A molecular dynamics study of a miRNA:mRNA interaction

In this paper we present a methodology to evaluate the binding free energy of a miRNA:mRNA complex through molecular dynamics (MD)–thermodynamic integration (TI) simulations. We applied our method to the Caenorhabditis elegans let-7 miRNA:lin-41 mRNA complex—a validated miRNA:mRNA interaction—in order to estimate the energetic stability of the structure. To make the miRNA:mRNA simulation possible and realistic, the methodology introduces specific solutions to overcome some of the general challenges of nucleic acid simulations and binding free energy computations that have been discussed widely in many previous research reports. The main features of the proposed methodology are: (1) positioning of the restraints imposed on the simulations in order to guarantee complex stability; (2) optimal sampling of the phase space to achieve satisfactory accuracy in the binding energy value; (3) determination of a suitable trade-off between computational costs and accuracy of binding free energy computation by the assessment of the scalability characteristics of the parallel simulations required for the TI. The experiments carried out demonstrate that MD simulations are a viable strategy for the study of miRNA binding characteristics, opening the way to the development of new computational target prediction methods based on three-dimensional structure information.     

Evaluation of the Adaptive Umbrella Sampling Method

Abstract

The adaptive umbrella sampling technique, introduced recently to improve the probability ratio method and found to perform more reliably than the customary harmonic umbrella sampling, is tested and compared with other free energy methods. One of the tests applies the method to a transition involving a chemical change: calculation of the hydration free energy difference between acetone and dimethylamine and the other test calculates the conformational free energy difference between the C ₇ and α_R conformations of the alanide dipeptide. The dipeptide problem is also treated by two types of thermodynamic integrations and by the perturbation method. The result for the acetone-dimethylamine problem is compared with previous calculations on the same system using the perturbation method, overlap ratio method and finite difference thermodynamic integration. Enhancements to the adaptive umbrella sampling method are also presented.     

Hysteresis and Statistical Errors in Free Energy Perturbation L to D Amino Acid Conversion

Abstract

A theory based on a Langevin equation along the reaction coordinate is developed to explain and calculate systematic and statistical errors in free energy perturbation simulations. The errors are calculated exactly when both the perturbation potential and the mean potential from the surrounding degrees of freedom are harmonic in the reaction coordinate. The effect of the mean potential is small as long as the force constant is small compared to the force constant of the perturbation potential. This indicates that the results obtained with zero mean force may still be valid as long as the second derivate of the mean potential is small compared to that of the perturbation potential. The theory is applied to conversion between L and D amino acids by changing the position of the minimum of the harmonic improper dihedral potential between ±35.264 degrees. For phenylalanine bound in the active site of a protein (thermolysin) we find from 20 psec. simulations statistical errors and hysteresis that both are about 2.5 kJ/mol in agreement with what is obtained from the theoretical predictions. The statistical errors are proportional to the square root of the coupling to the heat bath and inversely proportional to the square root of integration time while the (positive) hysteresis due to that the reaction coordinate lags behind is linear in the same quantities. This shows that the systematic errors will dominate in short simulations while the statistical ones will dominate for long simulations. The treatment is based on that the systematic influence of the surroundings can be represented by a mean force upon the reaction coordinate. If the relaxation processes of the environment are slow this may not be true. Then additional errors have to be considered.     

Classical cumulant dynamics for statistical chemical physics

Abstract

We developed classical cumulant dynamics for statistical mechanics in order to evaluate thermal equilibrium properties of a given system. The equations of motion (EOMs) for momentum and position were formulated together with those for second-order cumulant variables, which are functions of second-order moments. From the Kramers equation, and simplified EOMs were obtained by assuming a stationary state limit. The present method combined with the umbrella integration method was applied to evaluate free energy surface of a seven-particle Morse cluster. With low computational costs, the present approach gave almost equivalent free energy barrier those by conventional classical molecular dynamics.     

Role of a reaction coordinate in free energy calculations

Abstract

The free energy calculation method emerges as a viable technique for ‘in-silico’ calorimetry. Efficient sampling techniques and the good choice of a reaction path connecting the reactant and the product state enable accurate computations of the free energy differences. We argue that in many cases the thermodynamic integration technique has the lowest variance when the transformation between the reactant and the product state proceeds along the natural path of the studied chemical reaction. We provide examples of free energy calculations for the fragmentation of the charged clusters and the swapping reaction of oligomer formation in proteins that follow a tentative reaction mechanism.     

