Number Of Native Contacts Research Articles

Energy- and evolution-based design of inulosucrase for enhanced thermostability and inulin production.

Inulosucrase from Lactobacillus reuteri 121 (LrInu) exhibits promise in the synthesis of prebiotic inulin and fructooligosaccharides. However, for its use in industry, LrInu's thermostability is a crucial consideration. In this study, the computational program FireProt was used to predict the thermostable variants of LrInu. Using rational criteria, nine variants were selected for protein expression and characterization. The G237P variant was determined to be the greatest designed candidate due to its greatly enhanced stability and activity in comparison to the wild-type enzyme. The optimum temperature of G237P increased from 50 to 60°C, with an over 5-fold increase in the half-life. Spectroscopy studies revealed that the G237P mutation could prevent the structural change in LrInu caused by heat or urea treatment. Molecular dynamics (MD) simulations showed that the enhanced thermostability of the G237P variant resulted from an increase in structural rigidity and the number of native contacts within the protein molecule. In addition, G237P variant synthesizes inulin with greater efficiency than WT. KEY POINTS: • Thermostable inulosucrase variant(s) were designed by Fireprot server. • G237P variant showed significantly improved thermostability compared to the wild type. • Inulin is synthesized more efficiently by G237P variant.

Thermodynamics and Kinetics of Single-Chain Monellin Folding with Structural Insights into Specific Collapse in the Denatured State Ensemble

Proteins, which behave as random coils in high denaturant concentrations undergo collapse transition similar to polymers on denaturant dilution. We study collapse in the denatured ensemble of single-chain monellin (MNEI) using a coarse-grained protein model and molecular dynamics simulations. The model is validated by quantitatively comparing the computed guanidinium chloride and pH-dependent thermodynamic properties of MNEI folding with the experiments. The computed properties such as the fraction of the protein in the folded state and radius of gyration (Rg) as function of [GuHCl] are in good agreement with the experiments. The folded state of MNEI is destabilized with an increase in pH due to the deprotonation of the residues Glu24 and Cys42. On decreasing [GuHCl], the protein in the unfolded ensemble showed specific compaction. The Rg of the protein decreased steadily with [GuHCl] dilution due to increase in the number of native contacts in all the secondary structural elements present in the protein. MNEI folding kinetics is complex with multiple folding pathways and transiently stable intermediates are populated in these pathways. In strong stabilizing conditions, the protein in the unfolded ensemble showed transition to a more compact unfolded state where Rg decreased by ≈17% due to the formation of specific native contacts in the protein. The intermediate populated in the dominant MNEI folding pathway satisfies the structural features of the dry molten globule inferred from experiments.

Pressure Effects on Dissociation of CheY-FliM Complex Studied by Molecular Dynamics Simulations

The rotational switching of the bacteria flagella motor is controlled by binding of the signaling molecule CheY onto FliM which is a part of motor basal body. The rotational switching plays a central role in the bacterial chemotaxis. Recently, it was reported that high hydrostatic pressures of >120 MPa can induce the rotational switching even in the absence of CheY [1]. It was also suggested that hydration of the switch complex at high pressure induces structural changes similar to those caused by the binding of CheY. To gain further insights into the high pressure effect on the motor switching, we investigated differences in conformation of monomeric CheY and also CheY-FliM complex at different pressure conditions using molecular dynamics (MD) simulations. Then, pressure effects on the binding stability of the CheY-FliM complex was studied by dissociating the complex. The dissociation of the protein complex was observed using an efficient sampling method, PaCS-MD (Parallel Cascade Selection Molecular Dynamics) [2]. In PaCS-MD, the cycle of short MD simulations and selection of the structures close to the product structure for the next cycle are repeated, which enhances the conformational transitions without any additional external biases. From the obtained MD trajectories, the dissociation behavior was characterized using coordinates such as the center of mass (COM) distance and the number of native contacts between CheY and FliM. Moreover, potentials of mean force along the COM distance were calculated from probability distributions in steady state obtained by Markov state models. Those potentials of mean force provided binding free energies of the protein complex. Based on the results, we will also discuss mechanisms underlying influences of high hydrostatic pressures on the binding. Such insights would provide a further understanding towards an accurate regulation of protein-protein interactions.[1] Nishiyama, M. et al. 2013. J. Bacteriol. 195:1809-1814. doi: 10.1128/JB.02139-12.[2] Harada, R. and Kitao, A. 2013. J. Chem. Phys. 139:035103. doi: 10.1063/1.4813023.

