Efficiency, selectivity, and robustness of nucleocytoplasmic transport

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.

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

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

Integrative spatiotemporal map of nucleocytoplasmic transport

The Nuclear Pore Complex (NPC) facilitates rapid and selective nucleocytoplasmic transport of molecules as large as ribosomal subunits and viral capsids. It is not clear how key emergent properties of this transport arise from the system components and their interactions. To address this question, we constructed an integrative coarse-grained Brownian dynamics model of transport through a single NPC, followed by coupling it with a kinetic model of Ran-dependent transport in an entire cell. The microscopic model parameters were fitted to reflect experimental data and theoretical information regarding the transport, without making any assumptions about its emergent properties. The resulting reductionist model is validated by reproducing several features of transport not used for its construction, such as the morphology of the central transporter, rates of passive and facilitated diffusion as a function of size and valency, in situ radial distributions of pre-ribosomal subunits, and active transport rates for viral capsids. The model suggests that the NPC functions essentially as a virtual gate whose flexible phenylalanine-glycine (FG) repeat proteins raise an entropy barrier to diffusion through the pore. Importantly, this core functionality is greatly enhanced by several key design features, including 'fuzzy' and transient interactions, multivalency, redundancy in the copy number of FG nucleoporins, exponential coupling of transport kinetics and thermodynamics in accordance with the transition state theory, and coupling to the energy-reliant RanGTP concentration gradient. These design features result in the robust and resilient rate and selectivity of transport for a wide array of cargo ranging from a few kilodaltons to megadaltons in size. By dissecting these features, our model provides a quantitative starting point for rationally modulating the transport system and its artificial mimics.

Counter-Intuitive Features of Particle Dynamics in Nanopores

Using the framework of a continuous diffusion model based on the Smoluchowski equation, we analyze particle dynamics in the confinement of a transmembrane nanopore. We briefly review existing analytical results to highlight consequences of interactions between the channel nanopore and the translocating particles. These interactions are described within a minimalistic approach by lumping together multiple physical forces acting on the particle in the pore into a one-dimensional potential of mean force. Such radical simplification allows us to obtain transparent analytical results, often in a simple algebraic form. While most of our findings are quite intuitive, some of them may seem unexpected and even surprising at first glance. The focus is on five examples: (i) attractive interactions between the particles and the nanopore create a potential well and thus cause the particles to spend more time in the pore but, nevertheless, increase their net flux; (ii) if the potential well-describing particle-pore interaction occupies only a part of the pore length, the mean translocation time is a non-monotonic function of the well length, first increasing and then decreasing with the length; (iii) when a rectangular potential well occupies the entire nanopore, the mean particle residence time in the pore is independent of the particle diffusivity inside the pore and depends only on its diffusivity in the bulk; (iv) although in the presence of a potential bias applied to the nanopore the "downhill" particle flux is higher than the "uphill" one, the mean translocation times and their distributions are identical, i.e., independent of the translocation direction; and (v) fast spontaneous gating affects nanopore selectivity when its characteristic time is comparable to that of the particle transport through the pore.

[Structural and mechanical plasticity of the nuclear pore]

The nuclear pore, which can be seen as the gateway to the cell nucleus, is central to many processes including gene regulation. It is a complex and dynamic structure composed of more than 30 proteins present in multiple copies that allows the selective and directional transport of RNA and proteins. As shown by recent studies, it is able to adapt its overall structure to the state of the cell. These results suggest that the structural and mechanical plasticity of the nuclear pore is important for its function but also in the development of cancer or viral infections.

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.

Bunyaviral N Proteins Localize at RNA Processing Bodies and Stress Granules: The Enigma of Cytoplasmic Sources of Capped RNA for Cap Snatching

Most cytoplasmic-replicating negative-strand RNA viruses (NSVs) initiate genome transcription by cap snatching. The source of host mRNAs from which the cytoplasmic NSVs snatch capped-RNA leader sequences has remained elusive. Earlier reports have pointed towards cytoplasmic-RNA processing bodies (P body, PB), although several questions have remained unsolved. Here, the nucleocapsid (N) protein of plant- and animal-infecting members of the order Bunyavirales, in casu Tomato spotted wilt virus (TSWV), Rice stripe virus (RSV), Sin nombre virus (SNV), Crimean-Congo hemorrhagic fever virus (CCHFV) and Schmallenberg virus (SBV) have been expressed and localized in cells of their respective plant and animal hosts. All N proteins localized to PBs as well as stress granules (SGs), but extensively to docking stages of PB and SG. TSWV and RSV N proteins also co-localized with Ran GTPase-activating protein 2 (RanGAP2), a nucleo-cytoplasmic shuttling factor, in the perinuclear region, and partly in the nucleus when co-expressed with its WPP domain containing a nuclear-localization signal. Upon silencing of PB and SG components individually or concomitantly, replication levels of a TSWV minireplicon, as measured by the expression of a GFP reporter gene, ranged from a 30% reduction to a four-fold increase. Upon the silencing of RanGAP homologs in planta, replication of the TSWV minireplicon was reduced by 75%. During in vivo cap-donor competition experiments, TSWV used transcripts destined to PB and SG, but also functional transcripts engaged in translation. Altogether, the results implicate a more complex situation in which, besides PB, additional cytoplasmic sources are used during transcription/cap snatching of cytoplasmic-replicating and segmented NSVs.

