Mechanics limits ecological diversity and promotes heterogeneity in confined bacterial communities.

Multispecies bacterial populations often inhabit confined and densely packed environments where spatial competition determines the ecological diversity of the community. However, the role of mechanical interactions in shaping the ecology is still poorly understood. Here, we study a model system consisting of two populations of nonmotile Escherichia coli bacteria competing within open, monolayer microchannels. The competitive dynamics is observed to be biphasic: After seeding, either one strain rapidly fixates or both strains orient into spatially stratified, stable communities. We find that mechanical interactions with other cells and local spatial constraints influence the resulting community ecology in unexpected ways, severely limiting the overall diversity of the communities while simultaneously allowing for the establishment of stable, heterogeneous populations of bacteria displaying disparate growth rates. Surprisingly, the populations have a high probability of coexisting even when one strain has a significant growth advantage. A more coccus morphology is shown to provide a selective advantage, but agent-based simulations indicate this is due to hydrodynamic and adhesion effects within the microchannel and not from breaking of the nematic ordering. Our observations are qualitatively reproduced by a simple Pólya urn model, which suggests the generality of our findings for confined population dynamics and highlights the importance of early colonization conditions on the resulting diversity and ecology of bacterial communities. These results provide fundamental insights into the determinants of community diversity in dense confined ecosystems where spatial exclusion is central to competition as in organized biofilms or intestinal crypts.

Self-regulation of the nuclear pore complex enables clogging-free crowded transport.

Nuclear pore complexes (NPCs) are the main conduits for macromolecular transport into and out of the nucleus of eukaryotic cells. The central component of the NPC transport mechanism is an assembly of intrinsically disordered proteins (IDPs) that fills the NPC channel. The channel interior is further crowded by large numbers of simultaneously translocating cargo-carrying and free transport proteins. How the NPC can efficiently, rapidly, and selectively transport varied cargoes in such crowded conditions remains ill understood. Past experimental results suggest that the NPC is surprisingly resistant to clogging and that transport may even become faster and more efficient as the concentration of transport protein increases. To understand the mechanisms behind these puzzling observations, we construct a computational model of the NPC comprising only a minimal set of commonly accepted consensus features. This model qualitatively reproduces the previous experimental results and identifies self-regulating mechanisms that relieve crowding. We show that some of the crowding-alleviating mechanisms-such as preventing saturation of the bulk flux-are "robust" and rely on very general properties of crowded dynamics in confined channels, pertaining to a broad class of selective transport nanopores. By contrast, the counterintuitive ability of the NPC to leverage crowding to achieve more efficient single-molecule translocation is "fine-tuned" and relies on the particular spatial architecture of the IDP assembly in the NPC channel.

Proofreading does not result in more reliable ligand discrimination in receptor signaling due to its inherent stochasticity.

Kinetic proofreading (KPR) has been used as a paradigmatic explanation for the high specificity of ligand discrimination by cellular receptors. KPR enhances the difference in the mean receptor occupancy between different ligands compared to a nonproofread receptor, thus potentially enabling better discrimination. On the other hand, proofreading also attenuates the signal and introduces additional stochastic receptor transitions relative to a nonproofreading receptor. This increases the relative magnitude of noise in the downstream signal, which can interfere with reliable ligand discrimination. To understand the effect of noise on ligand discrimination beyond the comparison of the mean signals, we formulate the task of ligand discrimination as a problem of statistical estimation of the receptor affinity of ligands based on the molecular signaling output. Our analysis reveals that proofreading typically worsens ligand resolution compared to a nonproofread receptor. Furthermore, the resolution decreases further with more proofreading steps under most commonly biologically considered conditions. This contrasts with the usual notion that KPR universally improves ligand discrimination with additional proofreading steps. Our results are consistent across a variety of different proofreading schemes and metrics of performance, suggesting that they are inherent to the KPR mechanism itself rather than any particular model of molecular noise. Based on our results, we suggest alternative roles for KPR schemes such as multiplexing and combinatorial encoding in multi-ligand/multi-output pathways.

