Event detection and sub‐state discovery from biomolecular simulations using higher‐order statistics: Application to enzyme adenylate kinase

Biomolecular simulations at millisecond and longer time‐scales can provide vital insights into functional mechanisms. Because post‐simulation analyses of such large trajectory datasets can be a limiting factor in obtaining biological insights, there is an emerging need to identify key dynamical events and relating these events to the biological function online, that is, as simulations are progressing. Recently, we have introduced a novel computational technique, quasi‐anharmonic analysis (QAA) (Ramanathan et al., PLoS One 2011;6:e15827), for partitioning the conformational landscape into a hierarchy of functionally relevant sub‐states. The unique capabilities of QAA are enabled by exploiting anharmonicity in the form of fourth‐order statistics for characterizing atomic fluctuations. In this article, we extend QAA for analyzing long time‐scale simulations online. In particular, we present HOST4MD—a higher‐order statistical toolbox for molecular dynamics simulations, which (1) identifies key dynamical events as simulations are in progress, (2) explores potential sub‐states, and (3) identifies conformational transitions that enable the protein to access those sub‐states. We demonstrate HOST4MD on microsecond timescale simulations of the enzyme adenylate kinase in its apo state. HOST4MD identifies several conformational events in these simulations, revealing how the intrinsic coupling between the three subdomains (LID, CORE, and NMP) changes during the simulations. Further, it also identifies an inherent asymmetry in the opening/closing of the two binding sites. We anticipate that HOST4MD will provide a powerful and extensible framework for detecting biophysically relevant conformational coordinates from long time‐scale simulations. Proteins 2012. © 2012 Wiley Periodicals, Inc.     

Thermodynamic and Kinetic Analyses of DNA Triplex Formation: Application of Filter-Binding Assay

Abstract

We have developed a simple and efficient method for studying equilibrium thermodynamics and kinetics of DNA triplex formation, which utilizes a filter-binding procedure. The application of this method to the triplex formation between a double-stranded homopurine-homopyrimidine and a single-stranded homopyrimidine oligonucleotides has demonstrated its ability in the quantitative estimation of equilibrium binding constants and rate constants under various conditions. Thus, this simple method can serve as a powerful tool for the systematic analysis of sequence and environmental effects on the equilibrium and kinetic quantities in the triplex formation.     

INDEX TO SUBJECTS,Volume 2

Abstract

The effect of U(34) dethiolation on the anticodon-anticodon association between E.coli tRNA(Glu) and yeast tRNA(Phe) has been studied by the temperature jump relaxation technique. An important destabilization upon replacement of the thioketo group of s²U(34) by a keto group, was revealed by a lowering of melting temperature of about 20° C. The measured kinetic parameters indicated that this destabilization effect was originated in an increase of dissociation and a decrease of association rate constants by a factor of 4 to 5. Modifications in both stacking interactions and flexibility in the anticodon loop would be responsible for this effect.     

Calculation of the Generalized Susceptibility for a Highly Supercooled Fluid Through Molecular-Dynamics Simulation

Abstract

A new method of computation of generalized susceptibility and dynamical structure factor through molecular dynamics (MD) simulation is proposed. This gives rise to a reliable and accurate result more than that calculated from a conventional method with a direct Fourier transformation. Computational results are presented for the imaginary part of the generalized susceptibility, X″ (ω), for a binary soft-sphere fluid with a super-long-time molecular dynamics (MD) simulation. Both α- and β-peaks in X″ (ω) in a supercooled fluid is shown for the first time through the present MD computation. The MD result obtained is in a good agreement with that obtained by the trapping diffusion model, which we have previously proposed for the glass transition.     

Kinetics of inhibition of alkaline phosphatase from green crab (Scylla serrata) by N-bromosuccinimide

The inactivation of alkaline phosphatase from green crab (Scylla serrata) by N-bromosuccinimide has been studied using the kinetic method of the substrate reaction during modification of enzyme activity previously described by Tsou [(1988),Adv. Enzymol. Related Areas Mol. Biol. 61, 381–436]. The results show that inactivation of the enzyme is a slow, reversible reaction. The microscopic rate constants for the reaction of the inactivator with free enzyme and the enzyme-substrate complex were determined. Comparison of these rate constants indicates that the presence of substrate offers marked protection of this enzyme against inactivation by N-bromosuccinimide. The above results suggest that the tryptophan residue is essential for activity and is situated at the active site of the enzyme.Abbreviations ALP alkaline phosphatase - PNPP p-nitrophenyl phosphate - NBS N-bromosuccinimide     

The Value of Mechanistic Biophysical Information for Systems-Level Understanding of Complex Biological Processes Such as Cytokinesis

This review illustrates the value of quantitative information including concentrations, kinetic constants and equilibrium constants in modeling and simulating complex biological processes. Although much has been learned about some biological systems without these parameter values, they greatly strengthen mechanistic accounts of dynamical systems. The analysis of muscle contraction is a classic example of the value of combining an inventory of the molecules, atomic structures of the molecules, kinetic constants for the reactions, reconstitutions with purified proteins and theoretical modeling to account for the contraction of whole muscles. A similar strategy is now being used to understand the mechanism of cytokinesis using fission yeast as a favorable model system.     

