Tube geometry controls protein cluster conformation and stability on the endoplasmic reticulum surface

The endoplasmic reticulum (ER), a cellular organelle that forms a cell-spanning network of tubes and sheets, is an important location of protein synthesis and folding. When the ER experiences sustained unfolded protein stress, IRE1 proteins embedded in the ER membrane activate and assemble into clusters as part of the unfolded protein response (UPR). We use kinetic Monte Carlo simulations to explore IRE1 clustering dynamics on the surface of ER tubes. While initially growing clusters are approximately round, once a cluster is sufficiently large a shorter interface length can be achieved by 'wrapping' around the ER tube. A wrapped cluster can grow without further interface length increases. Relative to wide tubes, narrower tubes enable cluster wrapping at smaller cluster sizes. Our simulations show that wrapped clusters on narrower tubes grow more rapidly, evaporate more slowly, and require a lower protein concentration to grow compared to equal-area round clusters on wider tubes. These results suggest that cluster wrapping, facilitated by narrower tubes, could be an important factor in the growth and stability of IRE1 clusters and thus impact the persistence of the UPR, connecting geometry to signaling behavior. This work is consistent with recent experimental observations of IRE1 clusters wrapped around narrow tubes in the ER network.

Quantitative modeling of EGF receptor ligand discrimination via internalization proofreading

The epidermal growth factor receptor (EGFR) is a central regulator of cell physiology that is stimulated by multiple distinct ligands. Although ligands bind to EGFR while the receptor is exposed on the plasma membrane, EGFR incorporation into endosomes following receptor internalization is an important aspect of EGFR signaling, with EGFR internalization behavior dependent upon the type of ligand bound. We develop quantitative modeling for EGFR recruitment to and internalization from clathrin domains, focusing on how internalization competes with ligand unbinding from EGFR. We develop two model versions: a kinetic model with EGFR behavior described as transitions between discrete states and a spatial model with EGFR diffusion to circular clathrin domains. We find that a combination of spatial and kinetic proofreading leads to enhanced EGFR internalization ratios in comparison to unbinding differences between ligand types. Various stages of the EGFR internalization process, including recruitment to and internalization from clathrin domains, modulate the internalization differences between receptors bound to different ligands. Our results indicate that following ligand binding, EGFR may encounter multiple clathrin domains before successful recruitment and internalization. The quantitative modeling we have developed describes competition between EGFR internalization and ligand unbinding and the resulting proofreading.

Confinement of unliganded EGFR by tetraspanin nanodomains gates EGFR ligand binding and signaling

The epidermal growth factor receptor (EGFR) is a central regulator of cell physiology. EGFR is activated by ligand binding, triggering receptor dimerization, activation of kinase activity, and intracellular signaling. EGFR is transiently confined within various plasma membrane nanodomains, yet how this may contribute to regulation of EGFR ligand binding is poorly understood. To resolve how EGFR nanoscale compartmentalization gates ligand binding, we developed single-particle tracking methods to track the mobility of ligand-bound and total EGFR, in combination with modeling of EGFR ligand binding. In comparison to unliganded EGFR, ligand-bound EGFR is more confined and distinctly regulated by clathrin and tetraspanin nanodomains. Ligand binding to unliganded EGFR occurs preferentially in tetraspanin nanodomains, and disruption of tetraspanin nanodomains impairs EGFR ligand binding and alters the conformation of the receptor's ectodomain. We thus reveal a mechanism by which EGFR confinement within tetraspanin nanodomains regulates receptor signaling at the level of ligand binding.

Mitochondrial mRNA localization is governed by translation kinetics and spatial transport

For many nuclear-encoded mitochondrial genes, mRNA localizes to the mitochondrial surface co-translationally, aided by the association of a mitochondrial targeting sequence (MTS) on the nascent peptide with the mitochondrial import complex. For a subset of these co-translationally localized mRNAs, their localization is dependent on the metabolic state of the cell, while others are constitutively localized. To explore the differences between these two mRNA types we developed a stochastic, quantitative model for MTS-mediated mRNA localization to mitochondria in yeast cells. This model includes translation, applying gene-specific kinetics derived from experimental data; and diffusion in the cytosol. Even though both mRNA types are co-translationally localized we found that the steady state number, or density, of ribosomes along an mRNA was insufficient to differentiate the two mRNA types. Instead, conditionally-localized mRNAs have faster translation kinetics which modulate localization in combination with changes to diffusive search kinetics across metabolic states. Our model also suggests that the MTS requires a maturation time to become competent to bind mitochondria. Our work indicates that yeast cells can regulate mRNA localization to mitochondria by controlling mitochondrial volume fraction (influencing diffusive search times) and gene translation kinetics (adjusting mRNA binding competence) without the need for mRNA-specific binding proteins. These results shed light on both global and gene-specific mechanisms that enable cells to alter mRNA localization in response to changing metabolic conditions.

