Entropy-enthalpy transduction caused by conformational shifts can obscure the forces driving protein-ligand binding.

Molecular dynamics simulations of unprecedented duration now can provide new insights into biomolecular mechanisms. Analysis of a 1-ms molecular dynamics simulation of the small protein bovine pancreatic trypsin inhibitor reveals that its main conformations have different thermodynamic profiles and that perturbation of a single geometric variable, such as a torsion angle or interresidue distance, can select for occupancy of one or another conformational state. These results establish the basis for a mechanism that we term entropy-enthalpy transduction (EET), in which the thermodynamic character of a local perturbation, such as enthalpic binding of a small molecule, is camouflaged by the thermodynamics of a global conformational change induced by the perturbation, such as a switch into a high-entropy conformational state. It is noted that EET could occur in many systems, making measured entropies and enthalpies of folding and binding unreliable indicators of actual thermodynamic driving forces. The same mechanism might also account for the high experimental variance of measured enthalpies and entropies relative to free energies in some calorimetric studies. Finally, EET may be the physical mechanism underlying many cases of entropy-enthalpy compensation.

Acoustofluidic chemical waveform generator and switch.

Eliciting a cellular response to a changing chemical microenvironment is central to many biological processes including gene expression, cell migration, differentiation, apoptosis, and intercellular signaling. The nature and scope of the response is highly dependent upon the spatiotemporal characteristics of the stimulus. To date, studies that investigate this phenomenon have been limited to digital (or step) chemical stimulation with little control over the temporal counterparts. Here, we demonstrate an acoustofluidic (i.e., fusion of acoustics and microfluidics) approach for generating programmable chemical waveforms that permits continuous modulation of the signal characteristics including the amplitude (i.e., sample concentration), shape, frequency, and duty cycle, with frequencies reaching up to 30 Hz. Furthermore, we show fast switching between multiple distinct stimuli, wherein the waveform of each stimulus is independently controlled. Using our device, we characterized the frequency-dependent activation and internalization of the ß2-adrenergic receptor (ß2-AR), a prototypic G-protein coupled receptor (GPCR), using epinephrine. The acoustofluidic-based programmable chemical waveform generation and switching method presented herein is expected to be a powerful tool for the investigation and characterization of the kinetics and other dynamic properties of many biological and biochemical processes.

The SAMPL4 hydration challenge: evaluation of partial charge sets with explicit-water molecular dynamics simulations.

We used blind predictions of the 47 hydration free energies in the SAMPL4 challenge to test multiple partial charge models in the context of explicit solvent free energy simulations with the general AMBER force field. One of the partial charge models, IPolQ-Mod, is a fast continuum solvent-based implementation of the IPolQ approach. The AM1-BCC, restrained electrostatic potential (RESP) and IpolQ-Mod approaches all perform reasonably well (R(2) > 0.8), while VCharge, though faster, gives less accurate results (R(2) of 0.5). The AM1-BCC results are more accurate than those of RESP for tertiary amines and nitrates, but the overall difference in accuracy between these methods is not statistically significant. Interestingly, the IPolQ-Mod method is found to yield partial charges in very close agreement with RESP. This observation suggests that the success of RESP may be attributed to its fortuitously approximating the arguably more rigorous IPolQ approach.

The SAMPL4 host-guest blind prediction challenge: an overview.

