Simple Model System Research Articles

Essential Considerations for Free Energy Calculations of RNA-Small Molecule Complexes: Lessons from the Theophylline-Binding RNA Aptamer.

Alchemical free energy calculations are widely used to predict the binding affinity of small molecule ligands to protein targets; however, the application of these methods to RNA targets has not been deeply explored. We systematically investigated how modeling decisions affect the performance of absolute binding free energy calculations for a relatively simple RNA model system: theophylline-binding RNA aptamer with theophylline and five analogs. The goal of this investigation was 2-fold: (1) understanding the performance levels we can expect from absolute free energy calculations for a simple RNA complex and (2) learning about practical modeling considerations that impact the success of RNA-binding predictions, which may be different from the best practices established for protein targets. We learned that magnesium ion (Mg2+) placement is a critical decision that impacts affinity predictions. When information regarding Mg2+ positions is lacking, implementing RNA backbone restraints is an alternative way of stabilizing the RNA structure that recapitulates prediction accuracy. Since mistakes in Mg2+ placement can be detrimental, omitting magnesium ions entirely and using RNA backbone restraints are attractive as a risk-mitigating approach. We found that predictions are sensitive to modeling experimental buffer conditions correctly, including salt type and ionic strength. We explored the effects of sampling in the alchemical protocol, choice of the ligand force field (GAFF2/OpenFF Sage), and water model (TIP3P/OPC) on predictions, which allowed us to give practical advice for the application of free energy methods to RNA targets. By capturing experimental buffer conditions and implementing RNA backbone restraints, we were able to compute binding affinities accurately (mean absolute error (MAE) = 2.2 kcal/mol, Pearson's correlation coefficient = 0.9, Kendall's τ = 0.7). We believe there is much to learn about how to apply free energy calculations for RNA targets and how to enhance their performance in prospective predictions. This study is an important first step for learning best practices and special considerations for RNA-ligand free energy calculations. Future studies will consider increasingly complicated ligands and diverse RNA systems and help the development of general protocols for therapeutically relevant RNA targets.

Flow Matching for Optimal Reaction Coordinates of Biomolecular Systems.

We present flow matching for reaction coordinates (FMRC), a novel deep learning algorithm designed to identify optimal reaction coordinates (RC) in biomolecular reversible dynamics. FMRC is based on the mathematical principles of lumpability and decomposability, which we reformulate into a conditional probability framework for efficient data-driven optimization using deep generative models. While FMRC does not explicitly learn the well-established transfer operator or its eigenfunctions, it can effectively encode the dynamics of leading eigenfunctions of the system transfer operator into its low-dimensional RC space. We further quantitatively compare its performance with several state-of-the-art algorithms by evaluating the quality of Markov state models (MSM) constructed in their respective RC spaces, demonstrating the superiority of FMRC in three increasingly complex biomolecular systems. In addition, we successfully demonstrated the efficacy of FMRC for bias deposition in the enhanced sampling of a simple model system. Finally, we discuss its potential applications in downstream applications such as enhanced sampling methods and MSM construction.

Exploring New Algorithms for Molecular Vibrational Spectroscopy Using Physics-Informed Program Synthesis.

Inductive program synthesis (PS) has recently begun to emerge as a useful new approach to automatically generate algorithms in quantum chemistry, as demonstrated in recent applications to the vibrational Schrödinger equation for simple model systems with one or two degrees-of-freedom. Here, we report a new physics-informed approach to inductive PS that is more conducive to the generation of discrete variable representation algorithms for real molecular systems. The new framework ensures separability of the kinetic and potential operators and does not require an exact solution to compare synthesized algorithmic predictions with. Algorithms with a tridiagonal matrix structure are generated via a variational-based stochastic optimization procedure. Crucially, through an extensive testing procedure, we demonstrate that variationally synthesized algorithms perform just as well as those generated using a target function. Assuming a direct product representation of normal coordinates, these algorithms are applied to three triatomic molecules. In total, we identify a set of seven PS algorithms that accurately reproduce the vibrational spectra of H2O, NO2, and SO2, as predicted by Colbert-Miller and sine-DVR algorithms.

The roles of blur and eye convergence in distance estimation in larval zebrafish

Animals use an array of visual cues to gauge distance, and their underlying neural mechanisms remain largely unknown. Zebrafish larvae execute different hunting behaviors depending on distance to the prey, providing a simple model system in which to study this process. To identify distance cues, we presented equivalent prey stimuli at increasing distance and recorded hunting behaviors. We found that the initial convergence angle was lower for more distant prey, suggesting that they are able to gauge distance to the prey via monocular cues. We investigated blur as a possible monocular cue, and found that by artificially blurring the stimulus, we were able to reduce initial convergence and strike probability. This implicates blur as a distance cue in zebrafish prey capture, adds to our knowledge of how larvae are able to visually target and accurately capture prey.

