Protein topology determines binding mechanism

Molecular mechanism of multispecific recognition of Calmodulin through conformational changes

Calmodulin (CaM) is found to have the capability to bind multiple targets. Investigations on the association mechanism of CaM to its targets are crucial for understanding protein-protein binding and recognition. Here, we developed a structure-based model to explore the binding process between CaM and skMLCK binding peptide. We found the cooperation between nonnative electrostatic interaction and nonnative hydrophobic interaction plays an important role in nonspecific recognition between CaM and its target. We also found that the conserved hydrophobic anchors of skMLCK and binding patches of CaM are crucial for the transition from high affinity to high specificity. Furthermore, this association process involves simultaneously both local conformational change of CaM and global conformational changes of the skMLCK binding peptide. We found a landscape with a mixture of the atypical "induced fit," the atypical "conformational selection," and "simultaneously binding-folding," depending on the synchronization of folding and binding. Finally, we extend our discussions on multispecific binding between CaM and its targets. These association characteristics proposed for CaM and skMLCK can provide insights into multispecific binding of CaM.

Binding of interferon reduces the force of unfolding for interferon receptor 1

Differential signaling of the type I interferon receptor (IFNAR) has been correlated with the ability of its subunit, IFNAR1, to differentially recognize a large spectrum of different ligands, which involves intricate conformational re-arrangements of multiple interacting domains. To shed light onto the structural determinants governing ligand recognition, we compared the force-induced unfolding of the IFNAR1 ectodomain when bound to interferon and when free, using the atomic force microscope and steered molecular dynamics simulations. Unexpectedly, we find that IFNAR1 is easier to mechanically unfold when bound to interferon than when free. Analysis of the structures indicated that the origin of the reduction in unfolding forces is a conformational change in IFNAR1 induced by ligand binding.

Mechanism of Human Apohemoglobin Unfolding

Removal of heme from human hemoglobin (Hb) results in formation of an apoglobin heterodimer. Titration of this apodimer with guanidine hydrochloride (GdnHCl) leads to biphasic unfolding curves indicating two distinct steps. Initially, the heme pocket unfolds and generates a dimeric intermediate in which ∼50% of the original helicity is lost, but the α₁β₁ interface is still intact. At higher GdnHCl concentrations, this intermediate dissociates into unfolded monomers. This structural interpretation was verified by comparing GdnHCl titrations for adult human hemoglobin A (HbA), recombinant fetal human hemoglobin (HbF), recombinant Hb cross-linked with a single glycine linker between the α chains, and recombinant Hbs with apolar heme pocket mutations that markedly stabilize native conformations in both subunits. The first phase of apoHb unfolding is independent of protein concentration, little affected by genetic cross-linking, but significantly shifted toward higher GdnHCl concentrations by the stabilizing distal pocket mutations. The second phase depends on protein concentration and is shifted to higher GdnHCl concentrations by genetic cross-linking. This model for apoHb unfolding allowed us to quantitate subtle differences in stability between apoHbA and apoHbF, which suggest that the β and γ heme pockets have similar stabilities, whereas the α₁γ₁ interface is more resistant to dissociation than the α₁β₁ interface.

Topological transformations in proteins: effects of heating and proximity of an interface

Using a structure-based coarse-grained model of proteins, we study the mechanism of unfolding of knotted proteins through heating. We find that the dominant mechanisms of unfolding depend on the temperature applied and are generally distinct from those identified for folding at its optimal temperature. In particular, for shallowly knotted proteins, folding usually involves formation of two loops whereas unfolding through high-temperature heating is dominated by untying of single loops. Untying the knots is found to generally precede unfolding unless the protein is deeply knotted and the heating temperature exceeds a threshold value. We then use a phenomenological model of the air-water interface to show that such an interface can untie shallow knots, but it can also make knots in proteins that are natively unknotted.

Scoring Functions of Protein-Ligand Interactions

Scoring function of protein-ligand interactions is used to recognize the “native” binding pose of a ligand on the protein and to predict the binding affinity, so that the active small molecules can be discriminated from the non-active ones. Scoring function is widely used in computationally molecular docking and structure-based drug discovery. The development and improvement of scoring functions have broad implications in pharmaceutical industry and academic research. During the past three decades, much progress have been made in methodology and accuracy for scoring functions, and many successful cases have be witnessed in virtual database screening. In this chapter, the authors introduced the basic types of scoring functions and their derivations, the commonly-used evaluation methods and benchmarks, as well as the underlying challenges and current solutions. Finally, the authors discussed the promising directions to improve and develop scoring functions for future molecular docking-based drug discovery.