Diffusive search and trajectories on tubular networks: a propagator approach

Several organelles in eukaryotic cells, including mitochondria and the endoplasmic reticulum, form interconnected tubule networks extending throughout the cell. These tubular networks host many biochemical pathways that rely on proteins diffusively searching through the network to encounter binding partners or localized target regions. Predicting the behavior of such pathways requires a quantitative understanding of how confinement to a reticulated structure modulates reaction kinetics. In this work, we develop both exact analytical methods to compute mean first passage times and efficient kinetic Monte Carlo algorithms to simulate trajectories of particles diffusing in a tubular network. Our approach leverages exact propagator functions for the distribution of transition times between network nodes and allows large simulation time steps determined by the network structure. The methodology is applied to both synthetic planar networks and organelle network structures, demonstrating key general features such as the heterogeneity of search times in different network regions and the functional advantage of broadly distributing target sites throughout the network. The proposed algorithms pave the way for future exploration of the interrelationship between tubular network structure and biomolecular reaction kinetics.

Design principles for the glycoprotein quality control pathway

Newly-translated glycoproteins in the endoplasmic reticulum (ER) often undergo cycles of chaperone binding and release in order to assist in folding. Quality control is required to distinguish between proteins that have completed native folding, those that have yet to fold, and those that have misfolded. Using quantitative modeling, we explore how the design of the quality-control pathway modulates its efficiency. Our results show that an energy-consuming cyclic quality-control process, similar to the observed physiological system, outperforms alternative designs. The kinetic parameters that optimize the performance of this system drastically change with protein production levels, while remaining relatively insensitive to the protein folding rate. Adjusting only the degradation rate, while fixing other parameters, allows the pathway to adapt across a range of protein production levels, aligning with in vivo measurements that implicate the release of degradation-associated enzymes as a rapid-response system for perturbations in protein homeostasis. The quantitative models developed here elucidate design principles for effective glycoprotein quality control in the ER, improving our mechanistic understanding of a system crucial to maintaining cellular health.

We explore the architecture and limitations of the quality-control pathway responsible for efficient folding of secretory proteins. Newly-synthesized proteins are tagged by the attachment of a ‘glycan’ sugar chain which facilitates their binding to a chaperone that assists protein folding. Removal of a specific sugar group on the glycan ends the interaction with the chaperone, and not-yet-folded proteins can be re-tagged for another round of chaperone binding. A degradation pathway acts in parallel with the folding cycle, to remove those proteins that have remained unfolded for a sufficiently long time. We develop and solve a mathematical model of this quality-control system, showing that the cyclical design found in living cells is uniquely able to maximize folded protein throughput while avoiding accumulation of unfolded proteins. Although this physiological model provides the best performance, its parameters must be adjusted to perform optimally under different protein production loads, and any single fixed set of parameters leads to poor performance when production rate is altered. We find that a single adjustable parameter, the protein degradation rate, is sufficient to allow optimal performance across a range of conditions. Interestingly, observations of living cells suggest that the degradation speed is indeed rapidly adjusted.

Getting around the cell: physical transport in the intracellular world

Eukaryotic cells face the challenging task of transporting a variety of particles through the complex intracellular milieu in order to deliver, distribute, and mix the many components that support cell function. In this review, we explore the biological objectives and physical mechanisms of intracellular transport. Our focus is on cytoplasmic and intra-organelle transport at the whole-cell scale. We outline several key biological functions that depend on physically transporting components across the cell, including the delivery of secreted proteins, support of cell growth and repair, propagation of intracellular signals, establishment of organelle contacts, and spatial organization of metabolic gradients. We then review the three primary physical modes of transport in eukaryotic cells: diffusive motion, motor-driven transport, and advection by cytoplasmic flow. For each mechanism, we identify the main factors that determine speed and directionality. We also highlight the efficiency of each transport mode in fulfilling various key objectives of transport, such as particle mixing, directed delivery, and rapid target search. Taken together, the interplay of diffusion, molecular motors, and flows supports the intracellular transport needs that underlie a broad variety of biological phenomena.

Drive, filter, and stick: A protein sorting conspiracy in photoreceptors

The sorting of proteins into different functional compartments is a fundamental cellular task. In this issue, Maza et al. (2019. J. Cell Biol https://doi.org/10.1083/jcb.201906024) demonstrate that distinct protein populations are dynamically generated in specialized regions of photoreceptors via an interplay of protein-membrane affinity, impeded diffusion, and driven transport.

