Orientational Pathways during Protein Translocation through Polymer-Modified Nanopores.

Protein translocation through nanopores holds significant promise for applications in biotechnology, biomolecular analysis, and medicine. However, the interpretation of signals generated by the translocation of the protein remains challenging. In this way, it is crucial to gain a comprehensive understanding on how macromolecules translocate through a nanopore and to identify what are the critical parameters that govern the process. In this study, we investigate the interplay between protein charge regulation, orientation, and nanopore surface modifications using a theoretical framework that allows us to explicitly take into account the acid-base reactions of the titrable amino acids in the proteins and in the polyelectrolytes grafted to the nanopore surface. Our goal is to thoroughly characterize the translocation process of different proteins (GFP, ß-lactoglobulin, lysozyme, and RNase) through nanopores modified with weak polyacids. Our calculations show that the charge regulation mechanism exerts a profound effect on the translocation process. The pH-dependent interactions between proteins and charged polymers within the nanopore lead to diverse free energy landscapes with barriers, wells, and flat regions dictating translocation efficiency. Comparison of different proteins allows us to identify the significance of protein isoelectric point, size, and morphology in the translocation behavior. Taking advantage of these insights, we propose pH-responsive nanopores that can load proteins at one pH and release them at another, offering opportunities for controlled protein delivery, separation, and sensing applications.

Local Volume Concentration, Packing Domains and Scaling Properties of Chromatin.

We propose the Self Returning Excluded Volume (SR-EV) model for the structure of chromatin based on stochastic rules and physical interactions that can capture the observed behavior across imaging and sequencing based measures of chromatin organization. From nucleosome to chromosome scales, the model captures the overall chromatin organization as a corrugated system, with dense and dilute regions alternating in a manner that resembles the mixing of two disordered bi-continuous phases. This particular organizational topology is a consequence of the multiplicity of interactions and processes ocurring in the nuclei, and mimicked by the proposed return rules. Single configuration properties and ensemble averages show a robust agreement between theoretical and experimental results including chromatin volume concentration, contact probability, packing domain identification and size characterization, and packing scaling behavior. Model and experimental results suggest that there is an inherent chromatin organization regardless of the cell character and resistent to external forcings such as Rad21 degradation.

Local Volume Concentration, Packing Domains and Scaling Properties of Chromatin.

We propose the Self Returning Excluded Volume (SR-EV) model for the structure of chromatin based on stochastic rules and physical interactions that is able to capture the observed behavior across imaging and sequencing based measures of chromatin organization. The SR-EV model takes the return rules of the Self Returning Random Walk, incorporates excluded volume interactions, chain connectivity and expands the length scales range from 10 nm to over 1 micron. The model is computationally fast and we created thousands of configurations that we grouped in twelve different ensembles according to the two main parameters of the model. The analysis of the configurations was done in a way completely analogous to the experimental treatments used to determine chromatin volume concentration, contact probability, packing domain identification and size characterization, and packing scaling behavior. We find a robust agreement between the theoretical and experimental results. The overall organization of the model chromatin is corrugated, with dense packing domains alternating with a very dilute regions in a manner that resembles the mixing of two disordered bi-continuous phases. The return rules combined with excluded volume interactions lead to the formation of packing domains. We observed a transition from a short scale regime to a long scale regime occurring at genomic separations of ~ 4 × 104 base pairs or ~ 100 nm in distance. The contact probability reflects this transition with a change in the scaling exponent from larger than -1 to approximately -1. The analysis of the pair correlation function reveals that chromatin organizes following a power law scaling with exponent D∈{2,3} in the transition region between the short and long distance regimes.

Chromatin as self-returning walks: From population to single cell and back.

With a growing understanding of the chromatin structure, many efforts remain focused on bridging the gap between what is suggested by population-averaged data and what is visualized for single cells. A popular approach to traversing these scales is to fit a polymer model to Hi-C contact data. However, Hi-C is an average of millions to billions of cells, and each cell may not contain all population-averaged contacts. Therefore, we employ a novel approach of summing individual chromosome trajectories-determined by our Self-Returning Random Walk model-to create populations of cells. We allow single cells to consist of disparate structures and reproduce a variety of experimentally relevant contact maps. We show that the amount of shared topology between cells, and their mechanism of formation, changes the population-averaged structure. Therefore, we present a modeling technique that, with few constraints and little oversight, can be used to understand which single-cell chromatin structures underlie population-averaged behavior.

