How protein thermodynamics and folding mechanisms are altered by the chaperonin cage: molecular simulations

Investigation of Chemical Properties within Chaperonins in Stabilizing Substrate Protein Conformations Using Biomolecular Environment-Mimicking Model

Molecular chaperonins, such as GroEL/ES, are considered to assist in protein folding through both the confinement effect and chemical interactions provided by chaperonins themselves. Although the confinement effect on protein folding has been extensively investigated, the role of the chemical properties within chaperonins remains underexplored. To address this, we propose a Chaperonin Environment-Mimicking Model (CEMM) based on the effective radii and components of the GroEL/ES structure. Using enhanced molecular dynamics simulations, we compared the ability of CEMM with non-polar, polar uniform models and dilute environment to stabilize the experimental conformations of model substrate proteins. Consequently, the CEMM most effectively stabilized each experimental protein conformation, highlighting the importance of chemical properties within chaperonins in assisting protein folding. Furthermore, the analyses of the substrate proteins within each model suggest that the chemical diversity within chaperonins contributes to their ability to assist in protein folding.

Exploring Novel Antibiotics by Targeting the GroEL/GroES Chaperonin System

Infectious diseases have affected 13.7 million patients, placing a heavy burden on society. Furthermore, inappropriate and unrequited utilization of antibiotics has led to antimicrobial resistance worldwide. However, well-established targeted screening of environmental isolates or compound libraries has produced limited new drugs. The current situation, in which drug development is delayed, bacterial evolution is occurring, and drug resistance is emerging, requires the development of new targets and/or new strategies to combat infections. Some novel antibacterial strategies have been proposed, among which disruption of protein balance by inhibiting transcription and translation machinery is one of the proven effective antimicrobial strategies. Molecular chaperonins could mediate the correct folding of proteins, especially under conditions such as high temperature and pressure. The GroEL/ES system has been confirmed as one of the key molecular chaperones for bacterial viability. Recent data have revealed the antibacterial activities of GroEL/ES-targeted compounds, highlighting the potential role of GroEL/ES in the development of novel antibiotics. In this brief review, we discuss the function of the GroEL/ES system and summarize the inhibitors of the GroEL/ES system. The GroEL/ES system may represent a promising drug target for the exploration of novel antibiotics.

Scaling Laws for Protein Folding under Confinement

Spatial confinement significantly affects protein folding. Without the confinement provided by chaperones, many proteins cannot fold correctly. However, the quantitative effect of confinement on protein folding remains elusive. In this study, we observed scaling laws between the variation in folding transition temperature and the size of confinement, (Tf - Tfbulk)/Tfbulk ∼ L-ν. The scaling exponent v is significantly influenced by both the protein's topology and folding cooperativity. Specifically, for a given protein, v can decrease as the folding cooperativity of the model increases, primarily due to the heightened sensitivity of the unfolded state energy to changes in cage size. For proteins with diverse topologies, variations in topological complexity influence scaling exponents in multiple ways. Notably, v exhibits a clear positive correlation with contact order and the proportion of nonlocal contacts, as this complexity significantly enhances the sensitivity of entropy loss in the unfolded state. Furthermore, we developed a novel scaling argument yielding 5/3 ≤ ν ≤ 10/3, consistent with the simulation results.

Protecting Proteins from Desiccation Stress Using Molecular Glasses and Gels

Faced with desiccation stress, many organisms deploy strategies to maintain the integrity of their cellular components. Amorphous glassy media composed of small molecular solutes or protein gels present general strategies for protecting against drying. We review these strategies and the proposed molecular mechanisms to explain protein protection in a vitreous matrix under conditions of low hydration. We also describe efforts to exploit similar strategies in technological applications for protecting proteins in dry or highly desiccated states. Finally, we outline open questions and possibilities for future explorations.

Self-Assembled Artificial DNA Nanocompartments and Their Bioapplications

Compartmentalization is the strategy evolved by nature to control reactions in space and time. The ability to emulate this strategy through synthetic compartmentalization systems has rapidly evolved in the past years, accompanied by an increasing understanding of the effects of spatial confinement on the thermodynamic and kinetic properties of the guest molecules. DNA nanotechnology has played a pivotal role in this scientific endeavor and is still one of the most promising approaches for the construction of nanocompartments with programmable structural features and nanometer-scaled addressability. In this review, the design approaches, bioapplications, and theoretical frameworks of self-assembled DNA nanocompartments are surveyed. From DNA polyhedral cages to virus-like capsules, the construction principles of such intriguing architectures are illustrated. Various applications of DNA nanocompartments, including their use for programmable enzyme scaffolding, single-molecule studies, biosensing, and as artificial nanofactories, ending with an ample description of DNA nanocages for biomedical purposes, are then reported. Finally, the theoretical hypotheses that make DNA nanocompartments, and nanosystems in general, a topic of great interest in modern science, are described and the progresses that have been done until now in the comprehension of the peculiar phenomena that occur within nanosized environments are summarized.

Friends in need: How chaperonins recognize and remodel proteins that require folding assistance

