Titratable Martini model for constant pH simulations

Capturing chemical reactions inside biomolecular condensates with reactive Martini simulations

Biomolecular condensates are phase separated systems that play an important role in the spatio-temporal organisation of cells. Their distinct physico-chemical nature offers a unique environment for chemical reactions to occur. The compartmentalisation of chemical reactions is also believed to be central to the development of early life. To demonstrate how molecular dynamics may be used to capture chemical reactions in condensates, here we perform reactive molecular dynamics simulations using the coarse-grained Martini forcefield. We focus on the formation of rings of benzene-1,3-dithiol inside a synthetic peptide-based condensate, and find that the ring size distribution shifts to larger macrocycles compared to when the reaction takes place in an aqueous environment. Moreover, reaction rates are noticeably increased when the peptides simultaneously undergo phase separation, hinting that condensates may act as chaperones in recruiting molecules to reaction hubs.

Atomistic Molecular Dynamics Simulations of ABA-Type Polymer Peptide Conjugates: Insights into Supramolecular Structures and their Circular Dichroism Spectra

A combination of atomistic molecular dynamics (aMD) simulations and circular dichroism (CD) analysis is used to explore supramolecular structures of amphiphilic ABA-type triblock polymer peptide conjugates (PPC). Using the example of a recently introduced PPC with pH- and temperature responsive self-assembling behavior [Otter et al., Macromolecular Rapid Communications 2018, 39, 1800459], this study shows how molecular dynamics simulations of simplified fragment molecules can add crucial information to CD data, which helps to correctly identify the self-assembled structures and monitor the folding/unfolding pathways of the molecules. The findings offer insights into the nature of structural transitions induced by external stimuli, thus contributing to the understanding of the connection of microscopic structures with macroscopic properties.

Unveiling Interactions of Tumor-Targeting Nanoparticles with Lipid Bilayers Using a Titratable Martini Model

pH-responsive nanoparticles are ideal vehicles for drug delivery and are widely used in cell imaging in targeted therapy of cancer, which usually has a weakly acidic microenvironment. In this work, we constructed a titratable molecular model for nanoparticles grafted with ligands of pH-sensitive carboxylic acids and investigated the interactions between the nanoparticles and the lipid bilayer in varying pH environments. We mainly examined the effect of the grafting density of the pH-sensitive ligands of the nanoparticles on the interactions of the nanoparticles with the lipid bilayer. The results show that the nanoparticles can penetrate the lipid bilayer only when the pH value is lower than a critical value, which can be readily modulated to the specific pH value of the tumor microenvironment by changing the ligand grafting density. This work provides some insights into modulating the interactions between the pH-sensitive nanoparticles and cellular membranes to realize targeted drug delivery to tumors based on their specific pH environment.

Closing the Gap between Experiment and Simulation─A Holistic Study on the Complexation of Small Interfering RNAs with Polyethylenimine

Rational design is pivotal in the modern development of nucleic acid nanocarrier systems. With the rising prominence of polymeric materials as alternatives to lipid-based carriers, understanding their structure-function relationships becomes paramount. Here, we introduce a newly developed coarse-grained model of polyethylenimine (PEI) based on the Martini 3 force field. This model facilitates molecular dynamics simulations of true-sized PEI molecules, exemplified by molecules with molecular weights of 1.3, 5, 10, and 25 kDa, with degrees of branching between 50.0 and 61.5%. We employed this model to investigate the thermodynamics of small interfering RNA (siRNA) complexation with PEI. Our simulations underscore the pivotal role of electrostatic interactions in the complexation process. Thermodynamic analyses revealed a stronger binding affinity with increased protonation, notably in acidic (endosomal) pH, compared to neutral conditions. Furthermore, the molecular weight of PEI was found to be a critical determinant of binding dynamics: smaller PEI molecules closely enveloped the siRNA, whereas larger ones extended outward, facilitating the formation of complexes with multiple RNA molecules. Experimental validations, encompassing isothermal titration calorimetry and single-molecule fluorescence spectroscopy, aligned well with our computational predictions. Our findings not only validate the fidelity of our PEI model but also accentuate the importance of in silico data in the rational design of polymeric drug carriers. The synergy between computational predictions and experimental validations, as showcased here, signals a refined and precise approach to drug carrier design.