Analysis of three-dimensional chromatin packing domains by chromatin scanning transmission electron microscopy (ChromSTEM).

Chromatin organization over multiple length scales plays a critical role in the regulation of transcription. Deciphering the interplay of these processes requires high-resolution, three-dimensional, quantitative imaging of chromatin structure in vitro. Herein, we introduce ChromSTEM, a method that utilizes high-angle annular dark-field imaging and tomography in scanning transmission electron microscopy combined with DNA-specific staining for electron microscopy. We utilized ChromSTEM for an in-depth quantification of 3D chromatin conformation with high spatial resolution and contrast, allowing for characterization of higher-order chromatin structure almost down to the level of the DNA base pair. Employing mass scaling analysis on ChromSTEM mass density tomograms, we observed that chromatin forms spatially well-defined higher-order domains, around 80 nm in radius. Within domains, chromatin exhibits a polymeric fractal-like behavior and a radially decreasing mass-density from the center to the periphery. Unlike other nanoimaging and analysis techniques, we demonstrate that our unique combination of this high-resolution imaging technique with polymer physics-based analysis enables us to (i) investigate the chromatin conformation within packing domains and (ii) quantify statistical descriptors of chromatin structure that are relevant to transcription. We observe that packing domains have heterogeneous morphological properties even within the same cell line, underlying the potential role of statistical chromatin packing in regulating gene expression within eukaryotic nuclei.

Acid-Base Equilibrium and Dielectric Environment Regulate Charge in Supramolecular Nanofibers.

Peptide amphiphiles are a class of molecules that can self-assemble into a variety of supramolecular structures, including high-aspect-ratio nanofibers. It is challenging to model and predict the charges in these supramolecular nanofibers because the ionization state of the peptides are not fixed but liable to change due to the acid-base equilibrium that is coupled to the structural organization of the peptide amphiphile molecules. Here, we have developed a theoretical model to describe and predict the amount of charge found on self-assembled peptide amphiphiles as a function of pH and ion concentration. In particular, we computed the amount of charge of peptide amphiphiles nanofibers with the sequence C 16 - V 2 A 2 E 2. In our theoretical formulation, we consider charge regulation of the carboxylic acid groups, which involves the acid-base chemical equilibrium of the glutamic acid residues and the possibility of ion condensation. The charge regulation is coupled with the local dielectric environment by allowing for a varying dielectric constant that also includes a position-dependent electrostatic solvation energy for the charged species. We find that the charges on the glutamic acid residues of the peptide amphiphile nanofiber are much lower than the same functional group in aqueous solution. There is a strong coupling between the charging via the acid-base equilibrium and the local dielectric environment. Our model predicts a much lower degree of deprotonation for a position-dependent relative dielectric constant compared to a constant dielectric background. Furthermore, the shape and size of the electrostatic potential as well as the counterion distribution are quantitatively and qualitatively different. These results indicate that an accurate model of peptide amphiphile self-assembly must take into account charge regulation of acidic groups through acid-base equilibria and ion condensation, as well as coupling to the local dielectric environment.

Proteins Adsorbing onto Surface-Modified Nanoparticles: Effect of Surface Curvature, pH, and the Interplay of Polymers and Proteins Acid-Base Equilibrium.

Protein adsorption onto nanomaterials is a process of vital significance and it is commonly controlled by functionalizing their surface with polymers. The efficiency of this strategy depends on the design parameters of the nanoconstruct. Although significant amount of work has been carried out on planar surfaces modified with different types of polymers, studies investigating the role of surface curvature are not as abundant. Here, we present a comprehensive and systematic study of the protein adsorption process, analyzing the effect of curvature and morphology, the grafting of polymer mixtures, the type of monomer (neutral, acidic, basic), the proteins in solution, and the conditions of the solution. The theoretical approach we employed is based on a molecular theory that allows to explicitly consider the acid-base reactions of the amino acids in the proteins and the monomers on the surface. The calculations showed that surface curvature modulates the molecular organization in space, but key variables are the bulk pH and salt concentration (in the millimolar range). When grafting the NP with acidic or basic polymers, the surface coating could disfavor or promote adsorption, depending on the solution's conditions. When NPs are in contact with protein mixtures in solution, a nontrivial competitive adsorption process is observed. The calculations reflect the balance between molecular organization and chemical state of polymers and proteins, and how it is modulated by the curvature of the underlying surface.

