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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.

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 counter-intuitive 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.

Kinetic proofreading (KPR) has been used as a paradigmatic explanation for the high specificity of important biological processes including ligand discrimination by cellular receptors. Kinetic proofreading enhances the difference in the mean receptor occupancy between different ligands, thus potentially enabling better discrimination. On the other hand, proofreading also attenuates the signal, increasing the relative magnitude of noise in the downstream signal. This 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 molecular affinity of ligands. Our analysis reveals that proofreading typically worsens ligand resolution which decreases with the number of proofreading steps under most commonly considered conditions. This contrasts with the usual notion that kinetic proofreading universally improves ligand discrimination with additional proofreading steps. Our results are consistent across a variety of different proofreading schemes, 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 kinetic proofreading schemes such as multiplexing and combinatorial encoding in multi-ligand/multi-output pathways.

Competition is ubiquitous in microbial communities, shaping both their spatial and temporal structure and composition. Many classic minimal models, 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 a population. Informed by recent experimental studies of cellular competition in confined spaces, we extend the Moran model to explicitly incorporate spatial exclusion through mechanical interactions among cells within a one-dimensional, open microchannel. The results of our spatial exclusion model differ significantly from those of its classical counterpart. The fixation/extinction probability of a species sharply depends on the species’ initial relative abundance, and the mean time to fixation is greatly accelerated, scaling logarithmically, rather than algebraically, with the system size. In non-neutral cases, spatial exclusion tends to attenuate the effects of fitness differences on the probability of fixation, and the fixation times increase as the relative fitness differences between species increase. Successful fixation by invasive species, whether through mutation or immigration, are also less probable on average than in the Moran model. Surprisingly, in the spatial exclusion model, successful fixations occur on average more rapidly in longer channels. The mean time to fixation heuristically arises from the boundary between populations performing either quasi-neutral diffusion, near a semi-stable fixed point, or 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 ecosystems where spatial exclusion is central to the competition, such as in organized biofilms or intestinal crypts. The results may be broadly applied to any system displaying tug-of-war type dynamics with a region of quasi-neutral diffusion centered around regions of deterministic population collapse.Author summaryCompetition for territory between different species has far reaching consequences for the diversity and fate of bacterial communities. In this study, we theoretically and computationally study the competitive dynamics of two bacterial populations competing for space in confined environments. The model we develop extends classical models that have served as paradigms for understanding competitive dynamics but did not explicitly include spatial exclusion. We find that spatial effects drastically change the probability of one species successfully outcompeting the other and accelerates the mean time it takes for a species to exclude the other from the environment. In comparison to the predictions of population models that neglect spatial exclusion, species with higher selective advantages are less heavily favoured to outcompete their rival species. Moreover, spatial exclusion influences the success of an invasive species taking over a densely populated community. Compared to classical well-mixed models, there is a reduction in the effectiveness of an invaders fitness advantage at improving the chances of taking over the population. Our results show that spatial exclusion has rich and unexpected repercussions on species dominance and the long-time composition of populations. These must be considered when trying to understand complex bacterial ecosystems such as biofilms and intestinal flora.

Structure, composition and stability of ecological populations are shaped by the inter- and intra-species interactions within these communities. It remains to be fully understood how the interplay of these interactions with other factors, such as immigration, control the structure, 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 multi-species ecological communities that incorporates competition, immigration and demographic noise. We find that the complete phase diagram exhibits rich behavior with multiple regimes that go beyond the classical 'niche' and 'neutral' regimes, extending and modifying the 'neutral-like' or 'niche-like' dichotomy. In particular, we observe novel 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 they 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., Comment: Main: 13 pages, 5 figures. Supplementary: 12 pages, 6 figures

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.

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.