High Charge Density in Peptide Dendrimers is Required to Destabilize Membranes: Insights into Endosome Evasion

Peptide dendrimers are a type of branched, symmetric, and topologically well-defined molecule that have already been used as delivery systems for nucleic acid transfection. Several of the most promising sequences showed high efficiency in many key steps of transfection, namely, binding siRNA, entering cells, and evading the endosome. However, small changes to the peptide dendrimers, such as in the hydrophobic core, the amino acid chirality, or the total available charges, led to significantly different experimental results with unclear mechanistic insights. In this work, we built a computational model of several of those peptide dendrimers (MH18, MH13, and MH47) and some of their variants to study the molecular details of the structure and function of these molecules. We performed CpHMD simulations in the aqueous phase and in interaction with a lipid bilayer to assess how conformation and protonation are affected by pH in different environments. We found that while the different peptide dendrimer sequences lead to no substantial structural differences in the aqueous phase, the total charge and, more importantly, the total charge density are key for the capacity of the dendrimer to interact and destabilize the membrane. These dendrimers become highly charged when the pH changes from 7.5 to 4.5, and the presence of a high charge density, which is decreased for MH47 that has four fewer titratable lysines, is essential to trigger membrane destabilization. These findings are in excellent agreement with the experimental data and help us to understand the high efficiency of some dendrimers and why the dendrimer MH47 is unable to complete the transfection process. This evidence provides further understanding of the mode of action of these peptide dendrimers and will be pivotal for the future design of new sequences with improved transfection capabilities.

Assessment of the MARTINI 3 Performance for Short Peptide Self-Assembly

The coarse-grained MARTINI force field, initially developed for membranes, has proven to be an exceptional tool for investigating supramolecular peptide assemblies. Over the years, the force field underwent refinements to enhance accuracy, enabling, for example, the reproduction of protein-ligand interactions and constant pH behavior. However, these protein-focused improvements seem to have compromised its ability to model short peptide self-assembly. In this study, we assess the performance of MARTINI 3 in reproducing peptide self-assembly using the well-established diphenylalanine (FF) as our test case. Unlike its success in version 2.1, FF does not even exhibit aggregation in version 3. By systematically exploring parameters for the aromatic side chains and charged backbone beads, we established a parameter set that effectively reproduces tube formation. Remarkably, these parameter adjustments also replicate the self-assembly of other di- and tripeptides and coassemblies. Furthermore, our analysis uncovers pivotal insights for enhancing the performance of MARTINI in modeling short peptide self-assembly. Specifically, we identify issues stemming from overestimated hydrophilicity arising from charged termini and disruptions in π-stacking interactions due to insufficient planarity in aromatic groups and a discrepancy in intermolecular distances between this and backbone-backbone interactions. This investigation demonstrates that strategic modifications can harness the advancements offered by MARTINI 3 for the realm of short peptide self-assembly.

Capric Acid and Myristic Acid Permeability Enhancers in Curved Liposome Membranes

Liposomes are considered as advanced drug delivery systems for cancer treatment. A generation of pH-sensitive liposomes is being developed that use fatty acids (FAs) as a trigger for drug release in tumor tissues. However, FAs are also known to enhance permeability, and it is unclear whether FAs in liposomes may cause drug leakage or premature drug release. The passive permeability of the drug through the membrane of the liposome is thus a crucial factor for timely drug delivery. To investigate how the curvature and lipid composition of liposomes affect their passive permeability, coarse-grained molecular dynamics were performed. The permeability was determined with a counting method. Flat bilayers and three liposomes with varying diameters were studied, which had varying lipid compositions of dipalmitoylphosphatidylcholine, cholesterol, and deprotonated or neutral saturated FAs. The investigated permeants were water and two other small permeants, which have different free energy profiles (solubility) across the membrane. First, for the curvature effect, our results showed that curvature increases the water permeability by reducing the membrane thickness. The permeability increase for water is about a factor of 1.7 for the most curved membranes. However, a high curvature decreases permeability for permeants with free energy profiles that are a mix of wells and barriers in the headgroup region of the membrane. Importantly, the type of experimental setup is expected to play a dominant role in the permeability value, i.e., whether permeants are escaping or entering the liposomes. Second, for the composition effect, FAs decrease both the area per lipid (APL) and the membrane thickness, resulting in permeability increases of up to 55%. Cholesterol has a similar effect on the APL but has the opposite impact on membrane thickness and permeability. Therefore, FAs and cholesterol have opposing effects on permeability, with cholesterol's effect being slightly stronger in our simulated bilayers. As all permeability values were well within a factor of 2, and with liposomes usually being larger and less curved in experimental applications, it can be concluded that the passive drug release from a pH-sensitive liposome does not seem to be significantly affected by the presence of FAs.