Chaperonins are biological nanomachines that help newly translated proteins to fold by rescuing them from kinetically trapped misfolded states. Protein folding assistance by the chaperonin machinery is obligatory in vivo for a subset of proteins in the bacterial proteome. Chaperonins are large oligomeric complexes, with unusual seven fold symmetry (group I) or eight/nine fold symmetry (group II), that form double-ring constructs, enclosing a central cavity that serves as the folding chamber. Dramatic large-scale conformational changes, that take place during ATP-driven cycles, allow chaperonins to bind misfolded proteins, encapsulate them into the expanded cavity and release them back into the cellular environment, regardless of whether they are folded or not. The theory associated with the iterative annealing mechanism, which incorporated the conformational free energy landscape description of protein folding, quantitatively explains most, if not all, the available data. Misfolded conformations are associated with low energy minima in a rugged energy landscape. Random disruptions of these low energy conformations result in higher free energy, less folded, conformations that can stochastically partition into the native state. Two distinct mechanisms of annealing action have been described. Group I chaperonins (GroEL homologues in eubacteria and endosymbiotic organelles), recognize a large number of misfolded proteins non-specifically and operate through highly coordinated cooperative motions. By contrast, the less well understood group II chaperonins (CCT in Eukarya and thermosome/TF55 in Archaea), assist a selected set of substrate proteins. Sequential conformational changes within a CCT ring are observed, perhaps promoting domain-by-domain substrate folding. Chaperonins are implicated in bacterial infection, autoimmune disease, as well as protein aggregation and degradation diseases. Understanding the chaperonin mechanism and the specific proteins they rescue during the cell cycle is important not only for the fundamental aspect of protein folding in the cellular environment, but also for effective therapeutic strategies.

Macromolecular Crowding Is More than Hard-Core Repulsions

Cells are crowded, but proteins are almost always studied in dilute aqueous buffer. We review the experimental evidence that crowding affects the equilibrium thermodynamics of protein stability and protein association and discuss the theories employed to explain these observations. In doing so, we highlight differences between synthetic polymers and biologically relevant crowders. Theories based on hard-core interactions predict only crowding-induced entropic stabilization. However, experiment-based efforts conducted under physiologically relevant conditions show that crowding can destabilize proteins and their complexes. Furthermore, quantification of the temperature dependence of crowding effects produced by both large and small cosolutes, including osmolytes, sugars, synthetic polymers, and proteins, reveals enthalpic effects that stabilize or destabilize proteins. Crowding-induced destabilization and the enthalpic component point to the role of chemical interactions between and among the macromolecules, cosolutes, and water. We conclude with suggestions for future studies. Expected final online publication date for the Annual Review of Biophysics, Volume 51 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Spatiotemporal Control of Molecular Cascade Reactions by a Reconfigurable DNA Origami Domino Array

Inspired by efficient biomolecular reactions in the cell, versatile DNA nanostructures have been explored for manipulating the spatial position and regulating reactions at the molecular level. Spatially controlled arrangement of molecules on the artificial scaffolds generally leads to enhanced reaction activities. Especially, the rich toolset of dynamic DNA nanostructures provides a potential route towards more sophisticated and vigorous regulation of molecular reactions. Herein, reconfigurable DNA origami domino array (DODA) as dynamic scaffolds was adopted in this work for temporal-controlled and switchable molecular cascade reactions. Dynamic regulation of the assembly of G-quadruplex, hybridization of parallel-stranded duplex and assembly of binary DNAzyme were demonstrated. Molecular cascade reactions proceed on the triggered reconfiguration of DODAs were realized, resulting in more complex, dynamic, and switchable control over the reactions.

A general approach to protein folding using thermostable exoshells

In vitro protein folding is a complex process which often results in protein aggregation, low yields and low specific activity. Here we report the use of nanoscale exoshells (tES) to provide complementary nanoenvironments for the folding and release of 12 highly diverse protein substrates ranging from small protein toxins to human albumin, a dimeric protein (alkaline phosphatase), a trimeric ion channel (Omp2a) and the tetrameric tumor suppressor, p53. These proteins represent a unique diversity in size, volume, disulfide linkages, isoelectric point and multi versus monomeric nature of their functional units. Protein encapsulation within tES increased crude soluble yield (3-fold to >100-fold), functional yield (2-fold to >100-fold) and specific activity (3-fold to >100-fold) for all the proteins tested. The average soluble yield was 6.5 mg/100 mg of tES with charge complementation between the tES internal cavity and the protein substrate being the primary determinant of functional folding. Our results confirm the importance of nanoscale electrostatic effects and provide a solution for folding proteins in vitro.

β-Hairpin Miniprotein Stabilization in Trehalose Glass Is Facilitated by an Emergent Compact Non-Native State

From stem cell freeze-drying to organ storage, considerable recent efforts have been directed toward the development of new preservation technologies. A prominent protein stabilizing strategy involves vitrification in glassy matrices, most notably those formed of sugars such as the biologically relevant preservative trehalose. Here, we compare the folding thermodynamics of a model miniprotein in solution and in the glassy state of the sugars trehalose and glucose. Using synchrotron radiation circular dichroism (SRCD), we find that the same native structure persists in solution and glass. However, upon transition to the glass, a completely different, conformationally restricted unfolded state replaces the disordered denatured state found in solution, potentially inhibiting misfolding. Concomitantly, a large exothermic contribution is observed in glass, exposing the stabilizing effect of interactions with the sugar matrix on the native state. Our results shed light on the mechanism of protein stabilization in sugar glass and should aid in future preservation technologies.

Nascent Folding of Proteins Across the Three Domains of Life

We study the nascent behavior of three model coarse-grained proteins in six rigid all-atom structures representing ribosomes that come from three domains of life. The synthesis of the proteins is implemented as a growth process. The geometry of the exit tunnel is quantified and shown to differ between the domains of life: both in volume and the size of constriction sites. This results in different characteristic times of capture within the tunnel and various probabilities of the escape. One of the proteins studied is the bacterial YibK which is knotted in its native state. A fraction of the trajectories results in knotting and the probability of doing so is largest for the bacterial ribosomes. Relaxing the condition of the rigidness of the ribosomes should result in a better avoidance of trapping and better proper folding.