Nuclear pore complexes (NPCs) discriminate nonspecific macromolecules from importin and exportin receptors, collectively termed “karyopherins” (Kaps), that mediate nucleocytoplasmic transport. This selective barrier function is attributed to the behavior of intrinsically disordered phenylalanine-glycine nucleoporins (FG Nups) that guard the NPC channel. However, NPCs in vivo are typically enriched with different Kaps, and how they impact the NPC barrier remains unknown. Here, we show that two major Kaps, importinβ1/karyopherinβ1 (Kapβ1) and exportin 1/chromosomal maintenance 1 (CRM1), are required to fortify NPC barrier function in vivo. Their enrichment at the NPC is sustained by promiscuous binding interactions with the FG Nups, which enable CRM1 to compensate for the loss of Kapβ1 as a means to maintain NPC barrier function. However, such a compensatory mechanism is constrained by the cellular abundances and different binding kinetics for each respective Kap, as evidenced for importin-5. Consequently, we find that NPC malfunction and nucleocytoplasmic leakage result from poor Kap enrichment.

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.

To perform their functions in the environment, and in cell collectives, living cells require sensing of external molecular environment via cell surface receptors. In recent years, physical approaches have provided important insights into the problems of receptor sensing and recognition. Puzzlingly, in many contexts, cells can perform accurate, specific and sensitive of discrimination of receptor ligands in the presence of high levels of non-specific competition and molecular noise. In the first part, we review several approaches to accurate ligand concentration sensing in the presence of non-specific ligands based on Berg-Purcell theory. In the second part, we review extensions of Kinetic Proofreading models applied to specificity and sensitivity of TCR signaling and its ability to filter out non-specific ligands. We further discuss how the connections between abstract physical approaches and the more detailed molecular models provide insights into the general principles of accuracy, specificity, sensitivity, and noise filtering in receptor signaling pathways.

The Type I Interferon family of cytokines all act through the same cell surface receptor and induce phosphorylation of the same subset of response regulators of the STAT family. Despite their shared receptor, different Type I Interferons have different functions during immune response to infection. In particular, they differ in the potency of their induced anti-viral and anti-proliferative responses in target cells. It remains not fully understood how these functional differences can arise in a ligand-specific manner both at the level of STAT phosphorylation and the downstream function. We use a minimal computational model of Type I Interferon signaling, focusing on Interferon-α and Interferon-β. We validate the model with quantitative experimental data to identify the key determinants of specificity and functional plasticity in Type I Interferon signaling. We investigate different mechanisms of signal discrimination, and how multiple system components such as binding affinity, receptor expression levels and their variability, receptor internalization, short-term negative feedback by SOCS1 protein, and differential receptor expression play together to ensure ligand specificity on the level of STAT phosphorylation. Based on these results, we propose phenomenological functional mappings from STAT activation to downstream anti-viral and anti-proliferative activity to investigate differential signal processing steps downstream of STAT phosphorylation. We find that the negative feedback by the protein USP18, which enhances differences in signaling between Interferons via ligand-dependent refractoriness, can give rise to functional plasticity in Interferon-α and Interferon-β signaling, and explore other factors that control functional plasticity. Beyond Type I Interferon signaling, our results have a broad applicability to questions of signaling specificity and functional plasticity in signaling systems with multiple ligands acting through a bottleneck of a small number of shared receptors.

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.

Nuclear pore complex (NPC) is a biomolecular "nanomachine" that controls nucleocytoplasmic transport in eukaryotic cells. The key component of the functional architecture of the NPC is the assembly of intrinsically disordered proteins that line its passageway and play a central role in the NPC transport mechanism. Due to paucity of experimental methods capable to directly probe the morphology of this assembly in intact NPCs, much of our knowledge about its properties derives from in vitro experiments augmented by theoretical and computational modeling. I review the major insights into the biophysics of the assemblies of the intrinsically disordered proteins of the NPC arising from the theoretical analysis of the recent in vitro experimental results, with the emphasis on the phase separation and aggregation phenomena.