Effect of smectic polymers on cholesteric liquid crystals.

Composite materials made of polymers and liquid crystals have been widely employed in smart windows, optical filters, and bistable displays. However, it is often difficult to decipher the role of the polymer network architecture on the alignment and the texture of liquid crystals. In this study, we use a simple model system where a small amount of polymerizable liquid crystalline monomer is mixed in a liquid crystal that exhibits both a smectic phase and a cholesteric phase with a large helical pitch. By cross-linking the monomer in the smectic phase, the liquid crystal textures become significantly altered. The existence of a polymer network not only creates resistance to form a helix and therefore hinders the formation of cholesteric fingerprints but also modifies the structure of the cholesteric texture. We investigate the effects of changing the concentration of chiral dopant and monomer on the formation and growth of the cholesteric fingerprint texture during the phase transition and on the width of the fingerprints. We find that, within a certain parameter range, the cholesteric fingerprints do not depend on the concentration of the chiral dopant. We explain this phenomenon by hypothesizing that the polymer network acts as a bulk alignment field.

Statistical mechanics of crystal nuclei of hard spheres.

In the study of crystal nucleation via computer simulations, hard spheres are arguably the most extensively explored model system. Nonetheless, even in this simple model system, the complex thermodynamics of crystal nuclei can sometimes give rise to counterintuitive results, such as the recent observation that the pressure inside a critical nucleus is lower than that of the surrounding fluid, seemingly clashing with the strictly positive Young-Laplace pressure we would expect in liquid droplets. Here, we re-derive many of the founding equations associated with crystal nucleation and use the hard-sphere model to demonstrate how they give rise to this negative pressure difference. We exploit the fact that, in the canonical ensemble, a nucleus can be in a (meta)stable equilibrium with the fluid and measure the surface stress for both flat and curved interfaces. Additionally, we explain the effect of defects on the chemical potential inside the crystal nucleus. Finally, we present a simple, fitted thermodynamic model to capture the properties of the nucleus, including the work required to form critical nuclei.

Interaction of a pyrene derivative with cationic [60]fullerene in phospholipid membranes and its effects on photodynamic actions.

We have reported that upon visible light irradiation, ferrocene-porphyrin-[60]fullerene triad molecules yield long-lived charge-separated states, enabling the control of the plasma membrane potential (V m) in living cells. These previous studies indicated that the localization of the triad molecules in a specific intra-membrane orientation and the suppression of the photodynamic actions of the [60]fullerene (C60) moiety are likely important to achieve fast and safe control of V m, respectively. In this study, by mimicking our previous system of triad molecules and living cells, we report a simplified model system with a cationic C60 derivative (catC60) and a liposome with embedded 1-pyrenebutyric acid (PyBA) to demonstrate that the addition of PyBA was important to achieve fast and safer control of V m.

Disassembling one-dimensional chains in molybdenum oxides

Abstract The dimensionality of quantum materials strongly affects their physical properties. Although many emergent phenomena, such as charge-density wave and Luttinger liquid behavior, are well understood in one-dimensional (1D) systems, the generalization to explore them in higher dimensional systems is still a challenging task. In this study, we aim to bridge this gap by systematically investigating the crystal and electronic structures of molybdenum-oxide family compounds, where the contexture of 1D chains facilitates rich emergent properties. While the quasi-1D chains in these materials share general similarities, such as the motifs made up of MoO6 octahedrons, they exhibit vast complexity and remarkable tunability. We disassemble the 1D chains in molybdenum oxides with different dimensions and construct effective models to excellently fit their low-energy electronic structures obtained by ab initio calculations. Furthermore, we discuss the implications of such chains on other physical properties of the materials and the practical significance of the effective models. Our work establishes the molybdenum oxides as simple and tunable model systems for studying and manipulating the dimensionality in quantum systems.

Harnessing Competitive Interactions to Regulate Supramolecular "Micelle-Droplet-Fiber" Transition and Reversibility in Water.