Kinetics of Thermal Inactivation of Lactate Dehydrogenase from Rabbit Muscle

The kinetics of thermal inactivation of rabbit muscle lactate dehydrogenase at different temperatures has been studied using the kinetic method for the substrate reaction during irreversible inhibition of enzyme activity previously described by Tsou [Adv. Enzymol. Relat. Areas Mol. Biol. (1988), 61, 381–436]. The results show that thermal inactivation of the enzyme is an irreversible reaction. Microscopic rate constants were determined for thermal inactivation of the free enzyme and the enzyme–substrate complex. The inactivation rate constant of the free enzyme is much larger than the rate constant of the enzyme–substrate complex. The results suggest that the presence of the substrate has a certain protective effect against thermal inactivation of the enzyme.     

Kinetics of the course of reactivation of aminoacylase reconstituted using Mn2+ ions

The kinetic theory of the substrate reaction during irreversible change of enzyme activity previously described by Tsou (Tsou (1988),Adv. Enzymol. Relat. Areas Mol. Biol.61, 381–436] has been applied to a study of the kinetics of the course of reactivation during reconstitution of apo-aminoacylase using Mn²⁺ or Zn²⁺. The kinetic parameters for Mn²⁺-and Zn²⁺-reconstituted enzymes and the microscopic rate constants for reactivation during reconstitution were determined. The kinetic analysis suggests the presence of a second Mn²⁺ binding site in Mn²⁺-reconstituted aminoacylase.     

Computer Simulation of Two-Dimensional Continuum Flows by the Direct Simulation Monte Carlo Method

Abstract

Computer simulations using particles are an attractive method to extract microscopic information of flow phenomena [1]. The molecular dynamics (MD) method, in which Newton's equations of motions are integrated, gives the temporal development of the system. In the MD simulation of fluid flows, the computational region is limited to atomistic scales [2]. On the other hand, the direct simulation Monte Carlo (DSMC) method, in which collisions of particles are made on a probabilistic basis, has a potential of treating a realistic system with a macroscopic scale length retaining the atomistic details. The DSMC method provides an efficient way to integrate the Boltzmann equation from the rarefied gas to the near-continuum region. Bird clarified the validity of the DSMC method in the near-continuum flow region [3]. However, the DSMC method has not been applied to the continuum region and compared with the continuum hydrodynamics.     

Bayesian inference for parameter estimation in lactoferrin-mediated iron transport across blood-brain barrier

BackgroundIn neurodegenerative diseases such as Alzheimer's and Parkinson's, excessive irons as well as lactoferrin (Lf), but not transferrin (Tf), have been found in and around the affected regions of the brain. These evidences suggest that lactoferrin plays a critical role during neurodegenerative diseases, although Lf-mediated iron transport across blood-brain barrier (BBB) is negligible compared to that of transferrin in normal condition. However, the kinetics of lactoferrins and lactoferrin-mediated iron transport are still unknown.MethodTo determine the kinetic rate constants of lactoferrin-mediated iron transport through BBB, a mass-action based ordinary differential equation model has been presented. A Bayesian framework is developed to estimate the kinetic rate parameters from posterior probability density functions. The iron transport across BBB is studied by considering both Lf- and Tf-mediated pathways for both normal and pathologic conditions.ResultsUsing the point estimates of kinetic parameters, our model can effectively reproduce the experimental data of iron transport through BBB endothelial cells. The robustness of the model and parameter estimation process are further verified by perturbation of kinetic parameters. Our results show that surge in high-affinity receptor density increases lactoferrin as well as iron in the brain.ConclusionsDue to the lack of a feedback loop such as iron regulatory proteins (IRPs) for lactoferrin, iron can transport to the brain continuously, which might increase brain iron to pathological levels and can contribute to neurodegeneration.General significanceThis study provides an improved understanding of presence of lactoferrin and iron in the brain during neurodegenerative diseases.     

