Explicit spatiotemporal simulation of receptor-G protein coupling in rod cell disk membranes

An Unstructured Mesh Reaction-Drift-Diffusion Master Equation with Reversible Reactions

We develop a convergent reaction-drift-diffusion master equation (CRDDME) to facilitate the study of reaction processes in which spatial transport is influenced by drift due to one-body potential fields within general domain geometries. The generalized CRDDME is obtained through two steps. We first derive an unstructured grid jump process approximation for reversible diffusions, enabling the simulation of drift-diffusion processes where the drift arises due to a conservative field that biases particle motion. Leveraging the Edge-Averaged Finite Element method, our approach preserves detailed balance of drift-diffusion fluxes at equilibrium, and preserves an equilibrium Gibbs-Boltzmann distribution for particles undergoing drift-diffusion on the unstructured mesh. We next formulate a spatially-continuous volume reactivity particle-based reaction-drift-diffusion model for reversible reactions of the form A + B ↔ C . A finite volume discretization is used to generate jump process approximations to reaction terms in this model. The discretization is developed to ensure the combined reaction-drift-diffusion jump process approximation is consistent with detailed balance of reaction fluxes holding at equilibrium, along with supporting a discrete version of the continuous equilibrium state. The new CRDDME model represents a continuous-time discrete-space jump process approximation to the underlying volume reactivity model. We demonstrate the convergence and accuracy of the new CRDDME through a number of numerical examples, and illustrate its use on an idealized model for membrane protein receptor dynamics in T cell signaling.

Partial mean-field model for neurotransmission dynamics

This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from computational inefficiency if particle numbers and density get too large. Alternative coarse-grained-resolution models reduce computational effort tremendously, e.g., by replacing the particle distribution by a continuous concentration field governed by reaction-diffusion PDEs. We demonstrate how models on the different resolution levels can be combined into hybrid models that seamlessly combine the best of both worlds, describing molecular species with large copy numbers by macroscopic equations with spatial resolution while keeping the spatial-stochastic particle-based resolution level for the species with low copy numbers. To this end, we introduce a simple particle-based model for the binding dynamics of ions and vesicles at the heart of the neurotransmission process. Within this framework, we derive a novel hybrid model and present results from numerical experiments which demonstrate that the hybrid model allows for an accurate approximation of the full particle-based model in realistic scenarios.

Rhodopsin, light-sensor of vision

The light sensor of vertebrate scotopic (low-light) vision, rhodopsin, is a G-protein-coupled receptor comprising a polypeptide chain with bound chromophore, 11-cis-retinal, that exhibits remarkable physicochemical properties. This photopigment is extremely stable in the dark, yet its chromophore isomerises upon photon absorption with 70% efficiency, enabling the activation of its G-protein, transducin, with high efficiency. Rhodopsin's photochemical and biochemical activities occur over very different time-scales: the energy of retinaldehyde's excited state is stored in <1 ps in retinal-protein interactions, but it takes milliseconds for the catalytically active state to form, and many tens of minutes for the resting state to be restored. In this review, we describe the properties of rhodopsin and its role in rod phototransduction. We first introduce rhodopsin's gross structural features, its evolution, and the basic mechanisms of its activation. We then discuss light absorption and spectral sensitivity, photoreceptor electrical responses that result from the activity of individual rhodopsin molecules, and recovery of rhodopsin and the visual system from intense bleaching exposures. We then provide a detailed examination of rhodopsin's molecular structure and function, first in its dark state, and then in the active Meta states that govern its interactions with transducin, rhodopsin kinase and arrestin. While it is clear that rhodopsin's molecular properties are exquisitely honed for phototransduction, from starlight to dawn/dusk intensity levels, our understanding of how its molecular interactions determine the properties of scotopic vision remains incomplete. We describe potential future directions of research, and outline several major problems that remain to be solved.

A hybrid stochastic/deterministic model of single photon response and light adaptation in mouse rods

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A hybrid stochastic/deterministic model of mouse rod phototransduction is presented.

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Rod photocurrent to photovoltage conversion in darkness is accurately characterized.

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Photoresponses to dim and bright stimuli and in various mutants are well reproduced.

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Recently debated molecular mechanisms of the phototransduction cascade are examined.

