The cable equation is a proper framework for modeling electrical neural signalling that takes place at a timescale at which the ionic concentrations vary little. However, in neural tissue there are also key dynamic processes that occur at longer timescales. For example, endured periods of intense neural signaling may cause the local extracellular K(+)-concentration to increase by several millimolars. The clearance of this excess K(+) depends partly on diffusion in the extracellular space, partly on local uptake by astrocytes, and partly on intracellular transport (spatial buffering) within astrocytes. These processes, that take place at the time scale of seconds, demand a mathematical description able to account for the spatiotemporal variations in ion concentrations as well as the subsequent effects of these variations on the membrane potential. Here, we present a general electrodiffusive formalism for modeling of ion concentration dynamics in a one-dimensional geometry, including both the intra- and extracellular domains. Based on the Nernst-Planck equations, this formalism ensures that the membrane potential and ion concentrations are in consistency, it ensures global particle/charge conservation and it accounts for diffusion and concentration dependent variations in resistivity. We apply the formalism to a model of astrocytes exchanging ions with the extracellular space. The simulations show that K(+)-removal from high-concentration regions is driven by a local depolarization of the astrocyte membrane, which concertedly (i) increases the local astrocytic uptake of K(+), (ii) suppresses extracellular transport of K(+), (iii) increases axial transport of K(+) within astrocytes, and (iv) facilitates astrocytic relase of K(+) in regions where the extracellular concentration is low. Together, these mechanisms seem to provide a robust regulatory scheme for shielding the extracellular space from excess K(+).

The RNA polymerase II (Pol II) is a eukaryotic enzyme that catalyzes the synthesis of the messenger RNA using a DNA template. Despite numerous biochemical and biophysical studies, it remains elusive whether the "secondary channel" is the only route for NTP to reach the active site of the enzyme or if the "main channel" could be an alternative. On this regard, crystallographic structures of Pol II have been extremely useful to understand the structural basis of transcription, however, the conformation of the unpaired non-template DNA part of the full transcription bubble (TB) is still unknown. Since diffusion routes of the nucleoside triphosphate (NTP) substrate through the main channel might overlap with the TB region, gaining structural information of the full TB is critical for a complete understanding of Pol II transcription process. In this study, we have built a structural model of Pol II with a complete transcription bubble based on multiple sources of existing structural data and used Molecular Dynamics (MD) simulations together with structural analysis to shed light on NTP entry pathways. Interestingly, we found that although both channels have enough space to allow NTP loading, the percentage of MD conformations containing enough space for NTP loading through the secondary channel is twice higher than that of the main channel. Further energetic study based on MD simulations with NTP loaded in the channels has revealed that the diffusion of the NTP through the main channel is greatly disfavored by electrostatic repulsion between the NTP and the highly negatively charged backbones of nucleotides in the non-template DNA strand. Taken together, our results suggest that the secondary channel is the major route for NTP entry during Pol II transcription.

Polarity establishment, the spontaneous generation of asymmetric molecular distributions, is a crucial component of many cellular functions. Saccharomyces cerevisiae (yeast) undergoes directed growth during budding and mating, and is an ideal model organism for studying polarization. In yeast and many other cell types, the Rho GTPase Cdc42 is the key molecular player in polarity establishment. During yeast polarization, multiple patches of Cdc42 initially form, then resolve into a single front. Because polarization relies on strong positive feedback, it is likely that the amplification of molecular-level fluctuations underlies the generation of multiple nascent patches. In the absence of spatial cues, these fluctuations may be key to driving polarization. Here we used particle-based simulations to investigate the role of stochastic effects in a Turing-type model of yeast polarity establishment. In the model, reactions take place either between two molecules on the membrane, or between a cytosolic and a membrane-bound molecule. Thus, we developed a computational platform that explicitly simulates molecules at and near the cell membrane, and implicitly handles molecules away from the membrane. To evaluate stochastic effects, we compared particle simulations to deterministic reaction-diffusion equation simulations. Defining macroscopic rate constants that are consistent with the microscopic parameters for this system is challenging, because diffusion occurs in two dimensions and particles exchange between the membrane and cytoplasm. We address this problem by empirically estimating macroscopic rate constants from appropriately designed particle-based simulations. Ultimately, we find that stochastic fluctuations speed polarity establishment and permit polarization in parameter regions predicted to be Turing stable. These effects can operate at Cdc42 abundances expected of yeast cells, and promote polarization on timescales consistent with experimental results. To our knowledge, our work represents the first particle-based simulations of a model for yeast polarization that is based on a Turing mechanism.

