RNAs undergo phase transitions with lower critical solution temperatures.

Co-phase separation of RNAs and RNA-binding proteins drives the biogenesis of ribonucleoprotein granules. RNAs can also undergo phase transitions in the absence of proteins. However, the physicochemical driving forces of protein-free, RNA-driven phase transitions remain unclear. Here we report that various types of RNA undergo phase separation with system-specific lower critical solution temperatures. This entropically driven phase separation is an intrinsic feature of the phosphate backbone that requires Mg2+ ions and is modulated by RNA bases. RNA-only condensates can additionally undergo enthalpically favourable percolation transitions within dense phases. This is enabled by a combination of Mg2+-dependent bridging interactions between phosphate groups and RNA-specific base stacking and base pairing. Phase separation coupled to percolation can cause dynamic arrest of RNAs within condensates and suppress the catalytic activity of an RNase P ribozyme. Our work highlights the need to incorporate RNA-driven phase transitions into models for ribonucleoprotein granule biogenesis.

FIREBALL: A tool to fit protein phase diagrams based on mean-field theories for polymer solutions.

Biomolecular condensates form via phase transitions of condensate-specific biomacromolecules. Intrinsically disordered regions featuring the appropriate sequence grammars can contribute via homotypic and heterotypic interactions to the driving forces for phase separation of multivalent proteins. Experiments and computations have matured to the point where the concentrations of coexisting dense and dilute phases can be measured or computed for individual intrinsically disordered regions in complex milieus. For a macromolecule such as a disordered protein in a solvent, the locus of points that connects concentrations of the two coexisting phases defines a phase boundary, or binodal. Often, only a few points along the binodal are accessible via measurements. In such cases, and for quantitative and comparative analysis of parameters that describe the driving forces for phase separation, it is useful to fit measured or computed binodals to mean-field free energies for polymer solutions. The nonlinearity of the underlying free energy functions makes it challenging to put mean-field theories into practice. Here, we present FIREBALL, a suite of computational tools designed to enable efficient construction, analysis, and fitting to experimental or computed data of binodals. We show that depending on the theory being used, one can also extract information regarding coil-to-globule transitions of individual macromolecules.

FIREBALL: A tool to fit protein phase diagrams based on mean-field theories for polymer solutions.

Biomolecular condensates form via phase transitions of condensate-specific biomacromolecules. Intrinsically disordered regions (IDRs) featuring the appropriate sequence grammar can contribute homotypic and heterotypic interactions to the driving forces for phase separation of multivalent proteins. At this juncture, experiments and computations have matured to the point where the concentrations of coexisting dense and dilute phases can be quantified for individual IDRs in complex milieus both in vitro and in vivo . For a macromolecule such as a disordered protein in a solvent, the locus of points that connects concentrations of the two coexisting phases defines a phase boundary or binodal. Often, only a few points along the binodal, especially in the dense phase, are accessible for measurement. In such cases and for quantitative and comparative analysis of parameters that describe the driving forces for phase separation, it is useful to fit measured or computed binodals to well-known mean-field free energies for polymer solutions. Unfortunately, the non-linearity of the underlying free energy functions makes it challenging to put mean-field theories into practice. Here, we present FIREBALL, a suite of computational tools designed to enable efficient construction, analysis, and fitting to experimental or computed data of binodals. We show that depending on the theory being used, one can also extract information regarding coil-to-globule transitions of individual macromolecules. Here, we emphasize the ease-of-use and utility of FIREBALL using examples based on data for two different IDRs. Statement of Significance: Macromolecular phase separation drives the assembly of membraneless bodies known as biomolecular condensates. Measurements and computer simulations can now be brought to bear to quantify how the concentrations of macromolecules in coexisting dilute and dense phases vary with changes to solution conditions. These mappings can be fit to analytical expressions for free energies of solution to extract information regarding parameters that enable comparative assessments of the balance of macromolecule-solvent interactions across different systems. However, the underlying free energies are non-linear and fitting them to actual data is non-trivial. To enable comparative numerical analyses, we introduce FIREBALL, a user-friendly suite of computational tools that allows one to generate, analyze, and fit phase diagrams and coil-to-globule transitions using well-known theories.