Prospective validation of methods for computing binding affinities can help assess their predictive power and thus set reasonable expectations for their performance in drug design applications. Supramolecular host-guest systems are excellent model systems for testing such affinity prediction methods, because their small size and limited conformational flexibility, relative to proteins, allows higher throughput and better numerical convergence. The SAMPL4 prediction challenge therefore included a series of host-guest systems, based on two hosts, cucurbit[7]uril and octa-acid. Binding affinities in aqueous solution were measured experimentally for a total of 23 guest molecules. Participants submitted 35 sets of computational predictions for these host-guest systems, based on methods ranging from simple docking, to extensive free energy simulations, to quantum mechanical calculations. Over half of the predictions provided better correlations with experiment than two simple null models, but most methods underperformed the null models in terms of root mean squared error and linear regression slope. Interestingly, the overall performance across all SAMPL4 submissions was similar to that for the prior SAMPL3 host-guest challenge, although the experimentalists took steps to simplify the current challenge. While some methods performed fairly consistently across both hosts, no single approach emerged as consistent top performer, and the nonsystematic nature of the various submissions made it impossible to draw definitive conclusions regarding the best choices of energy models or sampling algorithms. Salt effects emerged as an issue in the calculation of absolute binding affinities of cucurbit[7]uril-guest systems, but were not expected to affect the relative affinities significantly. Useful directions for future rounds of the challenge might involve encouraging participants to carry out some calculations that replicate each others' studies, and to systematically explore parameter options.

Blind prediction of SAMPL4 cucurbit[7]uril binding affinities with the mining minima method.

Accurate methods for predicting protein-ligand binding affinities are of central interest to computer-aided drug design for hit identification and lead optimization. Here, we used the mining minima (M2) method to predict cucurbit[7]uril binding affinities from the SAMPL4 blind prediction challenge. We tested two different energy models, an empirical classical force field, CHARMm with VCharge charges, and the Poisson-Boltzmann surface area solvation model; and a semiempirical quantum mechanical (QM) Hamiltonian, PM6-DH+, coupled with the COSMO solvation model and a surface area term for nonpolar solvation free energy. Binding affinities based on the classical force field correlated strongly with the experiments with a correlation coefficient (R(2)) of 0.74. On the other hand, binding affinities based on the QM energy model correlated poorly with experiments (R(2) = 0.24), due largely to two major outliers. As we used extensive conformational search methods, these results point to possible inaccuracies in the PM6-DH+ energy model or the COSMO solvation model. Furthermore, the different binding free energy components, solute energy, solvation free energy, and configurational entropy showed significant deviations between the classical M2 and quantum M2 calculations. Comparison of different classical M2 free energy components to experiments show that the change in the total energy, i.e. the solute energy plus the solvation free energy, is the key driving force for binding, with a reasonable correlation to experiment (R(2) = 0.56); however, accounting for configurational entropy further improves the correlation.

Substrate stiffness regulates cellular uptake of nanoparticles.

Nanoparticle (NP)-bioconjugates hold great promise for more sensitive disease diagnosis and more effective anticancer drug delivery compared with existing approaches. A critical aspect in both applications is cellular internalization of NPs, which is influenced by NP properties and cell surface mechanics. Despite considerable progress in optimization of the NP-bioconjugates for improved targeting, the role of substrate stiffness on cellular uptake has not been investigated. Using polyacrylamide (PA) hydrogels as model substrates with tunable stiffness, we quantified the relationship between substrate stiffness and cellular uptake of fluorescent NPs by bovine aortic endothelial cells (BAECs). We found that a stiffer substrate results in a higher total cellular uptake on a per cell basis, but a lower uptake per unit membrane area. To obtain a mechanistic understanding of the cellular uptake behavior, we developed a thermodynamic model that predicts that membrane spreading area and cell membrane tension are two key factors controlling cellular uptake of NPs, both of which are modulated by substrate stiffness. Our experimental and modeling results not only open up new avenues for engineering NP-based cancer cell targets for more effective in vivo delivery but also contribute an example of how the physical environment dictates cellular behavior and function.

Enzyme molecules as nanomotors.

Using fluorescence correlation spectroscopy, we show that the diffusive movements of catalase enzyme molecules increase in the presence of the substrate, hydrogen peroxide, in a concentration-dependent manner. Employing a microfluidic device to generate a substrate concentration gradient, we show that both catalase and urease enzyme molecules spread toward areas of higher substrate concentration, a form of chemotaxis at the molecular scale. Using glucose oxidase and glucose to generate a hydrogen peroxide gradient, we induce the migration of catalase toward glucose oxidase, thereby showing that chemically interconnected enzymes can be drawn together.

