Dependence of Binding Free Energies between RNA Nucleobases and Protein Side Chains on Local Dielectric Properties

Protein compactness and interaction valency define the architecture of a biomolecular condensate across scales

Non-membrane-bound biomolecular condensates have been proposed to represent an important mode of subcellular organization in diverse biological settings. However, the fundamental principles governing the spatial organization and dynamics of condensates at the atomistic level remain unclear. The Saccharomyces cerevisiae Lge1 protein is required for histone H2B ubiquitination and its N-terminal intrinsically disordered fragment (Lge11-80) undergoes robust phase separation. This study connects single- and multi-chain all-atom molecular dynamics simulations of Lge11-80 with the in vitro behavior of Lge11-80 condensates. Analysis of modeled protein-protein interactions elucidates the key determinants of Lge11-80 condensate formation and links configurational entropy, valency, and compactness of proteins inside the condensates. A newly derived analytical formalism, related to colloid fractal cluster formation, describes condensate architecture across length scales as a function of protein valency and compactness. In particular, the formalism provides an atomistically resolved model of Lge11-80 condensates on the scale of hundreds of nanometers starting from individual protein conformers captured in simulations. The simulation-derived fractal dimensions of condensates of Lge11-80 and its mutants agree with their in vitro morphologies. The presented framework enables a multiscale description of biomolecular condensates and embeds their study in a wider context of colloid self-organization.

Coding From Binding? Molecular Interactions at the Heart of Translation

The mechanism and the evolution of DNA replication and transcription, the key elements of the central dogma of biology, are fundamentally well explained by the physicochemical complementarity between strands of nucleic acids. However, the determinants that have shaped the third part of the dogma-the process of biological translation and the universal genetic code-remain unclear. We review and seek parallels between different proposals that view the evolution of translation through the prism of weak, noncovalent interactions between biological macromolecules. In particular, we focus on a recent proposal that there exists a hitherto unrecognized complementarity at the heart of biology, that between messenger RNA coding regions and the proteins that they encode, especially if the two are unstructured. Reflecting the idea that the genetic code evolved from intrinsic binding propensities between nucleotides and amino acids, this proposal promises to forge a link between the distant past and the present of biological systems.

Multiscale Modeling of Protein-RNA Condensation in and Out of Equilibrium

A vast number of intracellular membraneless bodies also known as biomolecular condensates form through a liquid-liquid phase separation (LLPS) of biomolecules. To date, phase separation has been identified as the main driving force for a membraneless organelles such as nucleoli, Cajal bodies, stress granules, and chromatin compartments. Recently, the protein-RNA condensation is receiving increased attention, because it is closely related to the biological function of cells such as transcription, translation, and RNA metabolism. Despite the multidisciplinary efforts put forth to study the biophysical properties of protein-RNA condensates, there are many fundamental unanswered questions regarding the mechanism of formation and regulation of protein-RNA condensates in eukaryotic cells. Major challenges in studying protein-RNA condensation stem from (i) the molecular heterogeneity and conformational flexibility of RNA and protein chains and (ii) the nonequilibrium nature of transcription and cellular environment. Computer simulations, bioinformatics, and mathematical models are uniquely positioned for shedding light on the microscopic nature of protein-RNA phase separation. To this end, there is an urgent need for innovative models with the right spatiotemporal resolution for confronting the experimental observables in a comprehensive and physics-based manner. In this chapter, we will summarize the currently emerging research efforts, which employ atomistic and coarse-grained molecular models and field theoretical models to understand equilibrium and nonequilibrium aspects of protein-RNA condensation.

Interaction preferences between protein side chains and key epigenetic modifications 5-methylcytosine, 5-hydroxymethycytosine and N6-methyladenine

Covalent modifications of standard DNA/RNA nucleobases affect epigenetic regulation of gene expression by modulating interactions between nucleic acids and protein readers. We derive here the absolute binding free energies and analyze the binding modalities between key modified nucleobases 5-methylcytosine (5mC), 5-hydroxymethylcytosine (5hmC) and N⁶-methyladenine (m⁶A) and all non-prolyl/non-glycyl protein side chains using molecular dynamics simulations and umbrella sampling in both water and methanol, the latter mimicking the low dielectric environment at the dehydrated nucleic-acid/protein interfaces. We verify the derived affinities by comparing against a comprehensive set of high-resolution structures of nucleic-protein complexes involving 5mC. Our analysis identifies protein side chains that are highly tuned for detecting cytosine methylation as a function of the environment and can thus serve as microscopic readers of epigenetic marks. Conversely, we show that the relative ordering of sidechain affinities for 5hmC and m⁶A does not differ significantly from those for their precursor bases, cytosine and adenine, respectively, especially in the low dielectric environment. For those two modified bases, the effect is more nuanced and manifests itself primarily at the level of absolute changes in the binding free energy. Our results contribute towards establishing a quantitative foundation for understanding, predicting and modulating the interactions between modified nucleic acids and proteins at the atomistic level.