Programmable synthetic biomolecular condensates for cellular control.

The formation of biomolecular condensates mediated by a coupling of associative and segregative phase transitions plays a critical role in controlling diverse cellular functions in nature. This has inspired the use of phase transitions to design synthetic systems. While design rules of phase transitions have been established for many synthetic intrinsically disordered proteins, most efforts have focused on investigating their phase behaviors in a test tube. Here, we present a rational engineering approach to program the formation and physical properties of synthetic condensates to achieve intended cellular functions. We demonstrate this approach through targeted plasmid sequestration and transcription regulation in bacteria and modulation of a protein circuit in mammalian cells. Our approach lays the foundation for engineering designer condensates for synthetic biology applications.

Developments in describing equilibrium phase transitions of multivalent associative macromolecules.

Biomolecular condensates are distinct cellular bodies that form and dissolve reversibly to organize cellular matter and biochemical reactions in space and time. Condensates are thought to form and dissolve under the influence of spontaneous and driven phase transitions of multivalent associative macromolecules. These include phase separation, which is defined by segregation of macromolecules from the solvent or from one another, and percolation or gelation, which is an inclusive networking transition driven by reversible associations among multivalent macromolecules. Considerable progress has been made to model sequence-specific phase transitions, especially for intrinsically disordered proteins. Here, we summarize the state-of-the-art of theories and computations aimed at understanding and modeling sequence-specific, thermodynamically controlled, coupled associative and segregative phase transitions of archetypal multivalent macromolecules.

Competing interactions give rise to two-state behavior and switch-like transitions in charge-rich intrinsically disordered proteins.

The most commonly occurring intrinsically disordered proteins (IDPs) are polyampholytes, which are defined by the duality of low net charge per residue and high fractions of charged residues. Recent experiments have uncovered nuances regarding sequence­ensemble relationships of model polyampholytic IDPs. These include differences in conformational preferences for sequences with lysine vs. arginine and the suggestion that well-mixed sequences form a range of conformations, including globules, conformations with ensemble averages that are reminiscent of ideal chains, or self-avoiding walks. Here, we explain these observations by analyzing results from atomistic simulations. We find that polyampholytic IDPs generally sample two distinct stable states, namely, globules and self-avoiding walks. Globules are favored by electrostatic attractions between oppositely charged residues, whereas self-avoiding walks are favored by favorable free energies of hydration of charged residues. We find sequence-specific temperatures of bistability at which globules and self-avoiding walks can coexist. At these temperatures, ensemble averages over coexisting states give rise to statistics that resemble ideal chains without there being an actual counterbalancing of intrachain and chain-solvent interactions. At equivalent temperatures, arginine-rich sequences tilt the preference toward globular conformations whereas lysine-rich sequences tilt the preference toward self-avoiding walks. We also identify differences between aspartate- and glutamate-containing sequences, whereby the shorter aspartate side chain engenders preferences for metastable, necklace-like conformations. Finally, although segregation of oppositely charged residues within the linear sequence maintains the overall two-state behavior, compact states are highly favored by such systems.

Uncovering Differences in Hydration Free Energies and Structures for Model Compound Mimics of Charged Side Chains of Amino Acids.