Energy landscape remodeling mechanism of Hsp70-chaperone-accelerated protein folding

Hsp70 chaperone is one of the key protein machines responsible for the quality control of protein production in cells. Facilitating in vivo protein folding by counteracting misfolding and aggregation is the essence of its biological function. Although the allosteric cycle during its functional actions has been well characterized both experimentally and computationally, the mechanism by which Hsp70 assists protein folding is still not fully understood. In this work, we studied the Hsp70-mediated folding of model proteins with rugged energy landscape by using molecular simulations. Different from the canonical scenario of Hsp70 functioning, which assumes that folding of substrate proteins occurs spontaneously after releasing from chaperones, our results showed that the substrate protein remains in contacts with the chaperone during its folding process. The direct chaperone-substrate interactions in the open conformation of Hsp70 tend to shield the substrate sites prone to form non-native contacts, which therefore avoids the frustrated folding pathway, leading to a higher folding rate and less probability of misfolding. Our results suggest that in addition to the unfoldase and holdase functions widely addressed in previous studies, Hsp70 can facilitate the folding of its substrate proteins by remodeling the folding energy landscape and directing the folding processes, demonstrating the foldase scenario. These findings add new, to our knowledge, insights into the general molecular mechanisms of chaperone-mediated protein folding.

Retardation of Folding Rates of Substrate Proteins in the Nanocage of GroEL

The Escherichia coli ATP-consuming chaperonin machinery, a complex between GroEL and GroES, has evolved to facilitate folding of substrate proteins (SPs) that cannot do so spontaneously. A series of kinetic experiments show that the SPs are encapsulated in the GroEL/ES nanocage for a short duration. If confinement of the SPs is the mechanism by which GroEL/ES facilitates folding, it follows that the assisted folding rate, relative to the bulk value, should always be enhanced. Here, we show that this is not the case for the folding of rhodanese in the presence of the full machinery of GroEL/ES and ATP. The assisted folding rate of rhodanese decreases. On the basis of our finding and those reported in other studies, we suggest that the ATP-consuming chaperonin machinery has evolved to optimize the product of the folding rate and the yield of the folded SPs on the biological time scale. Neither the rate nor the yield is separately maximized.

Duplex DNA Is Weakened in Nanoconfinement

For proteins and DNA secondary structures such as G-quadruplexes and i-motifs, nanoconfinement can facilitate their folding and increase structural stabilities. However, the properties of the physiologically prevalent B-DNA duplex have not been elucidated inside the nanocavity. Using a 17-bp DNA duplex in the form of a hairpin stem, here, we probed folding and unfolding transitions of the hairpin DNA duplex inside a DNA origami nanocavity. Compared to the free solution, the DNA hairpin inside the nanocage with a 15 × 15 nm cross section showed a drastic decrease in mechanical (20 → 9 pN) and thermodynamic (25 → 6 kcal/mol) stabilities. Free energy profiles revealed that the activation energy of unzipping the hairpin DNA duplex decreased dramatically (28 → 8 kcal/mol), whereas the transition state moved closer to the unfolded state inside the nanocage. All of these indicate that nanoconfinement weakens the stability of the hairpin DNA duplex to an unexpected extent. In a DNA hairpin made of a stem that contains complementary telomeric G-quadruplex (GQ) and i-motif (iM) forming sequences, formation of the Hoogsteen base pairs underlining the GQ or iM is preferred over the Watson-Crick base pairs in the DNA hairpin. These results shed light on the behavior of DNA in nanochannels, nanopores, or nanopockets of various natural or synthetic machineries. It also elucidates an alternative pathway to populate noncanonical DNA over B-DNA in the cellular environment where the nanocavity is abundant.

All-or-none folding of a flexible polymer chain in cylindrical nanoconfinement

Geometric confinement of a polymer chain results in a loss of conformational entropy. For a chain that can fold into a compact native state via a first-order-like transition, as is the case for many small proteins, confinement typically provides an entropic stabilization of the folded state, thereby shifting the location of the transition. This allows for the possibility of confinement (entropy) driven folding. Here, we investigate such confinement effects for a flexible square-well-sphere N-mer chain (monomer diameter σ) confined within a long cylindrical pore (diameter D) or a closed cylindrical box (height H = D). We carry out Wang-Landau simulations to construct the density of states, which provides access to the complete thermodynamics of the system. For a wide pore, an entropic stabilization of the folded state is observed. However, as the pore diameter approaches the size of the folded chain (D ∼ N^1/3σ), we find a destabilization effect. For pore diameters smaller than the native ground-state, the chain folds into a different, higher energy, ground state ensemble and the T vs D phase diagram displays non-monotonic behavior as the system is forced into different ground states for different ranges of D. In this regime, isothermal reduction of the confinement dimension can induce folding, unfolding, or crystallite restructuring. For the cylindrical box, we find a monotonic stabilization effect with decreasing D. Scaling laws for the confinement free energy in the athermal limit are also investigated.

Chaperonin-assisted protein folding: a chronologue

This chronologue seeks to document the discovery and development of an understanding of oligomeric ring protein assemblies known as chaperonins that assist protein folding in the cell. It provides detail regarding genetic, physiologic, biochemical, and biophysical studies of these ATP-utilizing machines from both in vivo and in vitro observations. The chronologue is organized into various topics of physiology and mechanism, for each of which a chronologic order is generally followed. The text is liberally illustrated to provide firsthand inspection of the key pieces of experimental data that propelled this field. Because of the length and depth of this piece, the use of the outline as a guide for selected reading is encouraged, but it should also be of help in pursuing the text in direct order.

