Coarse-Grained Potentials for Local Interactions in Unfolded Proteins

C9orf72 polyPR directly binds to various nuclear transport components

The disruption of nucleocytoplasmic transport (NCT) is an important mechanism in neurodegenerative diseases. In the case of C9orf72-ALS, trafficking of macromolecules through the nuclear pore complex (NPC) might get frustrated by the binding of C9orf72-translated arginine-containing dipeptide repeat proteins (R-DPRs) to the Kapβ family of nuclear transport receptors. Besides Kapβs, several other types of transport components have been linked to NCT impairments in R-DPR-expressed cells, but the molecular origin of these observations has not been clarified. Here, we adopt a coarse-grained molecular dynamics model at amino acid resolution to study the direct interaction between polyPR, the most toxic DPR, and various nuclear transport components to elucidate the binding mechanisms and provide a complete picture of potential polyPR-mediated NCT defects. We found polyPR to directly bind to several isoforms of the Impα family, CAS (the specific exporter of Impα) and RanGAP. We observe no binding between polyPR and Ran. Longer polyPRs at lower salt concentrations also make contact with RanGEF and NTF2. Analyzing the polyPR contact sites on the transport components reveals that polyPR potentially interferes with RanGTP/RanGDP binding, with nuclear localization signal (NLS)-containing cargoes (cargo-NLS) binding to Impα, with cargo-NLS release from Impα, and with Impα export from the nucleus. The abundance of polyPR-binding sites on multiple transport components combined with the inherent polyPR length dependence makes direct polyPR interference of NCT a potential mechanistic pathway of C9orf72 toxicity.

Diameter dependence of transport through nuclear pore complex mimics studied using optical nanopores

The nuclear pore complex (NPC) regulates the selective transport of large biomolecules through the nuclear envelope. As a model system for nuclear transport, we construct NPC mimics by functionalizing the pore walls of freestanding palladium zero-mode waveguides with the FG-nucleoporin Nsp1. This approach enables the measurement of single-molecule translocations through individual pores using optical detection. We probe the selectivity of Nsp1-coated pores by quantitatively comparing the translocation rates of the nuclear transport receptor Kap95 to the inert probe BSA over a wide range of pore sizes from 35 nm to 160 nm. Pores below 55 ± 5 nm show significant selectivity that gradually decreases for larger pores. This finding is corroborated by coarse-grained molecular dynamics simulations of the Nsp1 mesh within the pore, which suggest that leakage of BSA occurs by diffusion through transient openings within the dynamic mesh. Furthermore, we experimentally observe a modulation of the BSA permeation when varying the concentration of Kap95. The results demonstrate the potential of single-molecule fluorescence measurements on biomimetic NPCs to elucidate the principles of nuclear transport.

Structural properties of the HNF-1A transactivation domain

Hepatocyte nuclear factor 1α (HNF-1A) is a transcription factor with important gene regulatory roles in pancreatic β-cells. HNF1A gene variants are associated with a monogenic form of diabetes (HNF1A-MODY) or an increased risk for type 2 diabetes. While several pancreatic target genes of HNF-1A have been described, a lack of knowledge regarding the structure-function relationships in HNF-1A prohibits a detailed understanding of HNF-1A-mediated gene transcription, which is important for precision medicine and improved patient care. Therefore, we aimed to characterize the understudied transactivation domain (TAD) of HNF-1A in vitro. We present a bioinformatic approach to dissect the TAD sequence, analyzing protein structure, sequence composition, sequence conservation, and the existence of protein interaction motifs. Moreover, we developed the first protocol for the recombinant expression and purification of the HNF-1A TAD. Small-angle X-ray scattering and synchrotron radiation circular dichroism suggested a disordered conformation for the TAD. Furthermore, we present functional data on HNF-1A undergoing liquid-liquid phase separation, which is in line with in silico predictions and may be of biological relevance for gene transcriptional processes in pancreatic β-cells.

Choosing the right density for a concentrated protein system like gluten in a coarse-grained model

Large coarse-grained simulations are often conducted with an implicit solvent, which makes it hard to assess the water content of the sample and the effective concentration of the system. Here the number and the size of cavities and entanglements in the system, together with density profiles, are used to asses the homogeneity and interconnectedness of gluten. This is a continuation of an earlier article, "Viscoelastic properties of wheat gluten in a molecular dynamics study" (Mioduszewski and Cieplak 2021b). It turns out there is a wide range of densities (between 1 residue per cubic nanometer and 3 residues/nm[Formula: see text]) where the system is interconnected, but not homogeneous: there are still large empty spaces, surrounded by an entangled protein network. Those findings should be of importance to any coarse-grained simulation of large protein systems.

A One-Bead-Per-Saccharide (1BPS) Model for Glycosaminoglycans

Glycosaminoglycans (GAGs) are polysaccharide compounds that play key roles in various biological processes. GAGs are important structural components of cartilage and the extracellular matrix of the brain. Due to the large size of these polysaccharides, coarse-grained approaches are indispensable for modeling these biopolymers. We develop a one-bead-per-saccharide model of chondroitin sulfates and hyaluronic acid based on an existing three-bead-per-saccharide coarse-grained model. Our coarse graining is carried out by using iterative Boltzmann inversion (IBI), including an additional coupling potential to incorporate the correlation between dihedral angles. The predictions of the model are verified against those of the existing three-bead-per-saccharin model and the experimental radius of gyration for hyaluronic acid.

