Accurate Boundary Integral Formulations for the Calculation of Electrostatic Forces with an Implicit-Solvent Model.

An accurate force calculation with the Poisson-Boltzmann equation is challenging, as it requires the electric field on the molecular surface. Here we present a calculation of the electric field on the solute-solvent interface that is exact for piecewise linear variations of the potential and analyze four different alternatives to compute the force using a boundary element method. We performed a verification exercise for two cases: the isolated and two interacting molecules. Our results suggest that the boundary element method outperforms the finite difference method, as the latter needs a much finer mesh than in solvation energy calculations to get acceptable accuracy in the force, whereas the same surface mesh as in a standard energy calculation is appropriate for the boundary element method. Among the four evaluated alternatives of force calculation, we saw that the most accurate one is based on the Maxwell stress tensor. However, for a realistic application, like the barnase-barstar complex, the approach based on variations of the energy functional, which is less accurate, gives equivalent results. This analysis is useful toward using the Poisson-Boltzmann equation for force calculations in applications where high accuracy is key, for example, to feed molecular dynamics models or to enable the study of the interaction between large molecular structures, like viruses adsorbed onto substrates.

Single-chain models illustrate the 3D RNA folding shape during translation.

The three-dimensional conformation of RNA is important in the function and fate of the molecule. The common conformation of mRNA is formed based on the closed-loop structure and internal base pairings with the activity of the ribosome movements. However, recent reports suggest that the closed-loop structure might not be formed in many mRNAs. This implies that mRNA can be considered as a single polymer in the cell. Here, we introduce the Three-dimensional RNA Illustration Program (TRIP) to model the three-dimensional RNA folding shape based on single-chain models and angle restriction of each bead component from previously reported single-molecule fluorescence in situ hybridization (smFISH) experimental data. This simulation method was able to recapitulate the mRNA conformation change of the translation activity and three-dimensional positional interaction between an organelle and its localized mRNAs as end-to-end distances. Within the analyzed cases, base-pairing interactions only have minor effects on the three-dimensional mRNA conformation, and instead single-chain polymer characteristics have a more significant impact on the conformation. This top-down method will be used to interpret the aggregation mechanism of mRNA under different cellular conditions such as nucleolus and phase-separated granules.

Quantitative electrostatic force tomography for virus capsids in interaction with an approaching nanoscale probe.

Electrostatic interactions are crucial for the assembly, disassembly and stability of proteinaceous viral capsids. Moreover, at the molecular scale, elucidating the organization and structure of the capsid proteins in response to an approaching nanoprobe is a major challenge in biomacromolecular research. Here, we report on a generalized electrostatic model, based on the Poisson-Boltzmann equation, that quantifies the subnanometric electrostatic interactions between an AFM tip and a proteinaceous capsid from molecular snapshots. This allows us to describe the contributions of specific amino acids and atoms to the interaction force. We show validation results in terms of total electrostatic forces with previous semi-empirical generalized models at available length scales (d > 1 nm). Then, we studied the interaction of the Zika capsid with conical and spherical AFM tips in a tomography-type analysis to identify the most important residues and atoms, showing the localized nature of the interaction. This method can be employed for the interpretation of force microscopy experiments in fundamental virological characterization and in diverse nanomedicine applications, where specific regions of the protein cages are aimed to electrostatically interact with molecular sized functionalized inhibitors, or tailoring protein-cage functional properties for nucleic acid delivery.

Tuning Contact Angles of Aqueous Droplets on Hydrophilic and Hydrophobic Surfaces by Surfactants.

Adsorption of small amphiphilic molecules occurs in various biological and technological processes, sometimes desired while other times unwanted (e.g., contamination). Surface-active molecules preferentially bind to interfaces and affect their wetting properties. We use molecular dynamics simulations to study the adsorption of short-chained alcohols (simple surfactants) to the water-vapor interface and solid surfaces of various polarities. With a theoretical analysis, we derive an equation for the adsorption coefficient, which scales exponentially with the molecular surface area and the surface wetting coefficient and is in good agreement with the simulation results. We apply the outcomes to aqueous sessile droplets containing surfactants, where the competition of surfactant adsorptions to both interfaces alters the contact angle in a nontrivial way. The influence of surfactants is the strongest on very hydrophilic and hydrophobic surfaces, whereas droplets on moderately hydrophilic surfaces are less affected.