The electrostatic response of water to neutral polar solutes: implications for continuum solvent modeling.

Continuum solvation models are widely used to estimate the hydration free energies of small molecules and proteins, in applications ranging from drug design to protein engineering, and most such models are based on the approximation of a linear dielectric response by the solvent. We used explicit-water molecular dynamics simulations with the TIP3P water model to probe this linear response approximation in the case of neutral polar molecules, using miniature cucurbituril and cyclodextrin receptors and protein side-chain analogs as model systems. We observe supralinear electrostatic solvent responses, and this nonlinearity is found to result primarily from waters' being drawn closer and closer to the solutes with increased solute-solvent electrostatic interactions; i.e., from solute electrostriction. Dielectric saturation and changes in the water-water hydrogen bonding network, on the other hand, play little role. Thus, accounting for solute electrostriction may be a productive approach to improving the accuracy of continuum solvation models.

Tuning membrane phase separation using nonlipid amphiphiles.

Lipid phase separation may be a mechanism by which lipids participate in sorting membrane proteins and facilitate membrane-mediated biochemical signaling in cells. To provide new tools for membrane lipid phase manipulation that avoid direct effects on protein activity and lipid composition, we studied phase separation in binary and ternary lipid mixtures under the influence of three nonlipid amphiphiles, vitamin E (VE), Triton-X (TX)-100, and benzyl alcohol (BA). Mechanisms of additive-induced phase separation were elucidated using coarse-grained molecular dynamics simulations of these additives in a liquid bilayer made from 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and 1,2-dilinoleoyl-sn-glycero-3-phosphocholine [corrected]. From simulations, the additive's partitioning preference, changes in membrane thickness, and alterations in lipid order were quantified. Simulations showed that VE favored the DPPC phase but partitioned predominantly to the domain boundaries and lowered the tendency for domain formation, and therefore acted as a linactant. This simulated behavior was consistent with experimental observations in which VE promoted lipid mixing and dispersed domains in both gel/liquid and liquid-ordered/liquid-disordered systems. From simulation, BA partitioned predominantly to the DUPC phase, decreased lipid order there, and thinned the membrane. These actions explain why, experimentally, BA promoted phase separation in both binary and ternary lipid mixtures. In contrast, TX, a popular detergent used to isolate raft membranes in cells, exhibited equal preference for both phases, as demonstrated by simulations, but nonetheless, was a strong domain promoter in all lipid mixtures. Further analysis showed that TX increased membrane thickness of the DPPC phase to a greater extent than the DUPC phase and thus increased hydrophobic mismatch, which may explain experimental observation of phase separation in the presence of TX. In summary, these nonlipid amphiphiles provide new tools to tune domain formation in model vesicle systems and could provide the means to form or disperse membrane lipid domains in cells, in addition to the well-known methods involving cholesterol enrichment and sequestration.

Prediction of SAMPL3 host-guest binding affinities: evaluating the accuracy of generalized force-fields.

We used the second-generation mining minima method (M2) to compute the binding affinities of the novel host-guest complexes in the SAMPL3 blind prediction challenge. The predictions were in poor agreement with experiment, and we conjectured that much of the error might derive from the force field, CHARMm with Vcharge charges. Repeating the calculations with other generalized force-fields led to no significant improvement, and we observed that the predicted affinities were highly sensitive to the choice of force-field. We therefore embarked on a systematic evaluation of a set of generalized force fields, based upon comparisons with PM6-DH2, a fast yet accurate semi-empirical quantum mechanics method. In particular, we compared gas-phase interaction energies and entropies for the host-guest complexes themselves, as well as for smaller chemical fragments derived from the same molecules. The mean deviations of the force field interaction energies from the quantum results were greater than 3 kcal/mol and 9 kcal/mol, for the fragments and host-guest systems respectively. We further evaluated the accuracy of force-fields for computing the vibrational entropies and found the mean errors to be greater than 4 kcal/mol. Given these errors in energy and entropy, it is not surprising in retrospect that the predicted binding affinities deviated from the experiment by several kcal/mol. These results emphasize the need for improvements in generalized force-fields and also highlight the importance of systematic evaluation of force-field parameters prior to evaluating different free-energy methods.