Pragmatic Coarse-Graining of Proteins: Models and Applications

The molecular details involved in the folding, dynamics, organization, and interaction of proteins with other molecules are often difficult to assess by experimental techniques. Consequently, computational models play an ever-increasing role in the field. However, biological processes involving large-scale protein assemblies or long time scale dynamics are still computationally expensive to study in atomistic detail. For these applications, employing coarse-grained (CG) modeling approaches has become a key strategy. In this Review, we provide an overview of what we call pragmatic CG protein models, which are strategies combining, at least in part, a physics-based implementation and a top-down experimental approach to their parametrization. In particular, we focus on CG models in which most protein residues are represented by at least two beads, allowing these models to retain some degree of chemical specificity. A description of the main modern pragmatic protein CG models is provided, including a review of the most recent applications and an outlook on future perspectives in the field.

Recent advances on molecular dynamics-based techniques to address drug membrane permeability with atomistic detail

Several factors affect the passive membrane permeation of small molecules, including size, charge, pH, or the presence of specific chemical groups. Understanding these features is paramount to identifying or designing drug candidates with optimal ADMET properties and this can be achieved through experimental/knowledge-based methodologies or using computational approaches. Empirical methods often lack detailed information about the underlying molecular mechanism. In contrast, Molecular Dynamics-based approaches are a powerful strategy, providing an atomistic description of this process. This technique is continuously growing, featuring new related methodologies. In this work, the recent advances in this research area will be discussed.

Reactive Martini: Chemical Reactions in Coarse-Grained Molecular Dynamics Simulations

Chemical reactions are ubiquitous in both materials and the biophysical sciences. While coarse-grained (CG) molecular dynamics simulations are often needed to study the spatiotemporal scales present in these fields, chemical reactivity has not been explored thoroughly in CG models. In this work, a new approach to model chemical reactivity is presented for the widely used Martini CG Martini model. Employing tabulated potentials with a single extra particle for the angle dependence, the model provides a generic framework for capturing bonded topology changes using nonbonded interactions. As a first example application, the reactive model is used to study the macrocycle formation of benzene-1,3-dithiol molecules through the formation of disulfide bonds. We show that starting from monomers, macrocycles with sizes in agreement with experimental results are obtained using reactive Martini. Overall, our reactive Martini framework is general and can be easily extended to other systems. All of the required scripts and tutorials to explain its use are provided online.

PolySMart: a general coarse-grained molecular dynamics polymerization scheme

The development of simulation methods to study the structure and dynamics of a macroscopically sized piece of polymer material is important as such methods can elucidate structure-property relationships. Several methods have been reported to construct initial structures for homo- and co-polymers; however, most of them are only useful for short linear polymers since one needs to pack and equilibrate the far-from-equilibrium initial structures, which is a tedious task for long or hyperbranched polymers and unfeasible for polymer networks. In this method article, we present PolySMart, i.e., an open-source python package, which can effectively produce fully equilibrated homo- and hetero-polymer melts and solutions with no limitation on the polymer topology and size, at a coarse-grained resolution and through a bottom-up approach. This python package is also capable of exploring the polymerization kinetics through its reactive scheme in realistic conditions so that it can model the multiple co-occurring polymerization reactions (with different reaction rates) as well as consecutive polymerizations under stoichiometric and non-stoichiometric conditions. Thus, the equilibrated polymer models are generated through correct polymerization kinetics. A benchmark and verification of the performance of the program for several realistic cases, i.e., for homo-polymers, co-polymers, and crosslinked networks, is given. We further discuss the capability of the program to contribute to the discovery and design of new polymer materials.

Partitioning into phosphatidylcholine-cholesterol membranes: liposome measurements, coarse-grained simulations, and implications for bioaccumulation

Membrane-water partitioning is an important physical property for the assessment of bioaccumulation and environmental impact. Here, we advance simulation methodology for predicting the partitioning of small molecules into lipid membranes and compare the computational predictions to experimental measurements in liposomes. As a step towards high-throughput screening, we present an automated mapping and parametrization procedure to produce coarse-grained models compatible with the Martini 3 force field. The methodology is general and can also be used for other applications where coarse-grained simulations are appropriate. This article addresses the effect on membrane-water partitioning of adding cholesterol to POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) membranes. Nine contrasting neutral, zwitterionic and charged solutes are tested. Agreement between experiment and simulation is generally good, with the most challenging cases being permanently charged solutes. For all solutes, partitioning is found to be insensitive to membrane cholesterol concentration up to 25% mole fraction. Hence, for assessment of bioaccumulation into a range of membranes (such as those found in fish), partitioning data measured in pure lipid membranes are still informative.

