Computational assessment of folding energy landscapes in heterodimeric coiled coils

The coiled coil structural motif consists of alpha helices supercoiling around each other to form staggered knobs‐into‐holes packing. Such structures are deceptively simple, especially as they often can be described with parametric equations, but are known to exist in various conformations. Even the simplest systems, consisting of 2 monomers, can assemble into a wide range of states. They can form canonical as well as noncanonical coiled coils, be parallel or antiparallel, where helices associate with different degrees of shift, tilt, and rotation. Here, we investigate the energy landscape of heterodimeric coiled coils by carrying out de novo folding simulations starting from amino acid sequence. We folded a diverse set of 22 heterodimers and demonstrate that the approach is capable of identifying the atomic details in the experimental structure in the majority of cases. Our methodology also enables exploration of alternative states that can be accessible in solution beyond the experimentally determined structure. For many systems, we observe folding energy landscapes with multiple energy minima and several isoenergetic states. By comparing coiled coils from single domains and those extracted from larger proteins, we find that standalone coiled coils have deeper energy wells at the experimentally determined conformation. By folding the competing homodimeric states in addition to the heterodimers, we observe that the structural specificity towards the heteromeric state is often small. Taken together, our results demonstrate that de novo folding simulations can be a powerful tool to characterize structural specificity of coiled coils when coupled to assessment of energy landscapes.     

Temperature dependence of the free energy landscape of the src-SH3 protein domain

The temperature dependence of the free energy landscape of the src-SH3 protein domain is investigated through fully atomic simulations in explicit solvent. Simulations are performed above and below the folding transition temperature, enabling an analysis of both protein folding and unfolding. The transition state for folding and unfolding, identified from the free energy surfaces, is found to be very similar, with structure in the central hydrophobic sheet and little structure throughout the rest of the protein. This is a result of a polarized folding (unfolding) mechanism involving early formation (late loss) of the central hydrophobic sheet at the transition state. Unfolding simulations map qualitatively well onto low-temperature free energy surfaces but appear, however, to miss important features observed in folding simulations. In particular, details of the folding mechanism involving the opening and closing of the hydrophobic core are not captured by unfolding simulations performed under strongly denaturing conditions. In addition, free energy surfaces at high temperatures do not display a desolvation barrier found at lower temperatures, involving the expulsion of water molecules from the hydrophobic core.     

Identification of protein-protein interaction sites from docking energy landscapes

Protein recognition is one of the most challenging and intriguing problems in structural biology. Despite all the available structural, sequence and biophysical information about protein-protein complexes, the physico-chemical patterns, if any, that make a protein surface likely to be involved in protein-protein interactions, remain elusive. Here, we apply protein docking simulations and analysis of the interaction energy landscapes to identify protein-protein interaction sites. The new protocol for global docking based on multi-start global energy optimization of an all-atom model of the ligand, with detailed receptor potentials and atomic solvation parameters optimized in a training set of 24 complexes, explores the conformational space around the whole receptor without restrictions. The ensembles of the rigid-body docking solutions generated by the simulations were subsequently used to project the docking energy landscapes onto the protein surfaces. We found that highly populated low-energy regions consistently corresponded to actual binding sites. The procedure was validated on a test set of 21 known protein-protein complexes not used in the training set. As much as 81% of the predicted high-propensity patch residues were located correctly in the native interfaces. This approach can guide the design of mutations on the surfaces of proteins, provide geometrical details of a possible interaction, and help to annotate protein surfaces in structural proteomics.     

Mapping protein energy landscapes with amide hydrogen exchange and mass spectrometry: I. A generalized model for a two-state protein and comparison with experiment