Non-genetic and genetic rewiring underlie adaptation to hypomorphic alleles of an essential gene

Adaptive evolution to cellular stress is a process implicated in a wide range of biological and clinical phenomena. Two major routes of adaptation have been identified: non-genetic changes, which allow expression of different phenotypes in novel environments, and genetic variation achieved by selection of fitter phenotypes. While these processes are broadly accepted, their temporal and epistatic features in the context of cellular evolution and emerging drug resistance are contentious. In this manuscript, we generated hypomorphic alleles of the essential nuclear pore complex (NPC) gene NUP58. By dissecting early and long-term mechanisms of adaptation in independent clones, we observed that early physiological adaptation correlated with transcriptome rewiring and upregulation of genes known to interact with the NPC; long-term adaptation and fitness recovery instead occurred via focal amplification of NUP58 and restoration of mutant protein expression. These data support the concept that early phenotypic plasticity allows later acquisition of genetic adaptations to a specific impairment. We propose this approach as a genetic model to mimic targeted drug therapy in human cells and to dissect mechanisms of adaptation.

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

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

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

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

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.

Stochastically gated diffusion model of selective nuclear transport

Nuclear pore complexes (NPCs) allow the selective exchange of molecules between the cytoplasm and cell nucleus. Although small molecules can diffuse freely through a NPC, the transport of proteins and nucleotides requires association with transport factors (kaps). The latter transiently bind to disordered flexible polymers within the NPC, known collectively as phenylalanine-glycine-nucleoporins (FG-Nups). It has recently been shown that transient binding combined with diffusion in the bound state is a sufficient mechanism for selective transport. However, selectivity is significantly reduced if the mobility of the bound state is too slow. In this paper we formulate the binding-diffusion mechanism of selective transport in terms of a "stochastically gated" diffusion process in which each bound particle undergoes confined diffusion within a subdomain of the NPC. This allows us to make explicit the fact that the diffusion of a particle when bound to a polymer tether is spatially confined rather than simply reduced. We calculate the selectivity of the NPC and explore its dependence on the size of the confinement domains. We then use probabilistic methods to determine the splitting probability and mean first passage time (MFPT) for an individual particle to pass through the pore. Our analysis establishes that spatial confinement can significantly reduce selectivity in a binding-diffusion model, suggesting that other biophysical mechanisms such as interchain transfer are required.

Modeling the nucleoporins that form the hairy pores

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

Different time scales in dynamic systems with multiple outcomes

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.

Molecular determinants of large cargo transport into the nucleus

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.

Impact of Interparticle Interaction on Thermodynamics of Nano-Channel Transport of Two Species

Understanding the function and control of channel transport is of paramount importance for cell physiology and nanotechnology. In particular, if several species are involved, the mechanisms of selectivity, competition, cooperation, pumping, and its modulation need to be understood. What lacks is a rigorous mathematical approach within the framework of stochastic thermodynamics, which explains the impact of interparticle in-channel interactions on the transport properties of the respective species. To achieve this, stochastic channel transport of two species is considered in a model, which different from mean field approaches, explicitly conserves the spatial correlation of the species within the channel by analysis of the stochastic dynamics within a state space, the elements of which are the channel's spatial occupation states. The interparticle interactions determine the stochastic transitions between these states. Local flow and entropy production in this state space reveal the respective particle flows through the channel and the intensity of the Brownian ratchet like rectifying forces, which these species exert mutually on each other, together with its thermodynamic effectiveness and costs. Perfect coupling of transport of the two species is realized by an attractive empty channel and strong repulsive forces between particles of the same species. This confines the state space to a subspace with circular topology, in which the concentration gradients as thermodynamic driving forces act in series, and channel flow of both species becomes equivalent. For opposing concentration gradients, this makes the species with the stronger gradient the driving, positive entropy producing one; the other is driven and produces negative entropy. Gradients equal in magnitude make all flows vanish, and thermodynamic equilibrium occurs. A differential interparticle interaction with less repulsive forces within particles of one species but maintenance of this interaction for the other species adds a bypass path to this circular subspace. On this path, which is not involved in coupling of the two species, a leak flow of the species with less repulsive interparticle interaction emerges, which is directed parallel to its concentration gradient and, hence, produces positive entropy here. Different from the situation with perfect coupling, appropriate strong opposing concentration gradients may simultaneously parallelize the flow of their respective species, which makes each species produce positive entropy. The rectifying potential of the species with the bypass option is diminished. This implies the existence of a gradient of the other species, above which its flow and gradient are parallel for any gradient of the less coupled species. The opposite holds for the less coupled species. Its flow may always be rectified and turned anti-parallel to its gradient by a sufficiently strong opposing gradient of the other one.

Bound-State Diffusion due to Binding to Flexible Polymers in a Selective Biofilter

Selective biofilters are used by cells to control the transport of proteins, nucleic acids, and other macromolecules. Biological filters demonstrate both high specificity and rapid motion or high flux of proteins. In contrast, high flux comes at the expense of selectivity in many synthetic filters. Binding can lead to selective transport in systems in which the bound particle can diffuse, but the mechanisms that lead to bound diffusion remain unclear. Previous theory has proposed a molecular mechanism of bound-state mobility based only on transient binding to flexible polymers. However, this mechanism has not been directly tested in experiments. We demonstrate that bound mobility via tethered diffusion can be engineered into a synthetic gel using protein fragments derived from the nuclear pore complex. The resulting bound-state diffusion is quantitatively consistent with theory. Our results suggest that synthetic biological filters can be designed to take advantage of tethered diffusion to give rapid, selective transport.