Exploring Intra- and Inter-Regional Interactions in the IDP α-Synuclein Using smFRET and MD Simulations

Theoretical concepts from polymer physics are often used to describe intrinsically disordered proteins (IDPs). However, amino acid interactions within and between regions of the protein can lead to deviations from typical polymer scaling behavior and even to short-lived secondary structures. To investigate the key interactions in the dynamic IDP α-synuclein (αS) at the amino acid level, we conducted single-molecule fluorescence resonance energy transfer (smFRET) experiments and coarse-grained molecular dynamics (CG-MD) simulations. We find excellent agreement between experiments and simulations. Our results show that a physiological salt solution is a good solvent for αS and that the protein is highly dynamic throughout its entire chain, with local intra- and inter-regional interactions leading to deviations from global scaling. Specifically, we observe expansion in the C-terminal region, compaction in the NAC region, and a slightly smaller distance between the C- and N-termini than expected. Our simulations indicate that the compaction in the NAC region results from hydrophobic aliphatic contacts, mostly between valine and alanine residues, and cation-π interactions between lysine and tyrosine. In addition, hydrogen bonds also seem to contribute to the compaction of the NAC region. The expansion of the C-terminal region is due to intraregional electrostatic repulsion and increased chain stiffness from several prolines. Overall, our study demonstrates the effectiveness of combining smFRET experiments with CG-MD simulations to investigate the key interactions in highly dynamic IDPs at the amino acid level.

Comparative Performance of Computer Simulation Models of Intrinsically Disordered Proteins at Different Levels of Coarse-Graining

Coarse-graining is commonly used to decrease the computational cost of simulations. However, coarse-grained models are also considered to have lower transferability, with lower accuracy for systems outside the original scope of parametrization. Here, we benchmark a bead-necklace model and a modified Martini 2 model, both coarse-grained models, for a set of intrinsically disordered proteins, with the different models having different degrees of coarse-graining. The SOP-IDP model has earlier been used for this set of proteins; thus, those results are included in this study to compare how models with different levels of coarse-graining compare. The sometimes naive expectation of the least coarse-grained model performing best does not hold true for the experimental pool of proteins used here. Instead, it showed the least good agreement, indicating that one should not necessarily trust the otherwise intuitive notion of a more advanced model inherently being better in model choice.

Molecular basis of C9orf72 poly-PR interference with the β-karyopherin family of nuclear transport receptors

Nucleocytoplasmic transport (NCT) is affected in several neurodegenerative diseases including C9orf72-ALS. It has recently been found that arginine-containing dipeptide repeat proteins (R-DPRs), translated from C9orf72 repeat expansions, directly bind to several importins. To gain insight into how this can affect nucleocytoplasmic transport, we use coarse-grained molecular dynamics simulations to study the molecular interaction of poly-PR, the most toxic DPR, with several Kapβs (importins and exportins). We show that poly-PR-Kapβ binding depends on the net charge per residue (NCPR) of the Kapβ, salt concentration of the solvent, and poly-PR length. Poly-PR makes contact with the inner surface of most importins, which strongly interferes with Kapβ binding to cargo-NLS, IBB, and RanGTP in a poly-PR length-dependent manner. Longer poly-PRs at higher concentrations are also able to make contact with the outer surface of importins that contain several binding sites to FG-Nups. We also show that poly-PR binds to exportins, especially at lower salt concentrations, interacting with several RanGTP and FG-Nup binding sites. Overall, our results suggest that poly-PR might cause length-dependent defects in cargo loading, cargo release, Kapβ transport and Ran gradient across the nuclear envelope.

Percolation transition prescribes protein size-specific barrier to passive transport through the nuclear pore complex

Nuclear pore complexes (NPCs) control biomolecular transport in and out of the nucleus. Disordered nucleoporins in the complex's pore form a permeation barrier, preventing unassisted transport of large biomolecules. Here, we combine coarse-grained simulations of experimentally derived NPC structures with a theoretical model to determine the microscopic mechanism of passive transport. Brute-force simulations of protein transport reveal telegraph-like behavior, where prolonged diffusion on one side of the NPC is interrupted by rapid crossings to the other. We rationalize this behavior using a theoretical model that reproduces the energetics and kinetics of permeation solely from statistics of transient voids within the disordered mesh. As the protein size increases, the mesh transforms from a soft to a hard barrier, enabling orders-of-magnitude reduction in permeation rate for proteins beyond the percolation size threshold. Our model enables exploration of alternative NPC architectures and sets the stage for uncovering molecular mechanisms of facilitated nuclear transport.

Crowding-induced phase separation of nuclear transport receptors in FG nucleoporin assemblies

The rapid (< 1 ms) transport of biological material to and from the cell nucleus is regulated by the nuclear pore complex (NPC). At the core of the NPC is a permeability barrier consisting of intrinsically disordered Phe-Gly (FG) nucleoporins (FG Nups). Various types of nuclear transport receptors (NTRs) facilitate transport by partitioning in the FG Nup assembly, overcoming the barrier by their affinity to the FG Nups, and comprise a significant fraction of proteins in the NPC barrier. In previous work Zahn et al. (2016), we revealed a universal physical behaviour in the experimentally observed binding of two well-characterized NTRs, NTF2 and the larger Importin-β, to different planar assemblies of FG Nups, with the binding behaviour defined by negative cooperativity. This was further validated by a minimal physical model that treated the FG Nups as flexible homopolymers and the NTRs as uniformly cohesive spheres. Here, we build upon our original study by first parametrizing our model to experimental data, and next predicting the effects of crowding by different types of NTRs. We show how varying the amounts of one type of NTR modulates how the other NTR penetrates the FG Nup assembly. Notably, at similar and physiologically relevant NTR concentrations, our model predicts demixed phases of NTF2 and Imp-β within the FG Nup assembly. The functional implication of NTR phase separation is that NPCs may sustain separate transport pathways that are determined by inter-NTR competition.