Protein amide hydrogen exchange (HDX) is a convoluted process, whose kinetics is determined by both dynamics of the protein and the intrinsic exchange rate of labile hydrogen atoms fully exposed to solvent. Both processes are influenced by a variety of intrinsic and extrinsic factors. A mathematical formalism initially developed to rationalize exchange kinetics of individual amide hydrogen atoms is now often used to interpret global exchange kinetics (e.g., as measured in HDX MS experiments). One particularly important advantage of HDX MS is direct visualization of various protein states by observing distinct protein ion populations with different levels of isotope labeling under conditions favoring correlated exchange (the so-called EX1 exchange mechanism). However, mildly denaturing conditions often lead to a situation where the overall HDX kinetics cannot be clearly classified as either EX1 or EX2. The goal of this work is to develop a framework for a generalized exchange model that takes into account multiple processes leading to amide hydrogen exchange, and does not require that the exchange proceed strictly via EX1 or EX2 kinetics. To achieve this goal, we use a probabilistic approach that assigns a transition probability and a residual protection to each equilibrium state of the protein. When applied to a small protein chymotrypsin inhibitor 2, the algorithm allows complex HDX patterns observed experimentally to be modeled with remarkably good fidelity. On the basis of the model we are now in a position to begin to extract quantitative dynamic information from convoluted exchange kinetics.     

Comparing the energy landscapes for native folding and aggregation of PrP

Protein sequences are evolved to encode generally one folded structure, out of a nearly infinite array of possible folds. Underlying this code is a funneled free energy landscape that guides folding to the native conformation. Protein misfolding and aggregation are also a manifestation of free-energy landscapes. The detailed mechanisms of these processes are poorly understood, but often involve rare, transient species and a variety of different pathways. The inherent complexity of misfolding has hampered efforts to measure aggregation pathways and the underlying energy landscape, especially using traditional methods where ensemble averaging obscures important rare and transient events. We recently studied the misfolding and aggregation of prion protein by examining 2 monomers tethered in close proximity as a dimer, showing how the steps leading to the formation of a stable aggregated state can be resolved in the single-molecule limit and the underlying energy landscape thereby reconstructed. This approach allows a more quantitative comparison of native folding versus misfolding, including fundamental differences in the dynamics for misfolding. By identifying key steps and interactions leading to misfolding, it should help to identify potential drug targets. Here we describe the importance of characterizing free-energy landscapes for aggregation and the challenges involved in doing so, and we discuss how single-molecule studies can help test proposed structural models for PrP aggregates.     

Bacterial protein meal in diets for growing pigs: effects on protein and energy metabolism

This experiment investigated the effects of increasing the dietary content of bacterial protein meal (BPM) on the protein and energy metabolism of pigs from weaning to a live weight of 80 kg. Four litters with four castrated male pigs in each litter were used. The litters were divided into two blocks according to age. One pig from each litter was fed one of the four experimental diets. Soya-bean meal was replaced with BPM on the basis of digestible protein, and the BPM contents in the four diets were 0% (BP0), 5% (BP5), 10% (BP10) and 15% (BP15), corresponding to 0%, 17%, 35% and 52% of the digestible nitrogen (N), respectively. Four balance periods were performed, at the start of which the pigs weighed 9.5 kg, 20.7 kg, 45.3 kg and 77.2 kg, respectively. Once during each balance period, 22-h respiration experiments were performed using indirect calorimetry. Daily weight gain, feed intake and feed conversion rate were the same for all diets. The apparent digestibility of N was lower on diet BP10 than on BP0 (P = 0.002), whereas the apparent digestibility of energy was similar on all diets. The retention of nitrogen did not differ between diets and was 1.50, 1.53, 1.33 and 1.46 g N per kg^0.75 per day on BP0, BP5, BP10 and BP15, respectively. Neither metabolisable energy intake nor heat production were affected by inclusion level of BPM. Retention of energy was 620 (BP0), 696 (BP5), 613 (BP10) and 664 kJ/kg^0.75 per day (BP15), the differences among diets being non-significant. The N-free respiratory quotient was similar on all diets. It was concluded that the overall protein and energy metabolism in growing pigs were not affected when up to 50% of dietary N was derived from BPM.     

Complexity of free energy landscapes of peptides revealed by nonlinear principal component analysis