Homodimeric Escherichia coli Toxin CcdB (Controller of Cell Division or Death B Protein) Folds via Parallel Pathways

The existence of parallel pathways in the folding of proteins seems intuitive, yet remains controversial. We explore the folding kinetics of the homodimeric Escherichia coli toxin CcdB (Controller of Cell Division or Death B protein) using multiple optical probes and approaches. Kinetic studies performed as a function of protein and denaturant concentrations demonstrate that the folding of CcdB is a four-state process. The two intermediates populated during folding are present on parallel pathways. Both form by rapid association of the monomers in a diffusion limited manner and appear to be largely unstructured, as they are silent to the optical probes employed in the current study. The existence of parallel pathways is supported by the insensitivity of the amplitudes of the refolding kinetic phases to the different probes used in the study. More importantly, interrupted refolding studies and ligand binding studies clearly demonstrate that the native state forms in a biexponential manner, implying the presence of at least two pathways. Our studies indicate that the CcdA antitoxin binds only to the folded CcdB dimer and not to any earlier folding intermediates. Thus, despite being part of the same operon, the antitoxin does not appear to modulate the folding pathway of the toxin encoded by the downstream cistron. This study highlights the utility of ligand binding in distinguishing between sequential and parallel pathways in protein folding studies, while also providing insights into molecular interactions during folding in Type II toxin-antitoxin systems.

A mechanism for propagated SOD1 misfolding from frustration analysis of a G85R mutant protein assembly

Application of landscape theory and the dehydron hypothesis to a crystal structure of a G85R mutant superoxide dismutase (SOD1) tetrameric complex allows for the description of a prion-like hypothesis that serves to explain propagated SOD1 misfolding. We have developed two conformational-change scenarios, one local to the ESL at the complex interface, and a second displacement at the ESL of the otherdimeric subunit. When taken together these provide for a prion-like mechanism that can serve to explain the observed conversion of wtSOD1 to a misfolded form by the G85R mutant.

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.

An Internal Disulfide Locks a Misfolded Aggregation-prone Intermediate in Cataract-linked Mutants of Human γD-Crystallin

Considerable mechanistic insight has been gained into amyloid aggregation; however, a large number of non-amyloid protein aggregates are considered "amorphous," and in most cases, little is known about their mechanisms. Amorphous aggregation of γ-crystallins in the eye lens causes cataract, a widespread disease of aging. We combined simulations and experiments to study the mechanism of aggregation of two γD-crystallin mutants, W42R and W42Q: the former a congenital cataract mutation, and the latter a mimic of age-related oxidative damage. We found that formation of an internal disulfide was necessary and sufficient for aggregation under physiological conditions. Two-chain all-atom simulations predicted that one non-native disulfide in particular, between Cys(32) and Cys(41), was likely to stabilize an unfolding intermediate prone to intermolecular interactions. Mass spectrometry and mutagenesis experiments confirmed the presence of this bond in the aggregates and its necessity for oxidative aggregation under physiological conditions in vitro Mining the simulation data linked formation of this disulfide to extrusion of the N-terminal β-hairpin and rearrangement of the native β-sheet topology. Specific binding between the extruded hairpin and a distal β-sheet, in an intermolecular chain reaction similar to domain swapping, is the most probable mechanism of aggregate propagation.

Energy Landscape Topography Reveals the Underlying Link Between Binding Specificity and Activity of Enzymes

Enzyme activity (often quantified by k_cat/K_m) is the main function of enzyme when it is active against the specific substrate. Higher or lower activities are highly desired for the design of novel enzyme and drug resistance. However, it is difficult to measure the activities of all possible variants and find the “hot-spot” within the limit of experimental time. In this study, we explore the underlying energy landscape of enzyme-substrate interactions and introduce the intrinsic specificity ratio (ISR), which reflects the landscape topography. By studying two concrete systems, we uncover the statistical correlation between the intrinsic specificity and the enzyme activity k_cat/K_m. This physics-based concept and method show that the energy landscape topography is valuable for understanding the relationship between enzyme specificity and activity. In addition, it can reveal the underlying mechanism of enzyme-substrate actions and has potential applications on enzyme design.

Protein Ensembles: How Does Nature Harness Thermodynamic Fluctuations for Life? The Diverse Functional Roles of Conformational Ensembles in the Cell

All soluble proteins populate conformational ensembles that together constitute the native state. Their fluctuations in water are intrinsic thermodynamic phenomena, and the distributions of the states on the energy landscape are determined by statistical thermodynamics; however, they are optimized to perform their biological functions. In this review we briefly describe advances in free energy landscape studies of protein conformational ensembles. Experimental (nuclear magnetic resonance, small-angle X-ray scattering, single-molecule spectroscopy, and cryo-electron microscopy) and computational (replica-exchange molecular dynamics, metadynamics, and Markov state models) approaches have made great progress in recent years. These address the challenging characterization of the highly flexible and heterogeneous protein ensembles. We focus on structural aspects of protein conformational distributions, from collective motions of single- and multi-domain proteins, intrinsically disordered proteins, to multiprotein complexes. Importantly, we highlight recent studies that illustrate functional adjustment of protein conformational ensembles in the crowded cellular environment. We center on the role of the ensemble in recognition of small- and macro-molecules (protein and RNA/DNA) and emphasize emerging concepts of protein dynamics in enzyme catalysis. Overall, protein ensembles link fundamental physicochemical principles and protein behavior and the cellular network and its regulation.

