Optimal specificity and function for flexible biomolecular recognition

Biomolecular associations often accompanied by large conformational changes, sometimes folding and unfolding. By exploring an exactly solvable model, we constructed the free energy landscape and established a general framework for studying the biomolecular flexible binding process. We derived an optimal criterion for the specificity and function for flexible biomolecular binding where the binding and conformational folding are coupled.

Configuration-dependent diffusion can shift the kinetic transition state and barrier height of protein folding

We show that diffusion can play an important role in protein-folding kinetics. We explicitly calculate the diffusion coefficient of protein folding in a lattice model. We found that diffusion typically is configuration- or reaction coordinate-dependent. The diffusion coefficient is found to be decreasing with respect to the progression of folding toward the native state, which is caused by the collapse to a compact state constraining the configurational space for exploration. The configuration- or position-dependent diffusion coefficient has a significant contribution to the kinetics in addition to the thermodynamic free-energy barrier. It effectively changes (increases in this case) the kinetic barrier height as well as the position of the corresponding transition state and therefore modifies the folding kinetic rates as well as the kinetic routes. The resulting folding time, by considering both kinetic diffusion and the thermodynamic folding free-energy profile, thus is slower than the estimation from the thermodynamic free-energy barrier with constant diffusion but is consistent with the results from kinetic simulations. The configuration- or coordinate-dependent diffusion is especially important with respect to fast folding, when there is a small or no free-energy barrier and kinetics is controlled by diffusion.Including the configurational dependence will challenge the transition state theory of protein folding.

Downhill kinetics of biomolecular interface binding: Globally connected scenario

We study the kinetics of the biomolecular binding process at the interface using energy landscape theory. The global kinetic connectivity case is considered for a downhill funneled energy landscape. By solving the kinetic master equation, the kinetic time for binding is obtained and shown to have a U-shape curve-dependence on the temperature. The kinetic minimum of the binding time monotonically decreases when the ratio of the underlying energy gap between native state and average non-native states versus the roughness or the fluctuations of the landscape increases. At intermediate temperatures,fluctuations measured by the higher moments of the binding time lead to non-Poissonian, non-exponential kinetics. At both high and very low temperatures, the kinetics is nearly Poissonian and exponential.

The complex kinetics of protein folding in wide temperature ranges

The complex protein folding kinetics in wide temperature ranges is studied through diffusive dynamics on the underlying energy landscape. The well-known kinetic chevron rollover behavior is recovered from the mean first passage time, with the U-shape dependence on temperature. The fastest folding temperature T-0 is found to be smaller than the folding transition temperature T-f. We found that the fluctuations of the kinetics through the distribution of first passage time show rather universal behavior, from high-temperature exponential Poissonian kinetics to the relatively low-temperature highly nonexponential kinetics. The transition temperature is at T-k and T-0, T-k, T-f. In certain low-temperature regimes, a power law behavior at long time emerges. At very low temperatures ( lower than trapping transition temperature T< T-0/(4&SIM;6)), the kinetics is an exponential Poissonian process again.

Probing the kinetics of single molecule protein folding

We propose an approach to integrate the theory, simulations, and experiments in protein-folding kinetics. This is realized by measuring the mean and high-order moments of the first-passage time and its associated distribution. The full kinetics is revealed in the current theoretical framework through these measurements. In the experiments, information about the statistical properties of first-passage times can be obtained from the kinetic folding trajectories of single molecule experiments ( for example, fluorescence). Theoretical/simulation and experimental approaches can be directly related. We study in particular the temperature-varying kinetics to probe the underlying structure of the folding energy landscape. At high temperatures, exponential kinetics is observed; there are multiple parallel kinetic paths leading to the native state. At intermediate temperatures, nonexponential kinetics appears, revealing the nature of the distribution of local traps on the landscape and, as a result, discrete kinetic paths emerge. At very low temperatures, exponential kinetics is again observed; the dynamics on the underlying landscape is dominated by a single barrier.

Quantifying the kinetic paths of flexible biomolecular recognition

Biomolecular recognition often involves large conformational changes, sometimes even local unfolding. The identification of kinetic pathways has become a central issue in understanding the nature of binding. A new approach is proposed here to study the dynamics of this binding-folding process through the establishment of a path-integral framework on the underlying energy landscape. The dominant kinetic paths of binding and folding can be determined and quantified. The significant coupling between the binding and folding of biomolecules often exists in many important cellular processes. In this case, the corresponding kinetic paths of binding are shown to be intimately correlated with those of folding and the dynamics becomes quite cooperative. This implies that binding and folding happen concurrently. When the coupling between binding and folding is weak (strong), the kinetic process usually starts with significant folding (binding) first, with the binding (folding) later proceeding to the end. The kinetic rate can be obtained through the contributions from the dominant paths. The rate is shown to have a bell-shaped dependence on temperature in the concentration-saturated regime consistent with experiment. The changes of the kinetics that occur upon changing the parameters of the underlying binding-folding energy landscape are studied.