Structure and dynamics of nanoconfined water and aqueous solutions.

This review is devoted to discussing recent progress on the structure, thermodynamic, reactivity, and dynamics of water and aqueous systems confined within different types of nanopores, synthetic and biological. Currently, this is a branch of water science that has attracted enormous attention of researchers from different fields interested to extend the understanding of the anomalous properties of bulk water to the nanoscopic domain. From a fundamental perspective, the interactions of water and solutes with a confining surface dramatically modify the liquid's structure and, consequently, both its thermodynamical and dynamical behaviors, breaking the validity of the classical thermodynamic and phenomenological description of the transport properties of aqueous systems. Additionally, man-made nanopores and porous materials have emerged as promising solutions to challenging problems such as water purification, biosensing, nanofluidic logic and gating, and energy storage and conversion, while aquaporin, ion channels, and nuclear pore complex nanopores regulate many biological functions such as the conduction of water, the generation of action potentials, and the storage of genetic material. In this work, the more recent experimental and molecular simulations advances in this exciting and rapidly evolving field will be reported and critically discussed.

Design of Multifunctional Nanopore Using Polyampholyte Brush with Composition Gradient.

Molecular organizations and charge patterns inside biological nanopores are optimized by evolution to enhance ionic and molecular transport. Inspired by the nuclear pore complex that employs asymmetrically arranged disordered proteins for its gating, we here design an artificial nanopore coated by an asymmetric polyampholyte brush as a model system to study the asymmetric mass transport under nanoconfinement. A nonequilibrium steady-state molecular theory is developed to account for the intricate charge regulation effect of the weak polyampholyte and to address the coupling between the polymer conformation and the external electric field. On the basis of this state-of-the-art theoretical method, we present a comprehensive theoretical description of the stimuli-responsive structural behaviors and transport properties inside the nanopore with all molecular details considered. Our model demonstrates that by incorporating a gradient of pH sensitivity into the polymer coatings of the nanopore, a variety of asymmetric charge patterns and functional structures can be achieved, in a pH-responsive manner that allows for multiple functions to be implemented into the designed system. The asymmetric charge pattern inside the nanopore leads to an electrostatic trap for major current carriers, which turns the nanopore into an ionic rectifier with a rectification factor above 1000 at optimized pH and salt concentration. Our theory further predicts that the nanopore design behaves like a double-gated nanofluidic device with pH-triggered opening of the gates, which can serve as an ion pump and pH-responsive molecular filter. These results deepen our understanding of asymmetric transport in nanoconfined systems and provide guidelines for designing polymer-coated smart nanopores.

Nanoscale chromatin imaging and analysis platform bridges 4D chromatin organization with molecular function.

Extending across multiple length scales, dynamic chromatin structure is linked to transcription through the regulation of genome organization. However, no individual technique can fully elucidate this structure and its relation to molecular function at all length and time scales at both a single-cell level and a population level. Here, we present a multitechnique nanoscale chromatin imaging and analysis (nano-ChIA) platform that consolidates electron tomography of the primary chromatin fiber, optical super-resolution imaging of transcription processes, and label-free nano-sensing of chromatin packing and its dynamics in live cells. Using nano-ChIA, we observed that chromatin is localized into spatially separable packing domains, with an average diameter of around 200 nanometers, sub-megabase genomic size, and an internal fractal structure. The chromatin packing behavior of these domains exhibits a complex bidirectional relationship with active gene transcription. Furthermore, we found that properties of PDs are correlated among progenitor and progeny cells across cell division.

Nanopore gates via reversible crosslinking of polymer brushes: a theoretical study.