The interior of a eukaryotic cell is a highly complex composite material which consists of water, structural scaffoldings, organelles, and various biomolecular solutes. All these components serve as obstacles that impede the motion of vesicles. Hence, it is hypothesized that any alteration of the cytoskeletal network may directly impact or even disrupt the vesicle transport. A disruption of the vesicle-mediated cell transport is thought to contribute to several severe diseases and disorders, such as diabetes, Parkinson's and Alzheimer's disease, emphasizing the clinical relevance. To address the outlined objective, a multiscale finite element model of the diffusive vesicle transport is proposed on the basis of the concept of homogenization, owed to the complexity of the cytoskeletal network. In order to study the microscopic effects of specific nanoscopic actin filament network alterations onto the vesicle transport, a parametrized three-dimensional geometrical model of the actin filament network was generated on the basis of experimentally observed filament densities and network geometries in an adenocarcinomic human alveolar basal epithelial cell. Numerical analyzes of the obtained effective diffusion properties within two-dimensional sampling domains of the whole cell model revealed that the computed homogenized diffusion coefficients can be predicted statistically accurate by a simple two-parameter power law as soon as the inaccessible area fraction, due to the obstacle geometries and the finite size of the vesicles, is known. This relationship, in turn, leads to a massive reduction in computation time and allows to study the impact of a variety of different cytoskeletal alterations onto the vesicle transport. Hence, the numerical simulations predicted a 35% increase in transport time due to a uniformly distributed four-fold increase of the total filament amount. On the other hand, a hypothetically reduced expression of filament cross-linking proteins led to sparser filament networks and, thus, a speed up of the vesicle transport.

Lévy flight is a type of random walk that characterizes the behaviour of many natural phenomena studied across a multiplicity of academic disciplines; within biology specifically, the behaviour of fish, birds, insects, mollusks, bacteria, plants, slime molds, t-cells, and human populations. The Lévy flight foraging hypothesis states that because Lévy flights can maximize an organism's search efficiency, natural selection should result in Lévy-like behaviour. Empirical and theoretical research has provided ample evidence of Lévy walks in both extinct and extant species, and its efficiency across models with a diversity of resource distributions. However, no model has addressed the maintenance of Lévy flight foraging through evolutionary processes, and existing models lack ecological breadth. We use numerical simulations, including lineage-based models of evolution with a distribution of move lengths as a variable and heritable trait, to test the Lévy flight foraging hypothesis. We include biological and ecological contexts such as population size, searching costs, lifespan, resource distribution, speed, and consider both energy accumulated at the end of a lifespan and averaged over a lifespan. We demonstrate that selection often results in Lévy-like behaviour, although conditional; smaller populations, longer searches, and low searching costs increase the fitness of Lévy-like behaviour relative to Brownian behaviour. Interestingly, our results also evidence a bet-hedging strategy; Lévy-like behaviour reduces fitness variance, thus maximizing geometric mean fitness over multiple generations.

Calcium/calmodulin-dependent protein kinase II (CaMKII) holoenzymes play a critical role in decoding Ca2+ signals in neurons. Understanding how this occurs has been the focus of numerous studies including many that use models. However, CaMKII is notoriously difficult to simulate in detail because of its multi-subunit nature, which causes a combinatorial explosion in the number of species that must be modeled. To study the Ca2+-calmodulin-CaMKII reaction network with detailed kinetics while including the effect of diffusion, we have customized an existing stochastic particle-based simulator, Smoldyn, to manage the problem of combinatorial explosion. With this new method, spatial and temporal aspects of the signaling network can be studied without compromising biochemical details. We used this new method to examine how calmodulin molecules, both partially loaded and fully loaded with Ca2+, choose pathways to interact with and activate CaMKII under various Ca2+ input conditions. We found that the dependence of CaMKII phosphorylation on Ca2+ signal frequency is intrinsic to the network kinetics and the activation pattern can be modulated by the relative amount of Ca2+ to calmodulin and by the rate of Ca2+ diffusion. Depending on whether Ca2+ influx is saturating or not, calmodulin molecules could choose different routes within the network to activate CaMKII subunits, resulting in different frequency dependence patterns. In addition, the size of the holoenzyme produces a subtle effect on CaMKII activation. The more extended the subunits are organized, the easier for calmodulin molecules to access and activate the subunits. The findings suggest that particular intracellular environmental factors such as crowding and calmodulin availability can play an important role in decoding Ca2+ signals and can give rise to distinct CaMKII activation patterns in dendritic spines, Ca2+ channel nanodomains and cytoplasm.