Compositional complementarity between genomic RNA and coat proteins in positive-sense single-stranded RNA viruses

During packaging in positive-sense single-stranded RNA (+ssRNA) viruses, coat proteins (CPs) interact directly with multiple regions in genomic RNA (gRNA), but the underlying physicochemical principles remain unclear. Here we analyze the high-resolution cryo-EM structure of bacteriophage MS2 and show that the gRNA/CP binding sites, including the known packaging signal, overlap significantly with regions where gRNA nucleobase-density profiles match the corresponding CP nucleobase-affinity profiles. Moreover, we show that the MS2 packaging signal corresponds to the global minimum in gRNA/CP interaction energy in the unstructured state as derived using a linearly additive model and knowledge-based nucleobase/amino-acid affinities. Motivated by this, we predict gRNA/CP interaction sites for a comprehensive set of 1082 +ssRNA viruses. We validate our predictions by comparing them with site-resolved information on gRNA/CP interactions derived in SELEX and CLIP experiments for 10 different viruses. Finally, we show that in experimentally studied systems CPs frequently interact with autologous coding regions in gRNA, in agreement with both predicted interaction energies and a recent proposal that proteins in general tend to interact with own mRNAs, if unstructured. Our results define a self-consistent framework for understanding packaging in +ssRNA viruses and implicate interactions between unstructured gRNA and CPs in the process.

Correcting electrostatic artifacts due to net-charge changes in the calculation of ligand binding free energies

Alchemically derived free energies are artifacted when the perturbed moiety has a nonzero net charge. The source of the artifacts lies in the effective treatment of the electrostatic interactions within and between the perturbed atoms and remaining (partial) charges in the simulated system. To treat the electrostatic interactions effectively, lattice-summation (LS) methods or cutoff schemes in combination with a reaction-field contribution are usually employed. Both methods render the charging component of the calculated free energies sensitive to essential parameters of the system like the cutoff radius or the box side lengths. Here, we discuss the results of three previously published studies of ligand binding. These studies presented estimates of binding free energies that were artifacted due to the charged nature of the ligands. We show that the size of the artifacts can be efficiently calculated and raw simulation data can be corrected. We compare the corrected results with experimental estimates and nonartifacted estimates from path-sampling methods. Although the employed correction scheme involves computationally demanding continuum-electrostatics calculations, we show that the correction estimate can be deduced from a small sample of configurations rather than from the entire ensemble. This observation makes the calculations of correction terms feasible for complex biological systems. To show the general applicability of the proposed procedure, we also present results where the correction scheme was used to correct independent free energies obtained from simulations employing a cutoff scheme or LS electrostatics. In this work, we give practical guidelines on how to apply the appropriate corrections easily.

Effective Estimation of Ligand-Binding Affinity Using Biased Sampling Method

The binding between two biomolecules is one of the most critical factors controlling many bioprocesses. Therefore, it is of great interest to derive a reliable method to calculate the free binding energy between two biomolecules. In this work, we have demonstrated that the binding affinity of ligands to proteins can be determined through biased sampling simulations. The umbrella sampling (US) method was applied on 20 protein-ligand complexes, including the cathepsin K (CTSK), type II dehydroquinase (DHQase), heat shock protein 90 (HSP90), and factor Xa (FXa) systems. The ligand-binding affinity was evaluated as the difference between the largest and smallest values of the free-energy curve, which was obtained via a potential of mean force analysis. The calculated affinities differ sizably from the previously reported experimental values, with an average difference of ∼3.14 kcal/mol. However, the calculated results are in good correlation with the experimental data, with correlation coefficients of 0.76, 0.87, 0.96, and 0.97 for CTSK, DHQase, HSP90, and FXa, respectively. Thus, the binding free energy of a new ligand can be reliably estimated using our US approach. Furthermore, the root-mean-square errors (RMSEs) of binding affinity of these systems are 1.13, 0.90, 0.37, and 0.25 kcal/mol, for CTSK, DHQase, HSP90, and FXa, respectively. The small RMSE values indicate the good precision of the biased sampling method that can distinguish the ligands exhibiting similar binding affinities.

RNA-protein interactions in an unstructured context

Despite their importance, our understanding of noncovalent RNA-protein interactions is incomplete. This especially concerns the binding between RNA and unstructured protein regions, a widespread class of such interactions. Here, we review the recent experimental and computational work on RNA-protein interactions in an unstructured context with a particular focus on how such interactions may be shaped by the intrinsic interaction affinities between individual nucleobases and protein side chains. Specifically, we articulate the claim that the universal genetic code reflects the binding specificity between nucleobases and protein side chains and that, in turn, the code may be seen as the Rosetta stone for understanding RNA-protein interactions in general.