Folding–unfolding transition in the mini-protein villin headpiece (HP35): An equilibrium study using the Wang–Landau algorithm

A computational study, using the Wang–Landau algorithm, is carried out for the 35 residue mini-protein villin headpiece (HP35) to investigate some equilibrium aspects of its folding–unfolding transition in water. The force field used is ECEPP/3 and a solvent-accessible surface area method is used to describe the interaction with water. The density of states and the conditional probabilities of some physically interesting geometrical descriptors of the molecule at various energies are calculated by analyzing the high-statistics data generated by the simulations. All canonical ensemble averages are subsequently calculated by using these data. The computed quantities include specific heat, radius of gyration, number of native contacts, number of helical residues and the potential of mean force for three pairs of geometric descriptors. High precision and a systematic check on the convergence of the computation are the two key points of our methodology.

Network Properties of the Ensemble of RNA Structures

We describe the first dynamic programming algorithm that computes the expected degree for the network, or graph G = (V, E) of all secondary structures of a given RNA sequence a = a 1, …, a n. Here, the nodes V correspond to all secondary structures of a, while an edge exists between nodes s, t if the secondary structure t can be obtained from s by adding, removing or shifting a base pair. Since secondary structure kinetics programs implement the Gillespie algorithm, which simulates a random walk on the network of secondary structures, the expected network degree may provide a better understanding of kinetics of RNA folding when allowing defect diffusion, helix zippering, and related conformation transformations. We determine the correlation between expected network degree, contact order, conformational entropy, and expected number of native contacts for a benchmarking dataset of RNAs. Source code is available at http://bioinformatics.bc.edu/clotelab/RNAexpNumNbors.

Phase diagram of the Wako-Saitô-Muñoz-Eaton β hairpin model obtained from the partition-function zeros

I study the partition-function zeros of the Wako-Saitô-Muñoz-Eaton (WSME) β hairpin model in the complex temperature plane when the number of native contacts is 10. For various values of the entropy cost of disordering a bond, the zeros show a clear locus corresponding to the folding transition. The result suggests a new definition of the transition temperature, the temperature obtained by extrapolating the locus to the positive real axis. By computing the transition temperature for various values of the entropy cost, we obtain the phase diagram of the WSME β hairpin model. I compare the present definition of the transition temperature with the transition midpoint temperature for several values of the entropy parameter and show that they are in a reasonably good agreement.

Wang-Landau density of states based study of the folding-unfolding transition in the mini-protein Trp-cage (TC5b).

We present the results of a high-statistics equilibrium study of the folding/unfolding transition for the 20-residue mini-protein Trp-cage (TC5b) in water. The ECEPP/3 force field is used and the interaction with water is treated by a solvent-accessible surface area method. A Wang-Landau type simulation is used to calculate the density of states and the conditional probabilities for the various values of the radius of gyration and the number of native contacts at fixed values of energy--along with a systematic check on their convergence. All thermodynamic quantities of interest are calculated from this information. The folding-unfolding transition corresponds to a peak in the temperature dependence of the computed specific heat. This is corroborated further by the structural signatures of folding in the distributions for radius of gyration and the number of native contacts as a function of temperature. The potentials of mean force are also calculated for these variables, both separately and jointly. A local free energy minimum, in addition to the global minimum, is found in a temperature range substantially below the folding temperature. The free energy at this second minimum is approximately 5 k(B)T higher than the value at the global minimum.

Transition paths, diffusive processes, and preequilibria of protein folding

Fundamental relationships between the thermodynamics and kinetics of protein folding were investigated using chain models of natural proteins with diverse folding rates by extensive comparisons between the distribution of conformations in thermodynamic equilibrium and the distribution of conformations sampled along folding trajectories. Consistent with theory and single-molecule experiment, duration of the folding transition paths exhibits only a weak correlation with overall folding time. Conformational distributions of folding trajectories near the overall thermodynamic folding/unfolding barrier show significant deviations from preequilibrium. These deviations, the distribution of transition path times, and the variation of mean transition path time for different proteins can all be rationalized by a diffusive process that we modeled using simple Monte Carlo algorithms with an effective coordinate-independent diffusion coefficient. Conformations in the initial stages of transition paths tend to form more nonlocal contacts than typical conformations with the same number of native contacts. This statistical bias, which is indicative of preferred folding pathways, should be amenable to future single-molecule measurements. We found that the preexponential factor defined in the transition state theory of folding varies from protein to protein and that this variation can be rationalized by our Monte Carlo diffusion model. Thus, protein folding physics is different in certain fundamental respects from the physics envisioned by a simple transition-state picture. Nonetheless, transition state theory can be a useful approximate predictor of cooperative folding speed, because the height of the overall folding barrier is apparently a proxy for related rate-determining physical properties.