The propagation of epileptic seizure activity in the brain is a widespread pathophysiology that, in principle, should yield to intervention techniques guided by mathematical models of neuronal ensemble dynamics. During a seizure, neural activity will deviate from its current dynamical regime to one in which there are significant signal fluctuations. In silico treatments of neural activity are an important tool for the understanding of how the healthy brain can maintain stability, as well as of how pathology can lead to seizures. The hope is that, contained within the mathematical foundations of such treatments, there lie potential strategies for mitigating instabilities, e.g. via external stimulation. Here, we demonstrate that the dynamic causal modelling neuronal state equation generalises to a Fokker-Planck formalism if one extends the framework to model the ways in which activity propagates along the structural connections of neural systems. Using the Jacobian of this generalised state equation, we show that an initially unstable system can be rendered stable via a reduction in diffusivity-i.e., by lowering the rate at which neuronal fluctuations disperse to neighbouring regions. We show, for neural systems prone to epileptic seizures, that such a reduction in diffusivity can be achieved via external stimulation. Specifically, we show that this stimulation should be applied in such a way as to temporarily mirror the activity profile of a pathological region in its functionally connected areas. This counter-intuitive method is intended to be used pre-emptively-i.e., in order to mitigate the effects of the seizure, or ideally even prevent it from occurring in the first place. We offer proof of principle using simulations based on functional neuroimaging data collected from patients with idiopathic generalised epilepsy, in which we successfully suppress pathological activity in a distinct sub-network prior to seizure onset. Our hope is that this technique can form the basis for future real-time monitoring and intervention devices that are capable of treating epilepsy in a non-invasive manner.

The optomotor response (OMR) is central to the locomotory behavior in diverse animal species including insects, fish and mammals. Furthermore, the study of the OMR in larval zebrafish has become a key model system for investigating the neural basis of sensorimotor control. However, a comprehensive understanding of the underlying control algorithms is still outstanding. In fish it is often assumed that the OMR, by reducing average optic flow across the retina, serves to stabilize position with respect to the ground. Yet the degree to which this is achieved, and how it could emerge from the intermittent burst dynamics of larval zebrafish swimming, are unclear. Here, we combine detailed computational modeling with a new approach to free-swimming experiments in which we control the amount of visual feedback produced by a given motor effort by varying the height of the larva above a moving grid stimulus. We develop an account of underlying feedback control mechanisms that describes both the bout initiation process and the control of swim speed during bouts. We observe that the degree to which fish stabilize their position is only partial and height-dependent, raising questions about its function. We find the relative speed profile during bouts follows a fixed temporal pattern independent of absolute bout speed, suggesting that bout speed and bout termination are not separately controlled. We also find that the reverse optic flow, experienced when the fish is swimming faster than the stimulus, plays a minimal role in control of the OMR despite carrying most of the sensory information about self-movement. These results shed new light on the underlying dynamics of the OMR in larval zebrafish and will be crucial for future work aimed at identifying the neural basis of this behavior.