Design principles of selective transport through biopolymer barriers

In biological systems, polymeric materials block the movement of some macromolecules while allowing the selective passage of others. In some cases, binding enables selective transport, while in others the most inert particles appear to transit most rapidly. To study the general principles of filtering, we develop a model motivated by features of the nuclear pore complex (NPC) which are highly conserved and could potentially be applied to other biological systems. The NPC allows selective transport of proteins called transport factors, which transiently bind to disordered flexible proteins called phenylalanine-glycine-nucleoporins. While the NPC is tuned for transport factors and their cargo, we show that a single feature is sufficient for selective transport: the bound-state motion resulting from transient binding to flexible filaments. Interchain transfer without unbinding can further improve selectivity, especially for cross-linked chains. We generalize this observation to model nanoparticle transport through mucus and show that bound-state motion accelerates transport of transient nanoparticle application, even with clearance by mucus flow. Our model provides a framework to control binding-induced selective transport in biopolymeric materials.

Enhanced Nucleocytoplasmic Transport due to Competition for Elastic Binding Sites

Nuclear pore complexes (NPCs) control all traffic into and out of the cell nucleus. NPCs are molecular machines that simultaneously achieve high selectivity and high transport rates. The biophysical details of how cargoes rapidly traverse the pore remain unclear but are known to be mediated by interactions between cargo-binding chaperone proteins and natively unstructured nucleoporin proteins containing many phenylalanine-glycine repeats (FG nups) that line the pore's central channel. Here, we propose a specific and detailed physical mechanism for the high speed of nuclear import based on the elasticity of FG nups and on competition between individual chaperone proteins for FG nup binding. We develop a mathematical model to support our proposed mechanism. We suggest that the recycling of nuclear import factors back to the cytoplasm is important for driving high-speed import and predict the existence of an optimal cytoplasmic concentration of cargo for enhancing the rate of import over a purely diffusive rate.

Polymer translocation through a hairy channel mimicking the inner plug of a nuclear pore complex

A microscopic transport model of a polymer translocating through a nuclear pore complex (NPC) is presented based on self-consistent field theory (SCFT), with the NPC and its nucleoporins mimicked by a hairy channel. Multiple cell environment effects (electrolyte effect, excluded volume effect, NPC drag effect, and hydrophobic effect) are all considered in this hairy channel model. The influence of various parameters (polymer chain length, length of NPC, strength of hydrophobic effect, and excluded volume effect) on translocation time is studied through theoretical analysis and numerical calculation. Numerical simulation results show that an area of low nucleoporin number density exists in the NPC, which facilitates the translocation of the polymer. The results also show that the translocation time curves with increasing NPC length and polymer charge number are concave. In addition, there are critical values for NPC length and polymer charge number for which the translocation time has a minimal value. The translocation time decreases with the increasing strength of the hydrophobic effect and excluded volume effect.

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.

Interactions between a fluctuating polymer barrier and transport factors together with enzyme action are sufficient for selective and rapid transport through the nuclear pore complex

The nuclear pore complex, the only pathway for transport between the nucleus and cytoplasm, functions as a highly selective gate that blocks nonspecific macromolecules while allowing the rapid transport of tagged [transport factor (TF) bound] cargo up to an order of magnitude larger. The mechanism of this gate's operation is not yet fully understood and progress has been primarily hindered by the inherent complexity and multiscale nature of the problem. One needs to consider the hundreds of disordered proteins (phenylalanine glycine nucleoporins or FG nups) lining the pore, as well as their overall architecture and dynamics at the microsecond scale, while also accounting for transport at the millisecond scale across the entire pore. Here we formulate an approach that addresses transport properties over a large range of length and time scales. We do this by incorporating microscopic biophysical details, such as charge and specific TF-FG nup interactions, to compute the free energy landscape encountered by the cargo. We connect this to macroscopic transport by treating cargo translocation as a stochastic barrier crossing process and computing the current and the translocation time. We then identify distinct transport regimes (fast permeable, slow permeable, and impermeable) determined by the cargo size, TF affinity for FG nups, and the activity of the enzymes that cleave TFs from cargo. Our results, therefore provide an integrated picture of transport through the NPC, while highlighting how FG nup interactions with TFs and enzyme activity cooperate to produce selectivity and efficiency.

The exact phase diagram for a class of open multispecies asymmetric exclusion processes

The asymmetric exclusion process is an idealised stochastic model of transport, whose exact solution has given important insight into a general theory of nonequilibrium statistical physics. In this work, we consider a totally asymmetric exclusion process with multiple species of particles on a one-dimensional lattice in contact with reservoirs. We derive the exact nonequilibrium phase diagram for the system in the long time limit. We find two new phenomena in certain regions of the phase diagram: dynamical expulsion when the density of a species becomes zero throughout the system, and dynamical localisation when the density of a species is nonzero only within an interval far from the boundaries. We give a complete explanation of the macroscopic features of the phase diagram using what we call nested fat shocks.

A coarse-grained computational model of the nuclear pore complex predicts Phe-Gly nucleoporin dynamics

The phenylalanine-glycine–repeat nucleoporins are essential for transport through the nuclear pore complex. Pulupa et al. observe reptation of these nucleoporins on a physiological timescale in coarse-grained computational simulations.

The phenylalanine-glycine–repeat nucleoporins (FG-Nups), which occupy the lumen of the nuclear pore complex (NPC), are critical for transport between the nucleus and cytosol. Although NPCs differ in composition across species, they are largely conserved in organization and function. Transport through the pore is on the millisecond timescale. Here, to explore the dynamics of nucleoporins on this timescale, we use coarse-grained computational simulations. These simulations generate predictions that can be experimentally tested to distinguish between proposed mechanisms of transport. Our model reflects the conserved structure of the NPC, in which FG-Nup filaments extend into the lumen and anchor along the interior of the channel. The lengths of the filaments in our model are based on the known characteristics of yeast FG-Nups. The FG-repeat sites also bind to each other, and we vary this association over several orders of magnitude and run 100-ms simulations for each value. The autocorrelation functions of the orientation of the simulated FG-Nups are compared with in vivo anisotropy data. We observe that FG-Nups reptate back and forth through the NPC at timescales commensurate with experimental measurements of the speed of cargo transport through the NPC. Our results are consistent with models of transport where FG-Nup filaments are free to move across the central channel of the NPC, possibly informing how cargo might transverse the NPC.