The phototransduction cascade is paradigmatic for signaling pathways initiated by G protein-coupled receptors and is characterized by a fine regulation of photoreceptor sensitivity and electrical response to a broad range of light stimuli. Here, we present a biochemically comprehensive model of phototransduction in mouse rods based on a hybrid stochastic and deterministic mathematical framework, and a quantitatively accurate description of the rod impedance in the dark. The latter, combined with novel patch clamp recordings from rod outer segments, enables the interconversion of dim flash responses between photovoltage and photocurrent and thus direct comparison with the simulations. The model reproduces the salient features of the experimental photoresponses at very dim and bright stimuli, for both normal photoreceptors and those with genetically modified cascade components. Our modelling approach recapitulates a number of recent findings in vertebrate phototransduction. First, our results are in line with the recently established requirement of dimeric activation of PDE6 by transducin and further show that such conditions can be fulfilled at the expense of a significant excess of G protein activated by rhodopsin. Secondly, simulations suggest a crucial role of the recoverin-mediated Ca²⁺-feedback on rhodopsin kinase in accelerating the shutoff, when light flashes are delivered in the presence of a light background. Finally, stochastic simulations suggest that transient complexes between dark rhodopsin and transducin formed prior to light stimulation increase the reproducibility of single photon responses. Current limitations of the model are likely associated with the yet unknown mechanisms governing the shutoff of the cascade.

Supramolecular organization of rhodopsin in rod photoreceptor cell membranes

Rhodopsin is the light receptor in rod photoreceptor cells that initiates scotopic vision. Studies on the light receptor span well over a century, yet questions about the organization of rhodopsin within the photoreceptor cell membrane still persist and a consensus view on the topic is still elusive. Rhodopsin has been intensely studied for quite some time, and there is a wealth of information to draw from to formulate an organizational picture of the receptor in native membranes. Early experimental evidence in apparent support for a monomeric arrangement of rhodopsin in rod photoreceptor cell membranes is contrasted and reconciled with more recent visual evidence in support of a supramolecular organization of rhodopsin. What is known so far about the determinants of forming a supramolecular structure and possible functional roles for such an organization are also discussed. Many details are still missing on the structural and functional properties of the supramolecular organization of rhodopsin in rod photoreceptor cell membranes. The emerging picture presented here can serve as a springboard towards a more in-depth understanding of the topic.

Diffusion-influenced reaction rates in the presence of pair interactions

The kinetics of bimolecular reactions in solution depends, among other factors, on intermolecular forces such as steric repulsion or electrostatic interaction. Microscopically, a pair of molecules first has to meet by diffusion before the reaction can take place. In this work, we establish an extension of Doi's volume reaction model to molecules interacting via pair potentials, which is a key ingredient for interacting-particle-based reaction-diffusion (iPRD) simulations. As a central result, we relate model parameters and macroscopic reaction rate constants in this situation. We solve the corresponding reaction-diffusion equation in the steady state and derive semi-analytical expressions for the reaction rate constant and the local concentration profiles. Our results apply to the full spectrum from well-mixed to diffusion-limited kinetics. For limiting cases, we give explicit formulas, and we provide a computationally inexpensive numerical scheme for the general case, including the intermediate, diffusion-influenced regime. The obtained rate constants decompose uniquely into encounter and formation rates, and we discuss the effect of the potential on both subprocesses, exemplified for a soft harmonic repulsion and a Lennard-Jones potential. The analysis is complemented by extensive stochastic iPRD simulations, and we find excellent agreement with the theoretical predictions.

Rhodopsin Oligomerization and Aggregation

Rhodopsin is the light receptor in photoreceptor cells of the retina and a prototypical G protein-coupled receptor. Two types of quaternary structures can be adopted by rhodopsin. If rhodopsin folds and attains a proper tertiary structure, it can then form oligomers and nanodomains within the photoreceptor cell membrane. In contrast, if rhodopsin misfolds, it cannot progress through the biosynthetic pathway and instead will form aggregates that can cause retinal degenerative disease. In this review, emerging views are highlighted on the supramolecular organization of rhodopsin within the membrane of photoreceptor cells and the aggregation of rhodopsin that can lead to retinal degeneration.