Free energies of hydration are of fundamental interest for modeling and understanding conformational and phase equilibria of macromolecular solutes in aqueous phases. Of particular relevance to systems such as intrinsically disordered proteins are the free energies of hydration and hydration structures of model compounds that mimic charged side chains of Arg, Lys, Asp, and Glu. Here, we deploy a Thermodynamic Cycle-based Proton Dissociation (TCPD) approach in conjunction with data from direct measurements to obtain estimates for the free energies of hydration for model compounds that mimic the side chains of Arg+, Lys+, Asp-, and Glu-. Irrespective of the choice made for the hydration free energy of the proton, the TCPD approach reveals clear trends regarding the free energies of hydration for Arg+, Lys+, Asp-, and Glu-. These trends include asymmetries between the hydration free energies of acidic (Asp- and Glu-) and basic (Arg+ and Lys+) residues. Further, the TCPD analysis, which relies on a combination of experimental data, shows that the free energy of hydration of Arg+ is less favorable than that of Lys+. We sought a physical explanation for the TCPD-derived trends in free energies of hydration. To this end, we performed temperature-dependent calculations of free energies of hydration and analyzed hydration structures from simulations that use the polarizable Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field and water model. At 298 K, the AMOEBA model generates estimates of free energies of hydration that are consistent with TCPD values with a free energy of hydration for the proton of ca. -259 kcal/mol. Analysis of temperature-dependent simulations leads to a structural explanation for the observed differences in free energies of hydration of ionizable residues and reveals that the heat capacity of hydration is positive for Arg+ and Lys+ and negative for Asp- and Glu-.

Design of intrinsically disordered proteins that undergo phase transitions with lower critical solution temperatures.

Many naturally occurring elastomers are intrinsically disordered proteins (IDPs) built up of repeating units and they can demonstrate two types of thermoresponsive phase behavior. Systems characterized by lower critical solution temperatures (LCST) undergo phase separation above the LCST whereas systems characterized by upper critical solution temperatures (UCST) undergo phase separation below the UCST. There is congruence between thermoresponsive coil-globule transitions and phase behavior whereby the theta temperatures above or below which the IDPs transition from coils to globules serve as useful proxies for the LCST / UCST values. This implies that one can design sequences with desired values for the theta temperature with either increasing or decreasing radii of gyration above the theta temperature. Here, we show that the Monte Carlo simulations performed in the so-called intrinsic solvation (IS) limit version of the temperature-dependent the ABSINTH (self-Assembly of Biomolecules Studied by an Implicit, Novel, Tunable Hamiltonian) implicit solvation model, yields a useful heuristic for discriminating between sequences with known LCST versus UCST phase behavior. Accordingly, we use this heuristic in a supervised approach, integrate it with a genetic algorithm, combine this with IS limit simulations, and demonstrate that novel sequences can be designed with LCST phase behavior. These calculations are aided by direct estimates of temperature dependent free energies of solvation for model compounds that are derived using the polarizable AMOEBA (atomic multipole optimized energetics for biomolecular applications) forcefield. To demonstrate the validity of our designs, we calculate coil-globule transition profiles using the full ABSINTH model and combine these with Gaussian Cluster Theory calculations to establish the LCST phase behavior of designed IDPs.

Connecting Coil-to-Globule Transitions to Full Phase Diagrams for Intrinsically Disordered Proteins.

Phase separation is thought to underlie spatial and temporal organization that is required for controlling biochemical reactions in cells. Multivalence of interaction motifs, also known as stickers, is a defining feature of proteins that drive phase separation. Intrinsically disordered proteins with stickers uniformly distributed along the linear sequence can serve as scaffold molecules that drive phase separation. The sequence-intrinsic contributions of disordered proteins to phase separation can be discerned by computing or measuring sequence-specific phase diagrams. These help to delineate the combinations of protein concentration and a suitable control parameter, such as temperature, that support phase separation. Here, we present an approach that combines detailed simulations with a numerical adaptation of an analytical Gaussian cluster theory to enable the calculation of sequence-specific phase diagrams. Our approach leverages the known equivalence between the driving forces for single-chain collapse in dilute solutions and the driving forces for phase separation in concentrated solutions. We demonstrate the application of the theory-aided computations through calculation of phase diagrams for a set of archetypal intrinsically disordered low-complexity domains. We also leverage theories to compute sequence-specific percolation lines and thereby provide a thermodynamic framework for hardening transitions that have been observed for many biomolecular condensates.

Mechanistic Insights and Rational Design of a Versatile Surface with Cells/Bacteria Recognition Capability via Orientated Fusion Peptides.