Non-Boltzmann thermodynamic integration (NBTI) for macromolecular systems: relative free energy of binding of trypsin to benzamidine and benzylamine

The relative free energies of binding of trypsin to two amine inhibitors, benzamidine (BZD) and benzylamine (BZA), were calculated using non-Boltzmann thermodynamic integration (NBTI). Comparison of the simulations with the crystal structures of both complexes, trypsin-BZD and trypsin-BZA, shows that NBTI simulations better sample conformational space relative to thermodynamic integration (TI) simulations. The relative binding free energy calculated using NBTI was much closer to the experimentally determined value than that obtained using TI. The error in the TI simulation was found to be primarily due to incorrect sampling of BZA's conformation in the binding pocket. In contrast, NBTI produces a smooth mutation from BZD to BZA using a surrogate potential, resulting in a much closer agreement between the inhibitors' conformations and the omit electron density maps. This superior agreement between experiment and simulation, of both relative binding free energy differences and conformational sampling, demonstrates NBTI's usefulness for free energy calculations in macromolecular simulations.     

Computing free energies using nested sampling-based approaches

Abstract

Nested sampling (NS) has emerged as a powerful statistical mechanical sampling technique to compute the partition function of atomic and molecular systems. From the partition function all thermodynamic quantities can be calculated in absolute terms, including absolute free energies and entropies. In this article, we provide a brief overview of NS within a Bayesian context, as well as overviews of how NS is used to compute the partition functions and thermodynamic quantities in the canonical and isothermal-isobaric ensembles. Then we introduce a new scheme, Coupling Parameter Path Nested Sampling, to estimate the free energy difference between two systems with different potential energy functions. The method uses a NS simulation to traverse the same path through phase space as would be covered in traditional coupling parameter-based methods such as thermodynamic integration and perturbation approaches. We demonstrate the new method with two case studies and confirm its accuracy by comparison to conventional methods, including Widom test particle insertion and thermodynamic integration. The proposed method provides a powerful alternative to traditional coupling parameter-based free energy simulation methods.     

A Comparison of Seven Fast but Approximate Methods to Compute the Free Energy of Deprotonation for Amino Acids in Aqueous Solution

Abstract

In recent years, a variety of methods based on statistical mechanics have been successfully applied to calculate free energy differences of chemical reactions from molecular simulation. The accuracy and computational efficiency vary strongly between these methods. Seven approximate but fast methods to calculate free energy differences are compared in terms of accuracy and efficiency with the accurate but expensive thermodynamic integration method as reference, using 28 protonation and deprotonation reactions of aspartic acid in aqueous solution as test cases. At least two simulations are required to obtain an accurate free energy difference between two states of the system. Both, the averaged one-step perturbation method and the linear response method yield the most accurate results, while the latter method shows the fastest convergence.     

Sparse sampling of water density fluctuations near liquid-vapor coexistence

Abstract

The free energetics of water density fluctuations in bulk water, at interfaces, and in hydrophobic confinement inform the hydration of hydrophobic solutes as well as their interactions and assembly. The characterisation of such free energetics is typically performed using enhanced sampling techniques such as umbrella sampling. In umbrella sampling, order parameter distributions obtained from adjacent biased simulations must overlap in order to estimate free energy differences between biased ensembles. Many biased simulations are typically required to ensure such overlap, which exacts a steep computational cost. We recently introduced a sparse sampling method, which circumvents the overlap requirement by using thermodynamic integration to estimate free energy differences between biased ensembles. Here we build upon and generalise sparse sampling for characterising the free energetics of water density fluctuations in systems near liquid-vapor coexistence. We also introduce sensible heuristics for choosing the biasing potential parameters and strategies for adaptively refining them, which facilitate the estimation of such free energetics accurately and efficiently. We illustrate the method by characterising the free energetics of cavitation in a large volume in bulk water. We also use sparse sampling to characterise the free energetics of capillary evaporation for water confined between two hydrophobic plates. In both cases, sparse sampling is nearly two orders of magnitude faster than umbrella sampling. Given its efficiency, the sparse sampling method is particularly well suited for characterising free energy landscapes for systems wherein umbrella sampling is prohibitively expensive.     