ReaDDy 2: Fast and flexible software framework for interacting-particle reaction dynamics

Interacting-particle reaction dynamics (iPRD) combines the simulation of dynamical trajectories of interacting particles as in molecular dynamics (MD) simulations with reaction kinetics, in which particles appear, disappear, or change their type and interactions based on a set of reaction rules. This combination facilitates the simulation of reaction kinetics in crowded environments, involving complex molecular geometries such as polymers, and employing complex reaction mechanisms such as breaking and fusion of polymers. iPRD simulations are ideal to simulate the detailed spatiotemporal reaction mechanism in complex and dense environments, such as in signalling processes at cellular membranes, or in nano- to microscale chemical reactors. Here we introduce the iPRD software ReaDDy 2, which provides a Python interface in which the simulation environment, particle interactions and reaction rules can be conveniently defined and the simulation can be run, stored and analyzed. A C++ interface is available to enable deeper and more flexible interactions with the framework. The main computational work of ReaDDy 2 is done in hardware-specific simulation kernels. While the version introduced here provides single- and multi-threading CPU kernels, the architecture is ready to implement GPU and multi-node kernels. We demonstrate the efficiency and validity of ReaDDy 2 using several benchmark examples. ReaDDy 2 is available at the https://readdy.github.io/ website.

Effect of the Organization of Rhodopsin on the Association between Transducin and a Photoactivated Receptor

After photoactivation, rhodopsin (R), a G-protein-coupled receptor, rapidly activates multiple transducin G-proteins (G) in an initial amplification step of phototransduction. G-protein activation requires diffusion-mediated association with an active rhodopsin (R*) at the rod disk membrane. Different organizations of R within the membrane have been revealded by several microscopy studies, including static and freely diffusing situations. However, it is unclear how such different scenarios influence the activation rate of G proteins. Through Monte Carlo simulations, we study the association reaction between a photoactivated rhodopsin and transducin under different reported receptor organizations including (a) R monomers diffusing freely, (b) R forming static dispersed crystalline domains made of rows of dimers, and (c) R arranged in static tracks formed by two adjacent rows of dimers. A key parameter in our simulations is the probability of binding following a collision ( p). For high p, the association rate between R* and G is higher in the freely diffusive system than in the static organizations, but for low collision efficiencies, the static organizations can result in faster association rates than the mobile system. We also observe that with low p, increasing the concentration of R increases the association rate significantly in the dispersed crystals configuration and just slightly in the free diffusive system. In summary, the lateral organization of rhodopsin influences the association rate between R* and G in a manner strongly dependent on the collision efficiency.

Reversible Interacting-Particle Reaction Dynamics

Interacting-particle reaction dynamics (iPRD) simulates the spatiotemporal evolution of particles that experience interaction forces and can react with one another. The combination of interaction forces and reactions enables a wide range of complex reactive systems in biology and chemistry to be simulated, but gives rise to new questions such as how to evolve the dynamical equations in a computationally efficient and statistically correct manner. Here we consider reversible reactions such as A + B ⇄ C with interacting particles and derive expressions for the microscopic iPRD simulation parameters such that desired values for the equilibrium constant and the dissociation rate are obtained in the dilute limit. We then introduce a Monte Carlo algorithm that ensures detailed balance in the iPRD time-evolution (iPRD-DB). iPRD-DB guarantees the correct thermodynamics at all concentrations and maintains the desired kinetics in the dilute limit, where chemical rates are well-defined and kinetic measurement experiments usually operate. We show that in dense particle systems, the incorporation of detailed balance is essential to obtain physically realistic solutions. iPRD-DB is implemented in ReaDDy 2.

It takes two transducins to activate the cGMP-phosphodiesterase 6 in retinal rods

Among cyclic nucleotide phosphodiesterases (PDEs), PDE6 is unique in serving as an effector enzyme in G protein-coupled signal transduction. In retinal rods and cones, PDE6 is membrane-bound and activated to hydrolyse its substrate, cGMP, by binding of two active G protein α-subunits (Gα*). To investigate the activation mechanism of mammalian rod PDE6, we have collected functional and structural data, and analysed them by reaction-diffusion simulations. Gα* titration of membrane-bound PDE6 reveals a strong functional asymmetry of the enzyme with respect to the affinity of Gα* for its two binding sites on membrane-bound PDE6 and the enzymatic activity of the intermediary 1 : 1 Gα* · PDE6 complex. Employing cGMP and its 8-bromo analogue as substrates, we find that Gα* · PDE6 forms with high affinity but has virtually no cGMP hydrolytic activity. To fully activate PDE6, it takes a second copy of Gα* which binds with lower affinity, forming Gα* · PDE6 · Gα*. Reaction-diffusion simulations show that the functional asymmetry of membrane-bound PDE6 constitutes a coincidence switch and explains the lack of G protein-related noise in visual signal transduction. The high local concentration of Gα* generated by a light-activated rhodopsin molecule efficiently activates PDE6, whereas the low density of spontaneously activated Gα* fails to activate the effector enzyme.