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.

Cooperative Interactions between Different Classes of Disordered Proteins Play a Functional Role in the Nuclear Pore Complex of Baker's Yeast

Nucleocytoplasmic transport is highly selective, efficient, and is regulated by a poorly understood mechanism involving hundreds of disordered FG nucleoporin proteins (FG nups) lining the inside wall of the nuclear pore complex (NPC). Previous research has concluded that FG nups in Baker's yeast (S. cerevisiae) are present in a bimodal distribution, with the "Forest Model" classifying FG nups as either di-block polymer like "trees" or single-block polymer like "shrubs". Using a combination of coarse-grained modeling and polymer brush modeling, the function of the di-block FG nups has previously been hypothesized in the Di-block Copolymer Brush Gate (DCBG) model to form a higher-order polymer brush architecture which can open and close to regulate transport across the NPC. In this manuscript we work to extend the original DCBG model by first performing coarse grained simulations of the single-block FG nups which confirm that they have a single block polymer structure rather than the di-block structure of tree nups. Our molecular simulations also demonstrate that these single-block FG nups are likely cohesive, compact, collapsed coil polymers, implying that these FG nups are generally localized to their grafting location within the NPC. We find that adding a layer of single-block FG nups to the DCBG model increases the range of cargo sizes which are able to translocate the pore through a cooperative effect involving single-block and di-block FG nups. This effect can explain the puzzling connection between single-block FG nup deletion mutants in S. cerevisiae and the resulting failure of certain large cargo transport through the NPC. Facilitation of large cargo transport via single-block and di-block FG nup cooperativity in the nuclear pore could provide a model mechanism for designing future biomimetic pores of greater applicability.

Dependence of the Enzymatic Velocity on the Substrate Dissociation Rate

Enzymes are biological catalysts that play a fundamental role in all living systems by supporting the selectivity and the speed for almost all cellular processes. While the general principles of enzyme functioning are known, the specific details of how they work at the microscopic level are not always available. Simple Michaelis-Menten kinetics assumes that the enzyme-substrate complex has only one conformation that decays as a single exponential. As a consequence, the enzymatic velocity decreases as the dissociation (off) rate constant of the complex increases. Recently, Reuveni et al. [ Proc. Natl. Acad. Sci. USA 2014 , 111 , 4391 - 4396 ] showed that it is possible for the enzymatic velocity to increase when the off rate becomes higher, if the enzyme-substrate complex has many conformations which dissociate with the same off rate constant. This was done using formal mathematical arguments, without specifying the nature of the dynamics of the enzyme-substrate complex. In order to provide a physical basis for this unexpected result, we derive an analytical expression for the enzymatic velocity assuming that the enzyme-substrate complex has multiple states and its conformational dynamics is described by rate equations with arbitrary rate constants. By applying our formalism to a complex with two conformations, we show that the unexpected off rate dependence of the velocity can be readily understood: If one of the conformations is unproductive, the system can escape from this "trap" by dissociating, thereby giving the enzyme another chance to form the productive enzyme-substrate complex. We also demonstrate that the nonmonotonic off rate dependence of the enzymatic velocity is possible not only when all off rate constants are identical, but even when they are different. We show that for typical experimentally determined rate constants, the nonmonotonic off rate dependence can occur for micromolar substrate concentrations. Finally, we discuss the relation of this work to the problem of optimizing the flux through singly occupied membrane channels and transporters.

Simple rules for passive diffusion through the nuclear pore complex

Passive macromolecular diffusion through nuclear pore complexes is thought to decrease dramatically beyond ∼40 kD. Using time-resolved fluorescence microscopy and Brownian dynamics simulations, Timney et al. show that this barrier is in fact much softer, decreasing along a continuum.

Passive macromolecular diffusion through nuclear pore complexes (NPCs) is thought to decrease dramatically beyond a 30–60-kD size threshold. Using thousands of independent time-resolved fluorescence microscopy measurements in vivo, we show that the NPC lacks such a firm size threshold; instead, it forms a soft barrier to passive diffusion that intensifies gradually with increasing molecular mass in both the wild-type and mutant strains with various subsets of phenylalanine-glycine (FG) domains and different levels of baseline passive permeability. Brownian dynamics simulations replicate these findings and indicate that the soft barrier results from the highly dynamic FG repeat domains and the diffusing macromolecules mutually constraining and competing for available volume in the interior of the NPC, setting up entropic repulsion forces. We found that FG domains with exceptionally high net charge and low hydropathy near the cytoplasmic end of the central channel contribute more strongly to obstruction of passive diffusion than to facilitated transport, revealing a compartmentalized functional arrangement within the NPC.

The selective permeability barrier in the nuclear pore complex

The nuclear pore complex (NPC) mediates the shuttle transport of macromolecules between the nucleus and cytoplasm in eukaryotic cells. The permeability barrier formed by intrinsically disordered phenylalanine-glycine-rich nucleoporins (FG-Nups) in the NPC functions as the critical selective control for nucleocytoplasmic transport. Signal-independent small molecules (< 40 kDa) passively diffuse through the pore, but passage of large cargo molecules is inhibited unless they are chaperoned by nuclear transport receptors (NTRs). NTRs are capable of interacting with FG-Nups and guide the cargos to cross the barrier by facilitated diffusion. The native conformation of the FG-Nups permeability barrier and the competition among multiple NTRs interacting with this barrier in the native NPCs are the 2 core questions still being highly debated in the field. Recently, we applied high-speed super-resolution fluorescence microscopy to map out the natural structure of the FG-Nups barrier and determined the competition among multiple NTRs as they interact with the barrier in the native NPCs. In this extra-view article, we will review the current understanding in the configuration and function of FG-Nups barrier and highlight the new evidence obtained recently to answer the core questions in nucleocytoplasmic transport.