Thermal decomposition behaviour of polyethylene in oxygen-free and low oxygen content circumstances by reactive molecular dynamic simulation

In the present study, the thermal decomposition characteristics of polyethylene (PE) in oxygen-free and low oxygen content circumstances were examined by molecular dynamic (MD) simulations at atomic scale using reactive force field (ReaxFF). Temporal evolutions of species were captured reasonably during the processes of thermal decomposition. The effects of oxygen content, temperature and heating rate were also analysed. In addition, the kinetic properties were predicted with reliable parameters. The results show good agreements with the available ones, which illustrate that the species with two carbon atoms are the vast majority of final products. Higher oxygen content and temperature promote the generation of small molecules with carbon atom number less than or equal to 10. In the presence of oxygen, greater activation energy span and reaction order are calculated with lower adjust R², which indicates complex reactions according to kinetic analysis. The initial decomposition temperature of PE is proportional to the heating rate owing to heat transfer lag.     

Molecular Dynamics Simulations for 1:1 Solvent Primitive Model Electrolyte Solutions

Abstract

Molecular dynamics (MD) simulations at constant temperature have been carried out for systems of 1:1 solvent primitive model (SPM) electrolyte solutions. Equilibrium thermodynamics, mean cluster size, self-diffusion coefficients, and collision frequencies were computed to examine the electrostatic effects on the structural and dynamical properties. Coherent ionic cluster motion was deduced from a cluster analysis and from the dependence of the velocity and force autocorrelation functions (FACFs). The resulting MD data for the collision frequencies and self-diffusivities of both ions and hard-spheres were shown to be in good agreement with the theoretical predictions.     

Blue Moon Approach to Rare Events

The "Blue Moon" ensemble is a computationally efficient molecular dynamics method to estimate the rate constants of rare activated events when the process can be described by a reaction coordinate ξ(r), a well-defined function in configuration space. By means of holonomic constraints a number of values of ξ(r) can be prescribed along the relevant path to identify the "bottleneck" region first and to sample an ensemble of starting conditions to generate activated trajectories. These MD trajectories sample phase space according to a biased configurational distribution. With a suitable re-weighting of averages from such ensemble of trajectories one can characterize completely rare events.     

A continuum-atomistic method for incorporating Joule heating into classical molecular dynamics simulations

A hybrid atomistic-continuum method is presented for incorporating Joule heating into large-scale molecular dynamics (MD) simulations. When coupled to a continuum thermostat, the method allows resistive heating and heat transport in metals to be modeled without explicitly including electronic degrees of freedom. Atomic kinetic energies in a MD simulation are coupled via an ad hoc feedback loop to continuum current and heat transfer equations that are solved numerically on a finite difference grid (FDG). For resistive heating, the resistance in each region of the FDG is calculated from the experimental resistivity, atomic density, and average kinetic energy in the MD simulation. A network of resistors is established from which the potential at every FDG region is calculated given an applied voltage. The potential differences and the resistance between connected FDG regions are used to calculate the current between the two points and the heat generated from that current. This information is then added back into the atomic simulation. The method is demonstrated by simulating Joule heating and melting, along with associated changes in current, of single and bundles of metal nanowires, as well as a “pinched” wire under applied strain.     

Muscarinic binding to mouse brain receptor sites

In mouse brain the binding of [³H]-Atropine to the muscarinic receptor seems to be a simple mass-action determined process as gauged both by approach to equilibrium kinetics and binding at equilibrium. In contrast, using isotopic dilution technique, dissociation measurements indicate the existence of two receptor-ligand complexes. It would appear that association and dissociation rates of binding of the muscarinic antagonists atropine, scopolamine, N-methyl-4-piperidyl benzilate (4NMPB) and 3-quinuclidinyl benzilate (QNB) decrease with increasing affinity based on comparisons of kinetic binding data. The differences between the association rate constants are small whereas those between the dissociation rate constants differ markedly. This kinetic behavior is similar to the well-known time profile of antimuscarinic activity in isolated tissues. These phenomena are discussed in terms of possible isomerization of the receptor-ligand complex, as has been proposed recently for [³H]-scopolamine and [³H]-4NMPB binding.     