Particle-based membrane model for mesoscopic simulation of cellular dynamics

We present a simple and computationally efficient coarse-grained and solvent-free model for simulating lipid bilayer membranes. In order to be used in concert with particle-based reaction-diffusion simulations, the model is purely based on interacting and reacting particles, each representing a coarse patch of a lipid monolayer. Particle interactions include nearest-neighbor bond-stretching and angle-bending and are parameterized so as to reproduce the local membrane mechanics given by the Helfrich energy density over a range of relevant curvatures. In-plane fluidity is implemented with Monte Carlo bond-flipping moves. The physical accuracy of the model is verified by five tests: (i) Power spectrum analysis of equilibrium thermal undulations is used to verify that the particle-based representation correctly captures the dynamics predicted by the continuum model of fluid membranes. (ii) It is verified that the input bending stiffness, against which the potential parameters are optimized, is accurately recovered. (iii) Isothermal area compressibility modulus of the membrane is calculated and is shown to be tunable to reproduce available values for different lipid bilayers, independent of the bending rigidity. (iv) Simulation of two-dimensional shear flow under a gravity force is employed to measure the effective in-plane viscosity of the membrane model and show the possibility of modeling membranes with specified viscosities. (v) Interaction of the bilayer membrane with a spherical nanoparticle is modeled as a test case for large membrane deformations and budding involved in cellular processes such as endocytosis. The results are shown to coincide well with the predicted behavior of continuum models, and the membrane model successfully mimics the expected budding behavior. We expect our model to be of high practical usability for ultra coarse-grained molecular dynamics or particle-based reaction-diffusion simulations of biological systems.

An efficient multi-scale Green's function reaction dynamics scheme

Molecular Dynamics-Green's Function Reaction Dynamics (MD-GFRD) is a multiscale simulation method for particle dynamics or particle-based reaction-diffusion dynamics that is suited for systems involving low particle densities. Particles in a low-density region are just diffusing and not interacting. In this case, one can avoid the costly integration of microscopic equations of motion, such as molecular dynamics (MD), and instead turn to an event-based scheme in which the times to the next particle interaction and the new particle positions at that time can be sampled. At high (local) concentrations, however, e.g., when particles are interacting in a nontrivial way, particle positions must still be updated with small time steps of the microscopic dynamical equations. The efficiency of a multi-scale simulation that uses these two schemes largely depends on the coupling between them and the decisions when to switch between the two scales. Here we present an efficient scheme for multi-scale MD-GFRD simulations. It has been shown that MD-GFRD schemes are more efficient than brute-force molecular dynamics simulations up to a molar concentration of 10² μM. In this paper, we show that the choice of the propagation domains has a relevant impact on the computational performance. Domains are constructed using a local optimization of their sizes and a minimal domain size is proposed. The algorithm is shown to be more efficient than brute-force Brownian dynamics simulations up to a molar concentration of 10³ μM and is up to an order of magnitude more efficient compared with previous MD-GFRD schemes.

Excluded volume effects in on- and off-lattice reaction-diffusion models

Mathematical models are important tools to study the excluded volume effects on reaction-diffusion systems, which are known to play an important role inside living cells. Detailed microscopic simulations with off-lattice Brownian dynamics become computationally expensive in crowded environments. In this study, the authors therefore investigate to which extent on-lattice approximations, the so-called cellular automata models, can be used to simulate reactions and diffusion in the presence of crowding molecules. They show that the diffusion is most severely slowed down in the off-lattice model, since randomly distributed obstacles effectively exclude more volume than those ordered on an artificial grid. Crowded reaction rates can be both increased and decreased by the grid structure and it proves important to model the molecules with realistic sizes when excluded volume is taken into account. The grid artefacts increase with increasing crowder density and they conclude that the computationally more efficient on-lattice simulations are accurate approximations only for low crowder densities.