Blind prediction of host-guest binding affinities: a new SAMPL3 challenge.

The computational prediction of protein-ligand binding affinities is of central interest in early-stage drug-discovery, and there is a widely recognized need for improved methods. Low molecular weight receptors and their ligands--i.e., host-guest systems--represent valuable test-beds for such affinity prediction methods, because their small size makes for fast calculations and relatively facile numerical convergence. The SAMPL3 community exercise included the first ever blind prediction challenge for host-guest binding affinities, through the incorporation of 11 new host-guest complexes. Ten participating research groups addressed this challenge with a variety of approaches. Statistical assessment indicates that, although most methods performed well at predicting some general trends in binding affinity, overall accuracy was not high, as all the methods suffered from either poor correlation or high RMS errors or both. There was no clear advantage in using explicit versus implicit solvent models, any particular force field, or any particular approach to conformational sampling. In a few cases, predictions using very similar energy models but different sampling and/or free-energy methods resulted in significantly different results. The protonation states of one host and some guest molecules emerged as key uncertainties beyond the choice of computational approach. The present results have implications for methods development and future blind prediction exercises.

Atomistic simulation of lipid and DiI dynamics in membrane bilayers under tension.

Membrane tension modulates cellular processes by initiating changes in the dynamics of its molecular constituents. To quantify the precise relationship between tension, structural properties of the membrane, and the dynamics of lipids and a lipophilic reporter dye, we performed atomistic molecular dynamics (MD) simulations of DiI-labeled dipalmitoylphosphatidylcholine (DPPC) lipid bilayers under physiological lateral tensions ranging from -2.6 mN m(-1) to 15.9 mN m(-1). Simulations showed that the bilayer thickness decreased linearly with tension consistent with volume-incompressibility, and this thinning was facilitated by a significant increase in acyl chain interdigitation at the bilayer midplane and spreading of the acyl chains. Tension caused a significant drop in the bilayer's peak electrostatic potential, which correlated with the strong reordering of water and lipid dipoles. For the low tension regime, the DPPC lateral diffusion coefficient increased with increasing tension in accordance with free-area theory. For larger tensions, free area theory broke down due to tension-induced changes in molecular shape and friction. Simulated DiI rotational and lateral diffusion coefficients were lower than those of DPPC but increased with tension in a manner similar to DPPC. Direct correlation of membrane order and viscosity near the DiI chromophore, which was just under the DPPC headgroup, indicated that measured DiI fluorescence lifetime, which is reported to decrease with decreasing lipid order, is likely to be a good reporter of tension-induced decreases in lipid headgroup viscosity. Together, these results offer new molecular-level insights into membrane tension-related mechanotransduction and into the utility of DiI in characterizing tension-induced changes in lipid packing.

p38 MAP kinase is necessary for melanoma-mediated regulation of VE-cadherin disassembly.

Vascular endothelial (VE)-cadherin is localized to the endothelial borders and the adherens junctions, which are regulated by changes in mitogen-activated protein (MAP) kinases, GTPases, and intracellular calcium. We previously showed that melanoma cells induce VE-cadherin disassembly through contact with human umbilical vein endothelial cells in coculture. However, the exact mechanism by which melanoma cells signal endothelial cells to induce VE-cadherin junction disassembly is not well understood. In this study, VE-cadherin junction disassembly was further examined under fluorescence microscopy. We found that melanoma-induced VE-cadherin junction disassembly and upregulation of p38 MAP kinase in endothelial cells is regulated by both soluble factors from melanomas, particularly interleukin (IL)-8, IL-6, and IL-1beta, and through vascular cell adhesion molecule-1. Neutralizing melanoma-secreted soluble factors reduced endothelial gap formation. Endothelial cells transfected with MAP kinase kinase 6, a direct activator of p38 MAP kinase, increased VE-cadherin-mediated gap formation, facilitating melanoma transendothelial migration. In contrast, endothelial cells transfected with small-interfering RNA against p38 MAP kinase expression largely prevented melanoma transendothelial migration in Boyden chamber experiments. These findings indicate that p38 MAP kinase proteins regulate VE-cadherin junction disassembly, facilitating melanoma migration across endothelial cells.