Theory of Nonequilibrium Free Energy Transduction by Molecular Machines

Biomolecular machines are protein complexes that convert between different forms of free energy. They are utilized in nature to accomplish many cellular tasks. As isothermal nonequilibrium stochastic objects at low Reynolds number, they face a distinct set of challenges compared with more familiar human-engineered macroscopic machines. Here we review central questions in their performance as free energy transducers, outline theoretical and modeling approaches to understand these questions, identify both physical limits on their operational characteristics and design principles for improving performance, and discuss emerging areas of research.

High-resolution and high-accuracy topographic and transcriptional maps of the nucleosome barrier

Nucleosomes represent mechanical and energetic barriers that RNA Polymerase II (Pol II) must overcome during transcription. A high-resolution description of the barrier topography, its modulation by epigenetic modifications, and their effects on Pol II nucleosome crossing dynamics, is still missing. Here, we obtain topographic and transcriptional (Pol II residence time) maps of canonical, H2A.Z, and monoubiquitinated H2B (uH2B) nucleosomes at near base-pair resolution and accuracy. Pol II crossing dynamics are complex, displaying pauses at specific loci, backtracking, and nucleosome hopping between wrapped states. While H2A.Z widens the barrier, uH2B heightens it, and both modifications greatly lengthen Pol II crossing time. Using the dwell times of Pol II at each nucleosomal position we extract the energetics of the barrier. The orthogonal barrier modifications of H2A.Z and uH2B, and their effects on Pol II dynamics rationalize their observed enrichment in +1 nucleosomes and suggest a mechanism for selective control of gene expression.

Breaking time-reversal symmetry for ratchet models of molecular machines

Biomolecular machines transduce free energy from one form to another to fulfill many important roles inside cells, with dissipation required to achieve directed progress. We investigate how to break time-reversal symmetry at a given dissipation cost by using deterministic protocols to drive systems over sawtooth potentials, which have frequently been used to model molecular machines as ratchets. Time asymmetry increases for sawtooth potentials with higher barriers and for driving potentials of intermediate width. For systems driven over a sawtooth potential according to a protocol, we find that symmetric sawtooths maximize time asymmetry, whereas earlier work examining ratchet models of molecular machines required asymmetric sawtooth potentials to achieve directed behavior. This distinction arises because deterministically driven machines are externally provided with direction, whereas autonomous machines must generate directed behavior.

Allocating and Splitting Free Energy to Maximize Molecular Machine Flux

Biomolecular machines transduce between different forms of energy. These machines make directed progress and increase their speed by consuming free energy, typically in the form of nonequilibrium chemical concentrations. Machine dynamics are often modeled by transitions between a set of discrete metastable conformational states. In general, the free-energy change associated with each transition can increase the forward rate constant, decrease the reverse rate constant, or both. In contrast to previous optimizations, we find that in general flux is maximized neither by devoting all free-energy changes to increasing forward rate constants nor by solely decreasing reverse rate constants. Instead, the optimal free-energy splitting depends on the detailed dynamics. Extending our analysis to machines with vulnerable states (from which they can break down), in the strong driving corresponding to in vivo cellular conditions, processivity is maximized by reducing the occupation of the vulnerable state.

Effective dissipation: Breaking time-reversal symmetry in driven microscopic energy transmission

At molecular scales, fluctuations play a significant role and prevent biomolecular processes from always proceeding in a preferred direction, raising the question of how limited amounts of free energy can be dissipated to obtain directed progress. We examine the system and process characteristics that efficiently break time-reversal symmetry at fixed energy loss; in particular for a simple model of a molecular machine, an intermediate energy barrier produces unusually high asymmetry for a given dissipation. We relate the symmetry-breaking factors found in this model to recent observations of biomolecular machines.

Uniform spatial distribution of collagen fibril radii within tendon implies local activation of pC-collagen at individual fibrils

Collagen fibril cross-sectional radii show no systematic variation between the interior and the periphery of fibril bundles, indicating an effectively constant rate of collagen incorporation into fibrils throughout the bundle. Such spatially homogeneous incorporation constrains the extracellular diffusion of collagen precursors from sources at the bundle boundary to sinks at the growing fibrils. With a coarse-grained diffusion equation we determine stringent bounds, using parameters extracted from published experimental measurements of tendon development. From the lack of new fibril formation after birth, we further require that the concentration of diffusing precursors stays below the critical concentration for fibril nucleation. We find that the combination of the diffusive bound, which requires larger concentrations to ensure homogeneous fibril radii, and lack of nucleation, which requires lower concentrations, is only marginally consistent with fully processed collagen using conservative bounds. More realistic bounds may leave no consistent concentrations. Therefore, we propose that unprocessed pC-collagen diffuses from the bundle periphery followed by local C-proteinase activity and subsequent collagen incorporation at each fibril. We suggest that C-proteinase is localized within bundles, at fibril surfaces, during radial fibrillar growth. The much greater critical concentration of pC-collagen, as compared to fully processed collagen, then provides broad consistency between homogeneous fibril radii and the lack of fibril nucleation during fibril growth.