The supramolecular assembly of proteins into irreversible fibrils is often associated with diseases in which aberrant phase transitions occur. Due to the complexity of biological systems and their surrounding environments, the mechanism underlying phase separation-mediated supramolecular assembly is poorly understood, making the reversal of so-called irreversible fibrillization a significant challenge. Therefore, it is crucial to develop simple model systems that provide insights into the mechanistic process of monomers to phase-separated droplets and ordered supramolecular assemblies. Such models can help in investigating strategies to either reverse or modulate these states. Herein, we present a simple synthetic model system composed of three components, including a benzene-1,3,5-tricarboxamide-based supramolecular monomer, a surfactant, and water, to mimic the condensate pathway observed in biological systems. This highly dynamic system can undergo "micelle-droplet-fiber" transition over time and space with a concentration gradient field, regulated by competitive interactions. Importantly, manipulating these competitive interactions through guest molecules, temperature changes, and cosolvents can reverse ordered fibers into a disordered liquid or micellar state. Our model system provides new insights into the critical balance between various interactions among the three components that determine the pathway and reversibility of the process. Extending this "competitive interaction" approach from a simple model system to complex macromolecules, e.g., proteins, could open new avenues for biomedical applications, such as condensate-modifying therapeutics.

Application of Deconvolution in Path Integral Simulations.

In path integral molecular dynamics (PIMD) simulations, atoms are represented by several replicas connected with harmonic springs, so additional vibrations appear beyond the physical vibrations because of the normal mode frequencies coming from the springs of the ring polymer. In harmonic approximation, the frequencies of these internal modes can be determined exactly from the physical frequencies. We show that this formal effect of the path integral simulations on the vibrations can be considered as a convolution if we use the square of the frequency as an independent variable. This convolution can be represented as a matrix multiplication. The potential of the formalism is demonstrated in two applications. We present an alternative method to determine the power spectrum of thermostats used in PIMD simulations. We also show that in simple anharmonic model systems, the physical frequencies can be obtained from ring polymer molecular dynamics simulations by deconvolution, even in cases where spurious resonances appear.

RNA Polymerase II is a Polar Roadblock to a Progressing DNA Fork.

DNA replication and transcription occur simultaneously on the same DNA template, leading to inevitable conflicts between the replisome and RNA polymerase. These conflicts can stall the replication fork and threaten genome stability. Although numerous studies show that head-on conflicts are more detrimental and more prone to promoting R-loop formation than co-directional conflicts, the fundamental cause for the RNA polymerase roadblock polarity remains unclear, and the structure of these R-loops is speculative. In this work, we use a simple model system to address this complex question by examining the Pol II roadblock to a DNA fork advanced via mechanical unzipping to mimic the replisome progression. We found that the Pol II binds more stably to resist removal in the head-on configuration, even with minimal transcript size, demonstrating that the Pol II roadblock has an inherent polarity. However, an elongating Pol II with a long RNA transcript becomes an even more potent and persistent roadblock while retaining the polarity, and the formation of an RNA-DNA hybrid mediates this enhancement. Surprisingly, we discovered that when a Pol II collides with the DNA fork head-on and becomes backtracked, an RNA-DNA hybrid can form on the lagging strand in front of Pol II, creating a topological lock that traps Pol II at the fork. TFIIS facilitates RNA-DNA hybrid removal by severing the connection of Pol II with the hybrid. We further demonstrate that this RNA-DNA hybrid can prime lagging strand replication by T7 DNA polymerase while Pol II is still bound to DNA. Our findings capture basal properties of the interactions of Pol II with a DNA fork, revealing significant implications for transcription-replication conflicts.

Modelling structure-borne sound and radiation of submerged structures at high frequencies

Predicting the vibroacoustic behaviour of structures in contact with water and at high frequencies can be a complex task due to the fluid-structure interaction. Computation time increases with frequency and the complexity of the structure. Being able to predict the sound radiated by a naval vehicle in contact with water could help in improving passengers' comfort as well as the impact on the marine fauna. We use a prediction method called Dynamic Energy Analysis (DEA), so far emloyed mainly to assess the vibrational energy levels in the structure itself. DEA is a phase-space based ray tracing method determining energy densities in terms of the ray densities in a structure. The method can be applied on FEM-meshes and thus needs no SEA type substructuring. We expand the DEA methodology here to take into account radiation into the fluid in contact with the structure. From structure borne DEA calculations, we can determine directional sound radiation patterns both inside and outside the structure. We will demonstrate the new technique using some simple model systems.

A DFT Mechanistic Study on the Aza-Aldol Reaction of Boron Aza-Enolates: Relative Stability of Six-Membered Transition State and Its Relevance to the Coordination Mode of the Leaving Group.