Current methods for studying intracellular liquid-liquid phase separation

Liquid-liquid phase separation (LLPS) is a ubiquitous process that drives the formation of membrane-less intracellular compartments. This compartmentalization contains vastly different protein/RNA/macromolecule concentrations compared to the surrounding cytosol despite the absence of a lipid boundary. Because of this, LLPS is important for many cellular signaling processes and may play a role in their dysregulation. This chapter highlights recent advances in the understanding of intracellular phase transitions along with current methods used to identify LLPS in vitro and model LLPS in situ.

Nucleoporins' exclusive amino acid sequence features regulate their transient interaction with and selectivity of cargo complexes in the nuclear pore

Nucleocytoplasmic traffic of nucleic acids and proteins across the nuclear envelop via the nuclear pore complexes (NPCs) is vital for eukaryotic cells. NPCs screen transported macromolecules based on their morphology and surface chemistry. This selective nature of the NPC-mediated traffic is essential for regulating the fundamental functions of the nucleus, such as gene regulation, protein synthesis, and mechanotransduction. Despite the fundamental role of the NPC in cell and nuclear biology, the detailed mechanisms underlying how the NPC works have remained largely unknown. The critical components of NPCs enabling their selective barrier function are the natively unfolded phenylalanine- and glycine-rich proteins called “FG-nucleoporins” (FG Nups). These intrinsically disordered proteins are tethered to the inner wall of the NPC, and together form a highly dynamic polymeric meshwork whose physicochemical conformation has been the subject of intense debate. We observed that specific sequence features (called largest positive like-charge regions, or lpLCRs), characterized by extended subsequences that only possess positively charged amino acids, significantly affect the conformation of FG Nups inside the NPC. Here we investigate how the presence of lpLCRs affects the interactions between FG Nups and their interactions with the cargo complex. We combine coarse-grained molecular dynamics simulations with time-resolved force distribution analysis to disordered proteins to explore the behavior of the system. Our results suggest that the number of charged residues in the lpLCR domain directly governs the average distance between Phe residues and the intensity of interaction between them. As a result, the number of charged residues within lpLCR determines the balance between the hydrophobic interaction and the electrostatic repulsion and governs how dense and disordered the hydrophobic network formed by FG Nups is. Moreover, changing the number of charged residues in an lpLCR domain can interfere with ultrafast and transient interactions between FG Nups and the cargo complex.

Characterizing Binding Interactions That Are Essential for Selective Transport through the Nuclear Pore Complex

Specific macromolecules are rapidly transported across the nuclear envelope via the nuclear pore complex (NPC). The selective transport process is facilitated when nuclear transport receptors (NTRs) weakly and transiently bind to intrinsically disordered constituents of the NPC, FG Nups. These two types of proteins help maintain the selective NPC barrier. To interrogate their binding interactions in vitro, we deployed an NPC barrier mimic. We created the stationary phase by covalently attaching fragments of a yeast FG Nup called Nsp1 to glass coverslips. We used a tunable mobile phase containing NTR, nuclear transport factor 2 (NTF2). In the stationary phase, three main factors affected binding: the number of FG repeats, the charge of fragments, and the fragment density. We also identified three main factors affecting binding in the mobile phase: the avidity of the NTF2 variant for Nsp1, the presence of nonspecific proteins, and the presence of additional NTRs. We used both experimentally determined binding parameters and molecular dynamics simulations of Nsp1FG fragments to create an agent-based model. The results suggest that NTF2 binding is negatively cooperative and dependent on the density of Nsp1FG molecules. Our results demonstrate the strengths of combining experimental and physical modeling approaches to study NPC-mediated transport.

Coarse-grained simulations of phase separation driven by DNA and its sensor protein cGAS

The enzyme cGAS functions as a sensor that recognizes the cytosolic DNA from foreign pathogen. The activation of the protein triggers the transcription of inflammatory genes, leading into the establishment of an antipathogen state. An interesting new discovery is that the detection of DNA by cGAS induced the formation of liquid-like droplets. However how cells regulate the formation of these droplets is still not fully understood. In order to unravel the molecular mechanism beneath the DNA-mediated phase separation of cGAS, we developed a polymer-based coarse-grained model which takes into accounts the basic structural organization in DNA and cGAS, as well as the binding properties between these biomolecules. This model was further integrated into a hybrid simulation algorithm. With this computational method, a multi-step kinetic process of aggregation between cGAS and DNA was observed. Moreover, we systematically tested the model under different concentrations and binding parameters. Our simulation results show that phase separation requires both cGAS dimerization and protein-DNA interactions, whereas polymers can be kinetically trapped in small aggregates under strong binding affinities. Additionally, we demonstrated that supramolecular assembly can be facilitated by increasing the number of functional modules in protein or DNA polymers, suggesting that multivalency and intrinsic disordered regions play positive roles in regulating phase separation. This is consistent to previous experimental evidences. Taken together, this is, to the best of our knowledge, the first computational model to study condensation of cGAS-DNA complexes. While the method can reach the timescale beyond the capability of atomic-level MD simulations, it still includes information about spatial arrangement of functional modules in biopolymers that is missing in the mean-field theory. Our work thereby adds a useful dimension to a suite of existing experimental and computational techniques to study the dynamics of phase separation in biological systems.