Single file diffusion into a semi-infinite tube

We investigate single file diffusion (SFD) of large particles entering a semi-infinite tube, such as luminal diffusion of proteins into microtubules or flagella. While single-file effects have no impact on the evolution of particle density, we report significant single-file effects for individually tracked tracer particle motion. Both exact and approximate ordering statistics of particles entering semi-infinite tubes agree well with our stochastic simulations. Considering initially empty semi-infinite tubes, with particles entering at one end starting from an initial time t = 0, tracked particles are initially super-diffusive after entering the system, but asymptotically diffusive at later times. For finite time intervals, the ratio of the net displacement of individual single-file particles to the average displacement of untracked particles is reduced at early times and enhanced at later times. When each particle is numbered, from the first to enter (n = 1) to the most recent (n = N), we find good scaling collapse of this distance ratio for all n. Experimental techniques that track individual particles, or local groups of particles, such as photo-activation or photobleaching of fluorescently tagged proteins, should be able to observe these single-file effects. However, biological phenomena that depend on local concentration, such as flagellar extension or luminal enzymatic activity, should not exhibit single-file effects.

Cluster coarsening on drops exhibits strong and sudden size-selectivity

Autophagy, an important process for degradation of cellular components, requires the targeting of autophagy receptor proteins to potential substrates. Receptor proteins have been observed to form clusters on membranes. To understand how receptor clusters might affect autophagy selectivity, we model cluster coarsening on a polydisperse collection of spherical drop-like substrates. Our model receptor corresponds to NBR1, which supports peroxisome autophagy. We recover dynamical scaling of cluster sizes, but find that changing the drop size distribution changes the cluster-size scaling distribution. The magnitude of this effect is similar to how changing the spatial-dimension affects scaling in bulk systems. We also observe a sudden onset of size-selection of the remaining drops with clusters, due to clusters evaporating from smaller drops and growing on larger drops. This coarsening-driven size selection provides a physical mechanism for autophagy selectivity, and may explain reports of size selection during peroxisome degradation.

An equilibrium double-twist model for the radial structure of collagen fibrils

Mammalian tissues contain networks and ordered arrays of collagen fibrils originating from the periodic self-assembly of helical 300 nm long tropocollagen complexes. The fibril radius is typically between 25 to 250 nm, and tropocollagen at the surface appears to exhibit a characteristic twist-angle with respect to the fibril axis. Similar fibril radii and twist-angles at the surface are observed in vitro, suggesting that these features are controlled by a similar self-assembly process. In this work, we propose a physical mechanism of equilibrium radius control for collagen fibrils based on a radially varying double-twist alignment of tropocollagen within a collagen fibril. The free-energy of alignment is similar to that of liquid crystalline blue phases, and we employ an analytic Euler-Lagrange and numerical free energy minimization to determine the twist-angle between the molecular axis and the fibril axis along the radial direction. Competition between the different elastic energy components, together with a surface energy, determines the equilibrium radius and twist-angle at the fibril surface. A simplified model with a twist-angle that is linear with radius is a reasonable approximation in some parameter regimes, and explains a power-law dependence of radius and twist-angle at the surface as parameters are varied. Fibril radius and twist-angle at the surface corresponding to an equilibrium free-energy minimum are consistent with existing experimental measurements of collagen fibrils. Remarkably, in the experimental regime, all of our model parameters are important for controlling equilibrium structural parameters of collagen fibrils.