Simple biophysics underpins collective conformations of the intrinsically disordered proteins of the Nuclear Pore Complex

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

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

Deciphering the Structure and Function of Nuclear Pores Using Single-Molecule Fluorescence Approaches

Due to its central role in macromolecular trafficking and nucleocytoplasmic information transfer, the nuclear pore complex (NPC) has been studied in great detail using a wide spectrum of methods. Consequently, many aspects of its architecture, general function, and role in the life cycle of a cell are well understood. Over the last decade, fluorescence microscopy methods have enabled the real-time visualization of single molecules interacting with and transiting through the NPC, allowing novel questions to be examined with nanometer precision. While initial single-molecule studies focused primarily on import pathways using permeabilized cells, it has recently proven feasible to investigate the export of mRNAs in living cells. Single-molecule assays can address questions that are difficult or impossible to answer by other means, yet the complexity of nucleocytoplasmic transport requires that interpretation be based on a firm genetic, biochemical, and structural foundation. Moreover, conceptually simple single-molecule experiments remain technically challenging, particularly with regard to signal intensity, signal-to-noise ratio, and the analysis of noise, stochasticity, and precision. We discuss nuclear transport issues recently addressed by single-molecule microscopy, evaluate the limits of existing assays and data, and identify open questions for future studies. We expect that single-molecule fluorescence approaches will continue to be applied to outstanding nucleocytoplasmic transport questions, and that the approaches developed for NPC studies are extendable to additional complex systems and pathways within cells.

Evolutionarily Conserved Sequence Features Regulate the Formation of the FG Network at the Center of the Nuclear Pore Complex

The nuclear pore complex (NPC) is the portal for bidirectional transportation of cargos between the nucleus and the cytoplasm. While most of the structural elements of the NPC, i.e. nucleoporins (Nups), are well characterized, the exact transport mechanism is still under much debate. Many of the functional Nups are rich in phenylalanine-glycine (FG) repeats and are believed to play the key role in nucleocytoplasmic transport. We present a bioinformatics study conducted on more than a thousand FG Nups across 252 species. Our results reveal the regulatory role of polar residues and specific sequences of charged residues, named 'like charge regions' (LCRs), in the formation of the FG network at the center of the NPC. Positively charged LCRs prepare the environment for negatively charged cargo complexes and regulate the size of the FG network. The low number density of charged residues in these regions prevents FG domains from forming a relaxed coil structure. Our results highlight the significant role of polar interactions in FG network formation at the center of the NPC and demonstrate that the specific localization of LCRs, FG motifs, charged, and polar residues regulate the formation of the FG network at the center of the NPC.

Dissecting in vivo steady-state dynamics of karyopherin-dependent nuclear transport

The steady-state dynamics of karyopherin-dependent nuclear transport in a living cell is examined. The kinetic model established by a number of experimentally obtained parameters reveals how each step of the transport system contributes to maintaining steady-state cargo gradient and fluxes across the nuclear envelope.

Karyopherin-dependent molecular transport through the nuclear pore complex is maintained by constant recycling pathways of karyopherins coupled with the Ran-dependent cargo catch-and-release mechanism. Although many studies have revealed the bidirectional dynamics of karyopherins, the entire kinetics of the steady-state dynamics of karyopherin and cargo is still not fully understood. In this study, we used fluorescence recovery after photobleaching and fluorescence loss in photobleaching on live cells to provide convincing in vivo proof that karyopherin-mediated nucleocytoplasmic transport of cargoes is bidirectional. Continuous photobleaching of the cytoplasm of live cells expressing NLS cargoes led to progressive decrease of nuclear fluorescence signals. In addition, experimentally obtained kinetic parameters of karyopherin complexes were used to establish a kinetic model to explain the entire cargo import and export transport cycles facilitated by importin β. The results strongly indicate that constant shuttling of karyopherins, either free or bound to cargo, ensures proper balancing of nucleocytoplasmic distribution of cargoes and establishes effective regulation of cargo dynamics by RanGTP.

Importin-β modulates the permeability of the nuclear pore complex in a Ran-dependent manner

Soluble karyopherins of the importin-β (impβ) family use RanGTP to transport cargos directionally through the nuclear pore complex (NPC). Whether impβ or RanGTP regulate the permeability of the NPC itself has been unknown. In this study, we identify a stable pool of impβ at the NPC. A subpopulation of this pool is rapidly turned-over by RanGTP, likely at Nup153. Impβ, but not transportin-1 (TRN1), alters the pore's permeability in a Ran-dependent manner, suggesting that impβ is a functional component of the NPC. Upon reduction of Nup153 levels, inert cargos more readily equilibrate across the NPC yet active transport is impaired. When purified impβ or TRN1 are mixed with Nup153 in vitro, higher-order, multivalent complexes form. RanGTP dissolves the impβ•Nup153 complexes but not those of TRN1•Nup153. We propose that impβ and Nup153 interact at the NPC's nuclear face to form a Ran-regulated mesh that modulates NPC permeability.

DOI:http://dx.doi.org/10.7554/eLife.04052.001

In our cells, genetic material is contained within the nucleus, which is separated from the rest of the cell by a double-layered membrane called the nuclear envelope. Within this membrane there are pores that allow proteins and other molecules to enter and exit the nucleus.