Confinement and Crowding Effects on Folding of a Multidomain Y-Family DNA Polymerase

Proteins in vivo endure highly various interactions from the luxuriant surrounding macromolecular cosolutes. Confinement and macromolecular crowding are the two major effects that should be considered while comparing the results of protein dynamics from in vitro to in vivo. However, efforts have been largely focused on single domain protein folding up to now, and the quantifications of the in vivo effects in terms of confinements and crowders on modulating the structure and dynamics as well as the physical understanding of the underlying mechanisms on multidomain protein folding are still challenging. Here we developed a topology-based model to investigate folding of a multidomain Y-family DNA polymerase (DPO4) within spherical confined space and in the presence of repulsive and attractive crowders. We uncovered that the entropic component of the thermodynamic driving force led by confinements and repulsive crowders increases the stability of folded states relative to the folding intermediates and unfolded states, while the enthalpic component of the thermodynamic driving force led by attractive crowders gives rise to the opposite effects with less stability. We found that the shapes of DPO4 conformations influenced by the confinements and the crowders are quite different even when only the entropic component of the thermodynamic driving force is considered. We uncovered that under all in vivo conditions, the folding cooperativity of DPO4 decreases compared to that in bulk. We showed that the loss of folding cooperativity can promote the sequential domain-wise folding, which was widely found in cotranslational multidomain protein folding, and effectively prohibit the backtracking led by topological frustrations during multidomain protein folding processes.

Computational methods in the study of self-entangled proteins: a critical appraisal

The existence of self-entangled proteins, the native structure of which features a complex topology, unveils puzzling, and thus fascinating, aspects of protein biology and evolution. The discovery that a polypeptide chain can encode the capability to self-entangle in an efficient and reproducible way during folding, has raised many questions, regarding the possible function of these knots, their conservation along evolution, and their role in the folding paradigm. Understanding the function and origin of these entanglements would lead to deep implications in protein science, and this has stimulated the scientific community to investigate self-entangled proteins for decades by now. In this endeavour, advanced experimental techniques are more and more supported by computational approaches, that can provide theoretical guidelines for the interpretation of experimental results, and for the effective design of new experiments. In this review we provide an introduction to the computational study of self-entangled proteins, focusing in particular on the methodological developments related to this research field. A comprehensive collection of techniques is gathered, ranging from knot theory algorithms, that allow detection and classification of protein topology, to Monte Carlo or molecular dynamics strategies, that constitute crucial instruments for investigating thermodynamics and kinetics of this class of proteins.

Hydrophobic confinement modulates thermal stability and assists knotting in the folding of tangled proteins

There is growing support for the idea that the in vivo folding process of knotted proteins is assisted by chaperonins, but the mechanism of chaperonin assisted folding remains elusive. Here, we conduct extensive Monte Carlo simulations of lattice and off-lattice models to explore the effects of confinement and hydrophobic intermolecular interactions with the chaperonin cage in the folding and knotting processes. We find that moderate to high protein-cavity interactions (which are likely to be established in the beginning of the chaperonin working cycle) cause an energetic destabilization of the protein that overcomes the entropic stabilization driven by excluded volume, and leads to a decrease of the melting temperature relative to bulk conditions. Moreover, mild-to-moderate hydrophobic interactions with the cavity (which would be established later in the cycle) lead to a significant enhancement of knotting probability in relation to bulk conditions while simultaneously moderating the effect of steric confinement in the enhancement of thermal stability. Our results thus indicate that the chaperonin may be able to assist knotting without simultaneously thermally stabilizing potential misfolded states to a point that would hamper productive folding thus compromising its functional role.

Single-Molecule Investigations of G-Quadruplex

The genome-wide occurrence of G-quadruplexes and their demonstrated biological activities call for detailed understanding on the stability and transition kinetics of the structures. Although the core structural element in a G-quadruplex is simple and requires only four tandem repeats of Guanine rich sequences, there is rather rich conformational diversity in this structure. Corresponding to this structural diversity, it displays involved transition kinetics within individual G-quadruplexes and complicated interconversion among different G-quadruplex species. Due to the inherently high signal-to-noise ratio in the measurement, single-molecule tools offer a unique capability to investigate the thermodynamic, kinetic, and mechanical properties of G-quadruplexes with dynamic conformations. In this chapter, we describe different single molecule methods such as atomic-force microscopy (AFM), single-molecule fluorescence resonance energy transfer (smFRET), optical, magnetic, and magneto-optical tweezers to investigate G-quadruplex structures as well as their interactions with small-molecule ligands.

Chaperonin facilitates protein folding by avoiding initial polypeptide collapse

Chaperonins assist folding of many cellular proteins, including essential proteins for cell viability. However, it remains unclear how chaperonin-assisted folding is different from spontaneous folding. Chaperonin GroEL/GroES facilitates folding of denatured protein encapsulated in its central cage but the denatured protein often escapes from the cage to the outside during reaction. Here, we show evidence that the in-cage-folding and the escape occur diverging from the same intermediate complex in which polypeptide is tethered loosely to the cage and partly protrudes out of the cage. Furthermore, denatured proteins in the chaperonin cage are kept in more extended conformation than those initially formed in spontaneous folding. We propose that the formation of tethered intermediate of polypeptide is necessary to prevent polypeptide collapse at the expense of polypeptide escape. The tethering of polypeptide would allow freely mobile portions of tethered polypeptide to fold segmentally.

Effect of the geometry of confining media on the stability and folding rate of α -helix proteins

Protein folding in confined media has attracted wide attention over the past 15 years due to its importance to both in vivo and in vitro applications. It is generally believed that protein stability increases by decreasing the size of the confining medium, if the medium's walls are repulsive, and that the maximum folding temperature in confinement is in a pore whose size D ₀ is only slightly larger than the smallest dimension of a protein's folded state. Until recently, the stability of proteins in pores with a size very close to that of the folded state has not received the attention it deserves. In a previous paper [L. Javidpour and M. Sahimi, J. Chem. Phys. 135, 125101 (2011)], we showed that, contrary to the current theoretical predictions, the maximum folding temperature occurs in larger pores for smaller α-helices. Moreover, in very tight pores, the free energy surface becomes rough, giving rise to a new barrier for protein folding close to the unfolded state. In contrast to unbounded domains, in small nanopores proteins with an α-helical native state that contain the β structures are entropically stabilized implying that folding rates decrease notably and that the free energy surface becomes rougher. In view of the potential significance of such results to interpretation of many sets of experimental data that could not be explained by the current theories, particularly the reported anomalously low rates of folding and the importance of entropic effects on proteins' misfolded states in highly confined environments, we address the following question in the present paper: To what extent the geometry of a confined medium affects the stability and folding rates of proteins? Using millisecond-long molecular dynamics simulations, we study the problem in three types of confining media, namely, cylindrical and slit pores and spherical cavities. Most importantly, we find that the prediction of the previous theories that the dependence of the maximum folding temperature T _f on the size D of a confined medium occurs in larger media for larger proteins is correct only in spherical geometry, whereas the opposite is true in the two other geometries that we study. Also studied is the effect of the strength of the interaction between the confined media's walls and the proteins. If the walls are only weakly or moderately attractive, a complex behavior emerges that depends on the size of the confining medium.