Substrate catalysis enhances single-enzyme diffusion.

We show that diffusion of single urease enzyme molecules increases in the presence of urea in a concentration-dependent manner and calculate the force responsible for this increase. Urease diffusion measured using fluorescence correlation spectroscopy increased by 16-28% over buffer controls at urea concentrations ranging from 0.001 to 1 M. This increase was significantly attenuated when urease was inhibited with pyrocatechol, demonstrating that the increase in diffusion was the result of enzyme catalysis of urea. Local molecular pH changes as measured using the pH-dependent fluorescence lifetime of SNARF-1 conjugated to urease were not sufficient to explain the increase in diffusion. Thus, a force generated by self-electrophoresis remains the most plausible explanation. This force, evaluated using Brownian dynamics simulations, was 12 pN per reaction turnover. These measurements demonstrate force generation by a single enzyme molecule and lay the foundation for a further understanding of biological force generation and the development of enzyme-driven nanomotors.

Photophysics of Cy3-encapsulated calcium phosphate nanoparticles.

Progress toward clinical application of biodegradable fluorescent calcium phosphate (CP) nanoparticles as a bioimaging agent requires detailed knowledge of chromophore interaction with CP. As readouts of this cargo-matrix interaction, we determined the principle photophysical properties of Cy3 encapsulated in CP nanparticles (CPNPs) using steady-state and time-resolved fluorescence spectroscopy. Fluorescence correlation spectroscopy (FCS)-determined diffusion coefficients and associated hydrodynamic radii confirmed the presence of highly monodisperse CPNPs with radii ranging from 7 to 10 nm. Single CP nanoparticles were 20 times brighter than free dye molecules because of a CP-induced 5-fold increase in quantum efficiency and encapsulation of four dye molecules per particle. Solvatochromic shifts resulting from hydrogen bonding between free dye and solvent or restricted intramolecular mobility by solvent viscosity were absent when Cy3 was encapsulated in CP. Encapsulation-mediated increases in radiative decay rates and decreases in nonradiative decay rates resulting in longer fluorescence lifetimes of Cy3 were attributed to solvent and CP-related local refractive indices and restricted flexibility of dye by rigid CP. Enhanced brightness of CPNPs enabled imaging of single nanoparticles under epifluorescence using both standard and total internal reflection fluorescence (TIRF) modes with camera exposure times on the order of tens of milliseconds. These enhanced photophysical properties together with excellent biocompatibility make CPNPs ideal for bioimaging applications ranging from single-molecule tracking to in vivo tumor detection and offer the possibility of timed codelivery of drugs to control cell function.

Data-Driven Mapping of Gas-Phase Quantum Calculations to General Force Field Lennard-Jones Parameters.

Molecular dynamics simulations are helpful tools for a range of applications, ranging from drug discovery to protein structure determination. The successful use of this technology largely depends on the potential function, or force field, used to determine the potential energy at each configuration of the system. Most force fields encode all of the relevant parameters to be used in distinct atom types, each associated with parameters for all parts of the force field, typically bond stretches, angle bends, torsions, and nonbonded terms accounting for van der Waals and electrostatic interactions. Much attention has been paid to the nonbonded parameters and their derivation, which are important in particular due to their governance of noncovalent interactions, such as protein-ligand binding. Parametrization involves adjusting the nonbonded parameters to minimize the error between simulation results and experimental properties, such as heats of vaporization and densities of neat liquids. In this setting, determining the best set of atom types is far from trivial, and the large number of parameters to be fit for the atom types in a typical force field can make it difficult to approach a true optimum. Here, we utilize a previously described Minimal Basis Iterative Stockholder (MBIS) method to carry out an atoms-in-molecules partitioning of electron densities. Information from these atomic densities is then mapped to Lennard-Jones parameters using a set of mapping parameters much smaller than the typical number of atom types in a force field. This approach is advantageous in two ways: it eliminates atom types by allowing each atom to have unique Lennard-Jones parameters, and it greatly reduces the number of parameters to be optimized. We show that this approach yields results comparable to those obtained with the typed GAFF 1.7 force field, even when trained on a relatively small amount of experimental data.