Structural Determinants of Misfolding in Multidomain Proteins

Recent single molecule experiments, using either atomic force microscopy (AFM) or Förster resonance energy transfer (FRET) have shown that multidomain proteins containing tandem repeats may form stable misfolded structures. Topology-based simulation models have been used successfully to generate models for these structures with domain-swapped features, fully consistent with the available data. However, it is also known that some multidomain protein folds exhibit no evidence for misfolding, even when adjacent domains have identical sequences. Here we pose the question: what factors influence the propensity of a given fold to undergo domain-swapped misfolding? Using a coarse-grained simulation model, we can reproduce the known propensities of multidomain proteins to form domain-swapped misfolds, where data is available. Contrary to what might be naively expected based on the previously described misfolding mechanism, we find that the extent of misfolding is not determined by the relative folding rates or barrier heights for forming the domains present in the initial intermediates leading to folded or misfolded structures. Instead, it appears that the propensity is more closely related to the relative stability of the domains present in folded and misfolded intermediates. We show that these findings can be rationalized if the folded and misfolded domains are part of the same folding funnel, with commitment to one structure or the other occurring only at a relatively late stage of folding. Nonetheless, the results are still fully consistent with the kinetic models previously proposed to explain misfolding, with a specific interpretation of the observed rate coefficients. Finally, we investigate the relation between interdomain linker length and misfolding, and propose a simple alchemical model to predict the propensity for domain-swapped misfolding of multidomain proteins.

Building a minimum frustration framework for brain functions over long time scales

The minimum frustration principle (MFP) is a computational approach stating that, over the long time scales of evolution, proteins' free energy decreases more than expected by thermodynamical constraints as their amino acids assume conformations progressively closer to the lowest energetic state. This Review shows that this general principle, borrowed from protein folding dynamics, can also be fruitfully applied to nervous function. Highlighting the foremost role of energetic requirements, macromolecular dynamics, and above all intertwined time scales in brain activity, the MFP elucidates a wide range of mental processes from sensations to memory retrieval. Brain functions are compared with trajectories that, over long nervous time scales, are attracted toward the low-energy bottom of funnel-like structures characterized by both robustness and plasticity. We discuss how the principle, derived explicitly from evolution and selection of a funneling structure from microdynamics of contacts, is unlike other brain models equipped with energy landscapes, such as the Bayesian and free energy principles and the Hopfield networks. In summary, we make available a novel approach to brain function cast in a biologically informed fashion, with the potential to be operationalized and assessed empirically. © 2016 Wiley Periodicals, Inc.

Interplay between binding affinity and kinetics in protein-protein interactions

To clarify the interplay between the binding affinity and kinetics of protein-protein interactions, and the possible role of intrinsically disordered proteins in such interactions, molecular simulations were carried out on 20 protein complexes. With bias potential and reweighting techniques, the free energy profiles were obtained under physiological affinities, which showed that the bound-state valley is deep with a barrier height of 12 - 33 RT. From the dependence of the affinity on interface interactions, the entropic contribution to the binding affinity is approximated to be proportional to the interface area. The extracted dissociation rates based on the Arrhenius law correlate reasonably well with the experimental values (Pearson correlation coefficient R = 0.79). For each protein complex, a linear free energy relationship between binding affinity and the dissociation rate was confirmed, but the distribution of the slopes for intrinsically disordered proteins showed no essential difference with that observed for ordered proteins. A comparison with protein folding was also performed. Proteins 2016; 84:920-933. © 2016 Wiley Periodicals, Inc.

Molecular Dynamics Simulations of Ligand-Induced Flap Conformational Changes in Cathepsin-D-A Comparative Study

The flap region in aspartic proteases is a unique structural feature to this class of enzymes, and found to have a profound impact on protein overall structure, function, and dynamics. Understanding the structure and dynamic behavior of the flap regions is crucial in the design of selective inhibitors against aspartic proteases. Cathepsin-D, an aspartic protease enzyme, has been implicated in a long list of degenerative diseases as well as breast cancer progression. Presented herein, for the first time, is a comprehensive description of the conformational flap dynamics of cathepsin-D using a comparative 50 ns "multiple" molecular dynamics simulations. Diverse collective metrics were proposed to accurately define flap dynamics. These are distance d1 between the flap tips residues (Gly79 and Met301); dihedral angle ϕ; in addition to TriCα angles Gly79-Asp33-Asp223, θ1 , and Gly79-Asp223-Met301, θ2 . The maximum distance attained throughout the simulation was 17.42 and 11.47 Å for apo and bound cathepsin-D, respectively, while the minimum distance observed was 8.75 and 6.32 Å for apo and bound cathepsin-D, respectively. The movement of the flap as well as the twist of the active pocket can properly be explained by measuring the angle, θ1 , between Gly79-Asp33-Met301 and correlating it with the distance Cα of the flap tip residues. The asymmetrical opening of the binding cavity was best described by the large shift of -6.26° to +20.94° in the dihedral angle, ϕ, corresponding to the full opening of the flap at a range of 31-33 ns. A wide-range of post-dynamic analyses was also applied in this report to supplement our findings. We believe that this report would augment current efforts in designing potent structure-based inhibitors against cathepsin-D in the treatment of breast cancer and other degenerative diseases. J. Cell. Biochem. 117: 2643-2657, 2016. © 2016 Wiley Periodicals, Inc.