Effect of Confinement on Melting in Slit-Shaped Pores: Experimental and Simulation Study of Aniline in Activated Carbon Fibers

Abstract

We report both experimental and molecular simulation studies of the melting behavior of aniline confined within an activated carbon fiber having slit-shaped pores. Dielectric relaxation spectroscopy is used to determine the transition temperatures and also the dielectric relaxation times over the temperature range 240 to 340 K. For the confined system two transitions were observed, one at 298 K and a second transition at 324 K. The measured relaxation times indicate that the low temperature phase (below 298 K) is a crystalline or partially crystalline solid phase, while that above 324 K is a liquid-like phase; for the intermediate phase, in the range 298–324 K, the relaxation times are of the order 10^?5s, which is typical of a hexatic phase. The melting temperature of the confined system is well above that of bulk aniline, which is 267 K. The simulations are carried out using the Grand Canonical Monte Carlo method together with Landau free energy calculations, and phase transitions are located as state points where the grand free energies of two confined phases are equal. The nature of these phases is determined by analysis of in-plane pair positional and orientational correlation functions. The simulations also show two transitions. The first is a transition from a two-dimensional hexagonal crystal phase to a hexatic phase at 296 K; the second transition is from the hexatic to a liquid-like phase at 336 K. Confinement within the slit-shaped pores appears to stabilize the hexatic phase, which is the stable phase over a wider temperature range than for quasi-two-dimensional thin films.     

Calculation of conformational free energies by confinement simulations in explicit water with implicit desolvation

Abstract

The confinement method is a robust and conceptually simple free energy simulation method that allows the calculation of conformational free energy differences between highly dissimilar states. Application of the method to explicitly solvated systems requires a multi-stage simulation protocol for the calculation of desolvation free energies. Here we show that these desolvation free energies can be readily obtained from an implicit treatment, which is simpler and less costly. The accuracy and robustness of this protocol was shown by the calculation of conformational free energy differences of a series of explicitly solvated test systems. Given the accuracy and ease by which these free energy differences were obtained, the confinement method is promising for the treatment of conformational changes in large and complex systems.     

Monte Carlo Simulations of the Chemical Potential and Free Energy for Trimer and Hexamer Rings

Abstract

The chemical potential of a trimer and hexamer model ring system was determined by computer simulation over a range of temperatures and densities. Such ring molecules are important as model aromatic and naphthenic hydrocarbons. Thermodynamic integration of the pressure along a reversible path, Widom's ghost particle insertion method and Kirkwood's charging parameter method were used over a molecular density range of 0.05 to 0.30. Data were obtained by Monte Carlo simulation of a 96 molecule system that was modelled with a Lennard-Jones 6-12 truncated potential. The original insertion method, which does not take into account the orientation of the molecule when it is inserted, gives results for the chemical potential which deviate from that obtained using the thermodynamic pressure integration. At high density or temperature the deviation is significant. We have modified the Widom insertion technique to account for this short range orientation and find good agreement between this technique and the thermodynamic integration method for the chemical potential. We also calculated the free energy difference between our model ring molecules and ring molecules made up of hard spheres.     

Molecular Dynamics Simulations of some Small Organic Molecules

Abstract

Free energy differences between different conformers of D-ribofuranose, L-malic acid and meso-tartaric acid in solution were calculated using Molecular Dynamics simulations. In case of ribose the α → β transition was studied. For the acids attention was focussed on the transitions between the three possible staggered conformers with respect to the central C-C bond. In all cases a thermodynamic integration method was employed to evaluate the free energy difference. The use of an alternative technique, umbrella sampling, for ribose did not give promising results.

It was shown that one needs a fairly accurate picture of the accessible conformational space in case of flexible molecules like the ones considered here before one can determine meaningful free energy differences. Large hysteresis effects between forward and reverse simulated transitions were observed, but contrary to the general belief they are no direct measure of the accuracy of the calculated ΔG values. In all cases the ΔG values resulting from the simulations and from NMR experiments agree within the, considerable, error limits and for the different forms of D-ribose, L-malic acid and L-tartaric acid the relative order of their populations is also correctly reproduced.     