Bind3P: Optimization of a Water Model Based on Host-Guest Binding Data.

We report a water model, Bind3P (Version 0.1), which was obtained by using sensitivity analysis to readjust the Lennard-Jones parameters of the TIP3P model against experimental binding free energies for six host-guest systems, along with pure liquid properties. Tests of Bind3P against >100 experimental binding free energies and enthalpies for host-guest systems distinct from the training set show a consistent drop in the mean signed error, relative to matched calculations with TIP3P. Importantly, Bind3P also yields some improvement in the hydration free energies of small organic molecules and preserves the accuracy of bulk water properties, such as density and the heat of vaporization. The same approach can be applied to more sophisticated water models that can better represent pure water properties. These results lend further support to the concept of integrating host-guest binding data into force field parametrization.

Selectively manipulable acoustic-powered microswimmers.

Selective actuation of a single microswimmer from within a diverse group would be a first step toward collaborative guided action by a group of swimmers. Here we describe a new class of microswimmer that accomplishes this goal. Our swimmer design overcomes the commonly-held design paradigm that microswimmers must use non-reciprocal motion to achieve propulsion; instead, the swimmer is propelled by oscillatory motion of an air bubble trapped within the swimmer's polymer body. This oscillatory motion is driven by the application of a low-power acoustic field, which is biocompatible with biological samples and with the ambient liquid. This acoustically-powered microswimmer accomplishes controllable and rapid translational and rotational motion, even in highly viscous liquids (with viscosity 6,000 times higher than that of water). And by using a group of swimmers each with a unique bubble size (and resulting unique resonance frequencies), selective actuation of a single swimmer from among the group can be readily achieved.

Quantum Mechanical Calculation of Noncovalent Interactions: A Large-Scale Evaluation of PMx, DFT, and SAPT Approaches.

Quantum mechanical (QM) calculations of noncovalent interactions are uniquely useful as tools to test and improve molecular mechanics force fields and to model the forces involved in biomolecular binding and folding. Because the more computationally tractable QM methods necessarily include approximations, which risk degrading accuracy, it is essential to evaluate such methods by comparison with high-level reference calculations. Here, we use the extensive Benchmark Energy and Geometry Database (BEGDB) of CCSD(T)/CBS reference results to evaluate the accuracy and speed of widely used QM methods for over 1200 chemically varied gas-phase dimers. In particular, we study the semiempirical PM6 and PM7 methods; density functional theory (DFT) approaches B3LYP, B97-D, M062X, and ωB97X-D; and symmetry-adapted perturbation theory (SAPT) approach. For the PM6 and DFT methods, we also examine the effects of post hoc corrections for hydrogen bonding (PM6-DH+, PM6-DH2), halogen atoms (PM6-DH2X), and dispersion (DFT-D3 with zero and Becke-Johnson damping). Several orders of the SAPT expansion are also compared, ranging from SAPT0 up to SAPT2+3, where computationally feasible. We find that all DFT methods with dispersion corrections, as well as SAPT at orders above SAPT2, consistently provide dimer interaction energies within 1.0 kcal/mol RMSE across all systems. We also show that a linear scaling of the perturbative energy terms provided by the fast SAPT0 method yields similar high accuracy, at particularly low computational cost. The energies of all the dimer systems from the various QM approaches are included in the Supporting Information, as are the full SAPT2+(3) energy decomposition for a subset of over 1000 systems. The latter can be used to guide the parametrization of molecular mechanics force fields on a term-by-term basis.