Low-mass molecular dynamics simulation for configurational sampling enhancement: More evidence and theoretical explanation

It has been reported recently that classical, isothermal–isobaric molecular dynamics (NTP MD) simulations at a time step of 1.00 fs of the standard-mass time (Δt=1.00 fs^smt) and a temperature of ≤340 K using uniformly reduced atomic masses by tenfold offers better configurational sampling than standard-mass NTP MD simulations at the same time step. However, it has long been reported that atomic masses can also be increased to improve configurational sampling because higher atomic masses permit the use of a longer time step. It is worth investigating whether standard-mass NTP MD simulations at Δt=2.00 or 3.16 fs^smt can offer better or comparable configurational sampling than low-mass NTP MD simulations at Δt=1.00 fs^smt. This article reports folding simulations of two β-hairpins showing that the configurational sampling efficiency of NTP MD simulations using atomic masses uniformly reduced by tenfold at Δt=1.00 fs^smt is statistically equivalent to and better than those using standard masses at Δt=3.16 and 2.00 fs^smt, respectively. The results confirm that, relative to those using standard masses at routine Δt=2.00 fs^smt, the low-mass NTP MD simulations at Δt=1.00 fs^smt are a simple and generic technique to enhance configurational sampling at temperatures of ≤340 K.     

Evaluation of droplet-based microfluidic platforms as a convenient tool for lipases and esterases assays

Abstract

The accurate estimation of kinetic parameters is of fundamental importance for biochemical studies for research and industry. In this paper, we demonstrate the application of a modular microfluidic system for execution of enzyme assays that allow determining the kinetic parameters of the enzymatic reactions such as V_max – the maximum rate of reaction and K_M – the Michaelis constant. For experiments, the fluorogenic carbonate as a probe for a rapid determination of the kinetic parameters of hydrolases, such as lipases and esterases, was used. The microfluidic system together with the method described yields the kinetic constants calculated from the concentration of enzymatic product changes via a Michaelis–Menten model using the Lambert function W(x). This modular microfluidic system was validated on three selected enzymes (hydrolases).     

Alkylboronic acids accelerate affinity labelling of acetylcholinesterase with N,N,-dimethyl-2-phenylaziridinium ion

The kinetics of acetylcholinesterase alkylation with N,N-dimethyl-2-phenylaziridinium ion, the anionic-site-directed affinity label, has been investigated in the presence of alkylboronic acids, which are known as the esteratic-site-directed reversible inhibitors of the enzyme. The ternary complex of the enzyme, the aziridinium ion and alkylboronic acid, are formed in this reaction. In the case of propylboronic acid, for which the complete kinetic analysis of the acceleration effect has been carried out, the 85-fold increase in the rate of the enzyme alkylation reaction has been found. This acceleration effect was connected with the alkylation step, whereas the non-covalent binding of the aziridinium ion in the enzyme active centre was even hindered by the alkylboronic acid. The possible mechanism of this kinetic acceleration phenomenon is discussed with special reference to the kinetic data for the spontaneous solvolysis reaction of the aziridinium ion in water and organic solvents.     

Study on properties of liquid ammonia via molecular dynamics simulation based on ABEEMσπ polarisable force field

Abstract

The molecular dynamics simulation has been performed to investigate the charge distribution, structural and dynamical properties of liquid ammonia at 273 K using a polarisable force field of the atom-bond electronegativity equalisation method (ABEEMσπ). One ammonia molecule in this model has eight charge sites, one N atomic site, three H atomic sites, three N–H bond sites and one lone-pair electron site. ABEEMσπ model can present the quantitative site charges of molecular ammonias in liquid and their changing in response to their surroundings. The radial distribution functions and dynamical properties are in fair agreement with the available experimental data. The first peak of g_NN(r) appears at N–N distance of ~3.50 ± 0.05 Å where most hydrogen bonds are formed. The average coordination number of the first shell is 13.0 ± 0.1 among which a central ammonia molecule intimately connects 3 ~ 4 ammonia molecules by hydrogen bonds. The power spectrum shows the vibrations of hydrogen bonds. For a reference, a simple estimation of the average hydrogen bonding energy in liquid ammonia is 6.5 ± 0.1 kcal/mol larger than 3.8 ± 0.3 kcal/mol in dimer ammonia. Our simulation results provide more detailed information about liquid ammonia.     

Irreversible kinetics of β-N-acetyl-d-glucosaminidase from prawn (Penaeus vannamei) inactivated by mercuric ion

Cysteine residues in prawn (Penaeus vannamei) β-N-acetyl-d-glucosaminidase (NAGase, EC 3.2.1.52) have been modified by p-chloromercuribenzoate (PCMB). The results show that sulfhydryl group is essential for the activity of the enzyme. Inactivation kinetics of the enzyme by mercuric chloride (HgCl₂) has been studied using the kinetic method of the substrate reaction during inactivation of enzyme previously described by Tsou. The kinetic results show that the inactivation of the enzyme is an irreversible reaction. The microscopic rate constants for the reaction of Hg²⁺ with free enzyme and with the enzyme-substrate complex are determined. Comparison of these rate constants indicates that the presence of substrate offers marked protection of this enzyme against inactivation by Hg²⁺. The above results suggest that the cysteine residue is essential for activity.