The folding pathways and thermodynamics of semiflexible polymers

Inspired by the protein folding and DNA packing, we have systematically studied the thermodynamic and kinetic behaviors of single semiflexible homopolymers by Langevin dynamics simulations. In line with experiments, a rich variety of folding products, such as rod-like bundles, hairpins, toroids, and a mixture of them, are observed in the complete diagram of states. Moreover, knotted structures with a significant population are found in a certain range of bending stiffness in thermal equilibrium. As the solvent quality becomes poorer, the population of the intermediate occurring in the folding process increases, which leads to a severe chevron rollover for the folding arm. However, the population of the intermediates in the unfolding process is very low, insufficient to induce unfolding arm rollover. The total types of folding pathways from the coil state to the toroidal state for a semiflexible polymer chain remain unchanged by varying the solvent quality or temperature, whereas the kinetic partitioning into different folding events can be tuned significantly. In the process of knotting, three types of mechanisms, namely, plugging, slipknotting, and sliding, are discovered. Along the folding evolution, a semiflexible homopolymer chain can knot at any stage of folding upon leaving the extended coil state, and the probability to find a knot increases with chain compactness. In addition, we find rich types of knotted topologies during the folding of a semiflexible homopolymer chain. This study should be helpful in gaining insight into the general principles of biopolymer folding.

Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions

We introduce new Langevin-type equations describing the rotational and translational motion of rigid bodies interacting through conservative and non-conservative forces and hydrodynamic coupling. In the absence of non-conservative forces, the Langevin-type equations sample from the canonical ensemble. The rotational degrees of freedom are described using quaternions, the lengths of which are exactly preserved by the stochastic dynamics. For the proposed Langevin-type equations, we construct a weak 2nd order geometric integrator that preserves the main geometric features of the continuous dynamics. The integrator uses Verlet-type splitting for the deterministic part of Langevin equations appropriately combined with an exactly integrated Ornstein-Uhlenbeck process. Numerical experiments are presented to illustrate both the new Langevin model and the numerical method for it, as well as to demonstrate how inertia and the coupling of rotational and translational motion can introduce qualitatively distinct behaviours.

The exclusive effects of chaperonin on the behavior of proteins with 52 knot

The folding of proteins with a complex knot is still an unresolved question. Based on representative members of Ubiquitin C-terminal Hydrolases (UCHs) that contain the 5₂ knot in the native state, we explain how UCHs are able to unfold and refold in vitro reversibly within the structure-based model. In particular, we identify two, topologically different folding/unfolding pathways and corroborate our results with experiment, recreating the chevron plot. We show that confinement effect of chaperonin or weak crowding greatly facilitates folding, simultaneously slowing down the unfolding process of UCHs, compared with bulk conditions. Finally, we analyze the existence of knots in the denaturated state of UCHs. The results of the work show that the crowded environment of the cell should have a positive effect on the kinetics of complex knotted proteins, especially when proteins with deeper knots are found in this family.

Self-tying of knotted proteins remains a challenge both for theoreticians and experimentalist. In this work, we study the proteins with complex, the 5₂ knot, in a bulk and confined within a chaperonin box. We show that in our model we recreate the experimental results, identify two topologically distinct folding pathways and explain the beneficial role of confinement for complex knotted proteins. Encapsulation provides a possibility to fold via alternative pathway—folding via trefoil intermediate knot (N-terminal pathway) from entropic reason while folding via the C-terminal (direct tying) appears with the same probability. The results of this work show, how crowded environment in the real cell may enhance self-tying of proteins. The results are also the first step to the identification of possible oligomerization-prone forms of UCHs, which may cause neurodegenerative diseases.

Steric confinement and enhanced local flexibility assist knotting in simple models of protein folding

The chaperonin complex GroEL-GroES is able to accelerate the folding process of knotted proteins considerably. However, the folding mechanism inside the chaperonin cage is elusive. Here we use a combination of lattice and off-lattice Monte Carlo simulations of simple Gō models to study the effect of physical confinement and local flexibility on the folding process of protein model systems embedding a trefoil knot in their native structure. This study predicts that steric confinement plays a specific role in the folding of knotted proteins by increasing the knotting probability for very high degrees of confinement. This effect is observed for protein MJ0366 even above the melting temperature for confinement sizes compatible with the size of the GroEL/GroES chaperonin cage. An enhanced local flexibility produces the same qualitative effects on the folding process. In particular, we observe that knotting probability increases up to 40% in the transition state of protein MJ0366 when flexibility is enhanced. This is underlined by a structural change in the transition state, which becomes devoid of helical content. No relation between the knotting mechanism and flexibility was found in the context of the off-lattice model adopted in this work.