Brain stimulation can modulate the activity of neural circuits impaired by Alzheimer's disease (AD), having promising clinical benefit. However, all individuals with the same condition currently receive identical brain stimulation, with limited theoretical basis for this generic approach. In this study, we introduce a control theory framework for obtaining exogenous signals that revert pathological electroencephalographic activity in AD at a minimal energetic cost, while reflecting patients' biological variability. We used anatomical networks obtained from diffusion magnetic resonance images acquired by the Alzheimer's Disease Neuroimaging Initiative (ADNI) as mediators for the interaction between Duffing oscillators. The nonlinear nature of the brain dynamics is preserved, given that we extend the so-called state-dependent Riccati equation control to reflect the stimulation objective in the high-dimensional neural system. By considering nonlinearities in our model, we identified regions for which control inputs fail to correct abnormal activity. There are changes to the way stimulated regions are ranked in terms of the energetic cost of controlling the entire network, from a linear to a nonlinear approach. We also found that limbic system and basal ganglia structures constitute the top target locations for stimulation in AD. Patients with highly integrated anatomical networks-namely, networks having low average shortest path length, high global efficiency-are the most suitable candidates for the propagation of stimuli and consequent success on the control task. Other diseases associated with alterations in brain dynamics and the self-control mechanisms of the brain can be addressed through our framework.

Nuclear pore complexes (NPCs) form gateways for material transfer across the nuclear envelope of eukaryotic cells. Disordered proteins, rich in phenylalanine-glycine repeat motifs (FG-nups), form the central transport channel. Understanding how nups are arranged in the interior of the NPC may explain how NPC functions as a selectivity filter for transport of large molecules and a sieve-like filter for diffusion of small molecules (<9 nm or 40 kDa). We employed molecular dynamics to model the structures formed by various assemblies of one kind of nup, namely the 609-aa-long FG domain of Nsp1 (Nsp1-FG). The simulations started from different initial conformations and geometrical arrangements of Nsp1-FGs. In all cases Nsp1-FGs collectively formed brush-like structures with bristles made of bundles of 2-27 nups, however, the bundles being cross-linked through single nups leaving one bundle and joining a nearby one. The degree of cross-linking varies with different initial nup conformations and arrangements. Structural analysis reveals that FG-repeats of the nups not only involve formation of bundle structures, but are abundantly present in cross-linking regions where the epitopes of FG-repeats are highly accessible. Large molecules that are assisted by transport factors (TFs) are selectively transported through NPC apparently by binding to FG-nups through populated FG-binding pockets on the TF surface. Therefore, our finding suggests that TFs bind concertedly to multiple FGs in cross-linking regions and break-up the bundles to create wide pores for themselves and their cargoes to pass. In addition, the cross-linking between Nsp1-FG bundles, arising from simulations, is found to set a molecular size limit of <9 nm (40 kDa) for passive diffusion of molecules. Our simulations suggest that the NPC central channel, near the periphery where tethering of nups is dominant, features brush-like moderately cross-linked bundles, but in the central region, where tethering loses its effect, features a sieve-like structure of bundles and frequent cross-links.

Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium 'sparks' as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell.

The metabolic capabilities of the species and the local environment shape the microbial interactions in a community either through the exchange of metabolic products or the competition for the resources. Cells are often arranged in close proximity to each other, creating a crowded environment that unevenly reduce the diffusion of nutrients. Herein, we investigated how the crowding conditions and metabolic variability among cells shape the dynamics of microbial communities. For this, we developed CROMICS, a spatio-temporal framework that combines techniques such as individual-based modeling, scaled particle theory, and thermodynamic flux analysis to explicitly incorporate the cell metabolism and the impact of the presence of macromolecular components on the nutrients diffusion. This framework was used to study two archetypical microbial communities (i) Escherichia coli and Salmonella enterica that cooperate with each other by exchanging metabolites, and (ii) two E. coli with different production level of extracellular polymeric substances (EPS) that compete for the same nutrients. In the mutualistic community, our results demonstrate that crowding enhanced the fitness of cooperative mutants by reducing the leakage of metabolites from the region where they are produced, avoiding the resource competition with non-cooperative cells. Moreover, we also show that E. coli EPS-secreting mutants won the competition against the non-secreting cells by creating less dense structures (i.e. increasing the spacing among the cells) that allow mutants to expand and reach regions closer to the nutrient supply point. A modest enhancement of the relative fitness of EPS-secreting cells over the non-secreting ones were found when the crowding effect was taken into account in the simulations. The emergence of cell-cell interactions and the intracellular conflicts arising from the trade-off between growth and the secretion of metabolites or EPS could provide a local competitive advantage to one species, either by supplying more cross-feeding metabolites or by creating a less dense neighborhood.

