Folding dynamics of Trp-cage in the presence of chemical interference and macromolecular crowding. I

Proteins from Thermophilic Thermus thermophilus Often Do Not Fold Correctly in a Mesophilic Expression System Such as Escherichia coli

Majority of protein structure studies use Escherichia coli (E. coli) and other model organisms as expression systems for other species' genes. However, protein folding depends on cellular environment factors, such as chaperone proteins, cytoplasmic pH, temperature, and ionic concentrations. Because of differences in these factors, especially temperature and chaperones, native proteins in organisms such as extremophiles may fold improperly when they are expressed in mesophilic model organisms. Here we present a methodology of assessing the effects of using E. coli as the expression system on protein structures. We compare these effects between eight mesophilic bacteria and Thermus thermophilus (T. thermophilus), a thermophile, and found that differences are significantly larger for T. thermophilus. More specifically, helical secondary structures in T. thermophilus proteins are often replaced by coil structures in E. coli. Our results show unique directionality in misfolding when proteins in thermophiles are expressed in mesophiles. This indicates that extremophiles, such as thermophiles, require unique protein expression systems in protein folding studies.

Modeling protein association from homogeneous to mixed environments: A reaction-diffusion dynamics approach

Protein-protein association in vivo occur in a crowded and complex environment. Theoretical models based on hard-core repulsion predict stabilization of the product under crowded conditions. Soft interactions, on the contrary, can either stabilize or destabilize the product formation. Here we modeled protein association in presence of crowders of varying size, shape, interaction potential and used different mixing parameters for constituent crowders to study the influence on the association reaction. It was found that size is a more dominant factor in crowder-induced stabilization than the shape. Furthermore, in a mixture of crowders having different sizes but identical interaction potential, the change of free energy is additive of the free energy changes produced by individual crowders. However, the free energy change is not additive if two crowders of same size interact via different interaction potentials. These findings provide a systematic understanding of crowding influences in heterogeneous medium.

The Zero-Order Loop in Apoazurin Modulates Folding Mechanism In Silico

Pseudomonas aeruginosa apoazurin (apo, without the copper cofactor) has a single disulfide bond between residues 3 and 26 and unfolds in a two-state reaction in vitro. The disulfide bond covalently connects the N-termini of β-strands 1 and 3; thereby, it creates a zero-order loop or a "cinch" that restricts conformational space. Covalent loops and threaded topologies are emerging as important structural elements in folded proteins and may be important for function. In order to understand the role of a zero-order loop in the folding process of a protein, here we used coarse-grained molecular dynamics (CGMD) simulations in silico to compare two variants of apoazurin: one named "loop" which contained the disulfide, and another named "open" in which the disulfide bond between residues 3 and 26 was removed. CGMD simulations were performed to probe the stability and unfolding pathway of the two apoazurin variants at different urea concentrations and temperatures. Our results show that the covalent loop plays a prominent role in the unfolding mechanism of apoazurin; its removal alters both the folding-transition state and the unfolded-state ensemble of conformations. We propose that modulation of azurin's folding landscape by the disulfide bridge may be related to both copper capturing and redox sensing.

Crowding-Induced Elongated Conformation of Urea-Unfolded Apoazurin: Investigating the Role of Crowder Shape in Silico

Here, we show by solution nuclear magnetic resonance measurements that the urea-unfolded protein apoazurin becomes elongated when the synthetic crowding agent dextran 20 is present, in contrast to the prediction from the macromolecular crowding effect based on the argument of volume exclusion. To explore the complex interactions beyond volume exclusion, we employed coarse-grained molecular dynamics simulations to explore the conformational ensemble of apoazurin in a box of monodisperse crowders under strong chemically denaturing conditions. The elongated conformation of unfolded apoazurin appears to result from the interplay of the effective attraction between the protein and crowders and the shape of the crowders. With a volume-conserving crowder model, we show that the crowder shape provides an anisotropic direction of the depletion force, in which a bundle of surrounding rodlike crowders stabilize an elongated conformation of unfolded apoazurin in the presence of effective attraction between the protein and crowders.