Universal statistical fluctuations in thermodynamics and kinetics of single molecular recognition

We investigated the main universal statistical distributions of single molecular recognition. The distributions of the single molecule binding free energy spectrum or density of states were characterized in the ligand-receptor binding energy landscape. The analytical results are consistent with the microscopic molecular simulations. The free energy distribution of different binding modes or states for a single molecule ligand receptor pair is approximately Gaussian near the mean and exponential at the tail. The equilibrium constant of single molecule binding is log-normal distributed near the mean and power law distributed near the tail. Additionally, we found that the kinetics distribution of single molecule ligand binding can be characterized by log-normal around the mean and power law distribution near the tail. This distribution is caused by exploration of the underlying inhomogeneous free energy landscape. Different ligand-receptor binding complexes have the same universal form of distribution but differ in parameters.

SMOG 2: A Versatile Software Package for Generating Structure-Based Models

Molecular dynamics simulations with coarse-grained or simplified Hamiltonians have proven to be an effective means of capturing the functionally important long-time and large-length scale motions of proteins and RNAs. Originally developed in the context of protein folding, structure-based models (SBMs) have since been extended to probe a diverse range of biomolecular processes, spanning from protein and RNA folding to functional transitions in molecular machines. The hallmark feature of a structure-based model is that part, or all, of the potential energy function is defined by a known structure. Within this general class of models, there exist many possible variations in resolution and energetic composition. SMOG 2 is a downloadable software package that reads user-designated structural information and user-defined energy definitions, in order to produce the files necessary to use SBMs with high performance molecular dynamics packages: GROMACS and NAMD. SMOG 2 is bundled with XML-formatted template files that define commonly used SBMs, and it can process template files that are altered according to the needs of each user. This computational infrastructure also allows for experimental or bioinformatics-derived restraints or novel structural features to be included, e.g. novel ligands, prosthetic groups and post-translational/transcriptional modifications. The code and user guide can be downloaded at http://smog-server.org/smog2.

Coupled folding and binding with 2D Window-Exchange Umbrella Sampling

Intrinsically disordered regions of proteins can gain structure by binding to a partner. This process, of coupled folding and binding (CFaB), is a fundamental part of many important biological processes. Structure-based models have proven themselves capable of revealing fundamental aspects of how CFaB occurs, however, typical methods to enhance the sampling of these transitions, such as replica exchange, do not adequately sample the transition state region of this extremely rare process. Here, we use a variant of Umbrella Sampling to enforce sampling of the transition states of CFaB of HdeA monomers at neutral pH, an extremely rare process that occurs over timescales ranging from seconds to hours. Using high resolution sampling in the transition state region, we cluster states along the principal transition path to obtain a detailed description of coupled binding and folding for the HdeA dimer, revealing new insight into the ensemble of states that are accessible to client recognition. We then demonstrate that exchanges between umbrella sampling windows, as done in previous work, significantly improve relaxation in variables orthogonal to the restraints used. Altogether, these results show that Window-Exchange Umbrella Sampling is a promising approach for systems that exhibit flexible binding, and can reveal transition state ensembles of these systems in high detail. © 2015 Wiley Periodicals, Inc.

The folding unit of phosphofructokinase-2 as defined by the biophysical properties of a monomeric mutant

Escherichia coli phosphofructokinase-2 (Pfk-2) is an obligate homodimer that follows a highly cooperative three-state folding mechanism N2 ↔ 2I ↔ 2U. The strong coupling between dissociation and unfolding is a consequence of the structural features of its interface: a bimolecular domain formed by intertwining of the small domain of each subunit into a flattened β-barrel. Although isolated monomers of E. coli Pfk-2 have been observed by modification of the environment (changes in temperature, addition of chaotropic agents), no isolated subunits in native conditions have been obtained. Based on in silico estimations of the change in free energy and the local energetic frustration upon binding, we engineered a single-point mutant to destabilize the interface of Pfk-2. This mutant, L93A, is an inactive monomer at protein concentrations below 30 μM, as determined by analytical ultracentrifugation, dynamic light scattering, size exclusion chromatography, small-angle x-ray scattering, and enzyme kinetics. Active dimer formation can be induced by increasing the protein concentration and by addition of its substrate fructose-6-phosphate. Chemical and thermal unfolding of the L93A monomer followed by circular dichroism and dynamic light scattering suggest that it unfolds noncooperatively and that the isolated subunit is partially unstructured and marginally stable. The detailed structural features of the L93A monomer and the F6P-induced dimer were ascertained by high-resolution hydrogen/deuterium exchange mass spectrometry. Our results show that the isolated subunit has overall higher solvent accessibility than the native dimer, with the exception of residues 240-309. These residues correspond to most of the β-meander module and show the same extent of deuterium uptake as the native dimer. Our results support the idea that the hydrophobic core of the isolated monomer of Pfk-2 is solvent-penetrated in native conditions and that the β-meander module is not affected by monomerizing mutations.