Hospital-acquired infection causes many deaths worldwide and calls for the urgent need for antibacterial biomaterials used in clinic that can selectively kill harmful bacteria. The present study rationally designs fusion peptides capable of undergoing 2D self-assembly on the poly(methyl methacrylate) surface to form a smart surface, which can maintain a desirable orientation via electrostatic interactions. The in vitro assay shows that the smart surface can recognize bacteria to exert antibacterial activity and is nontoxic toward mouse bone mesenchymal stem cells. Excitingly, the smart surface can distinguish different bacterial strains. This selective feature, from being broad-spectrum to being highly selective against S. aureus, can be altered by varying the number of amino acids in the recognition sequences. By all-atom molecular dynamics simulations, it is also found that the recognition sequence in the peptide is critical for the selectivity toward specific bacterial strains, in which a less accessible surface area for the bacteria in the antimicrobial peptide sequence is responsible for such selectivity. Finally, the smart surface can inhibit S. aureus infection in vivo with much more rapid tissue-healing compared to the control.

Modular functionalization of crystalline graphene by recombinant proteins: a nanoplatform for probing biomolecules.

Graphene, as well as other two-dimensional materials, is a promising candidate for use in bioimaging, therapeutic drug delivery, and bio-sensing applications. Here, we developed a protocol to functionalize graphene with recombinant proteins using genetically encoded SpyTag-SpyCatcher chemistry. SpyTag forms a covalent isopeptide bond with its genetically encoded partner SpyCatcher through spontaneous amidation under physiological conditions. The functionalization protocol developed is based on the use of short proteins as a linker, where two graphene-binding-peptides (GBPs) are attached to both ends of SpyTag (referred to as GStG), followed by the covalent conjugation with SpyCatcher-fusion proteins. The proposed method enables the decoration of crystalline graphene with various proteins, such as fluorescent proteins and affibody molecules that bind to cancerous cells. This scheme, which takes advantage of the cleanness of single-crystal graphene and the robustness of SpyTag-SpyCatcher chemistry, provides a versatile platform on which to study the biomolecule-surface and cell-substrate interactions and, indeed, may lead to a new way of designing biomedical devices. The interaction between peptides and graphene was clearly shown using molecular dynamics simulation and proven using specially designed experiments.

Improving the productivity of monodisperse polyhedral cages by the rational design of kinetic self-assembly pathways.

Hollow polyhedral cages hold great potential for application in nanotechnological and biomedical fields. Understanding the formation mechanism of these self-assembled structures could provide guidance for the rational design of the desired polyhedral cages. Here, by constructing kinetic network models from extensive coarse-grained molecular dynamics simulations, we elucidated the formation mechanism of the dodecahedral cage, which is formed by the self-assembly of patchy particles. We found that the dodecahedral cage is formed through increasing the aggregate size followed by structure rearrangement. Based on this mechanistic understanding, we improved the productivity of the dodecahedral cage through the rational design of the patch arrangement of patchy particles, which promotes the structural rearrangement process. Our results demonstrate that it should be a feasible strategy to achieve the rational design of the desired nanostructures via the kinetic analysis. We anticipate that this methodology could be extended to other self-assembly systems for the fabrication of functional nanomaterials.

Harnessing complexity in molecular self-assembly using computer simulations.

In molecular self-assembly, hundreds of thousands of freely-diffusing molecules associate to form ordered and functional architectures in the absence of an actuator. This intriguing phenomenon plays a critical role in biology and has become a powerful tool for the fabrication of advanced nanomaterials. Due to the limited spatial and temporal resolutions of current experimental techniques, computer simulations offer a complementary strategy to explore self-assembly with atomic resolution. Here, we review recent computational studies focusing on both thermodynamic and kinetic aspects. As we shall see, thermodynamic approaches based on modeling and statistical mechanics offer initial guidelines to design nanostructures with modest computational effort. Computationally more intensive analyses based on molecular dynamics simulations and kinetic network models (KNMs) reach beyond it, opening the door to the rational design of self-assembly pathways. Current limitations of these methodologies are discussed. We anticipate that the synergistic use of thermodynamic and kinetic analyses based on computer simulations will provide an important contribution to the de novo design of self-assembly.