Folding of poly-amino acids and intrinsically disordered proteins in overcrowded milieu induced by pH change

pH-induced structural changes of the synthetic homopolypeptides poly-E, poly-K, poly-R, and intrinsically disordered proteins (IDPs) prothymosin α (ProTα) and linker histone H1, in concentrated PEG solutions simulating macromolecular crowding conditions within the membrane-less organelles, were characterized. The conformational transitions of the studied poly-amino acids in the concentrated PEG solutions depend on the polymerization degree of these homopolypeptides, the size of their side chains, the charge distribution of the side chains, and the crowding agent concentration. The results obtained for poly-amino acids are valid for IDPs having a significant total charge. The overcrowded conditions promote a significant increase in the cooperativity of the pH-induced coil-α-helix transition of ProTα and provoke histone H1 aggregation. The most favorable conditions for the pH-induced structural transitions in concentrated PEG solutions are realized when the charged residues are grouped in blocks, and when the distance between the end of the side group carrying charge and the backbone is small. Therefore, the block-wise distribution of charged residues within the IDPs not only plays an important role in the liquid-liquid phase transitions, but may also define the expressivity of structural transitions of these proteins in the overcrowded conditions of the membrane-less organelles.

Towards developing principles of protein folding and dynamics in the cell

Proteins must fold and function in the immensely complex environment of a cell, i.e. the cytoplasm-this is far from the ideal test-tube setting of a dilute solution. Here we review the advances in protein folding and dynamics inside the cell. In developing principles of protein behavior in vivo, we also begin to understand the organization and dynamics of the cytoplasm, unifying the single protein scale with the many-protein architectures at the subcellular scale. Our group has significantly contributed to this frontier by characterizing the effect of macromolecular crowding on the distribution of protein conformations. Additionally, we provide a personal perspective on becoming a theoretical biological physicist in the era of interdisciplinary research that has been greatly influenced by Dr Kamal Shukla. We also share our view on the future direction of protein folding inside a cell.

Predicting Protein-protein Association Rates using Coarse-grained Simulation and Machine Learning

Protein–protein interactions dominate all major biological processes in living cells. We have developed a new Monte Carlo-based simulation algorithm to study the kinetic process of protein association. We tested our method on a previously used large benchmark set of 49 protein complexes. The predicted rate was overestimated in the benchmark test compared to the experimental results for a group of protein complexes. We hypothesized that this resulted from molecular flexibility at the interface regions of the interacting proteins. After applying a machine learning algorithm with input variables that accounted for both the conformational flexibility and the energetic factor of binding, we successfully identified most of the protein complexes with overestimated association rates and improved our final prediction by using a cross-validation test. This method was then applied to a new independent test set and resulted in a similar prediction accuracy to that obtained using the training set. It has been thought that diffusion-limited protein association is dominated by long-range interactions. Our results provide strong evidence that the conformational flexibility also plays an important role in regulating protein association. Our studies provide new insights into the mechanism of protein association and offer a computationally efficient tool for predicting its rate.

Structure and Conformational Properties of d-Glucose/d-Galactose-Binding Protein in Crowded Milieu

Conformational changes of d-glucose/d-galactose-binding protein (GGBP) were studied under molecular crowding conditions modeled by concentrated solutions of polyethylene glycols (PEG-12000, PEG-4000, and PEG-600), Ficoll-70, and Dextran-70, addition of which induced noticeable structural changes in the GGBP molecule. All PEGs promoted compaction of GGBP and lead to the increase in ordering of its structure. Concentrated solutions of PEG-12000 and PEG-4000 caused GGBP aggregation. Although Ficoll-70 and Dextran-70 also promoted increase in the GGBP ordering, the structural outputs were different for different crowders. For example, in comparison with the GGBP in buffer, the intrinsic fluorescence spectrum of this protein was shifted to short-wave region in the presence of PEGs but was red-shifted in the presence of Ficoll-70 and Dextran-70. It was hypothesized that this difference could be due to the specific interaction of GGBP with the sugar-based polymers (Ficoll-70 and Dextran-70), indicating that protein can adopt different conformations in solutions containing molecular crowders of different chemical nature. It was also shown that all tested crowding agents were able to stabilize GGBP structure shifting the GGBP guanidine hydrochloride (GdnHCl)-induced unfolding curves to higher denaturant concentrations, but their stabilization capabilities did not depend on the hydrodynamic dimensions of the polymers molecules. Refolding of GGBP was complicated by protein aggregation in all tested solutions of crowding agents. The lowest yield of refolded protein was achieved in the highly concentrated solutions of PEG-12000. These data support the previous notion that the influence of macromolecular crowders on proteins is rather complex phenomenon that extends beyond the excluded volume effects.