Topological constraints and modular structure in the folding and functional motions of GlpG, an intramembrane protease

We investigate the folding of GlpG, an intramembrane protease, using perfectly funneled structure-based models that implicitly account for the absence or presence of the membrane. These two models are used to describe, respectively, folding in detergent micelles and folding within a bilayer, which effectively constrains GlpG's topology in unfolded and partially folded states. Structural free-energy landscape analysis shows that although the presence of multiple folding pathways is an intrinsic property of GlpG's modular functional architecture, the large entropic cost of organizing helical bundles in the absence of the constraining bilayer leads to pathways that backtrack (i.e., local unfolding of previously folded substructures is required when moving from the unfolded to the folded state along the minimum free-energy pathway). This backtracking explains the experimental observation of thermodynamically destabilizing mutations that accelerate GlpG's folding in detergent micelles. In contrast, backtracking is absent from the model when folding is constrained within a bilayer, the environment in which GlpG has evolved to fold. We also characterize a near-native state with a highly mobile transmembrane helix 5 (TM5) that is significantly populated under folding conditions when GlpG is embedded in a bilayer. Unbinding of TM5 from the rest of the structure exposes GlpG's active site, consistent with studies of the catalytic mechanism of GlpG that suggest that TM5 serves as a substrate gate to the active site.

Cytochrome unfolding pathways from computational analysis of crystal structures

We have developed a model to study the role of geometrical factors in influencing the early stages of unfolding in three cytochromes: cyt c', cyt c-b562 and cyt c. Each stage in unfolding is quantified by the spatial extension λ̂i of n-residue segments, and by their angular extension 〈βn〉. Similarities and differences between and among the three cytochromes in the unfolding of helical and non-helical regions can be determined by analyzing the data for each signature separately. Definite conclusions can be drawn when spatial and angular changes are considered in tandem. To facilitate comparisons, we present graphical portraits of the three cytochromes at the same stage of unfolding, and in relation to their native state structures. We also display specific segments at different stages of unfolding to illustrate differences in stability of defined domains thereby allowing us to make specific predictions on the unfolding of corresponding internal and terminal helices in cyt c' and cyt c-b562. Our work accords with an earlier experimental report on the presence and persistence of a hydrophobic core in cyt c.

Reduction of All-Atom Protein Folding Dynamics to One-Dimensional Diffusion

Theoretical models have often modeled protein folding dynamics as diffusion on a low-dimensional free energy surface, a remarkable simplification. However, the accuracy of such an approximation and the number of dimensions required were not clear. For all-atom folding simulations of ten small proteins in explicit solvent we show that the folding dynamics can indeed be accurately described as diffusion on just a single coordinate, the fraction of native contacts (Q). The diffusion models reproduce both folding rates, and finer details such as transition-path durations and diffusive propagators. The Q-averaged diffusion coefficients decrease with chain length, as anticipated from energy landscape theory. Although the Q-diffusion model does not capture transition-path durations for the protein NuG2, we show that this can be accomplished by designing an improved coordinate Qopt. Overall, one-dimensional diffusion on a suitable coordinate turns out to be a remarkably faithful model for the dynamics of the proteins considered.

Lessons in Protein Design from Combined Evolution and Conformational Dynamics

Protein-protein interactions play important roles in the control of every cellular process. How natural selection has optimized protein design to produce molecules capable of binding to many partner proteins is a fascinating problem but not well understood. Here, we performed a combinatorial analysis of protein sequence evolution and conformational dynamics to study how calmodulin (CaM), which plays essential roles in calcium signaling pathways, has adapted to bind to a large number of partner proteins. We discovered that amino acid residues in CaM can be partitioned into unique classes according to their degree of evolutionary conservation and local stability. Holistically, categorization of CaM residues into these classes reveals enriched physico-chemical interactions required for binding to diverse targets, balanced against the need to maintain the folding and structural modularity of CaM to achieve its overall function. The sequence-structure-function relationship of CaM provides a concrete example of the general principle of protein design. We have demonstrated the synergy between the fields of molecular evolution and protein biophysics and created a generalizable framework broadly applicable to the study of protein-protein interactions.

Neither Two-State nor Three-State: Dimerization of Lambda Cro Repressor

Lambda Cro repressor is one of the best studied dimeric transcription factors. However, there has still been an unsettled debate for decades about whether it is a two-state dimer or three-state dimer. We provide a new mechanism model that can reconcile these seemingly conflicting (mutually exclusive) experimental results. From simulations with all-atom structure-based model, we observe that the dimerization process of Lambda Cro repressor starts from one folded monomer with one unfolded monomer. Intrasubunit folding and intersubunit binding are partially coupled, in a fly casting manner.

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.