Living cells sense their environment through the binding of extra-cellular molecular ligands to cell surface receptors. Puzzlingly, vast numbers of signaling pathways exhibit a high degree of cross talk between different signals whereby different ligands act through the same receptor or shared components downstream. It remains unclear how a cell can accurately process information from the environment in such cross-wired pathways. We show that a feature which commonly accompanies cross talk - signaling pleiotropy (the ability of a receptor to produce multiple outputs) - offers a solution to the cross talk problem. In a minimal model we show that a single pleiotropic receptor can simultaneously identify and accurately sense the concentrations of arbitrary unknown ligands present individually or in a mixture. We calculate the fundamental limits of the signaling specificity and accuracy of such signaling schemes. The model serves as an elementary "building block" towards understanding more complex cross-wired receptor-ligand signaling networks.

The local microenvironment of a tumor plays an important and commonly observed role in cancer development and progression. Dynamic changes in the tissue microenvironment are thought to epigenetically disrupt healthy cellular phenotypes and drive cancer incidence. Despite the experimental work in this area there are no conceptual models to understand the interplay between the epigenetic dysregulation in the microenvironment of early tumors and the appearance of cancer driver mutations. Here, we develop a minimal model of the tissue microenvironment which considers three interacting subpopulations: healthy, phenotypically dysregulated, and mutated cancer cells. Healthy cells can epigenetically (reversibly) transition to the dysregulated phenotype, and from there to the cancer state. The epigenetic transition rates of noncancer cells can be influenced by the number of cancer cells in the microenvironment (termed microenvironment feedback). Our model delineates the regime in which microenvironment feedback accelerates the rate of cancer initiation. In addition, the model shows when and how microenvironment feedback may inhibit cancer progression. We discuss how our framework may provide resolution to some of the puzzling experimental observations of slow cancer progression.

In the nuclear pore complex (NPC), 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. While such interactions can be modelled at different levels of coarse graining,in-vitroexperimental data have been quantitatively described by minimal models that describe FG Nups as cohesive homogeneous polymers and NTRs as uniformly cohesive spheres, where 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 non-cohesive polymer units, and at the NTR surface. Here, we develop computational and analytical models that do take into account such heterogeneity at a level of minimal complexity, and compare them to experimental data on single-molecule interactions between FG Nups and NTRs. Overall, we find that the heterogeneous nature of FG Nups and NTRs plays a minor role for their equilibrium binding properties, but is of significance when it comes to (un)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.

Stochastic biochemical and transport processes have various final outcomes, and they can be viewed as dynamic systems with multiple exits. Many current theoretical studies, however, typically consider only a single time scale for each specific outcome, effectively corresponding to a single-exit process and assuming the independence of each exit process. However, the presence of other exits influences the statistical properties and dynamics measured at any specific exit. Here, we present theoretical arguments to explicitly show the existence of different time scales, such as mean exit times and inverse exit fluxes, for dynamic processes with multiple exits. This implies that the statistics of any specific exit dynamics cannot be considered without taking into account the presence of other exits. Several illustrative examples are described in detail using analytical calculations, mean-field estimates, and kinetic Monte Carlo computer simulations. The underlying microscopic mechanisms for the existence of different time scales are discussed. The results are relevant for understanding the mechanisms of various biological, chemical, and industrial processes, including transport through channels and pores.