The relationship between the solvent-accessible surface area of a protein and the number of native contacts in its structure

The degree of protein folding is characterized either by the solvent-accessible surface area (S ASA ) or the actual number of native contacts (N cont). Evidently, these values should correlate with each other, as a decrease in S ASA caused by the change in protein conformation during its folding must be accompanied by the corresponding increase in the number of native contacts. It is shown that this correlation does exist and is very strong (the correlation coefficient exceeds 99%), which can be used for an accurate and rapid estimation of the protein surface area from the number of native contacts. Among the methods commonly used for calculating the native contacts, the atom-atom approach gives the best fit if hydrogen atoms are taken into account and the cutoff value for the distance between the centers of atoms is taken to be 8 A. The latter means that two layers of surface atoms are required to shield the protein core from the solvent.

Conformational Changes below the Tm: Molecular Dynamics Studies of the Thermal Pretransition of Ribonuclease A

Recent work suggests that some native conformations of proteins can vary with temperature. To obtain an atomic-level description of this structural and conformational variation, we have performed all-atom, explicit-solvent molecular dynamics simulations of bovine pancreatic ribonuclease A (RNase A) up to its melting temperature (Tm approximately 337 K). RNase A has a thermal pretransition near 320 K [Stelea, S. D., Pancoska, P., Benight, A. S., and Keiderling, T. A. (2001) Protein Sci. 10, 970-978]. Our simulations identify a conformational change that coincides with this pretransition. Between 310 and 320 K, there is a small but significant decrease in the number of native contacts, beta-sheet hydrogen bonding, and deviation of backbone conformation from the starting structure, and an increase in the number of nonnative contacts. Native contacts are lost in beta-sheet regions and in alpha1, partially due to movement of alpha1 away from the beta-sheet core. At 330 and 340 K, a nonnative helical segment of residues 15-20 forms, corresponding to a helix observed in the N-terminal domain-swapped dimer [Liu, Y. S., Hart, P. J., Schulnegger, M. P., and Eisenberg, D. (1998) Proc. Natl. Acad. Sci. U.S.A. 95, 3437-3432]. The conformations observed at the higher temperatures possess nativelike topology and overall conformation, with many native contacts, but they have a disrupted active site. We propose that these conformations may represent the native state at elevated temperature, or the N' state. These simulations show that subtle, functionally important changes in protein conformation can occur below the Tm.

Reaction coordinates and transition pathways of rare events via forward flux sampling

A new approach is developed for identifying suitable reaction coordinates to describe the progression of rare events in complex systems. The method is based on the forward flux sampling (FFS) technique and standard least-square estimation (LSE) and it is denoted as FFS-LSE. The FFS algorithm generates trajectories for the transition between stable states as chains of partially connected paths, which can then be used to obtain "on-the-fly" estimates for the committor probability to the final region, p(B). These p(B) data are then used to screen a set of candidate collective properties for an optimal order parameter (i.e., reaction coordinate) that depends on a few relevant variables. LSE is used to find the coefficients of the proposed reaction coordinate model and an analysis of variance is used to determine the significant terms in the model. The method is demonstrated for several test systems, including the folding of a lattice protein. It is shown that a simple approximation to p(B) via a model linear on energy and number of native contacts is sufficient to describe the intrinsic dynamics of the protein system and to ensure an efficient sampling of pathways. In addition, since the p(B) surface found from the FFS-LSE approach leads to the identification of the transition state ensemble, mechanistic details of the dynamics of the system can be readily obtained during a single FFS-type simulation without the need to perform additional committor simulations.