Topology of polymer chains under nanoscale confinement

Spatial confinement limits the conformational space accessible to biomolecules but the implications for bimolecular topology are not yet known. Folded linear biopolymers can be seen as molecular circuits formed by intramolecular contacts. The pairwise arrangement of intra-chain contacts can be categorized as parallel, series or cross, and has been identified as a topological property. Using molecular dynamics simulations, we determine the contact order distributions and topological circuits of short semi-flexible linear and ring polymer chains with a persistence length of l_p under a spherical confinement of radius R_c. At low values of l_p/R_c, the entropy of the linear chain leads to the formation of independent contacts along the chain and accordingly, increases the fraction of series topology with respect to other topologies. However, at high l_p/R_c, the fraction of cross and parallel topologies are enhanced in the chain topological circuits with cross becoming predominant. At an intermediate confining regime, we identify a critical value of l_p/R_c, at which all topological states have equal probability. Confinement thus equalizes the probability of more complex cross and parallel topologies to the level of the more simple, non-cooperative series topology. Moreover, our topology analysis reveals distinct behaviours for ring- and linear polymers under weak confinement; however, we find no difference between ring- and linear polymers under strong confinement. Under weak confinement, ring polymers adopt parallel and series topologies with equal likelihood, while linear polymers show a higher tendency for series arrangement. The radial distribution analysis of the topology reveals a non-uniform effect of confinement on the topology of polymer chains, thereby imposing more pronounced effects on the core region than on the confinement surface. Additionally, our results reveal that over a wide range of confining radii, loops arranged in parallel and cross topologies have nearly the same contact orders. Such degeneracy implies that the kinetics and transition rates between the topological states cannot be solely explained by contact order. We expect these findings to be of general importance in understanding chaperone assisted protein folding, chromosome architecture, and the evolution of molecular folds.

Confined space facilitates G-quadruplex formation

Molecular simulations suggest that the stability of a folded macromolecule increases in a confined space due to entropic effects. However, due to the interactions between the confined molecular structure and the walls of the container, clear-cut experimental evidence for this prediction is lacking. Here, using DNA origami nanocages, we show the pure effect of confined space on the property of individual human telomeric DNA G-quadruplexes. We induce targeted mechanical unfolding of the G-quadruplex while leaving the nanocage unperturbed. We find that the mechanical and thermodynamic stabilities of the G-quadruplex inside the nanocage increase with decreasing cage size. Compared to the case of diluted or molecularly crowded buffer solutions, the G-quadruplex inside the nanocage is significantly more stable, showing a 100 times faster folding rate. Our findings suggest the possibility of co-replicational or co-transcriptional folding of G-quadruplex inside the polymerase machinery in cells.

Knotting and unknotting proteins in the chaperonin cage: Effects of the excluded volume

Molecular dynamics simulations are used to explore the effects of chaperonin-like cages on knotted proteins with very low sequence similarity, different depths of a knot but with a similar fold, and the same type of topology. The investigated proteins are VirC2, DndE and MJ0366 with two depths of a knot. A comprehensive picture how encapsulation influences folding rates is provided based on the analysis of different cage sizes and temperature conditions. Neither of these two effects with regard to knotted proteins has been studied by means of molecular dynamics simulations with coarse-grained structure-based models before. We show that encapsulation in a chaperonin is sufficient to self-tie and untie small knotted proteins (VirC2, DndE), for which the equilibrium process is not accessible in the bulk solvent. Furthermore, we find that encapsulation reduces backtracking that arises from the destabilisation of nucleation sites, smoothing the free energy landscape. However, this effect can also be coupled with temperature rise. Encapsulation facilitates knotting at the early stage of folding and can enhance an alternative folding route. Comparison to unknotted proteins with the same fold shows directly how encapsulation influences the free energy landscape. In addition, we find that as the size of the cage decreases, folding times increase almost exponentially in a certain range of cage sizes, in accordance with confinement theory and experimental data for unknotted proteins.

Structural fluctuations and thermal stability of proteins in crowded environments: effects of the excluded volume

We perform molecular dynamics simulations for a simple coarse-grained model of a protein placed inside of a softly repulsive sphere of radius R. The protein is surrounded either by a number of same molecules or a number of spherical crowding particles that immitate other biomolecules such as the osmolytes. The two descriptions are shown to lead to distinct results when testing thermal stability as assessed by studying the unfolding times as a function of temperature. We consider three examples of proteins and show that crowding increases the thermal stability provided the inter-protein or protein-crowder interactions are repulsive. On the other hand, an introduction of attraction between the proteins is found to destabilize the proteins. Crowding by repulsive crowder particles is seen to enhance the RMSF in certain exposed regions. The effect grows on decreasing the size of the crowding particles. In the absence of crowding the RMSF anticorrelates with the coordination number related to the residue-residue interaction.

Determination of contact maps in proteins: A combination of structural and chemical approaches

Contact map selection is a crucial step in structure-based molecular dynamics modelling of proteins. The map can be determined in many different ways. We focus on the methods in which residues are represented as clusters of effective spheres. One contact map, denoted as overlap (OV), is based on the overlap of such spheres. Another contact map, named Contacts of Structural Units (CSU), involves the geometry in a different way and, in addition, brings chemical considerations into account. We develop a variant of the CSU approach in which we also incorporate Coulombic effects such as formation of the ionic bridges and destabilization of possible links through repulsion. In this way, the most essential and well defined contacts are identified. The resulting residue-residue contact map, dubbed repulsive CSU (rCSU), is more sound in its physico-chemical justification than CSU. It also provides a clear prescription for validity of an inter-residual contact: the number of attractive atomic contacts should be larger than the number of repulsive ones - a feature that is not present in CSU. However, both of these maps do not correlate well with the experimental data on protein stretching. Thus, we propose to use rCSU together with the OV map. We find that the combined map, denoted as OV+rCSU, performs better than OV. In most situations, OV and OV+rCSU yield comparable folding properties but for some proteins rCSU provides contacts which improve folding in a substantial way. We discuss the likely residue-specificity of the rCSU contacts. Finally, we make comparisons to the recently proposed shadow contact map, which is derived from different principles.