Polymer-brush-modified nanopores are synthetic structures inspired by the gated transport exhibited by their biological counterparts. This work theoretically analyzes how the reversible crosslinking of a polymer network by soluble species can be used to control transport through nanochannels and pores. The study was performed with a molecular theory that allows inhomogeneities in the three spatial dimensions and explicitly takes into account the size, shape and conformations of all molecular species, considers the intermolecular interactions between the polymers and the soluble crosslinkers and includes the presence of a translocating particle inside the pore. It is shown than increasing the concentration of the soluble crosslinkers in bulk solution leads to a gradual increase of its number within the pore until a critical bulk concentration is reached. At the critical concentration, the number of crosslinkers inside the pore increases abruptly. For long chains, this sudden transition triggers the collapse of the polymer brush to the center of the nanopore. The resulting structure increases the free-energy barrier that a translocating particle has to surmount to go across the pore and modifies the route of translocation from the axis of the pore to its walls. On the other hand, for short polymer chains the crosslinkers trigger the collapse of the brush to the pore walls, which reduces the translocation barrier.

Theoretical Modeling of Chemical Equilibrium in Weak Polyelectrolyte Layers on Curved Nanosystems.

Surface functionalization with end-tethered weak polyelectrolytes (PE) is a versatile way to modify and control surface properties, given their ability to alter their degree of charge depending on external cues like pH and salt concentration. Weak PEs find usage in a wide range of applications, from colloidal stabilization, lubrication, adhesion, wetting to biomedical applications such as drug delivery and theranostics applications. They are also ubiquitous in many biological systems. Here, we present an overview of some of the main theoretical methods that we consider key in the field of weak PE at interfaces. Several applications involving engineered nanoparticles, synthetic and biological nanopores, as well as biological macromolecules are discussed to illustrate the salient features of systems involving weak PE near an interface or under (nano)confinement. The key feature is that by confining weak PEs near an interface the degree of charge is different from what would be expected in solution. This is the result of the strong coupling between structural organization of weak PE and its chemical state. The responsiveness of engineered and biological nanomaterials comprising weak PE combined with an adequate level of modeling can provide the keys to a rational design of smart nanosystems.

Modeling the nucleoporins that form the hairy pores.

Sitting on the nuclear envelope, nuclear pore complexes (NPCs) control the molecular transport between the nucleus and the cytoplasm. Without definite open or close states, the NPC uses a family of intrinsically disordered nucleoporins called FG-Nups to construct a selective permeability barrier whose functional structure is unclear. Experimental advances have offered high-resolution molecular knowledge of the NPC scaffold and docking of the unfolded FG-Nups, however, the 'hairy' barrier structure still appears as blurred lobes even under the state-of-the-art microscopy. Without accurate experimental visualization, the molecular mechanism for the NPC-mediated transport remains a matter of debate. Modeling provides an alternative way to resolve this long-standing mystery. Here, we briefly review different methods employed in modeling the FG-Nups, arranging from all-atom molecular dynamics to mean-field theories. We discuss the advantage and limit of each modeling technique, and summarize the theoretical insights that, despite certain controversy, deepened our understanding of the hairy pore.

Physical and data structure of 3D genome.

With the textbook view of chromatin folding based on the 30-nm fiber being challenged, it has been proposed that interphase DNA has an irregular 10-nm nucleosome polymer structure whose folding philosophy is unknown. Nevertheless, experimental advances suggest that this irregular packing is associated with many nontrivial physical properties that are puzzling from a polymer physics point of view. Here, we show that the reconciliation of these exotic properties necessitates modularizing three-dimensional genome into tree data structures on top of, and in striking contrast to, the linear topology of DNA double helix. These functional modules need to be connected and isolated by an open backbone that results in porous and heterogeneous packing in a quasi-self-similar manner, as revealed by our electron and optical imaging. Our multiscale theoretical and experimental results suggest the existence of higher-order universal folding principles for a disordered chromatin fiber to avoid entanglement and fulfill its biological functions.

Disordered chromatin packing regulates phenotypic plasticity.

Three-dimensional supranucleosomal chromatin packing plays a profound role in modulating gene expression by regulating transcription reactions through mechanisms such as gene accessibility, binding affinities, and molecular diffusion. Here, we use a computational model that integrates disordered chromatin packing (CP) with local macromolecular crowding (MC) to study how physical factors, including chromatin density, the scaling of chromatin packing, and the size of chromatin packing domains, influence gene expression. We computationally and experimentally identify a major role of these physical factors, specifically chromatin packing scaling, in regulating phenotypic plasticity, determining responsiveness to external stressors by influencing both intercellular transcriptional malleability and heterogeneity. Applying CPMC model predictions to transcriptional data from cancer patients, we identify an inverse relationship between patient survival and phenotypic plasticity of tumor cells.