Reaction-diffusion basis of retroviral infectivity

Retrovirus particle (virion) infectivity requires diffusion and clustering of multiple transmembrane envelope proteins (Env₃) on the virion exterior, yet is triggered by protease-dependent degradation of a partially occluding, membrane-bound Gag polyprotein lattice on the virion interior. The physical mechanism underlying such coupling is unclear and only indirectly accessible via experiment. Modelling stands to provide insight but the required spatio-temporal range far exceeds current accessibility by all-atom or even coarse-grained molecular dynamics simulations. Nor do such approaches account for chemical reactions, while conversely, reaction kinetics approaches handle neither diffusion nor clustering. Here, a recently developed multiscale approach is considered that applies an ultra-coarse-graining scheme to treat entire proteins at near-single particle resolution, but which also couples chemical reactions with diffusion and interactions. A model is developed of Env₃ molecules embedded in a truncated Gag lattice composed of membrane-bound matrix proteins linked to capsid subunits, with freely diffusing protease molecules. Simulations suggest that in the presence of Gag but in the absence of lateral lattice-forming interactions, Env₃ diffuses comparably to Gag-absent Env₃ Initial immobility of Env₃ is conferred through lateral caging by matrix trimers vertically coupled to the underlying hexameric capsid layer. Gag cleavage by protease vertically decouples the matrix and capsid layers, induces both matrix and Env₃ diffusion, and permits Env₃ clustering. Spreading across the entire membrane surface reduces crowding, in turn, enhancing the effect and promoting infectivity.This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

Quaternary structures of opsin in live cells revealed by FRET spectrometry

Rhodopsin is a prototypical G-protein-coupled receptor (GPCR) that initiates phototransduction in the retina. The receptor consists of the apoprotein opsin covalently linked to the inverse agonist 11-cis retinal. Rhodopsin and opsin have been shown to form oligomers within the outer segment disc membranes of rod photoreceptor cells. However, the physiological relevance of the observed oligomers has been questioned since observations were made on samples prepared from the retina at low temperatures. To investigate the oligomeric status of opsin in live cells at body temperatures, we utilized a novel approach called Förster resonance energy transfer spectrometry, which previously has allowed the determination of the stoichiometry and geometry (i.e. quaternary structure) of various GPCRs. In the current study, we have extended the method to additionally determine whether or not a mixture of oligomeric forms of opsin exists and in what proportion. The application of this improved method revealed that opsin expressed in live Chinese hamster ovary (CHO) cells at 37°C exists as oligomers of various sizes. At lower concentrations, opsin existed in an equilibrium of dimers and tetramers. The tetramers were in the shape of a near-rhombus. At higher concentrations of the receptor, higher-order oligomers began to form. Thus, a mixture of different oligomeric forms of opsin is present in the membrane of live CHO cells and oligomerization occurs in a concentration-dependent manner. The general principles underlying the concentration-dependent oligomerization of opsin may be universal and apply to other GPCRs as well.

Molecular basis for photoreceptor outer segment architecture

To serve vision, vertebrate rod and cone photoreceptors must detect photons, convert the light stimuli into cellular signals, and then convey the encoded information to downstream neurons. Rods and cones are sensory neurons that each rely on specialized ciliary organelles to detect light. These organelles, called outer segments, possess elaborate architectures that include many hundreds of light-sensitive membranous disks arrayed one atop another in precise register. These stacked disks capture light and initiate the chain of molecular and cellular events that underlie normal vision. Outer segment organization is challenged by an inherently dynamic nature; these organelles are subject to a renewal process that replaces a significant fraction of their disks (up to ∼10%) on a daily basis. In addition, a broad range of environmental and genetic insults can disrupt outer segment morphology to impair photoreceptor function and viability. In this chapter, we survey the major progress that has been made for understanding the molecular basis of outer segment architecture. We also discuss key aspects of organelle lipid and protein composition, and highlight distributions, interactions, and potential structural functions of key OS-resident molecules, including: kinesin-2, actin, RP1, prominin-1, protocadherin 21, peripherin-2/rds, rom-1, glutamic acid-rich proteins, and rhodopsin. Finally, we identify key knowledge gaps and challenges that remain for understanding how normal outer segment architecture is established and maintained.