Phenomenology and dynamics of competitive ecosystems beyond the niche-neutral regimes.

Structure, composition, and stability of ecological populations are shaped by the inter- and intraspecies interactions within their communities. It remains to be fully understood how the interplay of these interactions with other factors, such as immigration, controls the structure, the diversity, and the long-term stability of ecological systems in the presence of noise and fluctuations. We address this problem using a minimal model of interacting multispecies ecological communities that incorporates competition, immigration, and demographic noise. We find that a complete phase diagram exhibits rich behavior with multiple regimes that go beyond the classical "niche" and "neutral" regimes, extending and modifying the "rare biosphere" or "niche-like" dichotomy. In particular, we observe regimes that cannot be characterized as either niche or neutral where a multimodal species abundance distribution is observed. We characterize the transitions between the different regimes and show how these arise from the underlying kinetics of the species turnover, extinction, and invasion. Our model serves as a minimal null model of noisy competitive ecological systems, against which more complex models that include factors such as mutations and environmental noise can be compared.

Kinetic cooperativity resolves bidirectional clogging within the nuclear pore complex.

As the main gatekeeper of the nucleocytoplasmic transport in eukaryotic cells, the nuclear pore complex (NPC) faces the daunting task of facilitating the bidirectional transport of a high volume of macromolecular cargoes while ensuring the selectivity, speed, and efficiency of this process. The competition between opposing nuclear import and export fluxes passing through the same channel is expected to pose a major challenge to transport efficiency. It has been suggested that phase separation-like radial segregation of import and export fluxes within the assembly of intrinsically disordered proteins that line the NPC pore could be a mechanism for ensuring efficient bidirectional transport. We examine the impact of radial segregation on the efficiency of bidirectional transport through the NPC using a coarse-grained computational model of the NPC. We find little evidence that radial segregation improves transport efficiency. By contrast, surprisingly, we find that NTR crowding may enhance rather than impair the efficiency of bidirectional transport although it decreases the available space in the pore. We identify mechanisms of this novel crowding-induced transport cooperativity through the self-regulation of cargo density and flux in the pore. These findings explain how the functional architecture of the NPC resolves the problem of efficient bidirectional transport, and provide inspiration for the alleviation of clogging in artificial selective nanopores.

Spatial exclusion leads to "tug-of-war" ecological dynamics between competing species within microchannels.

Competition is ubiquitous in microbial communities, shaping both their spatial and temporal structure and composition. Classical minimal models of competition, such as the Moran model, have been employed in ecology and evolutionary biology to understand the role of fixation and invasion in the maintenance of population diversity. Informed by recent experimental studies of cellular competition in confined spaces, we extend the Moran model to incorporate mechanical interactions between cells that divide within the limited space of a one-dimensional open microchannel. The model characterizes the skewed collective growth of the cells dividing within the channel, causing cells to be expelled at the channel ends. The results of this spatial exclusion model differ significantly from those of its classical well-mixed counterpart. The mean time to fixation of a species is greatly accelerated, scaling logarithmically, rather than algebraically, with the system size, and fixation/extinction probability sharply depends on the species' initial fractional abundance. By contrast, successful takeovers by invasive species, whether through mutation or immigration, are substantially less likely than in the Moran model. We also find that the spatial exclusion tends to attenuate the effects of fitness differences on the fixation times and probabilities. We find that these effects arise from the combination of the quasi-neutral "tug-of-war" diffusion dynamics of the inter-species boundary around an unstable equipoise point and the quasi-deterministic avalanche dynamics away from the fixed point. These results, which can be tested in microfluidic monolayer devices, have implications for the maintenance of species diversity in dense bacterial and cellular ecosystems where spatial exclusion is central to the competition, such as in organized biofilms or intestinal crypts.

