of the mitochondrial intermembrane space (IMS) oxidoreductase Mia40 are synthesized on cytosolic ribosomes and diffuse as intrinsically disordered proteins to the IMS, where they fold into their functional conformations; behaving thus as conditionally disordered proteins. It is not clear how the sequences of these polypeptides encode at the same time for their ability to adopt a folded structure and to remain unfolded. Here we characterize the disorder-to-order transition of a Mia40 substrate, the human small copper chaperone Cox17. Using an integrated real-time approach, including chromatography, fluorescence, CD, FTIR, SAXS, NMR, and MS analysis, we demonstrate that in this mitochondrial protein, the conformational switch between disordered and folded states is controlled by the formation of a single disulfide bond, both in the presence and in the absence of Mia40. We provide molecular details on how the folding of a conditionally disordered protein is tightly regulated in time and space, in such a way that the same sequence is competent for protein translocation and activity.

Disulfide driven folding for a conditionally disordered protein

Conditionally disordered proteins are either ordered or disordered depending on the environmental context. The substrates of the mitochondrial intermembrane space (IMS) oxidoreductase Mia40 are synthesized on cytosolic ribosomes and diffuse as intrinsically disordered proteins to the IMS, where they fold into their functional conformations; behaving thus as conditionally disordered proteins. It is not clear how the sequences of these polypeptides encode at the same time for their ability to adopt a folded structure and to remain unfolded. Here we characterize the disorder-to-order transition of a Mia40 substrate, the human small copper chaperone Cox17. Using an integrated real-time approach, including chromatography, fluorescence, CD, FTIR, SAXS, NMR, and MS analysis, we demonstrate that in this mitochondrial protein, the conformational switch between disordered and folded states is controlled by the formation of a single disulfide bond, both in the presence and in the absence of Mia40. We provide molecular details on how the folding of a conditionally disordered protein is tightly regulated in time and space, in such a way that the same sequence is competent for protein translocation and activity.

Protein folding transition path times from single molecule FRET

The transition path is the tiny segment of a single molecule trajectory when the free energy barrier between states is crossed and for protein folding contains all of the information about the self-assembly mechanism. As a first step toward obtaining structural information during the transition path from experiments, single molecule FRET spectroscopy has been used to determine average transition path times from a photon-by-photon analysis of fluorescence trajectories. These results, obtained for several different proteins, have already provided new and demanding tests that support both the accuracy of all-atom molecular dynamics simulations and the basic postulates of energy landscape theory of protein folding.

Temperature evolution of Trp-cage folding pathways: An analysis by dividing the probability flux field into stream tubes

Owing to its small size and very fast folding rate, the Trp-cage miniprotein has become a benchmark system to study protein folding. Two folding pathways were found to be characteristic of this protein: pathway I, in which the hydrophobic collapse precedes the formation of α-helix, and pathway II, in which the events occur in the reverse order. At the same time, the relative contribution of these pathways at different temperatures as well as the nature of transition from one pathway to the other remain unclear. To gain insight into this issue, we employ a recently proposed hydrodynamic description of protein folding, in which the process of folding is considered as a motion of a "folding fluid" (Chekmarev et al., Phys. Rev. Lett. 100(1), 018107 2008). Using molecular dynamics simulations, we determine the field of probability fluxes of transitions in a space of collective variables and divide it into stream tubes. Each tube contains a definite fraction of the total folding flow and can be associated with a certain pathway. Specifically, three temperatures were considered, T = 285K, T = 315K, and T = 325K. We have found that as the temperature increases, the contribution of pathway I, which is approximately 90% of the total folding flow at T = 285K, decreases to approximately 10% at T = 325K, i.e., pathway II becomes dominant. At T = 315K, both pathways contribute approximately equally. All these temperatures are found below the calculated melting point, which suggests that the Trp-cage folding mechanism is determined by kinetic factors rather than thermodynamics.