Small molecules can pass through these pores unaided, which is known as ‘passive’ transport. However, larger cargos need help from transport receptor proteins in a process called ‘active’ transport. Large cargos bind to transport receptors, such as importin-β, in the cytoplasm and are then guided through the pore. Once the cargo and importin-β are inside the nucleus, a protein called RanGTP binds to importin-β to release the cargo.

It is thought that importin-β and RanGTP are only important for the active transport of cargo. Here, Lowe et al. studied how importin-β interacts with the pore. The experiments show that in the absence of RanGTP, importin-β accumulates inside the pore and binds to a protein called Nup153, which is part of the complex of proteins that makes up the pore. However, when RanGTP is present, some of the importin-β is displaced from Nup153 and leaves the pore, which makes it easier for cargo to pass through.

Further experiments show that when Nup153 and importin-β are mixed, they associate into a gel-like material that can be ‘melted’ by RanGTP. Lowe et al. propose a model for how RanGTP may control the flow of cargo through the nuclear pore by affecting the binding of importin-β to Nup153. Lowe et al.'s findings suggest that passive and active transport of cargo across the nuclear pore are fundamentally connected and suggest that RanGTP provides the cell with an additional layer of control over nucleocytoplasmic transport.

DOI:http://dx.doi.org/10.7554/eLife.04052.002

Karyopherin-centric control of nuclear pores based on molecular occupancy and kinetic analysis of multivalent binding with FG nucleoporins

Intrinsically disordered Phe-Gly nucleoporins (FG Nups) within nuclear pore complexes exert multivalent interactions with transport receptors (Karyopherins (Kaps)) that orchestrate nucleocytoplasmic transport. Current FG-centric views reason that selective Kap translocation is promoted by alterations in the barrier-like FG Nup conformations. However, the strong binding of Kaps with the FG Nups due to avidity contradicts rapid Kap translocation in vivo. Here, using surface plasmon resonance, we innovate a means to correlate in situ mechanistic (molecular occupancy and conformational changes) with equilibrium (binding affinity) and kinetic (multivalent binding kinetics) aspects of Karyopherinβ1 (Kapβ1) binding to four different FG Nups. A general feature of the FxFG domains of Nup214, Nup62, and Nup153 is their capacity to extend and accommodate large numbers of Kapβ1 molecules at physiological Kapβ1 concentrations. A notable exception is the GLFG domain of Nup98, which forms a partially penetrable cohesive layer. Interestingly, we find that a slowly exchanging Kapβ1 phase forms an integral constituent within the FG Nups that coexists with a fast phase, which dominates transport kinetics due to limited binding with the pre-occupied FG Nups at physiological Kapβ1 concentrations. Altogether, our data reveal an emergent Kap-centric barrier mechanism that may underlie mechanistic and kinetic control in the nuclear pore complex.

Nuclear pore complex protein sequences determine overall copolymer brush structure and function

The transport of cargo across the nuclear membrane is highly selective and accomplished by a poorly understood mechanism involving hundreds of nucleoporins lining the inside of the nuclear pore complex (NPC). Currently, there is no clear picture of the overall structure formed by this collection of proteins within the pore, primarily due to their disordered nature. We perform coarse-grained simulations of both individual nucleoporins and grafted rings of nups mimicking the in vivo geometry of the NPC and supplement this with polymer brush modeling. Our results indicate that different regions or blocks of an individual NPC protein can have distinctly different forms of disorder and that this property appears to be a conserved functional feature. Furthermore, this block structure at the individual protein level is critical to the formation of a unique higher-order polymer brush architecture that can exist in distinct morphologies depending on the effective interaction energy between the phenylalanine glycine (FG) domains of different nups. Because the interactions between FG domains may be modulated by certain forms of transport factors, our results indicate that transitions between brush morphologies could play an important role in regulating transport across the NPC, suggesting novel forms of gated transport across membrane pores with wide biomimetic applicability.

Physical modelling of the nuclear pore complex

An in-depth discussion of nuclear pore complexes illustrates the importance of macromolecular confinement in biological systems.

Physically interesting behaviour can arise when soft matter is confined to nanoscale dimensions. A highly relevant biological example of such a phenomenon is the Nuclear Pore Complex (NPC) found perforating the nuclear envelope of eukaryotic cells. In the central conduit of the NPC, of ∼30–60 nm diameter, a disordered network of proteins regulates all macromolecular transport between the nucleus and the cytoplasm. In spite of a wealth of experimental data, the selectivity barrier of the NPC has yet to be explained fully. Experimental and theoretical approaches are complicated by the disordered and heterogeneous nature of the NPC conduit. Modelling approaches have focused on the behaviour of the partially unfolded protein domains in the confined geometry of the NPC conduit, and have demonstrated that within the range of parameters thought relevant for the NPC, widely varying behaviour can be observed. In this review, we summarise recent efforts to physically model the NPC barrier and function. We illustrate how attempts to understand NPC barrier function have employed many different modelling techniques, each of which have contributed to our understanding of the NPC.

Higher nucleoporin-Importinβ affinity at the nuclear basket increases nucleocytoplasmic import

Several in vitro studies have shown the presence of an affinity gradient in nuclear pore complex proteins for the import receptor Importinβ, at least partially contributing to nucleocytoplasmic transport, while others have historically argued against the presence of such a gradient. Nonetheless, the existence of an affinity gradient has remained an uncharacterized contributing factor. To shed light on the affinity gradient theory and better characterize how the existence of such an affinity gradient between the nuclear pore and the import receptor may influence the nucleocytoplasmic traffic, we have developed a general-purpose agent based modeling (ABM) framework that features a new method for relating rate constants to molecular binding and unbinding probabilities, and used our ABM approach to quantify the effects of a wide range of forward and reverse nucleoporin-Importinβ affinity gradients. Our results indicate that transport through the nuclear pore complex is maximized with an effective macroscopic affinity gradient of 2000 µM, 200 µM and 10 µM in the cytoplasmic, central channel and nuclear basket respectively. The transport rate at this gradient is approximately 10% higher than the transport rate for a comparable pore lacking any affinity gradient, which has a peak transport rate when all nucleoporins have an affinity of 200 µM for Importinβ. Furthermore, this optimal ratio of affinity gradients is representative of the ratio of affinities reported for the yeast nuclear pore complex – suggesting that the affinity gradient seen in vitro is highly optimized.