Employing the recently developed hierarchical nonlinear principal component analysis (NLPCA) method of Saegusa et al. (Neurocomputing 2004;61:57-70 and IEICE Trans Inf Syst 2005;E88-D:2242-2248), the complexities of the free energy landscapes of several peptides, including triglycine, hexaalanine, and the C-terminal beta-hairpin of protein G, were studied. First, the performance of this NLPCA method was compared with the standard linear principal component analysis (PCA). In particular, we compared two methods according to (1) the ability of the dimensionality reduction and (2) the efficient representation of peptide conformations in low-dimensional spaces spanned by the first few principal components. The study revealed that NLPCA reduces the dimensionality of the considered systems much better, than did PCA. For example, in order to get the similar error, which is due to representation of the original data of beta-hairpin in low dimensional space, one needs 4 and 21 principal components of NLPCA and PCA, respectively. Second, by representing the free energy landscapes of the considered systems as a function of the first two principal components obtained from PCA, we obtained the relatively well-structured free energy landscapes. In contrast, the free energy landscapes of NLPCA are much more complicated, exhibiting many states which are hidden in the PCA maps, especially in the unfolded regions. Furthermore, the study also showed that many states in the PCA maps are mixed up by several peptide conformations, while those of the NLPCA maps are more pure. This finding suggests that the NLPCA should be used to capture the essential features of the systems.     

A survey of flexible protein binding mechanisms and their transition states using native topology based energy landscapes

Many cellular functions rely on interactions between protein pairs and higher oligomers. We have recently shown that binding mechanisms are robust and owing to the minimal frustration principle, just as for protein folding, are governed primarily by the protein's native topology, which is characterized by the network of non-covalent residue-residue interactions. The detailed binding mechanisms of nine dimers, a trimer, and a tetramer, each involving different degrees of flexibility and plasticity during assembly, are surveyed here using a model that is based solely on the protein topology, having a perfectly funneled energy landscape. The importance of flexibility in binding reactions is manifested by the fly-casting effect, which is diminished in magnitude when protein flexibility is removed. Many of the grosser and finer structural aspects of the various binding mechanisms (including binding of pre-folded monomers, binding of intrinsically unfolded monomers, and binding by domain-swapping) predicted by the native topology based landscape model are consistent with the mechanisms found in the laboratory. An asymmetric binding mechanism is often observed for the formation of the symmetric homodimers where one monomer is more structured at the binding transition state and serves as a template for the folding of the other monomer. Phi values were calculated to show how the structure of the binding transition state ensemble would be manifested in protein engineering studies. For most systems, the simulated Phi values are reasonably correlated with the available experimental values. This agreement suggests that the overall binding mechanism and the nature of the binding transition state ensemble can be understood from the network of interactions that stabilize the native fold. The Phi values for the formation of an antibody-antigen complex indicate a possible role for solvation of the interface in biomolecular association of large rigid proteins.     

Fragment replica-exchange method for efficient protein conformation sampling

The native structure of proteins corresponds to the global minimum of the free energy. The replica-exchange method (REM) has been recently used to search for the energy minimum in a wide protein conformation space. For large systems, however, applying REM can be costly because the number of replicas required for conformational sampling increases. We have developed a variant of REM called fragment REM, which is based on the existence of correlations between the local amino acid sequence and the local structure. Equilibrium distributions for two peptides were computed by conventional molecular dynamics, REM and the proposed REM simulations. We found that the modified REM successfully reduces the number of replicas needed for the simulation.     

The importance of explicit chain representation in protein folding models: an examination of Ising-like models

A class of models that represents a protein chain as a sequence of "folded" and "unfolded" residues has recently been used to correlate rates and mechanisms of protein folding with the protein native structure. In order to better understand the conditions under which these "Ising-like" models apply, we compare results from this model to those obtained from an off-lattice model which uses the same potential function. We find that Ising-like models by construction impose folding via a highly sequential nucleation-condensation mechanism, which in turn leads to more rugged energy landscapes, fewer "pathways" to the native state, and in the specific case examined here, the cold shock protein A from Escherichia coli, a qualitative difference in the most likely order of events in folding.     

LMProt: an efficient algorithm for Monte Carlo sampling of protein conformational space

A new and efficient Monte Carlo algorithm for sampling protein configurations in the continuous space is presented; the efficiency of this algorithm, named Local Moves for Proteins (LMProt), was compared to other alternative algorithms. For this purpose, we used an intrachain interaction energy function that is proportional to the root mean square deviation (rmsd) with respect to alpha-carbons from native structures of real proteins. For phantom chains, the LMProt method is approximately 10(4) and 20 times faster than the algorithms Thrashing (no local moves) and Sevenfold Way (local moves), respectively. Additionally, the LMProt was tested for real chains (excluded-volume all-atoms model); proteins 5NLL (138 residues) and 1BFF (129 residues) were used to determine the folding success xi as a function of the number eta of residues involved in the chain movements, and as a function of the maximum amplitude of atomic displacement delta r(max). Our results indicate that multiple local moves associated with relative chain flexibility, controlled by appropriate adjustments for eta and delta r(max), are essential for configurational search efficiency.     