Relationships between the folding rate constant and the topological parameters of small two-state proteins based on general random walk model

In this paper, we propose an analytically tractable model of protein folding based on one-dimensional general random walk. A second-order differential equation for the mean folding time of a single protein is constructed which can be used to derive the observed relationship between the folding rate constant and the number of native contacts. The parameters appearing in the model can be determined by fitting the theoretical prediction to the experimental result. In addition, taking into account the fact that the number of native contacts is almost proportional to the relative contact order, we can also explain the observed relationship between the folding rate constant and the relative contact order.

How the folding rate constant of simple, single-domain proteins depends on the number of native contacts.

Experiments have shown that the folding rate constants of two dozen structurally unrelated, small, single-domain proteins can be expressed in terms of one quantity (the contact order) that depends exclusively on the topology of the folded state. Such dependence is unique in chemical kinetics. Here we investigate its physical origin and derive the approximate formula ln(k) = ln(N) + a + bN, were N is the number of contacts in the folded state, and a and b are constants whose physical meaning is understood. This formula fits well the experimentally determined folding rate constants of the 24 proteins, with single values for a and b.

Heat Capacity of Protein Folding

We construct a Hamiltonian for a single domain protein where the contact enthalpy and the chain entropy decrease linearly with the number of native contacts. The hydration effect upon protein unfolding is included by modeling water as ideal dipoles that are ordered around the unfolded surfaces, where the influence of these surfaces, covered with an “ice-like” shell of water, is represented by an effective field that directs the water dipoles. An intermolecular pair interaction between water molecules is also introduced. The heat capacity of the model exhibits, the common feature of small globular proteins, two peaks corresponding to cold and warm unfolding, respectively. By introducing ad hoc vibrational modes, we obtain quantitatively good accordance with experiments on myoglobin.

A minimalist model protein with multiple folding funnels

Kinetic and structural studies of wild-type proteins such as prions and amyloidogenic proteins provide suggestive evidence that proteins may adopt multiple long-lived states in addition to the native state. All of these states differ structurally because they lie far apart in configuration space, but their stability is not necessarily caused by cooperative (nucleation) effects. In this study, a minimalist model protein is designed to exhibit multiple long-lived states to explore the dynamics of the corresponding wild-type proteins. The minimalist protein is modeled as a 27-monomer sequence confined to a cubic lattice with three different monomer types. An order parameter-the winding index-is introduced to characterize the extent of folding. The winding index has several advantages over other commonly used order parameters like the number of native contacts. It can distinguish between enantiomers, its calculation requires less computational time than the number of native contacts, and reduced-dimensional landscapes can be developed when the native state structure is not known a priori. The results for the designed model protein prove by existence that the rugged energy landscape picture of protein folding can be generalized to include protein "misfolding" into long-lived states.

Review of the fourth Johns Hopkins Protein Folding Meeting

Review of the fourth Johns Hopkins Protein Folding Meeting

On the transition coordinate for protein folding

To understand the kinetics of protein folding, we introduce the concept of a “transition coordinate” which is defined to be the coordinate along which the system progresses most slowly. As a practical implementation of this concept, we define the transmission coefficient for any conformation to be the probability for a chain with the given conformation to fold before it unfolds. Since the transmission coefficient can serve as the best possible measure of kinetic distance for a system, we present two methods by which we can determine how closely any parameter of the system approximates the transmission coefficient. As we determine that the transmission coefficient for a short-chain heteropolymer system is dominated by entropic factors, we have chosen to illustrate the methods mentioned by applying them to geometrical properties of the system such as the number of native contacts and the looplength distribution. We find that these coordinates are not good approximations of the transmission coefficient and therefore, cannot adequately describe the kinetics of protein folding.

Comparison of lattice Monte Carlo dynamics and Brownian dynamics folding pathways of α-helical hairpins

In the context of dynamic Monte Carlo and Brownian dynamics, trajectories of the folding pathways of α-helical hairpin proteins have been computed by two very different models and simulation schemes. The dynamic process is monitored by following the number of native contacts and, in the case of Brownian dynamics, also the torsional angles found along the computed trajectories. An examination of the resulting pathways suggests that the on-site mechanism of assembly previously found in Monte Carlo diamond lattice simulations holds in general for the initial stages of protein folding, and validates their independence with respect to the lattice geometry and the local movements employed in Monte Carlo calculations. Thus, the essential physical character of the computationally very efficient dynamic Monte Carlo simulations is confirmed.