Assessing the Stability of Biological Fibrils by Molecular-Scale Simulations.

The nanomechanical characterization of several biological fibrils that are the result of protein aggregation via molecular dynamics simulation is nowadays feasible, and together with atomic force microscopy experiments has widened our understanding of the forces in the regime of pN-nN and system sizes of about hundreds of nanometers. Several methodologies have been developed to achieve this target, and they range from the atomistic representation via molecular force fields to coarse-grained strategies that provide comparable results with experiments in a systematic way. In this chapter, we discuss several methodologies for the calculation of mechanical parameters, such as the elastic constants of relevant biological systems. They are presented together with details about parameterization and current limitations. Then, we discuss some of the applications of such methodologies for the description of bacterial filament and ß-amyloid systems. Finally, the latest lines of development are discussed.

RNA Secondary Structures Regulate Adsorption of Fragments onto Flat Substrates.

RNA is a functionally rich molecule with multilevel, hierarchical structures whose role in the adsorption to molecular substrates is only beginning to be elucidated. Here, we introduce a multiscale simulation approach that combines a tractable coarse-grained RNA structural model with an interaction potential of a structureless flat adsorbing substrate. Within this approach, we study the specific role of stem-hairpin and multibranch RNA secondary structure motifs on its adsorption phenomenology. Our findings identify a dual regime of adsorption for short RNA fragments with and without the secondary structure and underline the adsorption efficiency in both cases as a function of the surface interaction strength. The observed behavior results from an interplay between the number of contacts formed at the surface and the conformational entropy of the RNA molecule. The adsorption phenomenology of RNA seems to persist also for much longer RNAs as qualitatively observed by comparing the trends of our simulations with a theoretical approach based on an ideal semiflexible polymer chain.

Structural 3D Domain Reconstruction of the RNA Genome from Viruses with Secondary Structure Models.

Three-dimensional RNA domain reconstruction is important for the assembly, disassembly and delivery functionalities of a packed proteinaceus capsid. However, to date, the self-association of RNA molecules is still an open problem. Recent chemical probing reports provide, with high reliability, the secondary structure of diverse RNA ensembles, such as those of viral genomes. Here, we present a method for reconstructing the complete 3D structure of RNA genomes, which combines a coarse-grained model with a subdomain composition scheme to obtain the entire genome inside proteinaceus capsids based on secondary structures from experimental techniques. Despite the amount of sampling involved in the folded and also unfolded RNA molecules, advanced microscope techniques can provide points of anchoring, which enhance our model to include interactions between capsid pentamers and RNA subdomains. To test our method, we tackle the satellite tobacco mosaic virus (STMV) genome, which has been widely studied by both experimental and computational communities. We provide not only a methodology to structurally analyze the tertiary conformations of the RNA genome inside capsids, but a flexible platform that allows the easy implementation of features/descriptors coming from both theoretical and experimental approaches.

Characterization of Structural and Energetic Differences between Conformations of the SARS-CoV-2 Spike Protein.

The novel coronavirus disease 2019 (COVID-19) pandemic has disrupted modern societies and their economies. The resurgence in COVID-19 cases as part of the second wave is observed across Europe and the Americas. The scientific response has enabled a complete structural characterization of the Severe Acute Respiratory Syndrome-novel Coronavirus 2 (SARS-CoV-2). Among the most relevant proteins required by the novel coronavirus to facilitate the cell entry mechanism is the spike protein. This protein possesses a receptor-binding domain (RBD) that binds the cellular angiotensin-converting enzyme 2 (ACE2) and then triggers the fusion of viral and host cell membranes. In this regard, a comprehensive characterization of the structural stability of the spike protein is a crucial step to find new therapeutics to interrupt the process of recognition. On the other hand, it has been suggested that the participation of more than one RBD is a possible mechanism to enhance cell entry. Here, we discuss the protein structural stability based on the computational determination of the dynamic contact map and the energetic difference of the spike protein conformations via the mapping of the hydration free energy by the Poisson-Boltzmann method. We expect our result to foster the discussion of the number of RBD involved during recognition and the repurposing of new drugs to disable the recognition by discovering new hotspots for drug targets apart from the flexible loop in the RBD that binds the ACE2.