Numerical simulation of peristalsis to study co-localization and intestinal distribution of a macromolecular drug and permeation enhancer

In this work, simulations of intestinal peristalsis are performed to investigate the intraluminal transport of macromolecules (MMs) and permeation enhancers (PEs). Properties of insulin and sodium caprate (C₁₀) are used to represent the general class of MM and PE molecules. Nuclear magnetic resonance spectroscopy was used to obtain the diffusivity of C₁₀, and coarse-grain molecular dynamics simulations were carried out to estimate the concentration-dependent diffusivity of C₁₀. A segment of the small intestine with the length of 29.75 cm was modeled. Peristaltic speed, pocket size, release location, and occlusion ratio of the peristaltic wave were varied to study the effect on drug transport. It was observed that the maximum concentration at the epithelial surface for the PE and the MM increased by 397 % and 380 %, respectively, when the peristaltic wave speed was decreased from 1.5 to 0.5 cm s^-1. At this wave speed, physiologically relevant concentrations of PE were found at the epithelial surface. However, when the occlusion ratio is increased from 0.3 to 0.7, the concentration approaches zero. These results suggest that a slower-moving and more contracted peristaltic wave leads to higher efficiency in transporting mass to the epithelial wall during the peristalsis phases of the migrating motor complex.

Short Peptide Self-Assembly in the Martini Coarse-Grain Force Field Family

ConspectusPivotal to the success of any computational experiment is the ability to make reliable predictions about the system under study and the time required to yield these results. Biomolecular interactions is one area of research that sits in every camp of resolution vs the time required, from the quantum mechanical level to in vivo studies. At an approximate midpoint, there is coarse-grained molecular dynamics, for which the Martini force fields have become the most widely used, fast enough to simulate the entire membrane of a mitochondrion though lacking atom-specific precision. While many force fields have been parametrized to account for a specific system under study, the Martini force field has aimed at casting a wider net with more generalized bead types that have demonstrated suitability for broad use and reuse in applications from protein-graphene oxide coassembly to polysaccharides interactions.In this Account, the progressive (Martini versions 1 through 3) and peripheral (Sour Martini, constant pH, Martini Straight, Dry Martini, etc.) developmental trajectory of the Martini force field will be analyzed in terms of self-assembling systems with a focus on short (two to three amino acids) peptide self-assembly in aqueous environments. In particular, this will focus on the effects of the Martini solvent model and compare how changes in bead definitions and mapping have effects on different systems. Considerable effort in the development of Martini has been expended to reduce the "stickiness" of amino acids to better simulate proteins in bilayers. We have included in this Account a short study of dipeptide self-assembly in water, using all mainstream Martini force fields, to examine their ability to reproduce this behavior. The three most recently released versions of Martini and variations in their solvents are used to simulate in triplicate all 400 dipeptides of the 20 gene-encoded amino acids. The ability of the force fields to model the self-assembly of the dipeptides in aqueoues environments is determined by the measurement of the aggregation propensity, and additional descriptors are used to gain further insight into the dipeptide aggregates.

Mesoscale simulations: An indispensable approach to understand biomembranes

Computer simulation techniques form a versatile tool, a computational microscope, for exploring biological processes. This tool has been particularly effective in exploring different features of biological membranes. In recent years, thanks to elegant multiscale simulation schemes, some fundamental limitations of investigations by distinct simulation techniques have been resolved. As a result, we are now capable of exploring processes spanning multiple scales beyond the capacity of any single technique. In this perspective, we argue that mesoscale simulations require more attention and must be further developed to fill evident gaps in a quest toward simulating and modeling living cell membranes.

Facilitating CG Simulations with MAD: The MArtini Database Server

The MArtini Database (MAD - https://mad.ibcp.fr) is a web server designed for the sharing of structures and topologies of molecules parametrized with the Martini coarse-grained (CG) force field. MAD can also convert atomistic structures into CG structures and prepare complex systems (including proteins, lipids, etc.) for molecular dynamics (MD) simulations at the CG level. It is dedicated to the generation of input files for Martini 3, the most recent version of this popular CG force field. Specifically, the MAD server currently includes tools to submit or retrieve CG models of a wide range of molecules (lipids, carbohydrates, nanoparticles, etc.), transform atomistic protein structures into CG structures and topologies, with fine control on the process and assemble biomolecules into large systems, and deliver all files necessary to start simulations in the GROMACS MD engine.

pH-Dependent Conformational Switch Impacts Stability of the PsbS Dimer

The photosystem II PsbS protein triggers the photoprotective mechanism of plants by sensing the acidification of the thylakoid lumen. Despite the mechanism of action of PsbS would require a pH-dependent monomerization of the dimeric form, a clear connection between the pH-induced structural changes and the dimer stability is missing. Here, by applying constant pH coarse-grained and all-atom molecular dynamics simulations, we investigate the pH-dependent structural response of the PsbS dimer. We find that the pH variation leads to structural changes in the lumen-exposed helices, located at the dimeric interface, providing an effective switch between PsbS inactive and active form. Moreover, the monomerization free energies reveal that in the neutral pH conformation, where the network of H-bond interactions at the dimeric interface is destroyed, the protein-protein interaction is weaker. Our results show how the pH-dependent conformations of PsbS affect their dimerization propensity, which is at the basis of the photoprotective mechanism.