The mechanism of the aza-aldol reaction between boron aza-enolate and benzaldehyde is investigated by using density functional theory calculations. The result shows that the syn-E isomer is preferentially formed, consistent with experimental observations. The six-membered ring transition state (TS) with the boat form leads to the E isomer, while the more unstable chair TS does to the Z isomer. The preference of the syn isomer is determined by the interactions between the substituents of aza-enolate and benzaldehyde. Structural distortion and intrinsic reaction coordinate analyses of simplified model systems provide insights into the origin of the relative stability of the rate-determining TS with boat and chair forms. The boat TS is an early TS; thus, minimal structural distortions of the reactant are required to reach this TS. The Lewis pair interactions between the boron and imine groups during B-N elimination also influenced the relative stability of the TSs. This interaction involves the nitrogen lone pair in the boat TS, while the π(N═C) orbital is involved in the chair TS. The Lewis pair with the lone pair stabilizes the TS more than that with the π orbital. The boron aza-enolate with 9-BBN generates an ate complex and forms C-C bonds sequentially, whereas that with Bpin does not generate an ate complex and exhibits the concerted formation of B-O and C-C bonds. Thus, the higher electrophilicity of boron such as 9-BBN enhances the reactivity by facilitating the formation of the ate complex. A reaction design is proposed to reverse the syn/anti selectivity. Proof-of-concept DFT calculations suggested that the modification of the imine group would change the relative stability of the boat/chair TSs and give the anti-product.

Naphthalimide-Based Amphiphiles: Synthesis and DFT Studies of the Aggregation and Interaction of a Simplified Model System with Water Molecules.

Systems containing amphiphilic/pathic molecules have the tremendous capacity to self-assemble under appropriate conditions to form morphologies with well-defined structural order (systematic arrangement), nanometer-scale dimensions, and unique properties. In this work, the synthesis of novel naphthalimide-based amphiphilic probes that have 1,8-naphthalimide as the fluorescence signal reporting group, octyl as hydrophobic head, and PEG as hydrophilic tail, is described. These designed molecules represent a new class of self-assembling structures with some promising features. The lack of literature data on the use of 1,8-naphthalimides with cyclic and acyclic hydrophilic PEG fragments as self-assembling structures gives us the opportunity to initiate a new field in materials science. The successful synthesis of such structures is fundamental to synthetic chemistry, and computational studies of the aggregation and binding of water molecules shed light on the ability of these new systems to function as membrane water channels. This study not only expands the list of 1,8-naphthalimide derivatives but may also serve as a new platform for the development of membrane additives based on PEG-functionalized naphthalimides.

Cm(III) speciation in the presence of citrate from neutral to hyperalkaline conditions and the effect of calcium

We investigated the binary Cm-citrate system using time-resolved laser fluorescence spectroscopy (TRLFS), parallel factor analysis (PARAFAC), and quantum chemical calculations. Evidence collectively suggests the stepwise coordination and deprotonation of citrate alcohol groups in Cm-cit complexes with two bound citrate moieties upon increasing pH, which is supported by a bathochromic shift in emission spectra, an observed increase in lifetime measurements, and lower energy minima for citrate alcohol involvement versus hydrolysis of the Cm-citrate species. Our PARAFAC results agree with a 3-component model for the Cm-citrate system and offer pure component decompositions, yielding fraction species across the studied pH range that have a correlated slope = 1 as a function of pH. For the first time, evidence of ternary Ca-Cm-citrate complexes was revealed by TRLFS with increasing calcium concentration at fixed pHm. The formation of these ternary complexes was substantiated with density functional theory (DFT) calculations on simple model systems of the complexes. Shared citrate carboxylate groups between calcium and curium were proposed for all three ternary Ca-Cm-cit complexes based on DFT-determined Ca–O and Cm–O distances. Moreover, we found that the ternary complex with both alcohol groups deprotonated is most stable when it shares both two carboxylate and two alcohol groups between Ca and Cm. The presence of shared functional groups highlights the enhanced stability of these ternary complexes. Additional work is warranted to further constrain the stoichiometry, stability constants and dependence on ionic strength of these complexes for purposes of thermodynamic modeling of repository settings.

Models to predict configurational adiabats of Lennard-Jones fluids and their transport coefficients.