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.

Analysing the impact of nucleo-cytoplasmic shuttling of β-catenin and its antagonists APC, Axin and GSK3 on Wnt/β-catenin signalling

The canonical Wnt signalling pathway plays a critical role in development and disease. The key player of the pathway is β-catenin. Its activity is mainly regulated by the destruction complex consisting of APC, Axin and GSK3. In the nucleus, the complex formation of β-catenin and TCF initiates target gene expression. Our study provides a comprehensive analysis of the role of nucleo-cytoplasmic shuttling of APC, Axin, and GSK3 and the inactivation of β-catenin by the destruction complex in Wnt/β-catenin signalling. We address the following questions: Can nucleo-cytoplasmic shuttling of APC, Axin and GSK3 increase the [β-catenin/TCF] concentration? And, how is the [β-catenin/TCF] concentration influenced by phosphorylation and subsequent degradation of nuclear β-catenin? Based on experimental findings, we develop a compartmental model and conduct several simulation experiments. Our analysis reveals the following key findings: 1) nucleo-cytoplasmic shuttling of β-catenin and its antagonists can yield a spatial separation between the said proteins, which results in a breakdown of β-catenin degradation, followed by an accumulation of β-catenin and hence leads to an increase of the [β-catenin/TCF] concentration. Our results strongly suggest that Wnt signalling can benefit from nucleo-cytoplasmic shuttling of APC, Axin and GSK3, although they are in general β-catenin antagonising proteins. 2) The total robustness of the [β-catenin/TCF] output is closely linked to its absolute concentration levels. We demonstrate that the compartmental separation of β-catenin and the destruction complex does not only lead to a maximization, but additionally to an increased robustness of [β-catenin/TCF] signalling against perturbations in the cellular environment. 3) A nuclear accumulation of the destruction complex renders the pathway robust against fluctuations in Wnt signalling and against changes in the compartmental distribution of β-catenin. 4) Elucidating the impact of destruction complex inhibition, we show that the [β-catenin/TCF] concentration is more effectively enhanced by inhibition of the kinase GSK3 rather than the binding of β-catenin to the destruction complex.

Tracer diffusion in a crowded cylindrical channel

Based on a coarse-grained model, we carry out molecular dynamics simulations to analyze the diffusion of a small tracer particle inside a cylindrical channel whose inner wall is covered with randomly grafted short polymeric chains. We observe an interesting transient subdiffusive behavior along the cylindrical axis at high attraction between the tracer and the chains, however, the long-time diffusion is always normal. This process is found to be enhanced for the case that we immobilize the grafted chains, i.e., the subdiffusive behavior sets in at an earlier time and spans over a longer time period before becoming diffusive. Even if the grafted chains are replaced with a frozen sea of repulsive, nonconnected particles in the background, a transient subdiffusion is observed. The intermediate subdiffusive behavior only disappears when the grafted chains are replaced with a mobile background sea of mutually repulsive particles. Overall, the long-time diffusion coefficient of the tracer along the cylinder axis decreases with an increase in system volume fraction, the strength of the attraction between the tracer and the background, and also on freezing the background.

Effect of charge, hydrophobicity, and sequence of nucleoporins on the translocation of model particles through the nuclear pore complex

The molecular structure of the yeast nuclear pore complex (NPC) and the translocation of model particles have been studied with a molecular theory that accounts for the geometry of the pore and the sequence and anchoring position of the unfolded domains of the nucleoporin proteins (the FG-Nups), which control selective transport through the pore. The theory explicitly models the electrostatic, hydrophobic, steric, conformational, and acid-base properties of the FG-Nups. The electrostatic potential within the pore, which arises from the specific charge distribution of the FG-Nups, is predicted to be negative close to pore walls and positive along the pore axis. The positive electrostatic potential facilitates the translocation of negatively charged particles, and the free energy barrier for translocation decreases for increasing particle hydrophobicity. These results agree with the experimental observation that transport receptors that form complexes with hydrophilic/neutral or positively charged proteins to transport them through the NPC are both hydrophobic and strongly negatively charged. The molecular theory shows that the effects of electrostatic and hydrophobic interactions on the translocating potential are cooperative and nonequivalent due to the interaction-dependent reorganization of the FG-Nups in the presence of the translocating particle. The combination of electrostatic and hydrophobic interactions can give rise to complex translocation potentials displaying a combination of wells and barriers, in contrast to the simple barrier potential observed for a hydrophilic/neutral translocating particle. This work demonstrates the importance of explicitly considering the amino acid sequence and hydrophobic, electrostatic, and steric interactions in understanding the translocation through the NPC.