Molecular determinants of the interactions between proteins and ssDNA

ssDNA binding proteins (SSBs) protect ssDNA from chemical and enzymatic assault that can derail DNA processing machinery. Complexes between SSBs and ssDNA are often highly stable, but predicting their structures is challenging, mostly because of the inherent flexibility of ssDNA and the geometric and energetic complexity of the interfaces that it forms. Here, we report a newly developed coarse-grained model to predict the structure of SSB-ssDNA complexes. The model is successfully applied to predict the binding modes of six SSBs with ssDNA strands of lengths of 6-65 nt. In addition to charge-charge interactions (which are often central to governing protein interactions with nucleic acids by means of electrostatic complementarity), an essential energetic term to predict SSB-ssDNA complexes is the interactions between aromatic residues and DNA bases. For some systems, flexibility is required from not only the ssDNA but also, the SSB to allow it to undergo conformational changes and the penetration of the ssDNA into its binding pocket. The association mechanisms can be quite varied, and in several cases, they involve the ssDNA sliding along the protein surface. The binding mechanism suggests that coarse-grained models are appropriate to study the motion of SSBs along ssDNA, which is expected to be central to the function carried out by the SSBs.

Dependence of internal friction on folding mechanism

An outstanding challenge in protein folding is understanding the origin of "internal friction" in folding dynamics, experimentally identified from the dependence of folding rates on solvent viscosity. A possible origin suggested by simulation is the crossing of local torsion barriers. However, it was unclear why internal friction varied from protein to protein or for different folding barriers of the same protein. Using all-atom simulations with variable solvent viscosity, in conjunction with transition-path sampling to obtain reaction rates and analysis via Markov state models, we are able to determine the internal friction in the folding of several peptides and miniproteins. In agreement with experiment, we find that the folding events with greatest internal friction are those that mainly involve helix formation, while hairpin formation exhibits little or no evidence of friction. Via a careful analysis of folding transition paths, we show that internal friction arises when torsion angle changes are an important part of the folding mechanism near the folding free energy barrier. These results suggest an explanation for the variation of internal friction effects from protein to protein and across the energy landscape of the same protein.

Dimer domain swapping versus monomer folding in apo-myoglobin studied by molecular simulations

Using a coarse-grained symmetrized Go model, we performed a series of folding simulations of two apo-myoglobin molecules restrained at a high density, addressing competition of formation of a domain-swapped dimer with folding to two monomer structures.

Interplay between partner and ligand facilitates the folding and binding of an intrinsically disordered protein

Protein-protein interactions are at the heart of regulatory and signaling processes in the cell. In many interactions, one or both proteins are disordered before association. However, this disorder in the unbound state does not prevent many of these proteins folding to a well-defined, ordered structure in the bound state. Here we examine a typical system, where a small disordered protein (PUMA, p53 upregulated modulator of apoptosis) folds to an α-helix when bound to a groove on the surface of a folded protein (MCL-1, induced myeloid leukemia cell differentiation protein). We follow the association of these proteins using rapid-mixing stopped flow, and examine how the kinetic behavior is perturbed by denaturant and carefully chosen mutations. We demonstrate the utility of methods developed for the study of monomeric protein folding, including β-Tanford values, Leffler α, Φ-value analysis, and coarse-grained simulations, and propose a self-consistent mechanism for binding. Folding of the disordered protein before binding does not appear to be required and few, if any, specific interactions are required to commit to association. The majority of PUMA folding occurs after the transition state, in the presence of MCL-1. We also examine the role of the side chains of folded MCL-1 that make up the binding groove and find that many favor equilibrium binding but, surprisingly, inhibit the association process.

Frustration in biomolecules

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their own structures and dynamics using as input seemingly random character strings of their sequence, following which they coalesce and perform integrated cellular functions. In large computational systems with finite interaction-codes, the appearance of conflicting goals is inevitable. Simple conflicting forces can lead to quite complex structures and behaviors, leading to the concept of frustration in condensed matter. We present here some basic ideas about frustration in biomolecules and how the frustration concept leads to a better appreciation of many aspects of the architecture of biomolecules, and especially how biomolecular structure connects to function by means of localized frustration. These ideas are simultaneously both seductively simple and perilously subtle to grasp completely. The energy landscape theory of protein folding provides a framework for quantifying frustration in large systems and has been implemented at many levels of description. We first review the notion of frustration from the areas of abstract logic and its uses in simple condensed matter systems. We discuss then how the frustration concept applies specifically to heteropolymers, testing folding landscape theory in computer simulations of protein models and in experimentally accessible systems. Studying the aspects of frustration averaged over many proteins provides ways to infer energy functions useful for reliable structure prediction. We discuss how frustration affects folding mechanisms. We review here how the biological functions of proteins are related to subtle local physical frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. In this review, we also emphasize that frustration, far from being always a bad thing, is an essential feature of biomolecules that allows dynamics to be harnessed for function. In this way, we hope to illustrate how Frustration is a fundamental concept in molecular biology.