A Molecular Theory of Polypeptide Adsorption at Inorganic Surfaces

A faithful description of polypeptide adsorption at ionizable surfaces remains a theoretical challenge from a molecular perspective due to the strong coupling of local thermodynamic nonideality and ionizations of both the adsorbate and substrate that are sensitive to the solution condition such as pH, ion valence, and salt concentration. Building upon a recently developed coarse-grained model for natural amino acids in bulk electrolyte solutions, here we report a molecular theory applicable to polypeptide adsorption on ionizable inorganic surfaces over a broad range of inhomogeneous conditions. Our thermodynamic model is able to account for diverse solution effects as well as the amino-acid sequence on polypeptide adsorption and surface association such as hydrogen bonding or bidentate coordination. The theoretical predictions have been validated by extensive comparison with experimental data for the adsorption isotherms of three representative polypeptides at a titanium surface.

Molecular Dynamics Study of the Aggregation Behavior of N,N,N',N'-Tetraoctyl Diglycolamide

Liquid–liquid extraction is a commonly used technique to separate metals and is a process that has particular relevance to the nuclear industry. There has been a drive to use environmentally friendly ligands composed only of carbon, hydrogen, nitrogen, and oxygen. One example is the i-SANEX process that has been developed to separate minor actinides from spent nuclear fuel. The underlying science of such processes, is, however, both complex and intriguing. Recent research indicates that the liquid phases involved are frequently structured fluids with a hierarchical organization of aggregates. Effective flow-sheet modeling of such processes is likely to benefit from the knowledge of the fundamental properties of these phases. As a stepping stone toward this, we have performed molecular dynamics simulations on a metal free i-SANEX system composed of the ligand N,N,N′,N′-tetraoctyl diglycolamide (TODGA), diluent hydrogenated tetrapropylene (TPH), and polar species water and nitric acid. We have also studied the effects of adding n-octanol and swapping TPH for n-dodecane. It would seem sensible to understand this simpler system before introducing metal complexes. Such an understanding would ideally arise from studying the system’s properties over a wide range of compositions. The large number of components, however, precludes a comprehensive scan of compositions, so we have chosen to study a fixed concentration of TODGA while varying the concentrations of water and nitric acid over a substantial range. Reverse aggregates are observed, with polar species in the interior in contact with the polar portions of the TODGA molecules and the organic diluent on the exterior in contact with the TODGA alkyl chains. These aggregates are irregular in shape and grow in size as the amount of water and nitric acid increases. At a sufficiently high polar content, a single extended cluster forms corresponding to the third phase formation. No well-defined bonding motifs were observed between the polar species and TODGA. The cluster size distribution fits an isodesmic model, where the Gibbs energy change of adding a TODGA molecule to a cluster ranges between 4.5 and 7.0 kJ mol^–1, depending on the system composition. The addition of n-octanol was found to reduce the degree of aggregation, with n-octanol acting as a co-surfactant. Exchanging the diluent TPH for n-dodecane also decreased the aggregation. We present evidence that this is due to the greater penetration of n-dodecane into the reverse aggregates. It is known, however, that the propensity for the third phase formation is greater with n-dodecane as the diluent than is the case with TPH, but we argue that these two results are not contradictory. This research casts light on the driving forces for aggregation, informs process engineers as to what species are present, and indicates that flow-sheet liquid–liquid extraction modeling might benefit by incorporating an isodesmic aggregation approach.

Polyethylenimine-DNA Nanoparticles under Endosomal Acidification and Implication to Gene Delivery

Non-viral gene delivery using polyethylenimine (PEI) has shown tremendous promise as a therapeutic technique. Through the formation of nanoparticles (NPs), PEIs protect genetic material such as DNA from degradation. Escape of the NPs from endosomes and lysosomes is facilitated by PEI's buffering capacity over a wide range of pH. However, little is known about the effects of endosomal acidification on the morphology of the NPs. In this work, large-scale coarse-grained simulations performed to mimic endosomal acidification reveal that NPs undergo a resizing process that is highly dependent on the N/P ratio (ratio of PEI nitrogen to DNA phosphate) at which they are prepared. With a low N/P ratio, NPs further aggregate after endosomal acidification, whereas with a high N/P ratio they dissociate. The mechanisms behind such NP resizing and its consequences on endosomal escape and nuclear trafficking are discussed. Based on the findings, suggestions are made on the PEI architecture that may enhance NP dissociation driven by endosomal acidification.