Nucleocytoplasmic transport is tightly regulated by the nuclear pore complex (NPC). Among the thousands of molecules that cross the NPC, even very large (>15 nm) cargoes such as pathogens, mRNAs and pre-ribosomes can pass the NPC intact. For these cargoes, there is little quantitative understanding of the requirements for their nuclear import, especially the role of multivalent binding to transport receptors via nuclear localisation sequences (NLSs) and the effect of size on import efficiency. Here, we assayed nuclear import kinetics of 30 large cargo models based on four capsid-like particles in the size range of 17–36 nm, with tuneable numbers of up to 240 NLSs. We show that the requirements for nuclear transport can be recapitulated by a simple two-parameter biophysical model that correlates the import flux with the energetics of large cargo transport through the NPC. Together, our results reveal key molecular determinants of large cargo import in cells., eLife digest Eukaryotes, such as animals, plants and fungi, store the genetic material within their cells inside a specific compartment called the nucleus. Surrounding the nucleus is a protective membrane which molecules must pass across in order to reach the cell’s DNA. Straddling the membrane are nuclear pore complexes, or NPCs for short, which act as the gatekeepers to the nucleus, shuttling thousands of different molecules back and forth whilst restricting access to others. Large cargoes need to have specific markers on their surface called nuclear localization signals in order to be transported by NPCs. Certain transporter proteins help the NPC carry large molecules across the membrane by binding to these signals. This generates the energy needed to overcome the barrier of transporting it across the membrane. Some viruses have nuclear localization signals of their own, which can exploit this transport system; these signals allow the virus to enter the nucleus and hijack the genetic machinery of the cell. It has been suggested that viruses have multiple copies of these surface signals to improve their chances of reaching the nucleus. However, it remained unclear how the number of nuclear localization signals affects the transport of large molecules into the nucleus. To answer this question, Paci et al. engineered a range of different sized particles derived from viral structures which had varying numbers of nuclear localization signals on their surface. These particles were inserted into human cell lines grown in the laboratory, and imaged to see how they were transported into the nucleus. The rate of nuclear transport was then measured for each particle, and this data was used to create a mathematical model. Paci et al. found that the larger the cargo, the more nuclear localization signals it needed to be efficiently transported across the membrane into the nucleus. This is because inserting big cargoes into the NPC requires more energy. Therefore, by increasing the number of surface signals transporter proteins can bind to, larger molecules are able to interact with the NPC and generate the energy required for crossing. These findings improve our current understanding of how nuclear transport could be hijacked by viruses. It could also help scientists who are developing targeted nanoparticles to deliver therapies for genetic conditions to the nucleus.

Unlike the well defined structures of classical natively folded proteins, Intrinsically Disordered Proteins (IDP) and Intrinsically Disordered Regions (IDR) 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, dynamics, and function. Multiple experimental and theoretical evidence points in many cases to the overall importance of the general properties of the amino acid sequence of the IPDs rather than their precise atomistic details. However, while different experimental techniques can probe aspects of the IDP conformations, often different techniques or conditions offer seemingly contradictory results. Using coarse-grained polymer models informed by experimental observations, we investigate the effects of several key variables on the dimensions and the dynamics of IDPs. The coarse-grained simulations are in a good agreement with the results of atomistic MD. 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 identify the conditions that allow mapping of highly heterogeneous sequences of IDPs onto averaged minimal polymer models. We discuss the implications of these results for the interpretation of the recent experimental measurements, and for further development of appropriate mesoscopic models of IDPs.

A significant challenge to delivering therapeutic doses of nanoparticles to targeted disease sites is the fact that most nanoparticles become trapped in the liver. Liver-resident macrophages, or Kupffer cells, are key cells in the hepatic sequestration of nanoparticles. However, the precise role that the macrophage phenotype plays in nanoparticle uptake is unknown. Here, we show that the human macrophage phenotype modulates hard nanoparticle uptake. Using gold nanoparticles, we examined uptake by human monocyte-derived macrophages that had been driven to a "regulatory" M2 phenotype or an "inflammatory" M1 phenotype and found that M2-type macrophages preferentially take up nanoparticles, with a clear hierarchy among the subtypes (M2c > M2 > M2a > M2b > M1). We also found that stimuli such as LPS/IFN-γ rather than with more "regulatory" stimuli such as TGF-β/IL-10 reduce per cell macrophage nanoparticle uptake by an average of 40%. Primary human Kupffer cells were found to display heterogeneous expression of M1 and M2 markers, and Kupffer cells expressing higher levels of M2 markers (CD163) take up significantly more nanoparticles than Kupffer cells expressing lower levels of surface CD163. Our results demonstrate that hepatic inflammatory microenvironments should be considered when studying liver sequestration of nanoparticles, and that modifying the hepatic microenvironment might offer a tool for enhancing or decreasing this sequestration. Our findings also suggest that models examining the nanoparticle/macrophage interaction should include studies with primary tissue macrophages.