Single-molecule dynamics reveals cooperative binding-folding in protein recognition

The study of associations between two biomolecules is the key to understanding molecular function and recognition. Molecular function is often thought to be determined by underlying structures. Here, combining a single-molecule study of protein binding with an energy-landscape-inspired microscopic model, we found strong evidence that biomolecular recognition is determined by flexibilities in addition to structures. Our model is based on coarse-grained molecular dynamics on the residue level with the energy function biased toward the native binding structure ( the Go model). With our model, the underlying free-energy landscape of the binding can be explored. There are two distinct conformational states at the free-energy minimum, one with partial folding of CBD itself and significant interface binding of CBD to Cdc42, and the other with native folding of CBD itself and native interface binding of CBD to Cdc42. This shows that the binding process proceeds with a significant interface binding of CBD with Cdc42 first, without a complete folding of CBD itself, and that binding and folding are then coupled to reach the native binding state.

First-passage time distribution and non-Markovian diffusion dynamics of protein folding

We study the kinetics of protein folding via statistical energy landscape theory. We concentrate on the local-connectivity case, where the configurational changes can only occur among neighboring states, with the folding progress described in terms of an order parameter given by the fraction of native conformations. The non-Markovian diffusion dynamics is analyzed in detail and an expression for the mean first-passage time (MFPT) from non-native unfolded states to native folded state is obtained. It was found that the MFPT has a V-shaped dependence on the temperature. We also find that the MFPT is shortened as one increases the gap between the energy of the native and average non-native folded states relative to the fluctuations of the energy landscape. The second- and higher-order moments are studied to infer the first-passage time distribution. At high temperature, the distribution becomes close to a Poisson distribution, while at low temperatures the distribution becomes a Levy-type distribution with power-law tails, indicating a nonself-averaging intermittent behavior of folding dynamics. We note the likely relevance of this result to single-molecule dynamics experiments, where a power law (Levy) distribution of the relaxation time of the underlined protein energy landscape is observed.

Temperature dependence of the distribution of the first passage time: Results from discontinuous molecular dynamics simulations of an all-atom model of the second beta-hairpin fragment of protein G

More than 22 000 folding kinetic simulations were performed to study the temperature dependence of the distribution of first passage time (FPT) for the folding of an all-atom Go-like model of the second beta-hairpin fragment of protein G. We find that the mean FPT (MFPT) for folding has a U (or V)-shaped dependence on the temperature with a minimum at a characteristic optimal folding temperature T-opt*. The optimal folding temperature T-opt* is located between the thermodynamic folding transition temperature and the solidification temperature based on the Lindemann criterion for the solid. Both the T-opt* and the MFPT decrease when the energy bias gap against nonnative contacts increases. The high-order moments are nearly constant when the temperature is higher than T-opt* and start to diverge when the temperature is lower than T-opt*. The distribution of FPT is close to a log-normal-like distribution at T* greater than or equal to T-opt*. At even lower temperatures, the distribution starts to develop long power-law-like tails, indicating the non-self-averaging intermittent behavior of the folding dynamics. It is demonstrated that the distribution of FPT can also be calculated reliably from the derivative of the fraction not folded (or fraction folded), a measurable quantity by routine ensemble-averaged experimental techniques at dilute protein concentrations.

Stochastic protein folding simulation in the three-dimensional HP-model

We present results from three-dimensional protein folding simulations in the HP-model on ten benchmark problems. The simulations are executed by a simulated annealing-based algorithm with a time-dependent cooling schedule. The neighbourhood relation is determined by the pull-move set. The results provide experimental evidence that the maximum depth D of local minima of the underlying energy landscape can be upper bounded by D < n(2/3). The local search procedure employs the stopping criterion (In/delta)(D/gamma) where m is an estimation of the average number of neighbouring conformations, gamma relates to the mean of non-zero differences of the objective function for neighbouring conformations, and 1-delta is the confidence that a minimum conformation has been found. The bound complies with the results obtained for the ten benchmark problems. (c) 2008 Elsevier Ltd. All rights reserved.