Dynamic conformational change regulates the protein-DNA recognition: an investigation on binding of a Y-family polymerase to its target DNA

Protein-DNA recognition is a central biological process that governs the life of cells. A protein will often undergo a conformational transition to form the functional complex with its target DNA. The protein conformational dynamics are expected to contribute to the stability and specificity of DNA recognition and therefore may control the functional activity of the protein-DNA complex. Understanding how the conformational dynamics influences the protein-DNA recognition is still challenging. Here, we developed a two-basin structure-based model to explore functional dynamics in Sulfolobus solfataricus DNA Y-family polymerase IV (DPO4) during its binding to DNA. With explicit consideration of non-specific and specific interactions between DPO4 and DNA, we found that DPO4-DNA recognition is comprised of first 3D diffusion, then a short-range adjustment sliding on DNA and finally specific binding. Interestingly, we found that DPO4 is under a conformational equilibrium between multiple states during the binding process and the distributions of the conformations vary at different binding stages. By modulating the strength of the electrostatic interactions, the flexibility of the linker, and the conformational dynamics in DPO4, we drew a clear picture on how DPO4 dynamically regulates the DNA recognition. We argue that the unique features of flexibility and conformational dynamics in DPO4-DNA recognition have direct implications for low-fidelity translesion DNA synthesis, most of which is found to be accomplished by the Y-family DNA polymerases. Our results help complete the description of the DNA synthesis process for the Y-family polymerases. Furthermore, the methods developed here can be widely applied for future investigations on how various proteins recognize and bind specific DNA substrates.

Protein-DNA recognition is crucial for many key biological processes in cells. Protein often undergoes large-scale conformational change during DNA recognition. However, the physical and global understanding of flexible protein-DNA binding is still challenging. Here, we developed a theoretical approach to investigate binding of a Y-family DNA polymerase to its target DNA during the DNA synthesis process. The results of electrostatic-controlled multi-step DNA binding process accompanied with multi-state conformational transition of protein occurring throughout are in remarkable agreement with experiments. During the process of protein-DNA recognition, the flexibility is found to facilitate both the conformational transition of protein (intra-chain dynamics) and DNA binding (inter-chain dynamics) simultaneously. Therefore, we provided a quantitative description of protein-DNA binding mechanism that flexibility or conformational change regulates DNA recognition dynamically, leading to high efficiency and specificity of function for protein-DNA recognition.

Specificity and affinity quantification of flexible recognition from underlying energy landscape topography

Flexibility in biomolecular recognition is essential and critical for many cellular activities. Flexible recognition often leads to moderate affinity but high specificity, in contradiction with the conventional wisdom that high affinity and high specificity are coupled. Furthermore, quantitative understanding of the role of flexibility in biomolecular recognition is still challenging. Here, we meet the challenge by quantifying the intrinsic biomolecular recognition energy landscapes with and without flexibility through the underlying density of states. We quantified the thermodynamic intrinsic specificity by the topography of the intrinsic binding energy landscape and the kinetic specificity by association rate. We found that the thermodynamic and kinetic specificity are strongly correlated. Furthermore, we found that flexibility decreases binding affinity on one hand, but increases binding specificity on the other hand, and the decreasing or increasing proportion of affinity and specificity are strongly correlated with the degree of flexibility. This shows more (less) flexibility leads to weaker (stronger) coupling between affinity and specificity. Our work provides a theoretical foundation and quantitative explanation of the previous qualitative studies on the relationship among flexibility, affinity and specificity. In addition, we found that the folding energy landscapes are more funneled with binding, indicating that binding helps folding during the recognition. Finally, we demonstrated that the whole binding-folding energy landscapes can be integrated by the rigid binding and isolated folding energy landscapes under weak flexibility. Our results provide a novel way to quantify the affinity and specificity in flexible biomolecular recognition.

Flexibility in biomolecular recognition is crucial for the function. Flexibility often leads to moderate binding affinity but high binding specificity, challenging the conventional wisdom that high specificity is guaranteed by high affinity. Currently, understanding of the relationship between affinity and specificity in flexible biomolecular recognition is still obscure, even in a qualitative way. By exploring the intrinsic biomolecular recognition energy landscapes, we provided a novel way to quantify the thermodynamic intrinsic specificity by energy landscape topography and kinetic specificity by association rate. We show quantitatively that flexibility decreases binding affinity while increases binding specificity, and the relative changes in affinity and specificity are strongly correlated with the degree of flexibility. Our results show that more (less) flexibility leads to weaker (stronger) coupling between affinity and specificity. Importantly, we demonstrated that flexibility modulates affinity and specificity through the underlying energy landscape. Our study establishes the quantitative relationship among flexibility, affinity and specificity, bridging the gap between theory and experiments.

Prepaying the entropic cost for allosteric regulation in KIX

The kinase-inducible domain interacting (KIX) domain of the CREB binding protein (CBP) is capable of simultaneously binding two intrinsically disordered transcription factors, such as the mixed-lineage leukemia (MLL) and c-Myb peptides, at isolated interaction sites. In vitro, the affinity for binding c-Myb is approximately doubled when KIX is in complex with MLL, which suggests a positive cooperative binding mechanism, and the affinity for MLL is also slightly increased when KIX is first bound by c-Myb. Expanding the scope of recent NMR and computational studies, we explore the allosteric mechanism at a detailed molecular level that directly connects the microscopic structural dynamics to the macroscopic shift in binding affinities. To this end, we have performed molecular dynamics simulations of free KIX, KIX-c-Myb, MLL-KIX, and MLL-KIX-c-Myb using a topology-based Gō-like model. Our results capture an increase in affinity for the peptide in the allosteric site when KIX is prebound by a complementary effector and both peptides follow an effector-independent folding-and-binding mechanism. More importantly, we discover that MLL binding lowers the entropic cost for c-Myb binding, and vice versa, by stabilizing the L12-G2 loop and the C-terminal region of the α3 helix on KIX. This work demonstrates the importance of entropy in allosteric signaling between promiscuous molecular recognition sites and can inform the rational design of small molecule stabilizers to target important regions of conformationally dynamic proteins.