Peptide folding in the presence of interacting protein crowders

Using Monte Carlo methods, we explore and compare the effects of two protein crowders, BPTI and GB1, on the folding thermodynamics of two peptides, the compact helical trp-cage and the β-hairpin-forming GB1m3. The thermally highly stable crowder proteins are modeled using a fixed backbone and rotatable side-chains, whereas the peptides are free to fold and unfold. In the simulations, the crowder proteins tend to distort the trp-cage fold, while having a stabilizing effect on GB1m3. The extent of the effects on a given peptide depends on the crowder type. Due to a sticky patch on its surface, BPTI causes larger changes than GB1 in the melting properties of the peptides. The observed effects on the peptides stem largely from attractive and specific interactions with the crowder surfaces, and differ from those seen in reference simulations with purely steric crowder particles.

Exploring the balance between folding and functional dynamics in proteins and RNA

As our understanding of biological dynamics continues to be refined, it is becoming clear that biomolecules can undergo transitions between ordered and disordered states as they execute functional processes. From a computational perspective, studying disorder events poses a challenge, as they typically occur on long timescales, and the associated molecules are often large (i.e., hundreds of residues). These size and time requirements make it advantageous to use computationally inexpensive models to characterize large-scale dynamics, where more highly detailed models can provide information about individual sub-steps associated with function. To reduce computational demand, one often uses a coarse-grained representation of the molecule or a simplified description of the energetics. In order to use simpler models to identify transient disorder in RNA and proteins, it is imperative that these models can accurately capture structural fluctuations about folded configurations, as well as the overall stability of each molecule. Here, we explore a class of simplified model for which all non-hydrogen atoms are explicitly represented. We find that this model can provide a consistent description of protein folding and native-basin dynamics for several representative biomolecules. We additionally show that the native-basin fluctuations of tRNA and the ribosome are robust to variations in the model. Finally, the extended variable loop in tRNAIle is predicted to be very dynamic, which may facilitate biologically-relevant rearrangements. Together, this study provides a foundation that will aid in the application of simplified models to study disorder during function in ribonucleoprotein (RNP) assemblies.

What protein folding teaches us about biological function and molecular machines

Protein folding was the first area of molecular biology for which a systematic statistical-mechanical analysis of dynamics was developed. As a result, folding is described as a process by which a disordered protein chain diffuses across a high-dimensional energy landscape and finally reaches the folded ensemble. Folding studies have produced countless theoretical concepts that are generalizable to other biomolecular processes, such as the functional dynamics of molecular assemblies. Common themes in folding and function include the dominant role of excluded volume, that a balance between energetic roughness and geometrical effects guides dynamics, and that folding/functional landscapes are relatively smooth. Here, we discuss how insights into protein folding have been applied to investigate the functional dynamics of biomolecular assemblies.

The growth of filaments under macromolecular confinement using scaling theory

Macromolecular confinement regulates the growth rate, structure, and length of the filaments, which can be quantitatively described using scaling theory.

Folding simulation of Trp-cage utilizing a new AMBER compatible force field with coupled main chain torsions

A newly developed AMBER compatible force field with coupled backbone torsion potential terms (AMBER032D) is utilized in a folding simulation of a mini-protein Trp-cage. Through replica exchange and direct molecular dynamics (MD) simulations, a multi-step folding mechanism with a synergetic folding of the hydrophobic core (HPC) and the α-helix in the final stage is suggested. The native structure has the lowest free energy and the melting temperature predicted from the specific heat capacity Cvis only 12 K higher than the experimental measurement. This study, together with our previous study, shows that AMBER032Dis an accurate force field that can be used for protein folding simulations.