Path lumping: An efficient algorithm to identify metastable path channels for conformational dynamics of multi-body systems.

Constructing Markov state models from large-scale molecular dynamics simulation trajectories is a promising approach to dissect the kinetic mechanisms of complex chemical and biological processes. Combined with transition path theory, Markov state models can be applied to identify all pathways connecting any conformational states of interest. However, the identified pathways can be too complex to comprehend, especially for multi-body processes where numerous parallel pathways with comparable flux probability often coexist. Here, we have developed a path lumping method to group these parallel pathways into metastable path channels for analysis. We define the similarity between two pathways as the intercrossing flux between them and then apply the spectral clustering algorithm to lump these pathways into groups. We demonstrate the power of our method by applying it to two systems: a 2D-potential consisting of four metastable energy channels and the hydrophobic collapse process of two hydrophobic molecules. In both cases, our algorithm successfully reveals the metastable path channels. We expect this path lumping algorithm to be a promising tool for revealing unprecedented insights into the kinetic mechanisms of complex multi-body processes.

Kinetics-Controlled Amphiphile Self-Assembly Processes.

Amphiphile self-assembly is an essential bottom-up approach of fabricating advanced functional materials. Self-assembled materials with desired structures are often obtained through thermodynamic control. Here, we demonstrate that the selection of kinetic pathways can lead to drastically different self-assembled structures, underlining the significance of kinetic control in self-assembly. By constructing kinetic network models from large-scale molecular dynamics simulations, we show that two largely similar amphiphiles, 1-[11-oxo-11-(pyren-1-ylmethoxy)-undecyl]pyridinium bromide (PYR) and 1-(11-((5a1,8a-dihydropyren-1-yl)methylamino)-11-oxoundecyl)pyridinium bromide (PYN), prefer distinct kinetic assembly pathways. While PYR prefers an incremental growth mechanism and forms a nanotube, PYN favors a hopping growth pathway leading to a vesicle. Such preference was found to originate from the subtle difference in the distributions of hydrophobic and hydrophilic groups in their chemical structures, which leads to different rates of the adhesion process among the aggregating micelles. Our results are in good agreement with experimental results, and accentuate the role of kinetics in the rational design of amphiphile self-assembly.

Achieving enhanced cell penetration of short conformationally constrained peptides through amphiphilicity tuning.

Due to their enhanced stability and cell permeability, cyclic cell-penetrating peptides have been widely used as delivery vectors for transporting cell-impermeable cargos into cells. In this study, we synthesized a panel of conformationally constrained peptides with either α-helix or ß-hairpin conformations. We tuned the amphiphilicity of these constrained peptides with different distributions of charged or hydrophobic residues and compared their cellular uptake efficiencies in different cell lines. We found that the amphipathicity of these conformationally constrained peptides correlates well with their cellular uptake efficiency. We proposed that peptides with larger hydrophobic moments (HMs) have stronger binding affinities with the cell membrane which further accelerates the endocytosis process. This finding should provide an approach towards the design of more potent conformationally constrained cell-penetrating peptides for biomedical applications.

Controlling the Integration of Polyvinylpyrrolidone onto Substrate by Quartz Crystal Microbalance with Dissipation To Achieve Excellent Protein Resistance and Detoxification.