PolyUbiquitin chain linkage topology selects the functions from the underlying binding landscape

Ubiquitin (Ub) can generate versatile molecular signals and lead to different celluar fates. The functional poly-valence of Ub is believed to be resulted from its ability to form distinct polymerized chains with eight linkage types. To provide a full picture of ubiquitin code, we explore the binding landscape of two free Ub monomers and also the functional landscapes of of all eight linkage types by theoretical modeling. Remarkably, we found that most of the compact structures of covalently connected dimeric Ub chains (diUbs) pre-exist on the binding landscape. These compact functional states were subsequently validated by corresponding linkage models. This leads to the proposal that the folding architecture of Ub monomer has encoded all functional states into its binding landscape, which is further selected by different topologies of polymeric Ub chains. Moreover, our results revealed that covalent linkage leads to symmetry breaking of interfacial interactions. We further propose that topological constraint not only limits the conformational space for effective switching between functional states, but also selects the local interactions for realizing the corresponding biological function. Therefore, the topological constraint provides a way for breaking the binding symmetry and reaching the functional specificity. The simulation results also provide several predictions that qualitatively and quantitatively consistent with experiments. Importantly, the K48 linkage model successfully predicted intermediate states. The resulting multi-state energy landscape was further employed to reconcile the seemingly contradictory experimental data on the conformational equilibrium of K48-diUb. Our results further suggest that hydrophobic interactions are dominant in the functional landscapes of K6-, K11-, K33- and K48 diUbs, while electrostatic interactions play a more important role in the functional landscapes of K27, K29, K63 and linear linkages.

Quantifying the Sources of Kinetic Frustration in Folding Simulations of Small Proteins

Experiments and atomistic simulations of polypeptides have revealed structural intermediates that promote or inhibit conformational transitions to the native state during folding. We invoke a concept of “kinetic frustration” to quantify the prevalence and impact of these behaviors on folding rates within a large set of atomistic simulation data for 10 fast-folding proteins, where each protein’s conformational space is represented as a Markov state model of conformational transitions. Our graph theoretic approach addresses what conformational features correlate with folding inhibition and therefore permits comparison among features within a single protein network and also more generally between proteins. Nonnative contacts and nonnative secondary structure formation can thus be quantitatively implicated in inhibiting folding for several of the tested peptides.

Discriminating binding mechanisms of an intrinsically disordered protein via a multi-state coarse-grained model

Many proteins undergo a conformational transition upon binding to their cognate binding partner, with intrinsically disordered proteins (IDPs) providing an extreme example in which a folding transition occurs. However, it is often not clear whether this occurs via an "induced fit" or "conformational selection" mechanism, or via some intermediate scenario. In the first case, transient encounters with the binding partner favour transitions to the bound structure before the two proteins dissociate, while in the second the bound structure must be selected from a subset of unbound structures which are in the correct state for binding, because transient encounters of the incorrect conformation with the binding partner are most likely to result in dissociation. A particularly interesting situation involves those intrinsically disordered proteins which can bind to different binding partners in different conformations. We have devised a multi-state coarse-grained simulation model which is able to capture the binding of IDPs in alternate conformations, and by applying it to the binding of nuclear coactivator binding domain (NCBD) to either ACTR or IRF-3 we are able to determine the binding mechanism. By all measures, the binding of NCBD to either binding partner appears to occur via an induced fit mechanism. Nonetheless, we also show how a scenario closer to conformational selection could arise by choosing an alternative non-binding structure for NCBD.

The power of coarse graining in biomolecular simulations

Computational modeling of biological systems is challenging because of the multitude of spatial and temporal scales involved. Replacing atomistic detail with lower resolution, coarse grained (CG), beads has opened the way to simulate large-scale biomolecular processes on time scales inaccessible to all-atom models. We provide an overview of some of the more popular CG models used in biomolecular applications to date, focusing on models that retain chemical specificity. A few state-of-the-art examples of protein folding, membrane protein gating and self-assembly, DNA hybridization, and modeling of carbohydrate fibers are used to illustrate the power and diversity of current CG modeling.

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Exploring multi-dimensional coordinate-dependent diffusion dynamics on the energy landscape of protein conformation change

We explore the multi-dimensional diffusion dynamics of protein conformational change. We found in general that the diffusion is anisotropic and inhomogeneous. The directional and positional dependence of diffusion have significant impacts on the protein conformational kinetics: the dominant kinetic path of conformational change is shifted from the naively expected steepest decent gradient paths. The kinetic transition state is shifted away from the transition state. The effective kinetic free energy barrier height, determining the kinetic rate of the conformational change, is shifted away from the one estimated from the thermodynamic free energy barrier. The shift of the transition state in position and value will modify the phi value analysis for identification of hot residues and interactions responsible for conformational dynamics. Ongoing and future experiments can test the predictions of the model.