Membrane omega-3 fatty acids modulate the oligomerisation kinetics of adenosine A2A and dopamine D2 receptors

Membrane levels of docosahexaenoic acid (DHA), an essential omega-3 polyunsaturated fatty acid (ω-3 PUFA), are decreased in common neuropsychiatric disorders. DHA modulates key cell membrane properties like fluidity, thereby affecting the behaviour of transmembrane proteins like G protein-coupled receptors (GPCRs). These receptors, which have special relevance for major neuropsychiatric disorders have recently been shown to form dimers or higher order oligomers, and evidence suggests that DHA levels affect GPCR function by modulating oligomerisation. In this study, we assessed the effect of membrane DHA content on the formation of a class of protein complexes with particular relevance for brain disease: adenosine A_2A and dopamine D₂ receptor oligomers. Using extensive multiscale computer modelling, we find a marked propensity of DHA for interaction with both A_2A and D₂ receptors, which leads to an increased rate of receptor oligomerisation. Bioluminescence resonance energy transfer (BRET) experiments performed on living cells suggest that this DHA effect on the oligomerisation of A_2A and D₂ receptors is purely kinetic. This work reveals for the first time that membrane ω-3 PUFAs play a key role in GPCR oligomerisation kinetics, which may have important implications for neuropsychiatric conditions like schizophrenia or Parkinson’s disease.

Protein and Signaling Networks in Vertebrate Photoreceptor Cells

Vertebrate photoreceptor cells are exquisite light detectors operating under very dim and bright illumination. The photoexcitation and adaptation machinery in photoreceptor cells consists of protein complexes that can form highly ordered supramolecular structures and control the homeostasis and mutual dependence of the secondary messengers cyclic guanosine monophosphate (cGMP) and Ca²⁺. The visual pigment in rod photoreceptors, the G protein-coupled receptor rhodopsin is organized in tracks of dimers thereby providing a signaling platform for the dynamic scaffolding of the G protein transducin. Illuminated rhodopsin is turned off by phosphorylation catalyzed by rhodopsin kinase (GRK1) under control of Ca²⁺-recoverin. The GRK1 protein complex partly assembles in lipid raft structures, where shutting off rhodopsin seems to be more effective. Re-synthesis of cGMP is another crucial step in the recovery of the photoresponse after illumination. It is catalyzed by membrane bound sensory guanylate cyclases (GCs) and is regulated by specific neuronal Ca²⁺-sensor proteins called guanylate cyclase-activating proteins (GCAPs). At least one GC (ROS-GC1) was shown to be part of a multiprotein complex having strong interactions with the cytoskeleton and being controlled in a multimodal Ca²⁺-dependent fashion. The final target of the cGMP signaling cascade is a cyclic nucleotide-gated (CNG) channel that is a hetero-oligomeric protein located in the plasma membrane and interacting with accessory proteins in highly organized microdomains. We summarize results and interpretations of findings related to the inhomogeneous organization of signaling units in photoreceptor outer segments.

ReaDDyMM: Fast interacting particle reaction-diffusion simulations using graphical processing units

ReaDDy is a modular particle simulation package combining off-lattice reaction kinetics with arbitrary particle interaction forces. Here we present a graphical processing unit implementation of ReaDDy that employs the fast multiplatform molecular dynamics package OpenMM. A speedup of up to two orders of magnitude is demonstrated, giving us access to timescales of multiple seconds on single graphical processing units. This opens up the possibility of simulating cellular signal transduction events while resolving all protein copies.

Spatial and Temporal Aspects of Signaling by G-Protein-Coupled Receptors

Signaling by G-protein-coupled receptors is often considered a uniform process, whereby a homogeneously activated proportion of randomly distributed receptors are activated under equilibrium conditions and produce homogeneous, steady-state intracellular signals. While this may be the case in some biologic systems, the example of rhodopsin with its strictly local single-quantum mode of function shows that homogeneity in space and time cannot be a general property of G-protein-coupled systems. Recent work has now revealed many other systems where such simplicity does not prevail. Instead, a plethora of mechanisms allows much more complex patterns of receptor activation and signaling: different mechanisms of protein-protein interaction; temporal changes under nonequilibrium conditions; localized receptor activation; and localized second messenger generation and degradation-all of which shape receptor-generated signals and permit the creation of multiple signal types. Here, we review the evidence for such pleiotropic receptor signaling in space and time.