Influence of the anion on the electrical conductivity and glass formation of 1-butyl-3-methylimidazolium ionic liquids

Six ionic liquids based on the 1-butyl-3-methylimidazolium cation have been studied. As anions Cl-, Br-, I-, [NCS](-), [N(CN)(2)](-), and [BF4](-) were selected. The electrical conductivities were determined between 173 and 393 K based on impedance measurements in the frequency range from 0.1 to 10(7) Hz. The electrical conductivity increases, whereas the glass transition temperature, the fragility, and the low temperature activation energy decrease with increasing anion size. The results can be understood from the changing anion-cation interaction strength with changing anion size and from the energy landscape interpretation of the glass transition dynamics. (C) 2010 American Institute of Physics. [doi:10.1063/1.3455892]

Reaction Mechanisms of Crotonaldehyde Hydrogenation on Pt(111): Density Functional Theory and Microkinetic Modeling

The microkinetics based on density function theory (DFT) calculations is utilized to investigate the reaction mechanism of crotonaldehyde hydrogenation on Pt(111) in the free energy landscape. The dominant reaction channel of each hydrogenation product is identified. Each of them begins with the first surface hydrogenation of the carbonyl oxygen of crotonaldehyde on the surface. A new mechanism, 1,4-addition mechanism generating enols (butenol), which readily tautomerize to saturated aldehydes (butanal), is identified as a primary mechanism to yield saturated aldehydes instead of the 3,4-addition via direct hydrogenation of the ethylenic bond. The calculation results also show that the full hydrogenation product, butylalcohol, mainly stems from the deep hydrogenation of surface open-shell dihydrogenation intermediates. It is found that the apparent barriers of the dominant pathways to yield three final products are similar on P(111), which makes it difficult to achieve a high selectivity to the desired crotyl alcohol (COL).

Numerical assessment of potential impacts of hydraulically fractured Bowland Shale on overlying aquifers

Natural gas extracted from hydraulically fractured shale formations potentially has a big impact on the global energy landscape. However, there are concerns of potential environmental impacts of hydraulic fracturing of the shale formations, particularly those related to water quality. To evaluate the potential impact of hydraulically fractured shale on overlying aquifers, we conduct realizations of numerical modeling simulations to assess fluid flow and chloride transport from a synthetic Bowland Shale over a period of 11,000 years. The synthetic fractured shale was represented by a three-dimensional discrete fracture model that was developed by using the data from a Bowland Shale gas exploration in Lancashire, UK. Chloride mass exchange between fractures and the rock matrix was fully accounted for in the model. The assessment was carried out to investigate fluid and chloride mass fluxes before, during, and after hydraulic fracturing of the Bowland Shale. Impacts of the upward fracture height and aperture, as well as hydraulic conductivity of the multilayered bedrock system, are also included this assessment. This modeling revealed that the hydraulically fractured Bowland Shale is unlikely to pose a risk to its overlying groundwater quality when the induced fracture aperture is ≤200 µm. With the fracture aperture ≥1000 µm, the upward chloride flux becomes very sensitive to the upward fracture height growth and hydraulic conductivity of the multilayered bedrock system. In the extremely unlikely event of the upward fracture growth directly connecting the shale formation to the overlying Sherwood Sandstone aquifer with the fracture aperture ≥1000 µm, the upward chloride mass flux could potentially pose risks to the overlying aquifer in 100 years. The model study also revealed that the upward mass flux is significantly intercepted by the horizontal mass flux within a high permeable layer between the Bowland Shale and its overlying aquifers, reducing further upward flux toward the overlying aquifers.

Electrical conductivity and glass formation in nitrile-functionalized pyrrolidinium bis(trifluoromethylsulfonyl)imide ionic liquids: chain length and odd–even effects of the alkyl spacer between the pyrrolidinium ring and the nitrile group

The electrical conductivity of a series of pyrrolidinium bis(trifluoromethylsulfonyl)imide ionic liquids, functionalized with a nitrile (cyano) group at the end of an alkyl chain attached to the cation, was studied in the temperature range between 173 K and 393 K. The glass formation of the ionic liquids is influenced by the length of the alkyl spacer separating the nitrile function from the pyrrolidinium ring. The electrical conductivity and the viscosity do not show a monotonic dependence on the alkyl spacer length, but rather an odd-even effect. An explanation for this behavior is given, including the potential energy landscape picture for the glass transition.

Probing the Unfolded Configurations of a β-Hairpin Using Sketch-Map

This work examines the conformational ensemble involved in β-hairpin folding by means of advanced molecular dynamics simulations and dimensionality reduction. A fully atomistic description of the protein and the surrounding solvent molecules is used, and this complex energy landscape is sampled by means of parallel tempering metadynamics simulations. The ensemble of configurations explored is analyzed using the recently proposed sketch-map algorithm. Further simulations allow us to probe how mutations affect the structures adopted by this protein. We find that many of the configurations adopted by a mutant are the same as those adopted by the wild-type protein. Furthermore, certain mutations destabilize secondary-structure-containing configurations by preventing the formation of hydrogen bonds or by promoting the formation of new intramolecular contacts. Our analysis demonstrates that machine-learning techniques can be used to study the energy landscapes of complex molecules and that the visualizations that are generated in this way provide a natural basis for examining how the stabilities of particular configurations of the molecule are affected by factors such as temperature or structural mutations.