Simulating movement of tRNA through the ribosome during hybrid-state formation

Biomolecular simulations provide a means for exploring the relationship between flexibility, energetics, structure, and function. With the availability of atomic models from X-ray crystallography and cryoelectron microscopy (cryo-EM), and rapid increases in computing capacity, it is now possible to apply molecular dynamics (MD) simulations to large biomolecular machines, and systematically partition the factors that contribute to function. A large biomolecular complex for which atomic models are available is the ribosome. In the cell, the ribosome reads messenger RNA (mRNA) in order to synthesize proteins. During this essential process, the ribosome undergoes a wide range of conformational rearrangements. One of the most poorly understood transitions is translocation: the process by which transfer RNA (tRNA) molecules move between binding sites inside of the ribosome. The first step of translocation is the adoption of a "hybrid" configuration by the tRNAs, which is accompanied by large-scale rotations in the ribosomal subunits. To illuminate the relationship between these rearrangements, we apply MD simulations using a multi-basin structure-based (SMOG) model, together with targeted molecular dynamics protocols. From 120 simulated transitions, we demonstrate the viability of a particular route during P/E hybrid-state formation, where there is asynchronous movement along rotation and tRNA coordinates. These simulations not only suggest an ordering of events, but they highlight atomic interactions that may influence the kinetics of hybrid-state formation. From these simulations, we also identify steric features (H74 and surrounding residues) encountered during the hybrid transition, and observe that flexibility of the single-stranded 3'-CCA tail is essential for it to reach the endpoint. Together, these simulations provide a set of structural and energetic signatures that suggest strategies for modulating the physical-chemical properties of protein synthesis by the ribosome.

Reaching new levels of realism in modeling biological macromolecules in cellular environments

An increasing number of studies are aimed at modeling cellular environments in a comprehensive and realistic fashion. A major challenge in these efforts is how to bridge spatial and temporal scales over many orders of magnitude. Furthermore, there are additional challenges in integrating different aspects ranging from questions about biomolecular stability in crowded environments to the description of reactive processes on cellular scales. In this review, recent studies with models of biomolecules in cellular environments at different levels of detail are discussed in terms of their strengths and weaknesses. In particular, atomistic models, implicit representations of cellular environments, coarse-grained and spheroidal models of biomolecules, as well as the inclusion of reactive processes via reaction-diffusion models are described. Furthermore, strategies for integrating the different models into a comprehensive description of cellular environments are discussed.

Where soft matter meets living matter--protein structure, stability, and folding in the cell

A protein is a biopolymer that self-assembles through the process of protein folding. A cell is a crowded space where the surrounding macromolecules of a protein can limit the number of ways of folding. These crowding macromolecules can also affect the shape and the size of a physically malleable, or 'soft, squishy', protein with regulatory purposes. In this review, we focus on the in silico approaches of coarse-grained molecular simulations that enable the investigation of protein folding in a cell-like environment. When these simulation results were compared with experimentally measured properties of a protein, such joint effort has yielded new ideas on the specific function of a protein in cells. We also highlighted the recent developments of computer modeling and simulations that encompass the importance of the shape of a macromolecule, the interactions between macromolecules, and the hydrodynamic interactions on the kinetics and thermodynamics of a protein in a high concentration of protein solution and in cytoplasmic environments.

Inactivation of recombinant human brain-type creatine kinase during denaturation by guanidine hydrochloride in a macromolecular crowding system

In this study, we quantitatively examined the effects of the macromolecular crowding agents, polyethylene glycol 2000 (PEG 2000) and dextran 70, on guanidine hydrochloride (GdnHCl)-induced denaturation of recombinant human brain-type creatine kinase (rHBCK). Our results showed that both PEG 2000 and dextran 70 had a protective effect on the inactivation of rHBCK induced by 0.5 M GdnHCl at 25 °C. The presence of 200 g/L PEG 2000 resulted in the retention of 35.33 % of rHBCK activity after 4 h of inactivation, while no rHBCK activity was observed after denaturation in the absence of macromolecular crowding agents. The presence of PEG 2000 and dextran 70 at a concentration of 100 g/L could decelerate the k (2) value of the slow track to 21 and 33 %, respectively, in comparison to values obtained in the absence of crowding agents. Interestingly, inactivation of rHBCK in the presence of 200 g/L PEG 2000 followed first-order monophasic kinetics, with an apparent rate constant of 8 × 10(-5) s(-1). The intrinsic fluorescence results showed that PEG 2000 was better than dextran 70 at stabilizing rHBCK conformation. In addition, the results of the phase diagram indicate that more intermediates may be captured when rHBCK is denatured in a macromolecular crowding system. Mixed crowding agents did not produce better results than single crowding agents, but the protective effects of PEG 2000 on the inactivation and unfolding of rHBCK tended to increase as the ratio of PEG 2000 increased in the mixed crowding agent solution. Though it is not clear which crowding agents more accurately simulated the intracellular environment, this study could lead to a better understanding of protein unfolding in the intracellular environment.