Physics of the Nuclear Pore Complex: Theory, Modeling and Experiment

The hallmark of eukaryotic cells is the nucleus that contains the genome, enclosed by a physical barrier known as the nuclear envelope (NE). On the one hand, this compartmentalization endows the eukaryotic cells with high regulatory complexity and flexibility. On the other hand, it poses a tremendous logistic and energetic problem of transporting millions of molecules per second across the nuclear envelope, to facilitate their biological function in all compartments of the cell. Therefore, eukaryotes have evolved a molecular "nanomachine" known as the Nuclear Pore Complex (NPC). Embedded in the nuclear envelope, NPCs control and regulate all the bi-directional transport between the cell nucleus and the cytoplasm. NPCs combine high molecular specificity of transport with high throughput and speed, and are highly robust with respect to molecular noise and structural perturbations. Remarkably, the functional mechanisms of NPC transport are highly conserved among eukaryotes, from yeast to humans, despite significant differences in the molecular components among various species. The NPC is the largest macromolecular complex in the cell. Yet, despite its significant complexity, it has become clear that its principles of operation can be largely understood based on fundamental physical concepts, as have emerged from a combination of experimental methods of molecular cell biology, biophysics, nanoscience and theoretical and computational modeling. Indeed, many aspects of NPC function can be recapitulated in artificial mimics with a drastically reduced complexity compared to biological pores. We review the current physical understanding of the NPC architecture and function, with the focus on the critical analysis of experimental studies in cells and artificial NPC mimics through the lens of theoretical and computational models. We also discuss the connections between the emerging concepts of NPC operation and other areas of biophysics and bionanotechnology.

A designer FG-Nup that reconstitutes the selective transport barrier of the nuclear pore complex

Nuclear Pore Complexes (NPCs) regulate bidirectional transport between the nucleus and the cytoplasm. Intrinsically disordered FG-Nups line the NPC lumen and form a selective barrier, where transport of most proteins is inhibited whereas specific transporter proteins freely pass. The mechanism underlying selective transport through the NPC is still debated. Here, we reconstitute the selective behaviour of the NPC bottom-up by introducing a rationally designed artificial FG-Nup that mimics natural Nups. Using QCM-D, we measure selective binding of the artificial FG-Nup brushes to the transport receptor Kap95 over cytosolic proteins such as BSA. Solid-state nanopores with the artificial FG-Nups lining their inner walls support fast translocation of Kap95 while blocking BSA, thus demonstrating selectivity. Coarse-grained molecular dynamics simulations highlight the formation of a selective meshwork with densities comparable to native NPCs. Our findings show that simple design rules can recapitulate the selective behaviour of native FG-Nups and demonstrate that no specific spacer sequence nor a spatial segregation of different FG-motif types are needed to create selective NPCs.

Viscoelastic properties of wheat gluten in a molecular dynamics study

Wheat (Triticum spp.) gluten consists mainly of intrinsincally disordered storage proteins (glutenins and gliadins) that can form megadalton-sized networks. These networks are responsible for the unique viscoelastic properties of wheat dough and affect the quality of bread. These properties have not yet been studied by molecular level simulations. Here, we use a newly developed α-C-based coarse-grained model to study ∼ 4000-residue systems. The corresponding time-dependent properties are studied through shear and axial deformations. We measure the response force to the deformation, the number of entanglements and cavities, the mobility of residues, the number of the inter-chain bonds, etc. Glutenins are shown to influence the mechanics of gluten much more than gliadins. Our simulations are consistent with the existing ideas about gluten elasticity and emphasize the role of entanglements and hydrogen bonding. We also demonstrate that the storage proteins in maize and rice lead to weaker elasticity which points to the unique properties of wheat gluten.

During the breadmaking process, expanding gas bubbles cause the dough to increase volume. Gluten proteins act as an elastic scaffold in that process, allowing the wheat dough to grow more than other kinds of dough. Thus, explaining the unique viscoelastic properties of gluten at the molecular level may be of great interest to the baking industry. Assessing the structural properties of gluten is difficult because its proteins are disordered. We provide the first molecular dynamics model of gluten elasticity, that is able to distinguish gluten and proteins from different plants, like maize and rice. Our model shows the structural changes the gluten proteins undergo during their deformation, which mimics the mixing of dough during kneading. It also allows for a determination of the force required to extend gluten proteins, as during baking. The data confirms existing theories about gluten, but it also provides molecular-level information about the extraordinary elasticity of gluten.

Coarse-grained simulation of the translational and rotational diffusion of globular proteins by dissipative particle dynamics

With simplified interactions and degrees of freedom, coarse-grained (CG) simulations have been successfully applied to study the translational and rotational diffusion of proteins in solution. However, in order to reach larger lengths and longer timescales, many CG simulations employ an oversimplified model for proteins or an implicit-solvent model in which the hydrodynamic interactions are ignored, and thus, the real kinetics are more or less unfaithful. In this work, we develop a CG model based on the dissipative particle dynamics (DPD) that can be universally applied to different types of proteins. The proteins are modeled as a group of rigid DPD beads without conformational changes. The fluids (including solvent and ions) are also modeled as DPD beads. The electrostatic interactions between charged species are explicitly considered by including charge distributions on DPD particles. Moreover, a surface friction between the protein and fluid beads is applied to control the slip boundary condition. With this model, we investigate the self-diffusion of a single globular protein in bulk solution. The translational and rotational diffusion coefficients of the protein can be tuned by the surface frictional constant to fit the predictions of the Stokes-Einstein (SE) relation. We find that both translational and rotational diffusion coefficients that meet with the prediction of the SE relation based on experimental results of the hydrodynamic radius are reached at almost the same frictional constant for different types of proteins. Such scaling behavior indicates that the model can be applied to simulate the translational and rotational diffusion together for various types of proteins.