Synergistic and antagonistic interactions in multi-species populations - such as resource sharing and competition - result in remarkably diverse behaviors in populations of interacting cells, such as in soil or human microbiomes, or clonal competition in cancer. The degree of inter- and intra-specific interaction can often be quantified through the notion of an ecological "niche". Typically, weakly interacting species that occupy largely distinct niches result in stable mixed populations, while strong interactions and competition for the same niche results in rapid extinctions of some species and fixations of others. We investigate the transition of a deterministically stable mixed population to a stochasticity-induced fixation as a function of the niche overlap between the two species. We also investigate the effect of the niche overlap on the population stability with respect to external invasions. Our results have important implications for a number of experimental systems., 32 pages, 12 figures

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 dominant mechanism of nanoparticle entry into solid tumours has now been shown to be an active trans-endothelial pathway rather than the currently established passive transport via inter-endothelial gaps.

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.

Characterization of the interactions between nanosize ligands and polymeric substrates is important for predictive design of nanomaterials and in biophysical applications. The multivalent nature of the polymer–nanoparticle interaction and the dynamics of multiple internal conformations of the polymer chains makes it difficult to infer microscopic interactions from macroscopic binding assays. Using coarse-grained simulations, we estimate the free energy of binding between a nanoparticle and a surface-grafted polymeric substrate as a function of pertinent parameters such as polymer chain length, nanoparticle size, and microscopic polymer–nanoparticle attraction. We also investigate how the presence of the nanoparticle affects the internal configurations of the polymeric substrate, and estimate the entropic cost of binding. The results have important implications for the understanding of complex macromolecular assemblies.

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.

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.

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.

Super-resolved localization microscopy (SLM) has the potential to serve as an accurate, singlecell 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 SLM 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 (CV) then, for the number of molecules M estimated from a given number of blinks B, scales like , 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.

Nuclear Pore Complexes (NPCs) are key cellular transporter that control nucleocytoplasmic transport in eukaryotic cells, but its transport mechanism is still not understood. The centerpiece of NPC transport is the assembly of intrinsically disordered polypeptides, known as FG nucleoporins, lining its passageway. Their conformations and collective dynamics during transport are difficult to assess in vivo. In vitro investigations provide partially conflicting results, lending support to different models of transport, which invoke various conformational transitions of the FG nucleoporins induced by the cargo-carrying transport proteins. We show that the spatial organization of FG nucleoporin assemblies with the transport proteins can be understood within a first principles biophysical model with a minimal number of key physical variables, such as the average protein interaction strengths and spatial densities. These results address some of the outstanding controversies and suggest how molecularly divergent NPCs in different species can perform essentially the same function. DOI: http://dx.doi.org/10.7554/eLife.10785.001, eLife digest Animal, plant and fungal cells contain a structure called the nucleus, inside which the genetic material of the cell is stored. For the cell to work properly, certain proteins and other molecules need to be able to enter and exit the nucleus. This transport is carried out by pore-like molecular “devices” known as Nuclear Pore Complexes, whose architecture and mode of operation are unique among cellular transporters. Nuclear Pore Complexes are charged with a daunting task of deciding which of the hundreds of molecules it conducts per second should go through and which should not. Small molecules can pass freely through Nuclear Pore Complexes. However, larger molecules can only pass through the pore efficiently if they are bound to specialized transport proteins that interact with the proteins – called FG nucleoporins – that line the pore. A unique feature of the FG nucleoporins is that, unlike typical proteins, they do not have a defined three-dimensional structure. Instead, they form a soft and pliable lining inside the Nuclear Pore Complex passageway. Exactly how interacting with transport proteins affects the structure and spatial arrangements of the FG nucleoporins in a way that allows them to control transport is not well understood. This is in part because existing experimental techniques are unable to study the structures of the FG nucleoporins in enough detail to track how they change during transport. The complexity and the diversity of the FG nucleoporins also make them difficult to model in detail. Vovk, Gu et al. have developed a theoretical model that is based on just three basic physical properties of the FG nucleoporins – their flexibility, their ability to interact with each other, and their binding with the transport proteins. Future work can refine the model by incorporating further molecular details about the interactions between FG nucleoporins and transport proteins. The predictions made by this simple model agree well with experimental results in a wide range of situations – from single molecules to complex spatial assemblies. They also explain why some of the experimental results appear to contradict each other and suggest how several outstanding controversies in the field can be reconciled. Because the model invokes only fundamental physical principles of FG nucleoporin assemblies, it shows that some of their general properties do not depend on the exact conditions. In particular, this might shed light on why Nuclear Pore Complexes in different organisms perform essentially the same function, although the details of their molecular structure may differ. This also suggests how the FG nucleoporins can be manipulated to build artificial devices based on the same principles. DOI: http://dx.doi.org/10.7554/eLife.10785.002