Dynamic structure factor of undulating vesicles: finite-size and spherical geometry effects with application to neutron spin echo experiments.

We consider the dynamic structure factor (DSF) of quasi-spherical vesicles and present a generalization of an expression that was originally formulated by Zilman and Granek (ZG) for scattering from isotropically oriented quasi-flat membrane plaquettes. The expression is obtained in the form of a multi-dimensional integral over the undulating membrane surface. The new expression reduces to the original stretched exponential form in the limit of sufficiently large vesicles, i.e., in the micron range or larger. For much smaller unilamellar vesicles, deviations from the asymptotic, stretched exponential equation are noticeable even if one assumes that the Seifert-Langer leaflet density mode is completely relaxed and membrane viscosity is neglected. To avoid the need for an exhaustive numerical integration while fitting to neutron spin echo (NSE) data, we provide a useful approximation for polydisperse systems that tests well against the numerical integration of the complete expression. To validate the new expression, we performed NSE experiments on variable-size vesicles made of a POPC/POPS lipid mixture and demonstrate an advantage over the original stretched exponential form or other manipulations of the original ZG expression that have been deployed over the years to fit the NSE data. In particular, values of the membrane bending rigidity extracted from the NSE data using the new approximations were insensitive to the vesicle radii and scattering wavenumber and compared very well with expected values of the effective bending modulus ([Formula: see text]) calculated from results in the literature. Moreover, the generalized scattering theory presented here for an undulating quasi-spherical shell can be easily extended to other models for the membrane undulation dynamics beyond the Helfrich Hamiltonian and thereby provides the foundation for the study of the nanoscale dynamics in more complex and biologically relevant model membrane systems.

Effects of Sequence Composition, Patterning and Hydrodynamics on the Conformation and Dynamics of Intrinsically Disordered Proteins.

Intrinsically disordered proteins (IDPs) and intrinsically disordered regions (IDRs) perform diverse functions in cellular organization, transport and signaling. Unlike the well-defined structures of the classical natively folded proteins, IDPs and IDRs dynamically span large conformational and structural ensembles. This dynamic disorder impedes the study of the relationship between the amino acid sequences of the IDPs and their spatial structures and dynamics, with different experimental techniques often offering seemingly contradictory results. Although experimental and theoretical evidence indicates that some IDP properties can be understood based on their average biophysical properties and amino acid composition, other aspects of IDP function are dictated by the specifics of the amino acid sequence. We investigate the effects of several key variables on the dimensions and the dynamics of IDPs using coarse-grained polymer models. We focus on the sequence "patchiness" informed by the sequence and biophysical properties of different classes of IDPs-and in particular FG nucleoporins of the nuclear pore complex (NPC). We show that the sequence composition and patterning are well reflected in the global conformational variables such as the radius of gyration and hydrodynamic radius, while the end-to-end distance and dynamics are highly sequence-specific. We find that in good solvent conditions highly heterogeneous sequences of IDPs can be well mapped onto averaged minimal polymer models for the purpose of prediction of the IDPs dimensions and dynamic relaxation times. The coarse-grained simulations are in a good agreement with the results of atomistic MD. We discuss the implications of these results for the interpretation of the recent experimental measurements, and for the further applications of mesoscopic models of FG nucleoporins and IDPs more broadly.

Physical modeling of multivalent interactions in the nuclear pore complex.