Integration of the M6 Cyberknife in the Moderato Monte Carlo platform and prediction of beam parameters using machine learning

PurposeThis work describes the integration of the M6 Cyberknife in the Moderato Monte Carlo platform, and introduces a machine learning method to accelerate the modelling of a linac.MethodsThe MLC-equipped M6 Cyberknife was modelled and integrated in Moderato, our in-house platform offering independent verification of radiotherapy dose distributions. The model was validated by comparing TPS dose distributions with Moderato and by film measurements. Using this model, a machine learning algorithm was trained to find electron beam parameters for other M6 devices, by simulating dose curves with varying spot size and energy. The algorithm was optimized using cross-validation and tested with measurements from other institutions equipped with a M6 Cyberknife.ResultsOptimal agreement in the Monte Carlo model was reached for a monoenergetic electron beam of 6.75 MeV with Gaussian spatial distribution of 2.4 mm FWHM. Clinical plan dose distributions from Moderato agreed within 2% with the TPS, and film measurements confirmed the accuracy of the model. Cross-validation of the prediction algorithm produced mean absolute errors of 0.1 MeV and 0.3 mm for beam energy and spot size respectively. Prediction-based simulated dose curves for other centres agreed within 3% with measurements, except for one device where differences up to 6% were detected.ConclusionsThe M6 Cyberknife was integrated in Moderato and validated through dose re-calculations and film measurements. The prediction algorithm was successfully applied to obtain electron beam parameters for other M6 devices. This method would prove useful to speed up modelling of new machines in Monte Carlo systems.     

Calculation of Solvation Free-Energy Differences for Large Solute Change from Computer Simulations with Quadrature-Based Nearly Linear Thermodynamic Integration

Abstract

The free-energy simulation methodology is reviewed from the point of view of calculating large free-energy differences. The advantages of the nearly linear thermodynamic integration based on Gaussian quadrature are highlighted and its performance is characterized on systems ranging from the Lennard-Jones fluid to the A to B transition of DNA oligomers. A technique for optimizing the runlength at each quadrature point is given. Examples for the sensitivity of the calculated free energy to the atomic charges used are also presented.     

Results of a 24-Week Trial of Technosphere Insulin Versus Insulin Aspart in Type 2 Diabetes

ObjectiveTo compare glycemic efficacy of Technosphere insulin (TI) versus that of insulin aspart (IA), each added to basal insulin, in type 2 diabetes.MethodsThis randomized, 24-week trial included subjects aged from 18 to 80 years who were treated with subcutaneous insulin for 3 months and had glycated hemoglobin (HbA1C) levels of 7.0% to 11.5%. After receiving stabilized insulin glargine doses during a 4-week lead in, the subjects were randomized to TI or IA. The primary end point was an HbA1C change from baseline, with the differences analyzed by equivalence analyses.ResultsIn the overall cohort (N = 309; males, 23.3%), mean (SD) age was 58.5 (8.4) years, body mass index was 30.8 (4.7) kg/m², weight was 82.2 (13.6) kg, and duration of diabetes was 12.2 (7.1) years. An intention-to-treat cohort had 150 subjects randomized to TI (mean [SD] HbA1C: 8.9% [1.1%]) and 154 randomized to IA (mean [SD] HbA1C: 9.0% [1.3%]). At 24 weeks, mean (SD) HbA1C value declined to 7.9% (1.3%) and 7.7% (1.1%) in the TI and IA cohorts, respectively. A treatment difference of 0.26% was not statistically significant, but the predefined equivalency margin was not met. Subjects receiving TI lost 0.78 kg compared to baseline; subjects receiving IA gained 0.23 kg (P =.0007). The incidence of mild/moderate hypoglycemia was lower for the TI cohort, though not statistically significant.ConclusionBoth TI and IA resulted in significant and clinically meaningful HbA1C reductions. TI also resulted in significant and clinically meaningful weight reductions. These data support the use of inhaled insulin as a treatment option for individuals with type 2 diabetes.     

Free energy calculations for theophylline binding to an RNA aptamer: Comparison of MM-PBSA and thermodynamic integration methods

We have applied the molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) method (J. Srinivasan, T. E. Cheatham, P. Cieplak, P. A. Kollman, and D. A. Case, Journal of the American Chemical Society, 1998, Vol. 120, pp. 9401-9409) to study the interaction of an RNA aptamer with theophylline and its analogs. The MM-PBSA free energy analysis provides a reasonable absolute binding free energy for the RNA aptamer-theophylline complex formation. Energetic analysis reveals that the van der Waals interaction and the nonpolar contribution to solvation provide the basis for the favorable absolute free energy of complex. This trend is similar to other protein-ligand interactions studied previously. The MM-PBSA method also ranks the relative binding energies of five theophylline analogs approximately correctly, but not as well as the more conventional thermodynamic integration calculations, which were carried out to convert theophylline into its analogs. The comparison of MM-PBSA with TI suggests that the MM-PBSA method has some difficulties with the first-solvation-shell energetics.     