Dynamic Crowding Regulates Transcription.

The nuclear environment is highly crowded by biological macromolecules, including chromatin and mobile proteins, which alter the kinetics and efficiency of transcriptional machinery. These alterations have been described, both theoretically and experimentally, for steady-state crowding densities; however, temporal changes in crowding density ("dynamic crowding") have yet to be integrated with gene expression. Dynamic crowding is pertinent to nuclear biology because processes such as chromatin translocation and protein diffusion lend to highly mobile biological crowders. Therefore, to capture such dynamic crowding and investigate its influence on transcription, we employ a three-pronged, systems-molecular approach. A system of chemical reactions represents the transcription pathway, the rates of which are determined by molecular-scale simulations; Brownian dynamics and Monte Carlo simulations quantify protein diffusion and DNA-protein binding affinity, dependent on macromolecular density. Altogether, this approach shows that transcription depends critically on dynamic crowding as the gene expression resultant from dynamic crowding can be profoundly different than that of steady-state crowding. In fact, expression levels can display both amplification and suppression and are notably different for genes or gene populations with different chemical and structural properties. These properties can be exploited to impose circadian expression, which is asymmetric and varies in strength, or to explain expression in cells under biomechanical stress. Therefore, this work demonstrates that dynamic crowding nontrivially alters transcription kinetics and presents dynamic crowding within the bulk nuclear nanoenvironment as a novel regulatory framework for gene expression.

Nanocompartmentalization of the Nuclear Pore Lumen.

The nuclear pore complex (NPC) employs the intrinsically disordered regions (IDRs) from a family of phenylalanine-glycine-rich nucleoporins (FG-Nups) to control nucleocytoplasmic transport. It has been a long-standing mystery how the IDR-mediated mass exchange can be rapid yet selective. Here, we use a computational microscope to show that nanocompartmentalization of IDR subdomains leads to a remarkably elaborate gating structure as programmed by the amino acid sequences. In particular, we reveal a heterogeneous permeability barrier that combines an inner ring barrier with two vestibular condensates. Throughout the NPC, we find a polarized electrostatic potential and a diffuse thermoreversible FG network featuring mosaic FG territories with low FG-FG pairing fraction. Our theoretical anatomy of the central transporter sheds light into the sequence-structure-function relationship of the FG-Nups and provides a picture of nucleocytoplasmic mass exchange that allows a reconciliation of transport efficiency and specificity.

Classification of RNA backbone conformations into rotamers using 13C' chemical shifts: exploring how far we can go.

The conformational space of the ribose-phosphate backbone is very complex as it is defined in terms of six torsional angles. To help delimit the RNA backbone conformational preferences, 46 rotamers have been defined in terms of these torsional angles. In the present work, we use the ribose experimental and theoretical 13C' chemical shifts data and machine learning methods to classify RNA backbone conformations into rotamers and families of rotamers. We show to what extent the experimental 13C' chemical shifts can be used to identify rotamers and discuss some problem with the theoretical computations of 13C' chemical shifts.

Preservation of cellular nano-architecture by the process of chemical fixation for nanopathology.

Transformation in chromatin organization is one of the most universal markers of carcinogenesis. Microscale chromatin alterations have been a staple of histopathological diagnosis of neoplasia, and nanoscale alterations have emerged as a promising marker for cancer prognostication and the detection of predysplastic changes. While numerous methods have been developed to detect these alterations, most methods for sample preparation remain largely validated via conventional microscopy and have not been examined with nanoscale sensitive imaging techniques. For these nanoscale sensitive techniques to become standard of care screening tools, new histological protocols must be developed that preserve nanoscale information. Partial Wave Spectroscopic (PWS) microscopy has recently emerged as a novel imaging technique sensitive to length scales ranging between 20 and 200 nanometers. As a label-free, high-throughput, and non-invasive imaging technique, PWS microscopy is an ideal tool to quantify structural information during sample preparation. Therefore, in this work we applied PWS microscopy to systematically evaluate the effects of cytological preparation on the nanoscales changes of chromatin using two live cell models: a drug-based model of Hela cells differentially treated with daunorubicin and a cell line comparison model of two cells lines with inherently distinct chromatin organizations. Notably, we show that existing cytological preparation can be modified in order to maintain clinically relevant nanoscopic differences, paving the way for the emerging field of nanopathology.