Phase Separation of Toxic Dipeptide Repeat Proteins Related to C9orf72 ALS/FTD

The expansion mutation in the C9orf72 gene is the most common known genetic cause for amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD). This mutation can produce five dipeptide repeat proteins (DPRs), of which three are known to be toxic: poly-PR, poly-GR, and poly-GA. The toxicity of poly-GA is attributed to its aggregation in the cytoplasm, whereas for poly-PR and poly-GR, several toxicity pathways have been proposed. The toxicity of the DPRs has been shown to depend on their length, but the underlying molecular mechanism of this length dependence is not well understood. To address the possible role of phase separation in DPR toxicity, a one-bead-per-amino-acid (1BPA) coarse-grained molecular dynamics model is used to study the single-molecule and phase-separation properties of the DPRs. We find a strong dependence of the phase-separation behavior on both DPR length and concentration, with longer DPRs having a higher propensity to phase separate and form condensed phases with higher concentrations. The critical lengths required for phase separation (25 for poly-PR and 50 for poly-GA) are comparable to the toxicity threshold limit of 30 repeats found for the expansion mutation in patient cells, suggesting that phase separation could play an important role in DPR toxicity.

Pseudo-Improper-Dihedral Model for Intrinsically Disordered Proteins

We present a new coarse-grained C_α-based protein model with a nonradial multibody pseudo-improper-dihedral potential that is transferable, time-independent, and suitable for molecular dynamics. It captures the nature of backbone and side-chain interactions between amino acid residues by adapting a simple improper dihedral term for a one-bead-per-residue model. It is parameterized for intrinsically disordered proteins and applicable to simulations of such proteins and their assemblies on millisecond time scales.

Transient knots in intrinsically disordered proteins and neurodegeneration

We provide a brief overview of the topological features found in structured proteins and of the dynamical processes that involve knots. We then discuss the knotted states that arise in the intrinsically disordered polyglutamine and α-synuclein. We argue that the existence of the knotted conformations stalls degradation by proteases and thus enhances aggregation. This mechanism works if the length of a peptide chain exceeds a threshold, as in the Huntington disease. We also study the cavities that form within the conformations of the disordered proteins. The volume of the cavities varies in time in a way that is different than that of the radius of gyration or the end-to-end distance. In addition, we study the traffic between the conformational basins and identify patterns associated with the deep and shallow knots. The results are obtained by molecular dynamics simulations that use coarse-grained and all-atom models (with and without the explicit solvent).

Flexible and Extended Linker Domains Support Efficient Targeting of Heh2 to the Inner Nuclear Membrane

The nuclear pore complex (NPC) is embedded in the nuclear envelope and forms the main gateway to the nuclear interior including the inner nuclear membrane (INM). Two INM proteins in yeast are selectively imported. Their sorting signals consist of a nuclear localization signal, separated from the transmembrane domain by a long intrinsically disordered (ID) linker. We used computational models to predict the dynamic conformations of ID linkers and analyzed the INM targeting efficiency of proteins with linker regions with altered Stokes radii and decreased flexibilities. We find that flexibility, Stokes radius, and the frequency at which the linkers are at an extended end-to-end distance larger than 25 nm are good predictors for the targeting of the proteins. The data are consistent with a transport mechanism in which INM targeting of Heh2 is dependent on an ID linker that facilitates the crossing of the approximately 25-nm thick NPC scaffold.

Intrinsically disordered nuclear pore proteins show ideal-polymer morphologies and dynamics

In the nuclear pore complex, intrinsically disordered nuclear pore proteins (FG Nups) form a selective barrier for transport into and out of the cell nucleus, in a way that remains poorly understood. The collective FG Nup behavior has long been conceptualized either as a polymer brush, dominated by entropic and excluded-volume (repulsive) interactions, or as a hydrogel, dominated by cohesive (attractive) interactions between FG Nups. Here we compare mesoscale computational simulations with a wide range of experimental data to demonstrate that FG Nups are at the crossover point between these two regimes. Specifically, we find that repulsive and attractive interactions are balanced, resulting in morphologies and dynamics that are close to those of ideal polymer chains. We demonstrate that this property of FG Nups yields sufficient cohesion to seal the transport barrier, and yet maintains fast dynamics at the molecular scale, permitting the rapid polymer rearrangements needed for transport events.

Protein droplets in systems of disordered homopeptides and the amyloid glass phase

We study phase diagrams and liquid droplet formation for systems of polyglutamine and polyalanine chains in a coarse-grained model.