Predicting repeat protein folding kinetics from an experimentally determined folding energy landscape

The Notch ankyrin domain is a repeat protein whose folding has been characterized through equilibrium and kinetic measurements. In previous work, equilibrium folding free energies of truncated constructs were used to generate an experimentally determined folding energy landscape (Mello and Barrick, Proc Natl Acad Sci USA 2004;101:14102–14107). Here, this folding energy landscape is used to parameterize a kinetic model in which local transition probabilities between partly folded states are based on energy values from the landscape. The landscape‐based model correctly predicts highly diverse experimentally determined folding kinetics of the Notch ankyrin domain and sequence variants. These predictions include monophasic folding and biphasic unfolding, curvature in the unfolding limb of the chevron plot, population of a transient unfolding intermediate, relative folding rates of 19 variants spanning three orders of magnitude, and a change in the folding pathway that results from C‐terminal stabilization. These findings indicate that the folding pathway(s) of the Notch ankyrin domain are thermodynamically selected: the primary determinants of kinetic behavior can be simply deduced from the local stability of individual repeats.     

Local interactions and the optimization of protein folding

The role of local interactions in protein folding has recently been the subject of some controversy. Here we investigate an extension of Zwanzig's simple and general model of folding in which local and nonlocal interactions are represented by functions of single and multiple conformational degrees of freedom, respectively. The kinetics and thermodynamics of folding are studied for a series of energy functions in which the energy of the native structure is fixed, but the relative contributions of local and nonlocal interactions to this energy are varied over a broad range. For funnel shaped energy landscapes, we find that 1) the rate of folding increases, but the stability of the folded state decreases, as the contribution of local interactions to the energy of the native structure increases, and 2) the amount of native structure in the unfolded state and the transition state vary considerably with the local interaction strength. Simple exponential kinetics and a well-defined free energy barrier separating folded and unfolded states are observed when nonlocal interactions make an appreciable contribution to the energy of the native structure; in such cases a transition state theory type approximation yields reasonably accurate estimates of the folding rate. Bumps in the folding funnel near the native state, which could result from desolvation effects, side chain freezing, or the breaking of nonnative contacts, significantly alter the dependence of the folding rate on the local interaction strength: the rate of folding decreases when the local interaction strength is increased beyond a certain point. A survey of the distribution of strong contacts in the protein structure database suggests that evolutionary optimization has involved both kinetics and thermodynamics: strong contacts are enriched at both very short and very long sequence separations. Proteins 29:282–291, 1997. © 1997 Wiley-Liss, Inc.     

Exploring the relationship between funneled energy landscapes and two-state protein folding

It should take an astronomical time span for unfolded protein chains to find their native state based on an unguided conformational random search. The experimental observation that folding is fast can be rationalized by assuming that protein energy landscapes are sloped towards the native state minimum, such that rapid folding can proceed from virtually any point in conformational space. Folding transitions often exhibit two-state behavior, involving extensively disordered and highly structured conformers as the only two observable kinetic species. This study employs a simple Brownian dynamics model of "protein particles" moving in a spherically symmetrical potential. As expected, the presence of an overall slope towards the native state minimum is an effective means to speed up folding. However, the two-state nature of the transition is eradicated if a significant energetic bias extends too far into the non-native conformational space. The breakdown of two-state cooperativity under these conditions is caused by a continuous conformational drift of the unfolded proteins. Ideal two-state behavior can only be maintained on surfaces exhibiting large regions that are energetically flat, a result that is supported by other recent data in the literature (Kaya and Chan, Proteins: Struct Funct Genet 2003;52:510-523). Rapid two-state folding requires energy landscapes exhibiting the following features: (i) A large region in conformational space that is energetically flat, thus allowing for a significant degree of random sampling, such that unfolded proteins can retain a random coil structure; (ii) a trapping area that is strongly sloped towards the native state minimum.     