In the nuclear pore complex, intrinsically disordered proteins (FG Nups), along with their interactions with more globular proteins called nuclear transport receptors (NTRs), are vital to the selectivity of transport into and out of the cell nucleus. Although such interactions can be modeled at different levels of coarse graining, in vitro experimental data have been quantitatively described by minimal models that describe FG Nups as cohesive homogeneous polymers and NTRs as uniformly cohesive spheres, in which the heterogeneous effects have been smeared out. By definition, these minimal models do not account for the explicit heterogeneities in FG Nup sequences, essentially a string of cohesive and noncohesive polymer units, and at the NTR surface. Here, we develop computational and analytical models that do take into account such heterogeneity in a minimal fashion and compare them with experimental data on single-molecule interactions between FG Nups and NTRs. Overall, we find that the heterogeneous nature of FG Nups and NTRs does play a role in determining equilibrium binding properties but is of much greater significance when it comes to unbinding and binding kinetics. Using our models, we predict how binding equilibria and kinetics depend on the distribution of cohesive blocks in the FG Nup sequences and of the binding pockets at the NTR surface, with multivalency playing a key role. Finally, we observe that single-molecule binding kinetics has a rather minor influence on the diffusion of NTRs in polymer melts consisting of FG-Nup-like sequences.

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.

The entry of nanoparticles into solid tumours.

The concept of nanoparticle transport through gaps between endothelial cells (inter-endothelial gaps) in the tumour blood vessel is a central paradigm in cancer nanomedicine. The size of these gaps was found to be up to 2,000 nm. This justified the development of nanoparticles to treat solid tumours as their size is small enough to extravasate and access the tumour microenvironment. Here we show that these inter-endothelial gaps are not responsible for the transport of nanoparticles into solid tumours. Instead, we found that up to 97% of nanoparticles enter tumours using an active process through endothelial cells. This result is derived from analysis of four different mouse models, three different types of human tumours, mathematical simulation and modelling, and two different types of imaging techniques. These results challenge our current rationale for developing cancer nanomedicine and suggest that understanding these active pathways will unlock strategies to enhance tumour accumulation.

The Role of Cohesiveness in the Permeability of the Spatial Assemblies of FG Nucleoporins.

Nuclear pore complexes (NPCs) conduct selective, bidirectional transport across the nuclear envelope. The NPC passageway is lined by intrinsically disordered proteins that contain hydrophobic phenylalanine-glycine (FG) motifs, known as FG nucleoporins (FG nups), that play the key role in the NPC transport mechanism. Cohesive interactions among the FG nups, which arise from the combination of hydrophobic, electrostatic, and other forces, have been hypothesized to control the morphology of the assemblies of FG nups in the NPC, as well as their permeability with respect to the transport proteins. However, the role of FG nup cohesiveness is still vigorously debated. Using coarse-grained polymer theory and numerical simulations, we study the effects of cohesiveness on the selective permeability of in vitro FG nup assemblies in different geometries that have served as proxies for the morphological and transport properties of the NPC. We show that in high-density FG nup assemblies, increase in cohesiveness leads to the decrease in their permeability, in accordance with the accepted view. On the other hand, the permeability of low-density assemblies is a nonmonotonic function of the cohesiveness, and a moderate increase in cohesiveness can enhance permeability. The density- and cohesiveness-dependent effects on permeability are explained by considering the free-energy cost associated with penetrating the FG nup assemblies. We discuss the implications of these findings for the organization and function of the NPC.

Anomalous viscosity-time behavior of polysaccharide dispersions.

Using viscosity and dynamic light scattering (DLS) measurements, we monitored the changes in the properties of dispersions of chitosan (a cationic polysaccharide) in acidic solution over a period of up to 700 h. Different polymer concentrations, weight average molecular weights, and degrees of deacetylation were examined. We found that the solution rheology and chitosan aggregates continue to change even up to 700 h. It was observed, remarkably, using both capillary and cone and plate viscometry that the viscosity decreased significantly during the storage period of the chitosan dispersions, with a rapid initial decrease and a slow approach to the steady state value. DLS measurements over this period could be interpreted in terms of a gradual decrease in the size of the chitosan aggregates in the dispersion. This behavior is puzzling, insofar as one expects the dissolution of compact polymer aggregates with time into individual polymer chains to increase the viscosity rather than decrease it as observed: We attribute this apparently anomalous behavior to the fact that the chitosan aggregates are rigid crystalline rod-like entities, which dissolved with time from dispersion of overlapping rods (with high viscosity) into solution of individual random coils (with lower viscosity). A detailed model comparing the hydrodynamic behavior of the initial overlapping rod-like aggregates with the subsequent free coils in solution is in semi-quantitative agreement with our observation.