Loop formation and translational diffusion of intrinsically disordered proteins

The conformational flexibility and dynamics of unfolded peptide chains is of major interest in the context of protein folding and protein functioning. The rate with which amino acids at different positions along the peptide chain meet sets an upper speed limit for protein folding. By using single-molecule photo-induced energy transfer spectroscopy, we have systematically measured end-to-end and end-to-internal site contact formation rates for several intrinsically disordered protein fragments (IDPs) (11 to 41 amino acids) and have also determined their hydrodynamic radius using dual-focus fluorescence correlation spectroscopy. For interpreting the measured values, we have developed a Brownian dynamics model (based on bead-rod chain dynamics in a thermal bath including hydrodynamic interactions) which quantitatively reproduces all measured data surprisingly well while requiring only two fit parameters. The model provides a complete picture of the peptides' dynamics and allows us to translate the experimental rates and radii into molecular properties of the peptides: We find a persistence length of l_{P}=5.2±1.9Å, a hydrodynamic radius of a=3.5±0.7Å per amino acid, and that excluded volume effects play an important role in the dynamics of IDPs.

Age-dependent deterioration of nuclear pore assembly in mitotic cells decreases transport dynamics

Nuclear transport is facilitated by the Nuclear Pore Complex (NPC) and is essential for life in eukaryotes. The NPC is a long-lived and exceptionally large structure. We asked whether NPC quality control is compromised in aging mitotic cells. Our images of single yeast cells during aging, show that the abundance of several NPC components and NPC assembly factors decreases. Additionally, the single-cell life histories reveal that cells that better maintain those components are longer lived. The presence of herniations at the nuclear envelope of aged cells suggests that misassembled NPCs are accumulated in aged cells. Aged cells show decreased dynamics of transcription factor shuttling and increased nuclear compartmentalization. These functional changes are likely caused by the presence of misassembled NPCs, as we find that two NPC assembly mutants show similar transport phenotypes as aged cells. We conclude that NPC interphase assembly is a major challenge for aging mitotic cells.

Simulation methods for liquid-liquid phase separation of disordered proteins

Liquid-liquid phase separation of intrinsically disordered proteins (IDPs) and other biomolecules is a highly complex but robust process used by living systems. Drawing inspiration from biology, phase separating proteins have been successfully utilized for promising applications in fields of materials design and drug delivery. These protein-based materials are advantageous due to the ability to finely tune their stimulus-responsive phase behavior and material properties, and the ability to encode biologically active motifs directly into the sequence. The number of possible protein sequences is virtually endless, which makes sequence-based design a rather daunting task, but also attractive due to the amount of control coming from exploration of this variable space. The use of computational methods in this field of research have come to the aid in several aspects, including interpreting experimental results, identifying important structural features and molecular mechanisms capable of explaining the phase behavior, and ultimately providing predictive frameworks for rational design of protein sequences. Here we provide an overview of computational studies focused on phase separating biomolecules and the tools that are available to researchers interested in this topic.

Thermodynamically driven assemblies and liquid-liquid phase separations in biology

The sustenance of life depends on the high degree of organization that prevails through different levels of living organisms, from subcellular structures such as biomolecular complexes and organelles to tissues and organs. The physical origin of such organization is not fully understood, and even though it is clear that cells and organisms cannot maintain their integrity without consuming energy, there is growing evidence that individual assembly processes can be thermodynamically driven and occur spontaneously due to changes in thermodynamic variables such as intermolecular interactions and concentration. Understanding the phase separation in vivo requires a multidisciplinary approach, integrating the theory and physics of phase separation with experimental and computational techniques. This paper aims at providing a brief overview of the physics of phase separation and its biological implications, with a particular focus on the assembly of membraneless organelles. We discuss the underlying physical principles of phase separation from its thermodynamics to its kinetics. We also overview the wide range of methods utilized for experimental verification and characterization of phase separation of membraneless organelles, as well as the utility of molecular simulations rooted in thermodynamics and statistical physics in understanding the governing principles of thermodynamically driven biological self-assembly processes.

The Effect of FG-Nup Phosphorylation on NPC Selectivity: A One-Bead-Per-Amino-Acid Molecular Dynamics Study

Nuclear pore complexes (NPCs) are large protein complexes embedded in the nuclear envelope separating the cytoplasm from the nucleoplasm in eukaryotic cells. They function as selective gates for the transport of molecules in and out of the nucleus. The inner wall of the NPC is coated with intrinsically disordered proteins rich in phenylalanine-glycine repeats (FG-repeats), which are responsible for the intriguing selectivity of NPCs. The phosphorylation state of the FG-Nups is controlled by kinases and phosphatases. In the current study, we extended our one-bead-per-amino-acid (1BPA) model for intrinsically disordered proteins to account for phosphorylation. With this, we performed molecular dynamics simulations to probe the effect of phosphorylation on the Stokes radius of isolated FG-Nups, and on the structure and transport properties of the NPC. Our results indicate that phosphorylation causes a reduced attraction between the residues, leading to an extension of the FG-Nups and the formation of a significantly less dense FG-network inside the NPC. Furthermore, our simulations show that upon phosphorylation, the transport rate of inert molecules increases, while that of nuclear transport receptors decreases, which can be rationalized in terms of modified hydrophobic, electrostatic, and steric interactions. Altogether, our models provide a molecular framework to explain how extensive phosphorylation of FG-Nups decreases the selectivity of the NPC.