Role of denatured-state properties in chaperonin action probed by single-molecule spectroscopy

The bacterial chaperonin GroEL/GroES assists folding of a broad spectrum of denatured and misfolded proteins. Here, we explore the limits of this remarkable promiscuity by mapping two denatured proteins with very different conformational properties, rhodanese and cyclophilin A, during binding and encapsulation by GroEL/GroES with single-molecule spectroscopy, microfluidic mixing, and ensemble kinetics. We find that both proteins bind to GroEL with high affinity in a reaction involving substantial conformational adaptation. However, whereas the compact denatured state of rhodanese is encapsulated efficiently upon addition of GroES and ATP, the more expanded and unstructured denatured cyclophilin A is not encapsulated but is expelled into solution. The origin of this surprising disparity is the weaker interactions of cyclophilin A with a transiently formed GroEL-GroES complex, which may serve as a crucial checkpoint for substrate discrimination.

Thermodynamics and structure of macromolecules from flat-histogram Monte Carlo simulations

Over the last decade flat-histogram Monte Carlo simulations, especially multi-canonical and Wang-Landau simulations, have emerged as a strong tool to study the statistical mechanics of polymer chains. These investigations have focused on coarse-grained models of polymers on the lattice and in the continuum. Phase diagrams of chains in bulk as well as chains attached to surfaces were studied, for homopolymers as well as for protein-like models. Also, aggregation behavior in solution of these models has been investigated. We will present here the theoretical background for these simulations, explain the algorithms used and discuss their performance and give an overview over the systems studied with these methods in the literature, where we will limit ourselves to studies of coarse-grained model systems. Implementations of these algorithms on parallel computers will be also briefly described. In parallel to the development of these simulation methods, the power of a micro-canonical analysis of such simulations has been recognized, and we present the current state of the art in applying the micro-canonical analysis to phase transitions in nanoscopic polymer systems.

Searching target sites on DNA by proteins: Role of DNA dynamics under confinement

DNA-binding proteins (DBPs) rapidly search and specifically bind to their target sites on genomic DNA in order to trigger many cellular regulatory processes. It has been suggested that the facilitation of search dynamics is achieved by combining 3D diffusion with one-dimensional sliding and hopping dynamics of interacting proteins. Although, recent studies have advanced the knowledge of molecular determinants that affect one-dimensional search efficiency, the role of DNA molecule is poorly understood. In this study, by using coarse-grained simulations, we propose that dynamics of DNA molecule and its degree of confinement due to cellular crowding concertedly regulate its groove geometry and modulate the inter-communication with DBPs. Under weak confinement, DNA dynamics promotes many short, rotation-decoupled sliding events interspersed by hopping dynamics. While this results in faster 1D diffusion, associated probability of missing targets by jumping over them increases. In contrast, strong confinement favours rotation-coupled sliding to locate targets but lacks structural flexibility to achieve desired specificity. By testing under physiological crowding, our study provides a plausible mechanism on how DNA molecule may help in maintaining an optimal balance between fast hopping and rotation-coupled sliding dynamics, to locate target sites rapidly and form specific complexes precisely.

Statistical radii associated with amino acids to determine the contact map: fixing the structure of a type I cohesin domain in the Clostridium thermocellum cellulosome

We propose to improve and simplify protein refinement procedures through consideration of which pairs of amino acid residues should form native contacts. We first consider 11 330 proteins from the CATH database to determine statistical distributions of contacts associated with a given type of amino acid. The distributions are set across the distances between the α-C atoms that are in contact. Based on this data, we determine typical radii of effective spheres that can be placed on the α-C atoms in order to reconstruct the distribution of the contact lengths. This is done by checking for overlaps with enlarged van der Waals spheres associated with heavy atoms on other amino acids.The resulting contacts can be used to identify non-native contacts that may arise during the time evolution of structure-based models. Here, the radii are used to guide reconstruction of nine missing side chains in a type I cohesin domain with the Protein Data Bank code 1AOH. We first identify the likely missing contacts and then sculpt the corresponding side chains by standard refinement tools to achieve consistency with the expected contact map. One ambiguity in refinement is resolved by determining all-atom conformational energies.

Aggregation of theta-polymers in spherical confinement

We investigate the aggregation transition of theta polymers in spherical confinement with multicanonical simulations. This allows for a systematic study of the effect of density on the aggregation transition temperature for up to 24 monodisperse polymers. Our results for solutions in the dilute regime show that polymers can be considered isolated for all temperatures larger than the aggregation temperature, which is shown to be a function of the density. The resulting competition between single-polymer collapse and aggregation yields the lower temperature bound of the isolated chain approximation. We provide entropic and energetic arguments to describe the density dependence and finite-size effects of the aggregation transition for monodisperse solutions in finite systems. This allows us to estimate the aggregation transition temperature of dilute systems in a spherical cavity, using a few simulations of small, sufficiently dilute polymer systems.

How do chaperonins fold protein?

Protein folding is a biological process that is essential for the proper functioning of proteins in all living organisms. In cells, many proteins require the assistance of molecular chaperones for their folding. Chaperonins belong to a class of molecular chaperones that have been extensively studied. However, the mechanism by which a chaperonin mediates the folding of proteins is still controversial. Denatured proteins are folded in the closed chaperonin cage, leading to the assumption that denatured proteins are completely encapsulated inside the chaperonin cage. In contrast to the assumption, we recently found that denatured protein interacts with hydrophobic residues at the subunit interfaces of the chaperonin, and partially protrude out of the cage. In this review, we will explain our recent results and introduce our model for the mechanism by which chaperonins accelerate protein folding, in view of recent findings.