Dynamical Organization of Syntaxin-1A at the Presynaptic Active Zone

Synaptic vesicle fusion is mediated by SNARE proteins forming in between synaptic vesicle (v-SNARE) and plasma membrane (t-SNARE), one of which is Syntaxin-1A. Although exocytosis mainly occurs at active zones, Syntaxin-1A appears to cover the entire neuronal membrane. By using STED super-resolution light microscopy and image analysis of Drosophila neuro-muscular junctions, we show that Syntaxin-1A clusters are more abundant and have an increased size at active zones. A computational particle-based model of syntaxin cluster formation and dynamics is developed. The model is parametrized to reproduce Syntaxin cluster-size distributions found by STED analysis, and successfully reproduces existing FRAP results. The model shows that the neuronal membrane is adjusted in a way to strike a balance between having most syntaxins stored in large clusters, while still keeping a mobile fraction of syntaxins free or in small clusters that can efficiently search the membrane or be traded between clusters. This balance is subtle and can be shifted toward almost no clustering and almost complete clustering by modifying the syntaxin interaction energy on the order of only 1 kBT. This capability appears to be exploited at active zones. The larger active-zone syntaxin clusters are more stable and provide regions of high docking and fusion capability, whereas the smaller clusters outside may serve as flexible reserve pool or sites of spontaneous ectopic release.

Higher-order architecture of rhodopsin in intact photoreceptors and its implication for phototransduction kinetics

The visual pigment rhodopsin belongs to the family of G protein-coupled receptors that can form higher oligomers. It is controversial whether rhodopsin forms oligomers and whether oligomers are functionally relevant. Here, we study rhodopsin organization in cryosections of dark-adapted mouse rod photoreceptors by cryoelectron tomography. We identify four hierarchical levels of organization. Rhodopsin forms dimers; at least ten dimers form a row. Rows form pairs (tracks) that are aligned parallel to the disk incisures. Particle-based simulation shows that the combination of tracks with fast precomplex formation, i.e. rapid association and dissociation between inactive rhodopsin and the G protein transducin, leads to kinetic trapping: rhodopsin first activates transducin from its own track, whereas recruitment of transducin from other tracks proceeds more slowly. The trap mechanism could produce uniform single-photon responses independent of rhodopsin lifetime. In general, tracks might provide a platform that coordinates the spatiotemporal interaction of signaling molecules.

Simulation tools for particle-based reaction-diffusion dynamics in continuous space

Particle-based reaction-diffusion algorithms facilitate the modeling of the diffusional motion of individual molecules and the reactions between them in cellular environments. A physically realistic model, depending on the system at hand and the questions asked, would require different levels of modeling detail such as particle diffusion, geometrical confinement, particle volume exclusion or particle-particle interaction potentials. Higher levels of detail usually correspond to increased number of parameters and higher computational cost. Certain systems however, require these investments to be modeled adequately. Here we present a review on the current field of particle-based reaction-diffusion software packages operating on continuous space. Four nested levels of modeling detail are identified that capture incrementing amount of detail. Their applicability to different biological questions is discussed, arching from straight diffusion simulations to sophisticated and expensive models that bridge towards coarse grained molecular dynamics.

Nanodomain organization of rhodopsin in native human and murine rod outer segment disc membranes

Biological membranes display distinct domains that organize membrane proteins and signaling molecules to facilitate efficient and reliable signaling. The organization of rhodopsin, a G protein-coupled receptor, in native rod outer segment disc membranes was investigated by atomic force microscopy. Atomic force microscopy revealed that rhodopsin is arranged into domains of variable size, which we refer to herein as nanodomains, in native membranes. Quantitative analysis of 150 disc membranes revealed that the physical properties of nanodomains are conserved in humans and mice and that the properties of individual disc membranes can be variable. Examining the variable properties of disc membranes revealed some of the factors contributing to the size of rod outer segment discs and the formation of nanodomains in the membrane. The diameter of rod outer segment discs was dependent on the number of rhodopsin molecules incorporated into the membrane but independent of the spatial density of rhodopsin. The number of nanodomains present in a single disc was also dependent on the number of rhodopsin molecules incorporated into the membrane. The size of the nanodomains was largely independent of the number or spatial density of rhodopsin in the membrane.