Key aspects of the past 30 years of protein design

Proteins are the workhorse of life. They are the building infrastructure of living systems; they are the most efficient molecular machines known, and their enzymatic activity is still unmatched in versatility by any artificial system. Perhaps proteins' most remarkable feature is their modularity. The large amount of information required to specify each protein's function is analogically encoded with an alphabet of just ∼20 letters. The protein folding problem is how to encode all such information in a sequence of 20 letters. In this review, we go through the last 30 years of research to summarize the state of the art and highlight some applications related to fundamental problems of protein evolution.

Constant pH Coarse-Grained Molecular Dynamics with Stochastic Charge Neutralization

pH dependence abounds in biochemical systems; however, many simulation methods used to investigate these systems do not consider this property. Using a modified version of the hybrid non-equilibrium molecular dynamics (MD)/Monte Carlo algorithm, we include a stochastic charge neutralization method, which is particularly suited to the MARTINI force field and enables artifact-free Ewald summation methods in electrostatic calculations. We demonstrate the efficacy of this method by reproducing pH-dependent self-assembly and self-organization behavior previously reported in experimental literature. In addition, we have carried out experimental oleic acid titrations where we report the results in a more relevant way for the comparison with computational methods than has previously been done.

Calculation of Permeability Coefficients from Solute Equilibration Dynamics: An Assessment of Various Methods

Predicting the rate at which substances permeate membrane barriers in vivo is crucial for drug development. Permeability coefficients obtained from in vitro studies are valuable for this goal. These are normally determined by following the dynamics of solute equilibration between two membrane-separated compartments. However, the correct calculation of permeability coefficients from such data is not always straightforward. To address these problems, here we develop a kinetic model for solute permeation through lipid membrane barriers that includes the two membrane leaflets as compartments in a four-compartment model. Accounting for solute association with the membrane allows assessing various methods in a wide variety of conditions. The results showed that the often-used expression Papp= β × r/3 is inapplicable to very large or very small vesicles, to moderately or highly lipophilic solutes, or when the development of a significant pH gradient opposes the solute’s flux. We establish useful relationships that overcome these limitations and allow predicting permeability in compartmentalised in vitro or in vivo systems with specific properties. Finally, from the parameters for the interaction of the solute with the membrane barrier, we defined an intrinsic permeability coefficient that facilitates quantitative comparisons between solutes.

Reactive Monte Carlo simulations for charge regulation of colloidal particles

We use a reactive Monte Carlo simulation method and the primitive model of electrolyte to study acid-base equilibrium that controls charge regulation in colloidal systems. The simulations are performed in a semi-grand canonical ensemble in which colloidal suspension is in contact with a reservoir of salt and strong acid. The interior of colloidal particles is modeled as a low dielectric medium, different from the surrounding water. The effective colloidal charge is calculated for different numbers of surface acidic groups, pH, salt concentrations, and types of electrolyte. In the case of potassium chloride, the titration curves are compared with the experimental measurements obtained using potentiometric titration. A good agreement is found between simulations and experiments. In the case of lithium chloride, the specific ionic adsorption is taken into account through the partial dehydration of lithium ion.

Improved Parameterization of Phosphatidylinositide Lipid Headgroups for the Martini 3 Coarse-Grain Force Field

Phosphoinositides are a family of membrane phospholipids that play crucial roles in membrane regulatory events. As such, these lipids are often a key part of molecular dynamics simulation studies of biological membranes, in particular of those employing coarse-grain models because of the potential long times and sizes of the involved membrane processes. Version 3 of the widely used Martini coarse-grain force field has been recently published, greatly refining many aspects of biomolecular interactions. In order to properly use it for lipid membrane simulations with phosphoinositides, we put forth the Martini 3-specific parameterization of inositol, phosphatidylinositol, and seven physiologically relevant phosphorylated derivatives of phosphatidylinositol. Compared to parameterizations for earlier Martini versions, focus was put on a more accurate reproduction of the behavior seen in both atomistic simulations and experimental studies, including the signaling-relevant phosphoinositide interaction with divalent cations. The models that we develop improve upon the conformational dynamics of phosphoinositides in the Martini force field and provide stable topologies at typical Martini time steps. They are able to reproduce experimentally known protein-binding poses as well as phosphoinositide aggregation tendencies. The latter was tested both in the presence and absence of calcium and included correct behavior of PI(4,5)P₂ calcium-induced clusters, which can be of relevance for regulation.