A system for predicting energy and protein requirements of wild ruminants

Wild ruminants require energy and protein for the normal function. I developed a system for predicting these energy and protein requirements across ruminant species and life stages. This system defines requirements on the basis of net energy (NE), net protein (NP), and ruminally degraded protein (RDP). Total NE and NP requirements are calculated as the sum of NE and NP required for several functions (maintenance, activity, thermoregulation, gain, lactation, and gestation). To estimate the requirements for each function, I collected data predominantly for wild species and then formulated allometric and other equations that predict requirements across species. I estimated RDP requirements using an equation for cattle. I then related NE, NP, and RDP to quantities more practical for diet formulation (e.g. dry matter intake). I tabulated requirements over a range of body mass and life stages (neonate, juvenile, nonproductive adult, lactating adult, and gestating adult). Tabulated requirements suggest that adults at peak lactation require greatest quantities of energy and neonates generally require greatest quantities of protein, agreeing with suggestions that lactation is energetically expensive and protein is most limiting during growth. Equations used in this system were precise (allometric equations had R² generally ≥0.89 and coefficient of variation <31.1%) and expected to reliably predict requirements across species. Results showed that a system for beef cattle would overestimate NE and either over‐ or underestimate NP for gain when applied to wild ruminants, showing that systems for wild ruminants should not extrapolate from requirements for domestic ruminants. One prominent system for wild ruminants predicted at times vastly different protein requirements from those predicted by the proposed system. The proposed system should be further evaluated and expanded to include other nutrients. Zoo Biol 30:165–188, 2011. © 2010 Wiley‐Liss, Inc.     

From coarse-grain to all-atom: toward multiscale analysis of protein landscapes

Multiscale methods are becoming increasingly promising as a way to characterize the dynamics of large protein systems on biologically relevant time-scales. The underlying assumption in multiscale simulations is that it is possible to move reliably between different resolutions. We present a method that efficiently generates realistic all-atom protein structures starting from the C(alpha) atom positions, as obtained for instance from extensive coarse-grain simulations. The method, a reconstruction algorithm for coarse-grain structures (RACOGS), is validated by reconstructing ensembles of coarse-grain structures obtained during folding simulations of the proteins src-SH3 and S6. The results show that RACOGS consistently produces low energy, all-atom structures. A comparison of the free energy landscapes calculated using the coarse-grain structures versus the all-atom structures shows good correspondence and little distortion in the protein folding landscape.     

Generation of an antibody with a designed specificity difference for protein C and activated protein C

Rabbit polyclonal antibodies to a synthetic peptide, NH₂-Asp-Thr-Asn-Gln-Val-Asp-Gln-Lys-Asp-Gln-Leu-Asp-Phe-Arg-CONH₂ (APep), have been produced. This sequence is identical to that contained in the tetradecapeptide released from bovine protein C (PC) as a result of its conversion to its activated form (APC), except that Phe₁₃ replaced the normal Pro₁₃, in order to discourage cross-reactivity of antibodies to the carboxylterminal portion of APep with PC. The antibody pool obtained reacted with PC and showed virtually no cross-reactivity toward either APC or several typical plasma proteins. This general approach should serve well as a means of production of antibodies with a designed specificity capable of distinguishing between forms of the same protein that arise by release of peptide material.     

Free energy simulations for protein ligand binding and stability

Abstract

We summarize several computational techniques to determine relative free energies for condensed-phase systems. The focus is on practical considerations which are capable of making direct contact with experiments. Particular applications include the thermodynamic stability of apo- and holo-myoglobin, insulin dimerization free energy, ligand binding in lysozyme, and ligand diffusion in globular proteins. In addition to provide differential free energies between neighboring states, converged umbrella sampling simulations provide insight into migration barriers and ligand dissociation barriers and analysis of the trajectories yield additional insight into the structural dynamics of fundamental processes. Also, such simulations are useful tools to quantify relative stability changes for situations where experiments are difficult. This is illustrated for NO-bound myoglobin. For the dissociation of benzonitrile from lysozyme it is found that long umbrella sampling simulations are required to approximately converge the free energy profile. Then, however, the resulting differential free energy between the bound and unbound state is in good agreement with estimates from molecular mechanics with generalized Born surface area simulations. Furthermore, comparing the barrier height for ligand escape suggests that ligand dissociation contains a non-equilibrium component.