Nuclear transport receptor binding avidity triggers a self-healing collapse transition in FG-nucleoporin molecular brushes

Conformational changes at supramolecular interfaces are fundamentally coupled to binding activity, yet it remains a challenge to probe this relationship directly. Within the nuclear pore complex, this underlies how transport receptors known as karyopherins proceed through a tethered layer of intrinsically disordered nucleoporin domains containing Phe-Gly (FG)-rich repeats (FG domains) that otherwise hinder passive transport. Here, we use nonspecific proteins (i.e., BSA) as innate molecular probes to explore FG domain conformational changes by surface plasmon resonance. This mathematically diminishes the surface plasmon resonance refractive index constraint, thereby providing the means to acquire and correlate height changes in a surface-tethered FG domain layer to Kap binding affinities in situ with respect to their relative spatial arrangements. Stepwise measurements show that FG domain collapse is caused by karyopherin β1 (Kapβ1) binding at low concentrations, but this gradually transitions into a reextension at higher Kapβ1 concentrations. This ability to self-heal is intimately coupled to Kapβ1-FG binding avidity that promotes the maximal incorporation of Kapβ1 into the FG domain layer. Further increasing Kapβ1 to physiological concentrations leads to a "pileup" of Kapβ1 molecules that bind weakly to unoccupied FG repeats at the top of the layer. Therefore, binding avidity does not hinder fast transport per se. Revealing the biophysical basis underlying the form-function relationship of Kapβ1-FG domain behavior results in a convergent picture in which transport and mechanistic aspects of nuclear pore complex functionality are reconciled.

The yeast nuclear pore complex and transport through it

Exchange of macromolecules between the nucleus and cytoplasm is a key regulatory event in the expression of a cell's genome. This exchange requires a dedicated transport system: (1) nuclear pore complexes (NPCs), embedded in the nuclear envelope and composed of proteins termed nucleoporins (or "Nups"), and (2) nuclear transport factors that recognize the cargoes to be transported and ferry them across the NPCs. This transport is regulated at multiple levels, and the NPC itself also plays a key regulatory role in gene expression by influencing nuclear architecture and acting as a point of control for various nuclear processes. Here we summarize how the yeast Saccharomyces has been used extensively as a model system to understand the fundamental and highly conserved features of this transport system, revealing the structure and function of the NPC; the NPC's role in the regulation of gene expression; and the interactions of transport factors with their cargoes, regulatory factors, and specific nucleoporins.

Bistable collective behavior of polymers tethered in a nanopore

Polymer-coated pores play a crucial role in nucleo-cytoplasmic transport and in a number of biomimetic and nanotechnological applications. Here we present Monte Carlo and Density Functional Theory approaches to identify different collective phases of end-grafted polymers in a nanopore and to study their relative stability as a function of intermolecular interactions. Over a range of system parameters that is relevant for nuclear pore complexes, we observe two distinct phases: one with the bulk of the polymers condensed at the wall of the pore, and the other with the polymers condensed along its central axis. The relative stability of these two phases depends on the interpolymer interactions. The existence the two phases suggests a mechanism in which marginal changes in these interactions, possibly induced by nuclear transport receptors, cause the pore to transform between open and closed configurations, which will influence transport through the pore.

Nuclear translocation of β-catenin is essential for glioma cell survival

Identification of molecular pathways that are essential for cancer cell survival is vital for understanding the underlying biology, as well as to design effective cancer therapeutics. β-catenin, a multifunctional oncogenic protein, participates in cell development. Its multifaceted functions primarily lie to the subcellular distribution. The present study demonstrated that β-catenin accumulated in the nucleus to a greater extent in high-grade gliomas compared with low-grade gliomas. In addition, nuclear localization correlated with a worse prognosis for patients, as determined by immunohistochemical analysis of 74 glioma samples. Nuclear expression of β-catenin was down-regulated in LN229 and U87 glioma cells by a small molecule inhibitor of β-catenin/TCF4 signaling, demonstrating strongly inhibited β-catenin/TCF4 transcriptional activity and STAT3 luciferase activity, as well as decreased mRNA and protein levels of nuclear β-catenin, TCF4, EGFR, AKT1, AKT2 and STAT3. Furthermore, repressed nuclear translocation of β-catenin resulted in inhibition of proliferation and invasiveness, and also induced apoptosis of glioma cells. Similar results were also observed in vivo; intratumoral injection of such small molecule inhibitor downregulated expression of nuclear β-catenin, TCF4, and components of the EGFR pathway, and also delayed tumor growth in nude mice harboring subcutaneous U87 xenografts. Results from the present study provided evidence that nuclear accumulation of β-catenin participated in malignant progression of gliomas and implicated poor prognosis, highlighting it as a potential therapeutic target for gliomas.

Nucleocytoplasmic transport: a role for nonspecific competition in karyopherin-nucleoporin interactions

Nucleocytoplasmic transport occurs through the nuclear pore complex (NPC), which in yeast is a ~50 MDa complex consisting of ~30 different proteins. Small molecules can freely exchange through the NPC, but macromolecules larger than ~40 kDa must be aided across by transport factors, most of which belong to a related family of proteins termed karyopherins (Kaps). These transport factors bind to the disordered phenylalanine-glycine (FG) repeat domains in a family of NPC proteins termed FG nups, and this specific binding allows the transport factors to cross the NPC. However, we still know little in terms of the molecular and kinetic details regarding how this binding translates to selective passage of transport factors across the NPC. Here we show that the specific interactions between Kaps and FG nups are strongly modulated by the presence of a cellular milieu whose proteins appear to act as very weak competitors that nevertheless collectively can reduce Kap/FG nup affinities by several orders of magnitude. Without such modulation, the avidities between Kaps and FG nups measured in vitro are too tight to be compatible with the rapid transport kinetics observed in vivo. We modeled the multivalent interactions between the disordered repeat binding sites in the FG nups and multiple cognate binding sites on Kap, showing that they should indeed be sensitive to even weakly binding competitors; the introduction of such competition reduces the availability of these binding sites, dramatically lowering the avidity of their specific interactions and allowing rapid nuclear transport.