Often sharp changes in cellular behavior are triggered by thresholded events, i.e., by the attainment of a threshold value of a relevant cellular or molecular dynamical variable. Since the governing variable itself typically undergoes noisy or stochastic dynamics, there is a corresponding variability in the times when the same change occurs in each cell of a population. This time is called the "first passage" time and the corresponding process is a "first passage" (FP) process, referring to the event when a random variable first passes the threshold value. In this review we first present and elucidate fundamentals of the FP formalism within a unified conceptual framework, which naturally integrates the existing techniques. We then discuss applications thereof, with emphasis on the practical use of FP techniques in biophysical systems. Our focus here is on covering a diverse set of analytical techniques; the number of reviewed biological applications is thus limited, out of necessity. We focus on three specific areas: channel transport; receptor binding and adhesion; and single-cell growth and division.

The ability of cells to sense remotely is critical for a large array of collagen-dependent processes including collective cell migration and cancer cell invasion. However, the impact of the physical properties of collagen, particularly inelasticity, on intercellular communication is not defined. We developed a molecular dynamics model of a fibrous collagen network for examining how inelasticity arising from fiber slippage affects mechanical interactions of adherent cells. Inelastic remodeling of the fibrous pericellular matrix enabled propagation of cell-induced matrix deformations over longer distances (>5 fold) than in linear elastic, or strain-stiffening matrices, which do not exhibit inelastic behavior. Cells generated >10 fold larger forces at distant sites (>5 cell diameters) in matrices that undergo inelastic remodeling compared with linear or nonlinear elastic matrices. The size of the cell-induced matrix deformation fields and the amplitude of forces, which were derived from measurements of force autocorrelation function at remote sites, were proportional to the inelasticity of the fibrous network. This model indicates that inelasticity in the fibrous collagen network enables long-range strain propagation while network stiffening accounts for the transmission of larger forces predicted from linear or nonlinear elastic hydrogels. We conclude that the unusual trait of inelasticity in non-cross-linked collagen arising from fiber slippage, enables long-range mechanosensing that is not observed in synthetic, linear elastic hydrogels or in cross-linked matrices exhibiting nonlinear elasticity.

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.

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.