Quantitative determination of mechanical stability in the novel coronavirus spike protein.

We report on the novel observation about the gain in nanomechanical stability of the SARS-CoV-2 (CoV2) spike (S) protein in comparison with SARS-CoV from 2002 (CoV1). Our findings have several biological implications in the subfamily of coronaviruses, as they suggest that the receptor binding domain (RBD) (∼200 amino acids) plays a fundamental role as a damping element of the massive viral particle's motion prior to cell-recognition, while also facilitating viral attachment, fusion and entry. The mechanical stability via pulling of the RBD is 250 pN and 200 pN for CoV2 and CoV1 respectively, and the additional stability observed for CoV2 (∼50 pN) might play a role in the increasing spread of COVID-19.

Free Energies of the Disassembly of Viral Capsids from a Multiscale Molecular Simulation Approach.

Molecular simulations of large biological systems, such as viral capsids, remains a challenging task in soft matter research. On one hand, coarse-grained (CG) models attempt to make the description of the entire viral capsid disassembly feasible. On the other hand, the permanent development of novel molecular dynamics (MD) simulation approaches, like enhanced sampling methods, attempt to overcome the large time scales required for such simulations. Those methods have a potential for delivering molecular structures and properties of biological systems. Nonetheless, exploring the process on how a viral capsid disassembles by all-atom MD simulations has been rarely attempted. Here, we propose a methodology to analyze the disassembly process of viral capsids from a free energy perspective, through an efficient combination of dynamics using coarse-grained models and Poisson-Boltzmann simulations. In particular, we look at the effect of pH and charge of the genetic material inside the capsid, and compute the free energy of a disassembly trajectory precalculated using CG simulations with the SIRAH force field. We used our multiscale approach on the Triatoma virus (TrV) as a test case, and find that even though an alkaline environment enhances the stability of the capsid, the resulting deprotonation of the genetic material generates a Coulomb-type electrostatic repulsion that triggers disassembly.

Mechanical and thermodynamic properties of Aß42, Aß40, and α-synuclein fibrils: a coarse-grained method to complement experimental studies.

We perform molecular dynamics simulation on several relevant biological fibrils associated with neurodegenerative diseases such as Aß40, Aß42, and α-synuclein systems to obtain a molecular understanding and interpretation of nanomechanical characterization experiments. The computational method is versatile and addresses a new subarea within the mechanical characterization of heterogeneous soft materials. We investigate both the elastic and thermodynamic properties of the biological fibrils in order to substantiate experimental nanomechanical characterization techniques that are quickly developing and reaching dynamic imaging with video rate capabilities. The computational method qualitatively reproduces results of experiments with biological fibrils, validating its use in extrapolation to macroscopic material properties. Our computational techniques can be used for the co-design of new experiments aiming to unveil nanomechanical properties of biological fibrils from a point of view of molecular understanding. Our approach allows a comparison of diverse elastic properties based on different deformations , i.e., tensile (Y L), shear (S), and indentation (Y T) deformation. From our analysis, we find a significant elastic anisotropy between axial and transverse directions (i.e., Y T > Y L) for all systems. Interestingly, our results indicate a higher mechanostability of Aß42 fibrils compared to Aß40, suggesting a significant correlation between mechanical stability and aggregation propensity (rate) in amyloid systems. That is, the higher the mechanical stability the faster the fibril formation. Finally, we find that α-synuclein fibrils are thermally less stable than ß-amyloid fibrils. We anticipate that our molecular-level analysis of the mechanical response under different deformation conditions for the range of fibrils considered here will provide significant insights for the experimental observations.

Scaling law to determine peak forces in tapping-mode AFM experiments on finite elastic soft matter systems.