Blood purification systems, in which the adsorbent removes exogenous and endogenous toxins from the blood, are widely used in clinical practice. To improve the protein resistance of and detoxification by the adsorbent, researchers can modify the adsorbent with functional molecules, such as polyvinylpyrrolidone (PVP). However, achieving precise control of the functional molecular density, which is crucial to the activity of the adsorbent, remains a significant challenge. In the present study, we prepared a model system for blood purification adsorbents in which we controlled the integration density of PVP molecules of different molecular weights on an Au substrate by quartz crystal microbalance with dissipation (QCM-D). We characterized the samples with atomic force microscopy, X-ray photoelectron spectroscopy, and QCM-D and found that the molecular density and the chain length of the PVP molecules played important roles in determining the properties of the sample. At the optimal condition, the modified sample demonstrated strong resistance to plasma proteins, decreasing the adsorption of human serum albumin (HSA) and fibrinogen (Fg) by 92.5% and 79.2%, respectively. In addition, the modified sample exhibited excellent detoxification, and the adsorption of bilirubin increased 2.6-fold. Interestingly, subsequent atomistic molecular dynamics simulations indicated that the favorable interactions between PVP and bilirubin were dominated by hydrophobic interactions. An in vitro platelet adhesion assay showed that the adhesion of platelets on the sample decreased and that the platelets were maintained in an inactivated state. The CCK-8 assay indicated that the modified sample exhibited negligible cytotoxicity to L929 cells. These results demonstrated that our method holds great potential for the modification of adsorbents in blood purification systems.

Elucidation of the conformational dynamics of multi-body systems by construction of Markov state models.

Constructing Markov State Models (MSMs) based on short molecular dynamics simulations is a powerful computational technique to complement experiments in predicting long-time kinetics of biomolecular processes at atomic resolution. Even though the MSM approach has been widely applied to study one-body processes such as protein folding and enzyme conformational changes, the majority of biological processes, e.g. protein-ligand recognition, signal transduction, and protein aggregation, essentially involve multiple entities. Here we review the attempts at constructing MSMs for multi-body systems, point out the challenges therein and discuss recent algorithmic progresses that alleviate these challenges. In particular, we describe an automatic kinetics based partitioning method that achieves optimal definition of the conformational states in a multi-body system, and discuss a novel maximum-likelihood approach that efficiently estimates the slow uphill kinetics utilizing pre-computed equilibrium populations of all states. We expect that these new algorithms and their combinations may boost investigations of important multi-body biological processes via the efficient construction of MSMs.

Elucidating dominant pathways of the nano-particle self-assembly process.

Self-assembly processes play a key role in the fabrication of functional nano-structures with widespread application in drug delivery and micro-reactors. In addition to the thermodynamics, the kinetics of the self-assembled nano-structures also play an important role in determining the formed structures. However, as the self-assembly process is often highly heterogeneous, systematic elucidation of the dominant kinetic pathways of self-assembly is challenging. Here, based on mass flow, we developed a new method for the construction of kinetic network models and applied it to identify the dominant kinetic pathways for the self-assembly of star-like block copolymers. We found that the dominant pathways are controlled by two competing kinetic parameters: the encounter time Te, characterizing the frequency of collision and the transition time Tt for the aggregate morphology change from rod to sphere. Interestingly, two distinct self-assembly mechanisms, diffusion of an individual copolymer into the aggregate core and membrane closure, both appear at different stages (with different values of Tt) of a single self-assembly process. In particular, the diffusion mechanism dominates the middle-sized semi-vesicle formation stage (with large Tt), while the membrane closure mechanism dominates the large-sized vesicle formation stage (with small Tt). Through the rational design of the hydrophibicity of the copolymer, we successfully tuned the transition time Tt and altered the dominant self-assembly pathways.

Stapling of unprotected helical peptides via photo-induced intramolecular thiol-yne hydrothiolation.

Peptide stapling emerged as a versatile strategy to recapitulate the bioactive helical conformation of unstructured short peptides in water to improve their therapeutic properties in targeting intracellular "undruggable" targets. Here, we describe the development of photo-induced intramolecular thiol-yne macrocyclization for rapid access to short stapled peptides with enhanced biophysical properties. This new peptide stapling technique provides rapid access to conformationally constrained helices with satisfying functional group tolerance. Notably, the vinyl sulfide linkage shows distinct lipophilicity with reduced membrane toxicity compared to the corresponding all-hydrocarbon analogue. As a proof of principle, we constructed stabilized helices modulating intracellular estrogen receptor (ER)-coactivator interactions with a nanomolar binding affinity, enhanced serum stability, a diffuse cellular distribution and selective cytotoxicity towards ER-positive MCF-7 cells.