Ultra Rapid-Acting Inhaled Insulin Improves Glucose Control in Patients With Type 2 Diabetes Mellitus

ObjectiveTo determine whether the use of an inhaled insulin would improve HbA1c.MethodsThis study was performed in 20 type 2 diabetes mellitus (T2DM) participants with HbA1c values ≥7.5 (58) to ≤11.5% (102 mmol/mol) on a variety of glucose-lowering regimens. Prandial Technosphere insulin (TI) was rapidly titrated based on a treatment algorithm using postprandial blood glucose to calculate premeal doses. A 2-week baseline period was followed by 12 weeks of active treatment with TI. The primary outcome was change in HbA1c. Secondary outcomes included glucose time in range (time in range: 70-180 mg/dL) obtained by a blinded continuous glucose monitoring during the baseline period and at the end of 12 weeks. Goals were to assess how to rapidly and safely initiate TI intensification, determine dosing requirements, and establish an effective dose range in uncontrolled T2DM.ResultsMean HbA1c decreased by −1.6% (−17 mmol/mol) from 9.0% (75 mmol/mol) at baseline to 7.4% (57 mmol/mol) at 12 weeks (P < .0001). Mean time in range increased from 42.2% to 65.7% (P < .0002). Mean prandial doses of TI were 18 or 19 units for all meals. Time below range was 1.1% baseline and 2.6% post treatment (P = .01).ConclusionTreatment with inhaled TI dosed using a simple algorithm improved glycemic control measured by both HbA1c and time in range, with low rates of hypoglycemia. These data add significantly to understanding TI in the management of T2DM patients for whom prandial insulin is a consideration.     

A Deep Learning-based correction to EPID dosimetry for attenuation and scatter in the Unity MR-Linac system

PurposeEPID dosimetry in the Unity MR-Linac system allows for reconstruction of absolute dose distributions within the patient geometry. Dose reconstruction is accurate for the parts of the beam arriving at the EPID through the MRI central unattenuated region, free of gradient coils, resulting in a maximum field size of ~10 × 22 cm² at isocentre. The purpose of this study is to develop a Deep Learning-based method to improve the accuracy of 2D EPID reconstructed dose distributions outside this central region, accounting for the effects of the extra attenuation and scatter.MethodsA U-Net was trained to correct EPID dose images calculated at the isocenter inside a cylindrical phantom using the corresponding TPS dose images as ground truth for training. The model was evaluated using a 5-fold cross validation procedure. The clinical validity of the U-Net corrected dose images (the so-called DEEPID dose images) was assessed with in vivo verification data of 45 large rectum IMRT fields. The sensitivity of DEEPID to leaf bank position errors (±1.5 mm) and ±5% MU delivery errors was also tested.ResultsCompared to the TPS, in vivo 2D DEEPID dose images showed an average γ-pass rate of 90.2% (72.6%–99.4%) outside the central unattenuated region. Without DEEPID correction, this number was 44.5% (4.0%–78.4%). DEEPID correctly detected the introduced delivery errors.ConclusionsDEEPID allows for accurate dose reconstruction using the entire EPID image, thus enabling dosimetric verification for field sizes up to ~19 × 22 cm² at isocentre. The method can be used to detect clinically relevant errors.     

On the Accuracy Of Some Common Molecular Dynamics Algorithms

Abstract

Attention is drawn to the fact that some of the algorithms used in the simulation of molecular dynamics are less accurate than is commonly believed. In particular, we show that many of the “Verlet-equivalent” integration schemes are not equivalent to the Verlet algorithm, and consequently are not necessarily third order schemes which exhibit exact time-reversal symmetry. Of this class of algorithms, only Beeman's technique is found to generate the optimal positions and velocities for a third order technique. It is also pointed out that the method of constraints introduces errors of O(τ³) into the calculated position, and hence limits the accuracy of simulations that employ this method to second order.