Analytical equations to estimate the peak force will facilitate the interpretation and the planning of amplitude-modulation force microscopy (tapping mode) experiments. A closed-form analytical equation to estimate the tip-sample peak forces while imaging soft materials in liquid environment and within an elastic deformation regime has been deduced. We have combined a multivariate regression method with input from the virial-dissipation equations and Tatara's bidimensional deformation contact mechanics model. The equation enables to estimate the peak force based on the tapping mode observables, probe characteristics and the material properties of the sample. The accuracy of the equation has been verified by comparing it to numerical simulations for the archetypical operating conditions to image soft matter with high spatial resolution in tapping-mode AFM.

Scalable and fast heterogeneous molecular simulation with predictive parallelization schemes.

Multiscale and inhomogeneous molecular systems are challenging topics in the field of molecular simulation. In particular, modeling biological systems in the context of multiscale simulations and exploring material properties are driving a permanent development of new simulation methods and optimization algorithms. In computational terms, those methods require parallelization schemes that make a productive use of computational resources for each simulation and from its genesis. Here, we introduce the heterogeneous domain decomposition approach, which is a combination of an heterogeneity-sensitive spatial domain decomposition with an a priori rearrangement of subdomain walls. Within this approach, the theoretical modeling and scaling laws for the force computation time are proposed and studied as a function of the number of particles and the spatial resolution ratio. We also show the new approach capabilities, by comparing it to both static domain decomposition algorithms and dynamic load-balancing schemes. Specifically, two representative molecular systems have been simulated and compared to the heterogeneous domain decomposition proposed in this work. These two systems comprise an adaptive resolution simulation of a biomolecule solvated in water and a phase-separated binary Lennard-Jones fluid.

Dynamic force microscopy simulator (dForce): A tool for planning and understanding tapping and bimodal AFM experiments.

We present a simulation environment, dForce, which can be used for a better understanding of dynamic force microscopy experiments. The simulator presents the cantilever-tip dynamics for two dynamic AFM methods, tapping mode AFM and bimodal AFM. It can be applied for a wide variety of experimental situations in air or liquid. The code provides all the variables and parameters relevant in those modes, for example, the instantaneous deflection and tip-surface force, velocity, virial, dissipated energy, sample deformation and peak force as a function of time or distance. The simulator includes a variety of interactions and contact mechanics models to describe AFM experiments including: van der Waals, Hertz, DMT, JKR, bottom effect cone correction, linear viscoelastic forces or the standard linear solid viscoelastic model. We have compared two numerical integration methods to select the one that offers optimal accuracy and speed. The graphical user interface has been designed to facilitate the navigation of non-experts in simulations. Finally, the accuracy of dForce has been tested against numerical simulations performed during the last 18 years.

Peak forces and lateral resolution in amplitude modulation force microscopy in liquid.

The peak forces exerted on soft and rigid samples by a force microscope have been modeled by performing numerical simulations of the tip motion in liquid. The forces are obtained by using two contact mechanics models, Hertz and Tatara. We present a comparison between the numerical simulations and three analytical models for a wide variety of probe and operational parameters. In general, the forces derived from analytical expressions are not in good quantitative agreement with the simulations when the Young modulus and the set-point amplitude are varied. The only exception is the parametrized approximation that matches the results given by Hertz contact mechanics for soft materials and small free amplitudes. We also study the elastic deformation of the sample as a function of the imaging conditions for materials with a Young modulus between 25 MPa and 2 GPa. High lateral resolution images are predicted by using both small free amplitudes (less than 2 nm for soft materials) and high set-point amplitudes.

Peak forces in high-resolution imaging of soft matter in liquid.

The maximum force exerted by the tip of a force microscope on the sample surface is a critical factor that determines the spatial resolution and the degree of invasiveness of the measurement, in particular, on soft materials. Here we determine the conditions needed to image soft matter in the 30-500 MPa range while applying very small forces. Imaging at sub-50 pN in the elastic regime can only be achieved under strict conditions in terms of force constant values (below 0.1 N/m) and free amplitudes (below 2 nm). The peak force depends on the operational parameters, probe properties, the elastic and/or viscoelastic response of the sample, and the contact mechanics model. Images of heterogeneous samples are never taken at a constant peak force. Under the same operational conditions, smaller forces are obtained on the more compliant materials. We also find that the viscoelastic response reduces the peak force with respect to the purely elastic regions. Our findings are summarized in three-dimensional maps that contain the operational conditions for imaging at low forces.