Explicit-pH Coarse-Grained Molecular Dynamics Simulations Enable Insights into Restructuring of Intestinal Colloidal Aggregates with Permeation Enhancers

Permeation enhancers (PEs) can increase the bioavailability of drugs. The mechanisms of action of these PEs are complex, but, typically, when used for oral administration, they can transiently induce the alteration of trans- and paracellular pathways, including increased solubilization and membrane fluidity, or the opening of the tight junctions. To elucidate these mechanistic details, it is important to understand the aggregation behavior of not only the PEs themselves but also other molecules already present in the intestine. Aggregation processes depend critically on, among other factors, the charge state of ionizable chemical groups, which is affected by the pH of the system. In this study, we used explicit-pH coarse-grained molecular dynamics simulations to investigate the aggregation behavior and pH dependence of two commonly used PEs—caprate and SNAC—together with other components of fasted- and fed-state simulated intestinal fluids. We also present and validate a coarse-grained molecular topology for the bile salt taurocholate suitable for the Martini3 force-field. Our results indicate an increase in the number of free molecules as a function of the system pH and for each combination of FaSSIF/FeSSIF and PEs. In addition, there are differences between caprate and SNAC, which are rationalized based on their different molecular structures and critical micelle concentrations.

Adsorption of lysozyme into a charged confining pore

Several applications arise from the confinement of proteins on surfaces because their stability and biological activity are enhanced. It is also known that the way in which a protein adsorbs on the surface is important for its biological function since its active sites should not be obstructed. In this study, the adsorption properties of hen egg-white lysozyme, HEWL, into a negatively charged silica pore is examined by employing a coarse-grained model and constant-pH Monte Carlo simulations. The role of electrostatic interactions is taken into account via including the Debye-Hückel potentials into the Cα structure-based model. We evaluate the effects of pH, salt concentration, and pore radius on the protein preferential orientation and spatial distribution of its residues regarding the pore surface. By mapping the residues that stay closer to the pore surface, we find that the increase of pH leads to orientational changes of the adsorbed protein when the solution pH gets closer to the HEWL isoelectric point. Under these conditions, the pK_a shift of these important residues caused by the adsorption into the charged confining surface results in a HEWL charge distribution that stabilizes the adsorption in the observed protein orientation. We compare our observations to the results of the pK_a shift for HEWL available in the literature and to some experimental data.

Site Correlations, Capacitance, and Polarizability From Protein Protonation Fluctuations

We generalize the Kirkwood-Shumaker theory of protonation fluctuation for an anisotropic distribution of dissociable charges on a globular protein. The fluctuations of the total charge and the total dipole moment, in contrast to their average values, depend on the same proton occupancy correlator, thus exhibiting a similar dependence also on the solution pH. This has important consequences for the Kirkwood-Shumaker interaction and its dependence on the bathing solution conditions.

Titr-DMD-A Rapid, Coarse-Grained Quasi-All-Atom Constant pH Molecular Dynamics Framework

The pH-dependence of enzyme fold stability and catalytic activity is a fundamentally dynamic, structural property which is difficult to study. The challenges and expense of investigating dynamic, atomic scale behavior experimentally means that computational methods, particularly constant pH molecular dynamics (CpHMD), are well situated tools for this. However, these methods often struggle with affordable sampling of sufficiently long time scales while also obtaining accurate pKa prediction and verifying the structures they generate. We introduce Titr-DMD, an affordable CpHMD method that combines the quasi-all-atom coarse-grained discrete molecular dynamics (DMD) method for conformational sampling with Propka for pKa prediction, to circumvent these issues. The combination enables rapid sampling on limited computational resources, while simulations are still performed on the atomic scale. We benchmark the method on a set of proteins with experimentally attested pKa and on the pH triggered conformational change in a staphylococcal nuclease mutant, a rare experimental study of such behavior. Our results show Titr-DMD to be an effective and inexpensive method to study pH-coupled protein dynamics.

The Martini Model in Materials Science

The Martini model, a coarse-grained force field initially developed with biomolecular simulations in mind, has found an increasing number of applications in the field of soft materials science. The model's underlying building block principle does not pose restrictions on its application beyond biomolecular systems. Here, the main applications to date of the Martini model in materials science are highlighted, and a perspective for the future developments in this field is given, particularly in light of recent developments such as the new version of the model, Martini 3.

Perspectives on High-Throughput Ligand/Protein Docking With Martini MD Simulations

Molecular docking is central to rational drug design. Current docking techniques suffer, however, from limitations in protein flexibility and solvation models and by the use of simplified scoring functions. All-atom molecular dynamics simulations, on the other hand, feature a realistic representation of protein flexibility and solvent, but require knowledge of the binding site. Recently we showed that coarse-grained molecular dynamics simulations, based on the most recent version of the Martini force field, can be used to predict protein/ligand binding sites and pathways, without requiring any a priori information, and offer a level of accuracy approaching all-atom simulations. Given the excellent computational efficiency of Martini, this opens the way to high-throughput drug screening based on dynamic docking pipelines. In this opinion article, we sketch the roadmap to achieve this goal.