Information sampling can reduce uncertainty in future decisions but is often costly. To maximize reward, people need to balance sampling cost and information gain. Here we aimed to understand how autistic traits influence the optimality of information sampling and to identify the particularly affected cognitive processes. Healthy human adults with different levels of autistic traits performed a probabilistic inference task, where they could sequentially sample information to increase their likelihood of correct inference and may choose to stop at any moment. We manipulated the cost and evidence associated with each sample and compared participants' performance to strategies that maximize expected gain. We found that participants were overall close to optimal but also showed autistic-trait-related differences. Participants with higher autistic traits had a higher efficiency of winning rewards when the sampling cost was zero but a lower efficiency when the cost was high and the evidence was more ambiguous. Computational modeling of participants' sampling choices and decision times revealed a two-stage decision process, with the second stage being an optional second thought. Participants may consider cost in the first stage and evidence in the second stage, or in the reverse order. The probability of choosing to stop sampling at a specific stage increases with increasing cost or increasing evidence. Surprisingly, autistic traits did not influence the decision in either stage. However, participants with higher autistic traits inclined to consider cost first, while those with lower autistic traits considered cost or evidence first in a more balanced way. This would lead to the observed autistic-trait-related advantages or disadvantages in sampling optimality, depending on whether the optimal sampling strategy is determined only by cost or jointly by cost and evidence.

Cortico-basal-ganglia-thalamic (CBGT) networks are critical for adaptive decision-making, yet how changes to circuit-level properties impact cognitive algorithms remains unclear. Here we explore how dopaminergic plasticity at corticostriatal synapses alters competition between striatal pathways, impacting the evidence accumulation process during decision-making. Spike-timing dependent plasticity simulations showed that dopaminergic feedback based on rewards modified the ratio of direct and indirect corticostriatal weights within opposing action channels. Using the learned weight ratios in a full spiking CBGT network model, we simulated neural dynamics and decision outcomes in a reward-driven decision task and fit them with a drift diffusion model. Fits revealed that the rate of evidence accumulation varied with inter-channel differences in direct pathway activity while boundary height varied with overall indirect pathway activity. This multi-level modeling approach demonstrates how complementary learning and decision computations can emerge from corticostriatal plasticity.

The actin cortex is an active adaptive material, embedded with complex regulatory networks that can sense, generate, and transmit mechanical forces. The cortex exhibits a wide range of dynamic behaviours, from generating pulsatory contractions and travelling waves to forming organised structures. Despite the progress in characterising the biochemical and mechanical components of the actin cortex, the emergent dynamics of this mechanochemical system is poorly understood. Here we develop a reaction-diffusion model for the RhoA signalling network, the upstream regulator for actomyosin assembly and contractility, coupled to an active actomyosin gel, to investigate how the interplay between chemical signalling and mechanical forces regulates stresses and patterns in the cortex. We demonstrate that mechanochemical feedback in the cortex acts to destabilise homogeneous states and robustly generate pulsatile contractions. By tuning active stress in the system, we show that the cortex can generate propagating contraction pulses, form network structures, or exhibit topological turbulence.

Many cognitive processes involve transformations of distributed representations in neural populations, creating a need for population-level models. Recurrent neural network models fulfill this need, but there are many open questions about how their connectivity gives rise to dynamics that solve a task. Here, we present a method for finding the connectivity of networks for which the dynamics are specified to solve a task in an interpretable way. We apply our method to a working memory task by synthesizing a network that implements a drift-diffusion process over a ring-shaped manifold. We also use our method to demonstrate how inputs can be used to control network dynamics for cognitive flexibility and explore the relationship between representation geometry and network capacity. Our work fits within the broader context of understanding neural computations as dynamics over relatively low-dimensional manifolds formed by correlated patterns of neurons.

Mechanical coherence of cell layers is essential for epithelia to function as tissue barriers and to control active tissue dynamics during morphogenesis. RhoA signaling at adherens junctions plays a key role in this process by coupling cadherin-based cell-cell adhesion together with actomyosin contractility. Here we propose and analyze a mathematical model representing core interactions involved in the spatial localization of junctional RhoA signaling. We demonstrate how the interplay between biochemical signaling through positive feedback, combined with diffusion on the cell membrane and mechanical forces generated in the cortex, can determine the spatial distribution of RhoA signaling at cell-cell junctions. This dynamical mechanism relies on the balance between a propagating bistable signal that is opposed by an advective flow generated by an actomyosin stress gradient. Experimental observations on the behavior of the system when contractility is inhibited are in qualitative agreement with the predictions of the model.