Biomolecular dynamics: order-disorder transitions and energy landscapes

While the energy landscape theory of protein folding is now a widely accepted view for understanding how relatively weak molecular interactions lead to rapid and cooperative protein folding, such a framework must be extended to describe the large-scale functional motions observed in molecular machines. In this review, we discuss (1) the development of the energy landscape theory of biomolecular folding, (2) recent advances toward establishing a consistent understanding of folding and function and (3) emerging themes in the functional motions of enzymes, biomolecular motors and other biomolecular machines. Recent theoretical, computational and experimental lines of investigation have provided a very dynamic picture of biomolecular motion. In contrast to earlier ideas, where molecular machines were thought to function similarly to macroscopic machines, with rigid components that move along a few degrees of freedom in a deterministic fashion, biomolecular complexes are only marginally stable. Since the stabilizing contribution of each atomic interaction is on the order of the thermal fluctuations in solution, the rigid body description of molecular function must be revisited. An emerging theme is that functional motions encompass order-disorder transitions and structural flexibility provides significant contributions to the free energy. In this review, we describe the biological importance of order-disorder transitions and discuss the statistical-mechanical foundation of theoretical approaches that can characterize such transitions.

Comparison of chemical and thermal protein denaturation by combination of computational and experimental approaches. II

Chemical and thermal denaturation methods have been widely used to investigate folding processes of proteins in vitro. However, a molecular understanding of the relationship between these two perturbation methods is lacking. Here, we combined computational and experimental approaches to investigate denaturing effects on three structurally different proteins. We derived a linear relationship between thermal denaturation at temperature T(b) and chemical denaturation at another temperature T(u) using the stability change of a protein (ΔG). For this, we related the dependence of ΔG on temperature, in the Gibbs-Helmholtz equation, to that of ΔG on urea concentration in the linear extrapolation method, assuming that there is a temperature pair from the urea (T(u)) and the aqueous (T(b)) ensembles that produces the same protein structures. We tested this relationship on apoazurin, cytochrome c, and apoflavodoxin using coarse-grained molecular simulations. We found a linear correlation between the temperature for a particular structural ensemble in the absence of urea, T(b), and the temperature of the same structural ensemble at a specific urea concentration, T(u). The in silico results agreed with in vitro far-UV circular dichroism data on apoazurin and cytochrome c. We conclude that chemical and thermal unfolding processes correlate in terms of thermodynamics and structural ensembles at most conditions; however, deviations were found at high concentrations of denaturant.

Crowding effects on the small, fast-folding protein lambda6-85

The microsecond folder lambda6-85 is a small (9.2 kDa = 9200 amu) five helix bundle protein. We investigated the stability of lambda6-85 in two different low-fluorescence crowding matrices: the large 70 kDa carbohydrate Ficoll 70, and the small 14 kDa thermophilic protein SubL. The same thermal stability of secondary structure was measured by circular dichroism in aqueous buffer, and at a crowding fraction phi = 15 +/- 1% of Ficoll 70. Tryptophan fluorescence detection (probing a tertiary contact) yielded the same thermal stability in Ficoll, but 4 degrees C lower in aqueous buffer. Temperature-jump kinetics revealed that the relaxation rate, corrected for bulk viscosity, was very similar in Ficoll and in aqueous buffer. Thus viscosity, hydrodynamics and crowding seem to compensate one another. However, a new fast phase was observed in Ficoll, attributed to crowding-induced downhill folding. We also measured the stability of lambda6-85 in phi = 14 +/- 1% SubL, which acts as a smaller more rigid crowder. Significantly greater stabilization (7 to 13 degrees C depending on probe) was observed than in the Ficoll matrix. The results highlight the importance of crowding agent choice for studies of small, fast-folding proteins amenable to comparison with molecular dynamics simulations.