Protein translocation without specific quality control in a computational model of the Tat system

The twin-arginine translocation (Tat) system transports folded proteins of various sizes across both bacterial and plant thylakoid membranes. The membrane-associated TatA protein is an essential component of the Tat translocon, and a broad distribution of different sized TatA-clusters is observed in bacterial membranes. We assume that the size dynamics of TatA clusters are affected by substrate binding, unbinding, and translocation to associated TatBC clusters, where clusters with bound translocation substrates favour growth and those without associated substrates favour shrinkage. With a stochastic model of substrate binding and cluster dynamics, we numerically determine the TatA cluster size distribution. We include a proportion of targeted but non-translocatable (NT) substrates, with the simplifying hypothesis that the substrate translocatability does not directly affect cluster dynamical rate constants or substrate binding or unbinding rates. This amounts to a translocation model without specific quality control. Nevertheless, NT substrates will remain associated with TatA clusters until unbound and so will affect cluster sizes and translocation rates. We find that the number of larger TatA clusters depends on the NT fraction f. The translocation rate can be optimized by tuning the rate of spontaneous substrate unbinding, [Formula: see text]. We present an analytically solvable three-state model of substrate translocation without cluster size dynamics that follows our computed translocation rates, and that is consistent with in vitro Tat-translocation data in the presence of NT substrates.

PEX5 and ubiquitin dynamics on mammalian peroxisome membranes

Peroxisomes are membrane-bound organelles within eukaryotic cells that post-translationally import folded proteins into their matrix. Matrix protein import requires a shuttle receptor protein, usually PEX5, that cycles through docking with the peroxisomal membrane, ubiquitination, and export back into the cytosol followed by deubiquitination. Matrix proteins associate with PEX5 in the cytosol and are translocated into the peroxisome lumen during the PEX5 cycle. This cargo translocation step is not well understood, and its energetics remain controversial. We use stochastic computational models to explore different ways the AAA ATPase driven removal of PEX5 may couple with cargo translocation in peroxisomal importers of mammalian cells. The first model considered is uncoupled, in which translocation is spontaneous, and does not immediately depend on PEX5 removal. The second is directly coupled, in which cargo translocation only occurs when its PEX5 is removed from the peroxisomal membrane. The third, novel, model is cooperatively coupled and requires two PEX5 on a given importomer for cargo translocation — one PEX5 with associated cargo and one with ubiquitin. We measure both the PEX5 and the ubiquitin levels on the peroxisomes as we vary the matrix protein cargo addition rate into the cytosol. We find that both uncoupled and directly coupled translocation behave identically with respect to PEX5 and ubiquitin, and the peroxisomal ubiquitin signal increases as the matrix protein traffic increases. In contrast, cooperatively coupled translocation behaves dramatically differently, with a ubiquitin signal that decreases with increasing matrix protein traffic. Recent work has shown that ubiquitin on mammalian peroxisome membranes can lead to selective degradation by autophagy, or ‘pexophagy.’ Therefore, the high ubiquitin level for low matrix cargo traffic with cooperatively coupled protein translocation could be used as a disuse signal to mediate pexophagy. This mechanism may be one way that cells could regulate peroxisome numbers.

Peroxisomes are small organelles that must continually import matrix proteins to contribute to cholesterol and bile acid synthesis, among other important functions. Cargo matrix proteins are shuttled to the peroxisomal membrane, but the only source of energy that has been identified to translocate the cargo into the peroxisome is consumed during the removal of the shuttle protein. Ubiquitin is used to recycle peroxisomal shuttle proteins, but is more generally used in cells to signal degradation of damaged or unneeded cellular components. How shuttle removal and cargo translocation are coupled energetically has been difficult to determine directly, so we investigate how different models of coupling would affect the measurable levels of ubiquitin on mammalian peroxisomes. We find that for the simplest models of coupling, ubiquitin levels decrease as cargo levels decrease. Conversely, for a novel cooperative model of coupling we find that ubiquitin levels increase as cargo levels decrease. This effect could allow the cell to degrade peroxisomes when they are not used, or to avoid degrading peroxisomes as cargo levels increase. Regardless of which model is found to be right, we have shown that ubiquitination levels of peroxisomes should respond to the changing traffic of matrix proteins into peroxisomes.

A concise review of the cost-effectiveness of coronary heart disease prevention

Coronary heart disease is one of the largest sources of morbidity, mortality, and health care expenditure in the United States. This article reviews a number of studies that estimate the cost per unit of health benefits associated with different primary and secondary prevention strategies for coronary heart disease. Although prevention does not provide a panacea for rising health care spending, many preventive strategies are cost-effective when compared to other common clinical interventions. Prevention should be incorporated into regular clinical practice.

Neonatal cleft lip repair in Ayrshire; a contribution to the debate

Neonatal cleft lip repair has been the normal practice in Ayrshire, Scotland, for the last 10 years. The surgical results are briefly presented. Anaesthetic and paediatric considerations are discussed. Assuming careful preoperative assessment is made, the procedure carries minimal morbidity, can give good results and is believed to offer distinct advantages to the parents and child.