Effects of cross-linking on partitioning of nanoparticles into a polymer brush: Coarse-grained simulations test simple approximate theories.

The effect of cohesive contacts or, equivalently, dynamical cross-linking on the equilibrium morphology of a polymer brush infiltrated by nanoparticles that are attracted to the polymer strands is studied for plane-grafted brushes using coarse-grained molecular dynamics and approximate statistical mechanical models. In particular, the Alexander-de Gennes (AdG) and Strong Stretching Theory (SST) mean-field theory (MFT) models are considered. It is found that for values of the MFT cross-link strength interaction parameter beyond a certain threshold, both AdG and SST models predict that the polymer brush will be in a compact state of nearly uniform density packed next to the grafting surface over a wide range of solution phase nanoparticle concentrations. Coarse grained molecular dynamics simulations confirm this prediction, for both small nanoparticles (nanoparticle volume = monomer volume) and large nanoparticles (nanoparticle volume = 27 × monomer volume). Simulation results for these cross-linked systems are compared with analogous results for systems with no cross-linking. At the same solution phase nanoparticle concentration, strong cross-linking results in additional compression of the brush relative to the non-crosslinked analog and, at all but the lowest concentrations, to a lesser degree of infiltration by nanoparticles. For large nanoparticles, the monomer density profiles show clear oscillations moving outwards from the grafting surface, corresponding to a degree of layering of the absorbed nanoparticles in the brush as they pack against the grafting surface.

Protein Transport by the Nuclear Pore Complex: Simple Biophysics of a Complex Biomachine.

In eukaryotic cells, transport of molecules between the nucleus and the cytoplasm is facilitated by highly selective and efficient biomachines known as nuclear pore complexes (NPCs). The structural details of NPCs vary across species, with many of their constituent proteins exhibiting relatively low sequence conservation; yet the NPC as a whole retains its general architecture and mechanism of action in all eukaryotes from yeast to humans. This functional conservation in the absence of precise molecular conservation suggests that many aspects of the NPC transport mechanism may be understood based on general biophysical considerations. Accordingly, some aspects of NPC function have been recapitulated in artificial nanochannel mimics, even though they lack certain molecular elements of the endogenous NPC. Herein, we review biophysical aspects of NPC architecture and function and cover recent progress in the field. We also review recent advances in man-made molecular filters inspired by NPCs, and their applications in nanotechnology. We conclude the review with an outlook on outstanding questions in the field and biomedical aspects of NPC transport.

Molecular Counting with Localization Microscopy: A Bayesian Estimate Based on Fluorophore Statistics.

Superresolved localization microscopy has the potential to serve as an accurate, single-cell technique for counting the abundance of intracellular molecules. However, the stochastic blinking of single fluorophores can introduce large uncertainties into the final count. Here we provide a theoretical foundation for applying superresolved localization microscopy to the problem of molecular counting based on the distribution of blinking events from a single fluorophore. We also show that by redundantly tagging single molecules with multiple, blinking fluorophores, the accuracy of the technique can be enhanced by harnessing the central limit theorem. The coefficient of variation then, for the number of molecules M estimated from a given number of blinks B, scales like ∼1/Nl, where Nl is the mean number of labels on a target. As an example, we apply our theory to the challenging problem of quantifying the cell-to-cell variability of plasmid copy number in bacteria.

Large cargo transport by nuclear pores: implications for the spatial organization of FG-nucleoporins.