A comparison is made between three simple approximate formulas for the configurational adiabat (i.e., constant excess entropy, sex) lines in a Lennard-Jones (LJ) fluid, one of which is an analytic formula based on a harmonic approximation, which was derived by Heyes et al. [J. Chem. Phys. 159, 224504 (2023)] (analytic isomorph line, AIL). Another is where the density is normalized by the freezing density at that temperature (freezing isomorph line, FIL). It is found that the AIL formula and the average of the freezing density and the melting density ("FMIL") are configurational adiabats at all densities essentially down to the liquid-vapor binodal. The FIL approximation departs from a configurational adiabat in the vicinity of the liquid-vapor binodal close to the freezing line. The self-diffusion coefficient, D, shear viscosity, ηs, and thermal conductivity, λ, in macroscopic reduced units are essentially constant along the AIL and FMIL at all fluid densities and temperatures, but departures from this trend are found along the FIL at high liquid state densities near the liquid-vapor binodal. This supports growing evidence that for simple model systems with no or few internal degrees of freedom, isodynes are lines of constant excess entropy. It is shown that for the LJ fluid, ηs and D can be predicted accurately by an essentially analytic procedure from the high temperature limiting inverse power fluid values (apart from at very low densities), and this is demonstrated quite well also for the experimental argon viscosity.

Temperature effects on the branching dynamics in the model ambimodal (6 + 4)/(4 + 2) intramolecular cycloaddition reaction.

C14H20 (tetradecapentaene) is a simple model system exhibiting post transition-state behavior, wherein both the (6 + 4) and (4 + 2) cycloaddition products are formed from one ambimocal transition state structure. We studied the bifurcation dynamics starting from the two ambimodal transition state structures, the chair-form and boat-form, using the quasi-classical trajectory, classical molecular dynamics, and ring-polymer molecular dynamics methods on the parameter-optimized semiempirical GFN2-xTB potential energy surface. It was found that the calculated branching fractions differ between the chair-form and boat-form due to the different nature in the IRC pathways. We also investigated the effects of temperature on bifurcation dynamics and found that, at higher temperatures, trajectories stay longer in the intermediate region of the potential energy surface.

Measurement of solubility product reveals the interplay of oligomerization and self-association for defining condensate formation.

Cellular condensates often consist of 10s to 100s of distinct interacting molecular species. Because of the complexity of these interactions, predicting the point at which they will undergo phase separation is daunting. Using experiments and computation, we therefore studied a simple model system consisting of polySH3 and polyPRM designed for pentavalent heterotypic binding. We tested whether the peak solubility product, or the product of the dilute phase concentration of each component, is a predictive parameter for the onset of phase separation. Titrating up equal total concentrations of each component showed that the maximum solubility product does approximately coincide with the threshold for phase separation in both experiments and models. However, we found that measurements of dilute phase concentration include small oligomers and monomers; therefore, a quantitative comparison of the experiments and models required inclusion of small oligomers in the model analysis. Even with the inclusion of small polyPRM and polySH3 oligomers, models did not predict experimental results. This led us to perform dynamic light scattering experiments, which revealed homotypic binding of polyPRM. Addition of this interaction to our model recapitulated the experimentally observed asymmetry. Thus, comparing experiments with simulation reveals that the solubility product can be predictive of the interactions underlying phase separation, even if small oligomers and low affinity homotypic interactions complicate the analysis.

Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks

ABSTRACT Thermal stratification plays a key role in lakes' ecosystems. In contrast to deep lakes, the thermal structure of shallow polymictic lakes is characterized by a weak stratification with an apparent diurnal cycle. Long-term changes in stratification are governed by climate change and anthropogenic effects such as water level regulation. We developed a simple and robust model system consisting of an energy balance model to estimate depth-averaged water temperatures and an artificial neural network (ANN) model to predict stratification with high temporal resolution. One novelty of our approach is that instead of directly estimating water temperatures at different depths, we simulated the potential energy anomaly index, the indicator of stratification's strength. The ANN-based model's performance was assessed against a physical-based one-dimensional model (General Ocean Turbulence Model) by modeling a 40-year-long period from 1981 to 2020. The new model accurately predicts a shallow lake's weak stratification and its diurnal cycle. Besides, the model proved reliable on longer time scales, capturing the effect of climate change, anthropogenic water level regulation, and their synergistic interaction on the change of stratification's intensity and duration.

POTENTIAL PARAMETERS FOR EVALUATING THE ACTIVATION CHARACTERISTICS OF ION DIFFUSION IN SOLID ELECTROLYTES BASED ON STABILIZED ZIRCONIUM OXIDE

The activation energy values of oxygen ion diffusion in yttria-stabilized zirconia (one of the most promising solid electrolytes for fuel cell technologies), estimated in molecular dynamics studies with the classical Buckingham potential, turn out to be significantly lower than experimental ones. A possible reason is the incorrect calibration of the potential, the parameters of which were selected earlier using simple model systems. In this paper, three sets of potential parameters have been developed based on the calibration of the interatomic potential based on the results of periodic DFT calculation in an extended system. The results of molecular dynamic modeling using the developed parameter sets reproduce much better the experimental values of activation energies with a variation of the molar fraction of the dopant in a solid electrolyte.