Polymer-grafted surfaces and channels are increasingly used for the design of responsive materials and sensors due to robust performance and ease of use. Various strategies for the control of the nanoscale morphologies of such materials and devices are being tested. Entropic repulsion between the polymer chains in a grafted brush of sufficient density causes the chains to extend in the direction perpendicular to the grafting surface in comparison to the position of unattached polymers. When nanoparticles having attractive interactions with the polymers are introduced into the solvent, these nanoparticles tend to infiltrate into the brush and reduce its extension. Under certain conditions, a sharp reduction in brush height extension can occur over a narrow range of nanoparticle concentrations in solution. We describe a way of controlling transport through polymer-functionalized nanochannels with nanoparticle additives, relying on the physics of nanoparticles and polymer brushes under confinement, and we suggest a blueprint for the creation of a tunable nanovalve. The nanovalve is modeled as a cylinder with a polymer brush grafted on its inside surface. Brush properties such as the chain length and the grafting density are chosen so that the brush chains extend into the center of the cylinder in the absence of nanoparticles, occluding the flux of analyte molecules through the pore. When nanoparticles that are attracted to the polymers are introduced into solution, they infiltrate into the brush and partially collapse it against the cylindrical grafting surface, opening space in the center of the cylinder through which analyte molecules can flow. The operation of such a nanovalve is analyzed via self-consistent field theory calculations in the strong-stretching approximation. Self-consistent field analysis is supported by Langevin dynamics simulations of the underlying coarse-grained model of the polymer-nanoparticle system.

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.

We predict the thermodynamic and structural behavior of solutions of long cross-linked filaments. We find that at the mean field level, the entropy of self-assembled junctions induces an effective attraction between the filaments that can result in a phase separation into a connected network, in equilibrium with a dilute phase. A connected network can also be formed in a non-thermodynamic transition upon increase of the chain, or cross link density, or with decreasing temperature. For rigid rods, at low temperatures, we predict a transition from an isotropic network, to anisotropic bundles of rods tightly bound by cross links, that is triggered by the interplay between the configurational entropy of the cross-link distribution among the rods, and the rotational and translational entropy of the rods., Comment: typos and graphics corrected; 6 pages 1 figure

Self-assembly in soft-matter systems often results in the formation of locally cylindrical or chain-like structures. We review the theory of these systems whose large-scale structure and properties depend on whether the chains are finite, with end-caps or join to form junctions that result in networks. Physical examples discussed here include physical gels, wormlike micelles, dipolar fluids and microemulsions. In all these cases, the competition between end-caps and junctions results in an entropic phase separation into junction-rich and junction-poor phases, as recently observed by electron microscopy and seen in computer simulations. A simple model that accounts for these phenomena is reviewed. Extensions of these ideas can be applied to treat network formation and phase separation in a system of telechelic (hydrophobically tipped, hydrophilic) polymers and oil-in-water microemulsions, as observed in recent experiments.

We investigate the short time and short scale dynamics of membrane phases. The dynamics of the two point displacement correlator of the membrane is shown to be dominated by the transverse mean-square displacement of a tagged membrane point and to vary with time t as ∼t2/3. As a result, the structure factor of oriented lamellar phases at nearly perpendicular orientations (mean membrane normal parallel to the wavevector k → ) decays as a stretched exponential S( k → ,t)∼ e −( Γ k z t) 2/3 with Γkz∼(T/κ)1/2(T/η)kz3. For isotropic systems, angular averaging retains the stretched exponential decay, S(k,t)∼e−(Γkt)α, but with α>2/3 and no longer universal. We also find Γk∼kz with z

Nuclear Pore Complex (NPC) is a biological “nano-machine” that controls the macromolecular transport between the cell nucleus and the cytoplasm. It is a remarkable device that combines selectivity with robustness and speed. Unlike many other biological nano-channels, it functions without direct input of metabolic energy and without transitions of the gate from a 'closed' to an 'open' state during transport. The key aspect of transport is the interaction of the cargo-carrying transport factors with the unfolded, natively unstructured proteins that partially occlude the channel of the NPC and its nuclear and cytoplasmic exits.Mechanistic understanding of the transport through the Nuclear Pore Complex, and in particular its selectivity, is still lacking. Conformational transitions of the unfolded proteins of the NPC, induced by the transport factors, have been hypothesized to underlie the transport mechanism and its selectivity. These conformational changes are hard to access in vivo; they have been investigated in vitro, generating apparently contradictory results.We have investigated the biophysical underpinning of these conformational changes, using computational modeling based on the ideas the ideas of the polymer physics. We show that the differences in the experimentally observed behaviors can be explained by rather general physical factors, such as the attraction strength between the transport factors and the unfolded chains, protein density and the transport factor size. We also show how these general behaviors can be modulated by molecule-specific details, such as the aminoacid sequence and the relative arrangement in space of the charged and hydrophobic residues. Finally, we extend the model into a realistic NPC geometry. These results provide new insights into the fundamental principles of transport through the NPC and the control of the behavior of natively unfolded proteins in general.