Nuclear pore complexes (NPCs) mediate cargo traffic between the nucleus and the cytoplasm of eukaryotic cells. Nuclear transport receptors (NTRs) carry cargos through NPCs by transiently binding to phenylalanine-glycine (FG) repeats on intrinsically disordered polypeptides decorating the NPCs. Major impediments to understand the transport mechanism are the thousands of FG binding sites on each NPC, whose spatial distribution is unknown, and multiple binding sites per NTR, which leads to multivalent interactions. Using single molecule fluorescence microscopy, we show that multiple NTR molecules are required for efficient transport of a large cargo, while a single NTR promotes binding to the NPC but not transport. Particle trajectories and theoretical modelling reveal a crucial role for multivalent NTR interactions with the FG network and indicate a non-uniform FG repeat distribution. A quantitative model is developed wherein the cytoplasmic side of the pore is characterized by a low effective concentration of free FG repeats and a weak FG-NTR affinity, and the centrally located dense permeability barrier is overcome by multivalent interactions, which provide the affinity necessary to permeate the barrier.

Mechanism of hard-nanomaterial clearance by the liver.

The liver and spleen are major biological barriers to translating nanomedicines because they sequester the majority of administered nanomaterials and prevent delivery to diseased tissue. Here we examined the blood clearance mechanism of administered hard nanomaterials in relation to blood flow dynamics, organ microarchitecture and cellular phenotype. We found that nanomaterial velocity reduces 1,000-fold as they enter and traverse the liver, leading to 7.5 times more nanomaterial interaction with hepatic cells relative to peripheral cells. In the liver, Kupffer cells (84.8 ± 6.4%), hepatic B cells (81.5 ± 9.3%) and liver sinusoidal endothelial cells (64.6 ± 13.7%) interacted with administered PEGylated quantum dots, but splenic macrophages took up less material (25.4 ± 10.1%) due to differences in phenotype. The uptake patterns were similar for two other nanomaterial types and five different surface chemistries. Potential new strategies to overcome off-target nanomaterial accumulation may involve manipulating intra-organ flow dynamics and modulating the cellular phenotype to alter hepatic cell interactions.

Absolute Ligand Discrimination by Dimeric Signaling Receptors.

Many signaling pathways act through shared components, where different ligand molecules bind the same receptors or activate overlapping sets of response regulators downstream. Nevertheless, different ligands acting through cross-wired pathways often lead to different outcomes in terms of the target cell behavior and function. Although a number of mechanisms have been proposed, it still largely remains unclear how cells can reliably discriminate different molecular ligands under such circumstances. Here we show that signaling via ligand-induced receptor dimerization-a very common motif in cellular signaling-naturally incorporates a mechanism for the discrimination of ligands acting through the same receptor.

Artificial nanopores that mimic the transport selectivity of the nuclear pore complex.

Nuclear pore complexes (NPCs) act as effective and robust gateways between the nucleus and the cytoplasm, selecting for the passage of particular macromolecules across the nuclear envelope. NPCs comprise an elaborate scaffold that defines a approximately 30 nm diameter passageway connecting the nucleus and the cytoplasm. This scaffold anchors proteins termed 'phenylalanine-glycine' (FG)-nucleoporins, the natively disordered domains of which line the passageway and extend into its lumen. Passive diffusion through this lined passageway is hindered in a size-dependent manner. However, transport factors and their cargo-bound complexes overcome this restriction by transient binding to the FG-nucleoporins. To test whether a simple passageway and a lining of transport-factor-binding FG-nucleoporins are sufficient for selective transport, we designed a functionalized membrane that incorporates just these two elements. Here we demonstrate that this membrane functions as a nanoselective filter, efficiently passing transport factors and transport-factor-cargo complexes that specifically bind FG-nucleoporins, while significantly inhibiting the passage of proteins that do not. This inhibition is greatly enhanced when transport factor is present. Determinants of selectivity include the passageway diameter, the length of the nanopore region coated with FG-nucleoporins, the binding strength to FG-nucleoporins, and the antagonistic effect of transport factors on the passage of proteins that do not specifically bind FG-nucleoporins. We show that this artificial system faithfully reproduces key features of trafficking through the NPC, including transport-factor-mediated cargo import.