Molecular Transfer Model for pH Effects on Intrinsically Disordered Proteins: Theory and Applications

We present a theoretical method to study how changes in pH shape the heterogeneous conformational ensemble explored by intrinsically disordered proteins (IDPs). The theory is developed in the context of coarse-grained models, which enable a fast, accurate, and extensive exploration of conformational space at a given protonation state. In order to account for pH effects, we generalize the molecular transfer model (MTM), in which conformations are re-weighted using the transfer free energy, which is the free energy necessary for bringing to equilibrium in a new environment a "frozen" conformation of the system. Using the semi-grand ensemble, we derive an exact expression of the transfer free energy, which amounts to the appropriate summation over all the protonation states. Because the exact result is computationally too demanding to be useful for large polyelectrolytes or IDPs, we introduce a mean-field (MF) approximation of the transfer free energy. Using a lattice model, we compare the exact and MF results for the transfer free energy and a variety of observables associated with the model IDP. We find that the precise location of the charged groups (the sequence), and not merely the net charge, determines the structural properties. We demonstrate that some of the limitations previously noted for MF theory in the context of globular proteins are mitigated when disordered polymers are studied. The excellent agreement between the exact and MF results poises us to use the method presented here as a computational tool to study the properties of IDPs and other biological systems as a function of pH.

Development of coarse-grained force field for alcohols: an efficient meta-multilinear interpolation parameterization algorithm

Coarse-grained (CG) molecular dynamics are powerful tools to access a mesoscopic phenomenon and simultaneously record microscopic details, but currently the CG force fields (FFs) are still limited by low parameterization efficiency and poor accuracy especially for polar molecules. In this work, we developed a Meta-Multilinear Interpolation Parameterization (Meta-MIP) algorithm to optimize the CG FFs for alcohols. This algorithm significantly boosts parameterization efficiency by constructing on-the-fly local databases to cover the global optimal parameterization path. In specific, an alcohol molecule is mapped to a heterologous model composed of an OH bead and a hydrocarbon portion which consists of alkane beads representing two to four carbon atoms. Non-bonded potentials are described by soft Morse functions that have no tail-corrections but can still retain good continuities at truncation distance. Nearly all of the properties in terms of density, heat of vaporization, surface tension, and solvation free energy for alcohols predicted by the current FFs deviate from experimental values by less than 7%. This Meta-MIP algorithm can be readily applied to force field development for a wide variety of molecules or functional groups, in many situations including but not limited to CG FFs.

Coarse-Grained Parameterization of Nucleotide Cofactors and Metabolites: Protonation Constants, Partition Coefficients, and Model Topologies

Nucleotides are structural units relevant not only in nucleic acids but also as substrates or cofactors in key biochemical reactions. The size- and timescales of such nucleotide-protein interactions fall well within the scope of coarse-grained molecular dynamics, which holds promise of important mechanistic insight. However, the lack of specific parameters has prevented accurate coarse-grained simulations of protein interactions with most nucleotide compounds. In this work, we comprehensively develop coarse-grained parameters for key metabolites/cofactors (FAD, FMN, riboflavin, NAD, NADP, ATP, ADP, AMP, and thiamine pyrophosphate) in different oxidation and protonation states as well as for smaller molecules derived from them (among others, nicotinamide, adenosine, adenine, ribose, thiamine, and lumiflavin), summing up a total of 79 different molecules. In line with the Martini parameterization methodology, parameters were tuned to reproduce octanol-water partition coefficients. Given the lack of existing data, we set out to experimentally determine these partition coefficients, developing two methodological approaches, based on ³¹P-NMR and fluorescence spectroscopy, specifically tailored to the strong hydrophilicity of most of the parameterized compounds. To distinguish the partition of each relevant protonation species, we further potentiometrically characterized the protonation constants of key molecules. This work successfully builds a comprehensive and relevant set of computational models that will boost the biochemical application of coarse-grained simulations. It does so based on the measurement of partition and acid-base physicochemical data that, in turn, covers important gaps in nucleotide characterization.

Protocol for Simulations of PEGylated Proteins with Martini 3

Enhancement of proteins by PEGylation is an active area of research. However, the interactions between polymer and protein are far from fully understood. To gain a better insight into these interactions or even make predictions, molecular dynamics (MD) simulations can be applied to study specific protein-polymer systems at molecular level detail. Here we present instructions on how to simulate PEGylated proteins using the latest iteration of the Martini coarse-grained (CG) force-field. CG MD simulations offer near atomistic information and at the same time allow to study complex biological systems over longer time and length scales than fully atomistic-level simulations.