We discuss the structure and the interaction of telechelic brushes. We show that the association of functionalized chain ends is capable of giving rise to attractive interactions between telechelic brush-covered surfaces, in contrast to conventional repulsion. Our predictions for the interaction free energy are in agreement with experimental data.

We consider a lamellar phase of bilayer membranes held between two parallel plates and subject to a steady shear. Accounting for the coupling with the shear flow of the short wavelength undulation modes that are responsible for the membrane excess area, we argue that the flow generates an effective force which acts to reduce the excess area. From the viewpoint of the macroscopic lamellar whose geometric dimensions are fixed, this force translates into an effective lateral pressure. At low shear rates $\dot \gamma$ this pressure is balanced by the elastic restoring forces of the lamellar. Above a critical shear rate $\dot \gamma _c \sim d^{ - 5/2} D^{ - 1/2}$ , where d is the interlayer distance and D is the gap spacing, the lamellar buckles into a harmonic shape modulation, and we predict its wavelength λc and amplitude U o. We show that our model is isomorphic to a dilative strain, which is known to induce a similar buckling (undulation) instability. Indeed, at threshold the wavelength is $\lambda _c \sim \sqrt {Dd}$ and is identical in both cases. Using a non-linear analysis, we discuss how the wavelength and amplitude vary with shear rate away from the threshold. For $\dot \gamma \gg \dot \gamma _c$ we find $\lambda _c \sim \dot \gamma ^{ - 1/3}$ and $U_o \sim \dot \gamma ^{2/3}$ . We then focus on the coupling of the buckling modulation itself with the flow, and obtain a criterion for the limit of its stability. Motivated by experiments of D. Roux and coworkers, we assume that at this limit of stability the lamellar breakups into “onion”-like, multilamellar, vesicles. The critical shear rate $\dot \gamma *$ for the formation of onions is predicted to scale as $\dot \gamma * \sim \dot \gamma _c \sim d^{ - 5/2} D^{ - 1/2}$ . The scaling with d is consistent with available experimental data.

The dynamics of flexible polymeric fractals in solutions is discussed using a linearization self-consistent approximation. When hydrodynamic interaction is not screened (Zimm model) we find that the mean square displacement $〈\ensuremath{\Delta}{(t)}^{2}〉$ of a monomer is anomalously increasing with time, $〈\ensuremath{\Delta}(\mathcal{t}{)}^{2}〉D\ensuremath{\sim}{t}^{\ensuremath{\alpha}}$ with a universal exponent $\ensuremath{\alpha}=2/d$ in $d$ dimensions, independent of the fractal ${(d}_{f})$ and spectral dimensions. The viscoelastic modulus behaves as $G(\ensuremath{\omega})\ensuremath{\sim}(i\ensuremath{\omega}{)}^{u},$ with ${u=d}_{f}/d.$ When hydrodynamics is screened (Rouse model) we find $\ensuremath{\alpha}{=2/(2+d}_{f})$ and ${u=d}_{f}{/(2+d}_{f}).$ We conclude that measurements of $\ensuremath{\alpha}=2/d$ indicate unambiguously that the Zimm model is applicable and thus should be correlated with ${u=d}_{f}/d$ in rheology measurements.