A Metastable Contact and Structural Disorder in the Estrogen Receptor Transactivation Domain

The N-terminal transactivation domain (NTD) of estrogen receptor alpha, a well-known member of the family of intrinsically disordered proteins, mediates the receptor's transactivation function. However, an accurate molecular dissection of NTD's structure-function relationships remains elusive. Here, we show that the NTD adopts a mostly disordered, unexpectedly compact conformation that undergoes structural expansion on chemical denaturation. By combining small-angle X-ray scattering, hydroxyl radical protein footprinting, and computational modeling, we derive the ensemble-structures of the NTD and determine its ensemble-contact map revealing metastable long-range contacts, e.g., between residues I33 and S118. We show that mutation at S118, a known phosphorylation site, promotes conformational changes and increases coactivator binding. We further demonstrate via fluorine-19 (¹⁹F) nuclear magnetic resonance that mutations near I33 alter ¹⁹F chemical shifts at S118, confirming the proposed I33-S118 contact in the ensemble of structural disorder. These findings extend our understanding of how specific contact metastability mediates critical functions of disordered proteins.

Disordered peptide chains in an α-C-based coarse-grained model

We construct a one-bead-per-residue coarse-grained dynamical model to describe intrinsically disordered proteins at significantly longer timescales than in the all-atom models. In this model, inter-residue contacts form and disappear during the course of the time evolution. The contacts may arise between the sidechains, the backbones or the sidechains and backbones of the interacting residues. The model yields results that are consistent with many all-atom and experimental data on these systems. We demonstrate that the geometrical properties of various homopeptides differ substantially in this model. In particular, the average radius of gyration scales with the sequence length in a residue-dependent manner.

DNA origami scaffold for studying intrinsically disordered proteins of the nuclear pore complex

The nuclear pore complex (NPC) is the gatekeeper for nuclear transport in eukaryotic cells. A key component of the NPC is the central shaft lined with intrinsically disordered proteins (IDPs) known as FG-Nups, which control the selective molecular traffic. Here, we present an approach to realize artificial NPC mimics that allows controlling the type and copy number of FG-Nups. We constructed 34 nm-wide 3D DNA origami rings and attached different numbers of NSP1, a model yeast FG-Nup, or NSP1-S, a hydrophilic mutant. Using (cryo) electron microscopy, we find that NSP1 forms denser cohesive networks inside the ring compared to NSP1-S. Consistent with this, the measured ionic conductance is lower for NSP1 than for NSP1-S. Molecular dynamics simulations reveal spatially varying protein densities and conductances in good agreement with the experiments. Our technique provides an experimental platform for deciphering the collective behavior of IDPs with full control of their type and position.

Spatial structure of disordered proteins dictates conductance and selectivity in nuclear pore complex mimics

Nuclear pore complexes (NPCs) lined with intrinsically disordered FG-domains act as selective gatekeepers for molecular transport between the nucleus and the cytoplasm in eukaryotic cells. The underlying physical mechanism of the intriguing selectivity is still under debate. Here, we probe the transport of ions and transport receptors through biomimetic NPCs consisting of Nsp1 domains attached to the inner surface of solid-state nanopores. We examine both wildtype FG-domains and hydrophilic SG-mutants. FG-nanopores showed a clear selectivity as transport receptors can translocate across the pore whereas other proteins cannot. SG mutant pores lack such selectivity. To unravel this striking difference, we present coarse-grained molecular dynamics simulations that reveal that FG-pores exhibit a high-density, nonuniform protein distribution, in contrast to a uniform and significantly less-dense protein distribution in the SG-mutant. We conclude that the sequence-dependent density distribution of disordered proteins inside the NPC plays a key role for its conductivity and selective permeability.

Looking "Under the Hood" of Cellular Mechanotransduction with Computational Tools: A Systems Biomechanics Approach across Multiple Scales

Signal modulation has been developed in living cells throughout evolution to promote utilizing the same machinery for multiple cellular functions. Chemical and mechanical modules of signal transmission and transduction are interconnected and necessary for organ development and growth. However, due to the high complexity of the intercommunication of physical intracellular connections with biochemical pathways, there are many missing details in our overall understanding of mechanotransduction processes, i.e., the process by which mechanical signals are converted to biochemical cascades. Cell-matrix adhesions are mechanically coupled to the nucleus through the cytoskeleton. This modulated and tightly integrated network mediates the transmission of mechanochemical signals from the extracellular matrix to the nucleus. Various experimental and computational techniques have been utilized to understand the basic mechanisms of mechanotransduction, yet many aspects have remained elusive. Recently, in silico experiments have made important contributions to the field of mechanobiology. Herein, computational modeling efforts devoted to understanding integrin-mediated mechanotransduction pathways are reviewed, and an outlook is presented for future directions toward using suitable computational approaches and developing novel techniques for addressing important questions in the field of mechanotransduction.

Energetics of Transport through the Nuclear Pore Complex

Molecular transport across the nuclear envelope in eukaryotic cells is solely controlled by the nuclear pore complex (NPC). The NPC provides two types of nucleocytoplasmic transport: passive diffusion of small molecules and active chaperon-mediated translocation of large molecules. It has been shown that the interaction between intrinsically disordered proteins that line the central channel of the NPC and the transporting cargoes is the determining factor, but the exact mechanism of transport is yet unknown. Here, we use coarse-grained molecular dynamics simulations to quantify the energy barrier that has to be overcome for molecules to pass through the NPC. We focus on two aspects of transport. First, the passive transport of model cargo molecules with different sizes is studied and the size selectivity feature of the NPC is investigated. Our results show that the transport probability of cargoes is significantly reduced when they are larger than ∼5 nm in diameter. Secondly, we show that incorporating hydrophobic binding spots on the surface of the cargo effectively decreases the energy barrier of the pore. Finally, a simple transport model is proposed which characterizes the energy barrier of the NPC as a function of diameter and hydrophobicity of the transporting particles.