Microbes acclimate to changes in substrate availability by altering the number of transporters on the cell surface, however there is some disagreement on just how. We revisit the physics of substrate uptake and consider the steady-state scenario whereby cells have acclimated to maximize fitness. Flux balance analysis of a stoichiometric model of Escherichia coli was used in conjunction with quantitative proteomics data and molecular modeling of membrane transporters to reconcile these opposing views. An emergent feature of the proposed model is a critical substrate concentration S*, which delineates two rate limits. At concentrations above S*, transporter abundance can be regulated to maintain uptake rates as demanded by maximal growth rates, whereas below S*, uptake rates are strictly diffusion limited. In certain scenarios, the proposed model can take on a qualitatively different shape from the familiar hyperbolic kinetics curves, instead resembling the long-forgotten Blackman kinetics.

Microbial communities have vital roles in systems essential to human health and agriculture, such as gut and soil microbiomes, and there is growing interest in engineering designer consortia for applications in biotechnology (e.g., personalized probiotics, bioproduction of high-value products, biosensing). The capacity to monitor and model metabolite exchange in dynamic microbial consortia can provide foundational information important to understand the community level behaviors that emerge, a requirement for building novel consortia. Where experimental approaches for monitoring metabolic exchange are technologically challenging, computational tools can enable greater access to the fate of both chemicals and microbes within a consortium. In this study, we developed an in-silico model of a synthetic microbial consortia of sucrose-secreting Synechococcus elongatus PCC 7942 and Escherichia coli W. Our model was built on the NUFEB framework for Individual-based Modeling (IbM) and optimized for biological accuracy using experimental data. We showed that the relative level of sucrose secretion regulates not only the steady-state support for heterotrophic biomass, but also the temporal dynamics of consortia growth. In order to determine the importance of spatial organization within the consortium, we fit a regression model to spatial data and used it to accurately predict colony fitness. We found that some of the critical parameters for fitness prediction were inter-colony distance, initial biomass, induction level, and distance from the center of the simulation volume. We anticipate that the synergy between experimental and computational approaches will improve our ability to design consortia with novel function.

Membrane proteins account for about one third of the cellular proteome, but it is still unclear how dynamic they are and how they establish functional contacts with cytoplasmic interaction partners. Here, we consider a membrane-integrated one-component receptor that also acts as a transcriptional activator, and analyze how it kinetically locates its specific binding site on the genome. We focus on the case of CadC, the pH receptor of the acid stress response Cad system in E. coli. CadC is a prime example of a one-component signaling protein that directly binds to its cognate target site on the chromosome to regulate transcription. We combined fluorescence microscopy experiments, mathematical analysis, and kinetic Monte Carlo simulations to probe this target search process. Using fluorescently labeled CadC, we measured the time from activation of the receptor until successful binding to the DNA in single cells, exploiting that stable receptor-DNA complexes are visible as fluorescent spots. Our experimental data indicate that CadC is highly mobile in the membrane and finds its target by a 2D diffusion and capture mechanism. DNA mobility is constrained due to the overall chromosome organization, but a labeled DNA locus in the vicinity of the target site appears sufficiently mobile to randomly come close to the membrane. Relocation of the DNA target site to a distant position on the chromosome had almost no effect on the mean search time, which was between four and five minutes in either case. However, a mutant strain with two binding sites displayed a mean search time that was reduced by about a factor of two. This behavior is consistent with simulations of a coarse-grained lattice model for the coupled dynamics of DNA within a cell volume and proteins on its surface. The model also rationalizes the experimentally determined distribution of search times. Overall our findings reveal that DNA target search does not present a much bigger kinetic challenge for membrane-integrated proteins than for cytoplasmic proteins. More generally, diffusion and capture mechanisms may be sufficient for bacterial membrane proteins to establish functional contacts with cytoplasmic targets.