Comparative modeling of proteins

Much of the biochemistry that underlies health, medicine, and numerous biotechnology applications is regulated by proteins, whereby the ability of proteins to effect such processes is dictated by the three-dimensional structural assembly of the proteins. Thus, a detailed understanding of biochemistry requires not only knowledge of the constituent sequence of proteins, but also a detailed understanding of how that sequence folds spatially. Three-dimensional analysis of protein structures is thus proving to be a critical mode of biological and medical discovery in the early twenty-first century, providing fundamental insight into function that produces useful biochemistry and dysfunction that leads to disease. The large number of distinct proteins precludes rigorous laboratory characterization of the complete structural proteome, but fortunately efficient in silico structure prediction is possible for many proteins that have not been experimentally characterized. One technique that continues to provide accurate and efficient protein structure predictions, called comparative modeling, has become a critical tool in many biological disciplines. The discussion herein is an updated version of a previous 2008 treatise focusing on the general philosophy of comparative modeling methods and on specific strategies for successfully achieving reliable and accurate models. The chapter discusses basic aspects of template selection, sequence alignment, spatial alignment, loop and gap modeling, side chain modeling, structural refinement and validation, and provides an important new discussion on automated computational tools for protein structure prediction.

Segregation and phase inversion of strongly and weakly fluctuating Brownian particle mixtures and a chain of such particle mixtures in spherical containers

We investigate the segregation pattern formation of strongly and weakly fluctuating Brownian particle mixtures confined in a three-dimensional spherical container. We consider systems where the particle motion is restricted by the harmonic external trapping potential and the container edge wall. In such systems, two segregation patterns are observed. When the container radius is sufficiently large, more weakly fluctuating particles accumulate near the center of the container than strongly fluctuating particles. On the other hand, the distributions of the strongly and weakly fluctuating particles are inverted when the container radius is small. With no external trapping potentials, we find similar segregation and phase inversion if the particles construct a chain (heterofluctuating polymer) and are confined in a three-dimensional spherical container. We could apply these phenomena in the study of biopolymer behavior, such as chromosomes in the cell nucleus.

Mechanistic insights into the folding of knotted proteins in vitro and in vivo

The importance of knots and entanglements in biological systems is increasingly being realized and the number of proteins with topologically complex knotted structures has risen. However, the mechanism as to how these proteins knot and fold efficiently remains unclear. Using a cell-free expression system and pulse-proteolysis experiments, we have investigated the mechanism of knotting and folding for two bacterial trefoil-knotted methyltransferases. This study provides the first experimental evidence for a knotting mechanism. Results on fusions of stable protein domains to N-terminus, C-terminus or both termini of the knotted proteins clearly demonstrate that threading of the nascent chain through a knotting loop occurs via the C-terminus. Our results strongly suggest that this mechanism occurs even when the C-terminus is severely hindered by the addition of a large stable structure, in contrast to some simulations indicating that even the folding pathways of knotted proteins have some plasticity. The same strategy was employed to probe the effects of GroEL-GroES. In this case, results suggest active mechanisms for the molecular chaperonin. We demonstrate that a simple model in which GroEL-GroES sterically confines the unknotted polypeptide chain thereby promoting knotting is unlikely, and we propose two alternatives: (a) the chaperonin facilitates unfolding of kinetically and topologically trapped intermediates or (b) the chaperonin stabilizes interactions that promote knotting. These findings provide mechanistic insights into the folding of knotted proteins both in vitro and in vivo, thus elucidating how they have withstood evolutionary pressures regardless of their complex topologies and intrinsically slow folding rates.

Structural and mechanistic insights into the bacterial amyloid secretion channel CsgG

Curli are functional amyloid fibres that constitute the major protein component of the extracellular matrix in pellicle biofilms formed by Bacteroidetes and Proteobacteria (predominantly of the α and γ classes). They provide a fitness advantage in pathogenic strains and induce a strong pro-inflammatory response during bacteraemia. Curli formation requires a dedicated protein secretion machinery comprising the outer membrane lipoprotein CsgG and two soluble accessory proteins, CsgE and CsgF. Here we report the X-ray structure of Escherichia coli CsgG in a non-lipidated, soluble form as well as in its native membrane-extracted conformation. CsgG forms an oligomeric transport complex composed of nine anticodon-binding-domain-like units that give rise to a 36-stranded β-barrel that traverses the bilayer and is connected to a cage-like vestibule in the periplasm. The transmembrane and periplasmic domains are separated by a 0.9-nm channel constriction composed of three stacked concentric phenylalanine, asparagine and tyrosine rings that may guide the extended polypeptide substrate through the secretion pore. The specificity factor CsgE forms a nonameric adaptor that binds and closes off the periplasmic face of the secretion channel, creating a 24,000 Å(3) pre-constriction chamber. Our structural, functional and electrophysiological analyses imply that CsgG is an ungated, non-selective protein secretion channel that is expected to employ a diffusion-based, entropy-driven transport mechanism.

Effect of interactions with the chaperonin cavity on protein folding and misfolding

Recent experimental and computational results have suggested that attractive interactions between a chaperonin and an enclosed substrate can have an important effect on the protein folding rate: it appears that folding may even be slower inside the cavity than under unconfined conditions, in contrast to what we would expect from excluded volume effects on the unfolded state. Here we examine systematically the dependence of the protein stability and folding rate on the strength of such attractive interactions between the chaperonin and substrate, by using molecular simulations of model protein systems in an idealised attractive cavity. Interestingly, we find a maximum in stability, and a rate which indeed slows down at high attraction strengths. We have developed a simple phenomenological model which can explain the variations in folding rate and stability due to differing effects on the free energies of the unfolded state, folded state, and transition state; changes in the diffusion coefficient along the folding coordinate are relatively small, at least for our simplified model. In order to investigate a possible role for these attractive interactions in folding, we have studied a recently developed model for misfolding in multidomain proteins. We find that, while encapsulation in repulsive cavities greatly increases the fraction of misfolded protein, sufficiently strong attractive protein-cavity interactions can strongly reduce the fraction of proteins reaching misfolded traps.