Nucleoporin's Like Charge Regions Are Major Regulators of FG Coverage and Dynamics Inside the Nuclear Pore Complex

Nucleocytoplasmic transport has been the subject of a large body of research in the past few decades. Recently, the focus of investigations in this field has shifted from studies of the overall function of the nuclear pore complex (NPC) to the examination of the role of different domains of phenylalanine-glycine nucleoporin (FG Nup) sequences on the NPC function. In our recent bioinformatics study, we showed that FG Nups have some evolutionarily conserved sequence-based features that might govern their physical behavior inside the NPC. We proposed the ‘like charge regions’ (LCRs), sequences of charged residues with only one type of charge, as one of the features that play a significant role in the formation of FG network inside the central channel. In this study, we further explore the role of LCRs in the distribution of FG Nups, using a recently developed coarse-grained molecular dynamics model. Our results demonstrate how LCRs affect the formation of two transport pathways. While some FG Nups locate their FG network at the center of the NPC forming a homogeneous meshwork of FG repeats, other FG Nups cover the space adjacent to the NPC wall. LCRs in the former group, i.e. FG Nups that form an FG domain at the center, tend to regulate the size of the highly dense, doughnut-shaped FG meshwork and leave a small low FG density area at the center of the pore for passive diffusion. On the other hand, LCRs in the latter group of FG Nups enable them to maximize their interactions and cover a larger space inside the NPC to increase its capability to transport numerous cargos at the same time. Finally, a new viewpoint is proposed that reconciles different models for the nuclear pore selective barrier function.

Quantifying the role of chaperones in protein translocation by computational modeling

The molecular chaperone Hsp70 plays a central role in the import of cytoplasmic proteins into organelles, driving their translocation by binding them from the organellar interior. Starting from the experimentally-determined structure of the E. coli Hsp70, we computed, by means of molecular simulations, the effective free-energy profile for substrate translocation upon chaperone binding. We then used the resulting free energy to quantitatively characterize the kinetics of the import process, whose comparison with unassisted translocation highlights the essential role played by Hsp70 in importing cytoplasmic proteins.

Probing the disordered domain of the nuclear pore complex through coarse-grained molecular dynamics simulations

The distribution of disordered proteins (FG-nups) that line the transport channel of the nuclear pore complex (NPC) is investigated by means of coarse-grained molecular dynamics simulations. A one-bead-per-amino-acid model is presented that accounts for the hydrophobic/hydrophilic and electrostatic interactions between different amino acids, polarity of the solvent, and screening of free ions. The results indicate that the interaction of the FG-nups forms a high-density, doughnut-like distribution inside the NPC, which is rich in FG-repeats. We show that the obtained distribution is encoded in the amino-acid sequence of the FG-nups and is driven by both electrostatic and hydrophobic interactions. To explore the relation between structure and function, we have systematically removed different combinations of FG-nups from the pore to simulate inviable and viable NPCs that were previously studied experimentally. The obtained density distributions show that the maximum density of the FG-nups inside the pore does not exceed 185 mg/mL in the inviable NPCs, whereas for the wild-type and viable NPCs, this value increases to 300 mg/mL. Interestingly, this maximum density is not correlated to the total mass of the FG-nups, but depends sensitively on the specific combination of essential Nups located in the central plane of the NPC.

Recent advances in transferable coarse-grained modeling of proteins

Computer simulations are indispensable tools for studying the structure and dynamics of biological macromolecules. Biochemical processes occur on different scales of length and time. Atomistic simulations cannot cover the relevant spatiotemporal scales at which the cellular processes occur. To address this challenge, coarse-grained (CG) modeling of the biological systems is employed. Over the last few years, many CG models for proteins continue to be developed. However, many of them are not transferable with respect to different systems and different environments. In this review, we discuss those CG protein models that are transferable and that retain chemical specificity. We restrict ourselves to CG models of soluble proteins only. We also briefly review recent progress made in the multiscale hybrid all-atom/CG simulations of proteins.

PRIMO: A Transferable Coarse-grained Force Field for Proteins

We describe here the PRIMO (PRotein Intermediate Model) force field, a physics-based fully transferable additive coarse-grained potential energy function that is compatible with an all-atom force field for multi-scale simulations. The energy function consists of standard molecular dynamics energy terms plus a hydrogen-bonding potential term and is mainly parameterized based on the CHARMM22/CMAP force field in a bottom-up fashion. The solvent is treated implicitly via the generalized Born model. The bonded interactions are either harmonic or distance-based spline interpolated potentials. These potentials are defined on the basis of all-atom molecular dynamics (MD) simulations of dipeptides with the CHARMM22/CMAP force field. The non-bonded parameters are tuned by matching conformational free energies of diverse set of conformations with that of CHARMM all-atom results. PRIMO is designed to provide a correct description of conformational distribution of the backbone (ϕ/ψ) and side chains (χ1) for all amino acids with a CMAP correction term. The CMAP potential in PRIMO is optimized based on the new CHARMM C36 CMAP. The resulting optimized force field has been applied in MD simulations of several proteins of 36-155 amino acids and shown that the root-mean-squared-deviation of the average structure from the corresponding crystallographic structure varies between 1.80 and 4.03 Å. PRIMO is shown to fold several small peptides to their native-like structures from extended conformations. These results suggest the applicability of the PRIMO force field in the study of protein structures in aqueous solution, structure predictions as well as ab initio folding of small peptides.