Signaling complexes: biophysical constraints on intracellular communication

Peptide-Based Inhibitors of the Induced Signaling Protein Interactions: Current State and Prospects

Formation of the transient protein complexes in response to activation of cellular receptors is a common mechanism by which cells respond to external stimuli. This article presents the concept of blocking interactions of signaling proteins by the peptide inhibitors, and describes the progress achieved to date in the development of signaling inhibitors that act by blocking the signal-dependent protein interactions.

Membrane localization accelerates association under conditions relevant to cellular signaling

Translocation of cytoplasmic molecules to the plasma membrane is commonplace in cell signaling. Membrane localization has been hypothesized to increase intermolecular association rates; however, it has also been argued that association should be faster in the cytosol because membrane diffusion is slow. Here, we directly compare an identical association reaction, the binding of complementary DNA strands, in solution and on supported membranes. The measured rate constants show that for a 10-µm-radius spherical cell, association is 22- to 33-fold faster at the membrane than in the cytoplasm. The kinetic advantage depends on cell size and is essentially negligible for typical ~1 µm prokaryotic cells. The rate enhancement is attributable to a combination of higher encounter rates in two dimensions and a higher reaction probability per encounter.

Lipid Binding of SH2 Domains

The Src homology 2 (SH2) domain is a modular protein interaction domain that specifically recognizes the phosphotyrosine (pY) motif of a target molecule. We recently reported that a large majority of human SH2 domains tightly bind membrane lipids, and many show high lipid specificity. Most of them can bind a lipid and the pY motif coincidently because their lipid-binding sites are topologically distinct from pY-binding pockets. Lipid binding of SH2 domain-containing kinases and phosphatases is functionally important because it exerts exquisite spatiotemporal control on protein-protein interaction and cell signaling activities mediated by these proteins. Here, we describe two assays, surface plasmon resonance analysis and fluorescence quenching analysis, which allow quantitative determination of the affinity and specificity of SH2-lipid interaction and high-throughput screening for SH2 domain-lipid-binding inhibitors.

Effect of Channel Radius on Fluorescent Nanoparticle Based Molecular Communication

The effect of the communication channel size on the transport and subsequent detection of chemical messengers is investigated on millimetric and micrometric channels. The transport of the information carriers, being characterized by an advective and a diffusive contribution, was simulated by varying the flow velocity and the diffusion coefficient. Then, to evaluate the information quality, the Intersymbol Interference (ISI) between two consecutive signals at a specific release delay was estimated. This allowed us to verify that operating under micrometric channel conditions has a larger flow velocity range to obtain completely separated successive signals and smaller release delays can be used between signals. The theoretical results were confirmed by developing a prototype molecular communication platform operating under microfluidic conditions, which enables communication through fluorescent nanoparticles, namely Carbon Quantum Dots (CQDs).

Novel Roles of SH2 and SH3 Domains in Lipid Binding

Signal transduction, the ability of cells to perceive information from the surroundings and alter behavior in response, is an essential property of life. Studies on tyrosine kinase action fundamentally changed our concept of cellular regulation. The induced assembly of subcellular hubs via the recognition of local protein or lipid modifications by modular protein interactions is now a central paradigm in signaling. Such molecular interactions are mediated by specific protein interaction domains. The first such domain identified was the SH2 domain, which was postulated to be a reader capable of finding and binding protein partners displaying phosphorylated tyrosine side chains. The SH3 domain was found to be involved in the formation of stable protein sub-complexes by constitutively attaching to proline-rich surfaces on its binding partners. The SH2 and SH3 domains have thus served as the prototypes for a diverse collection of interaction domains that recognize not only proteins but also lipids, nucleic acids, and small molecules. It has also been found that particular SH2 and SH3 domains themselves might also bind to and rely on lipids to modulate complex assembly. Some lipid-binding properties of SH2 and SH3 domains are reviewed here.

Multistage signal-interactive nanoparticles improve tumor targeting through efficient nanoparticle-cell communications

Communication between biological components is critical for homeostasis maintenance among the convergence of complicated bio-signals. For therapeutic nanoparticles (NPs), the general lack of effective communication mechanisms with the external cellular environment causes loss of homeostasis, resulting in deprived autonomy, severe macrophage-mediated clearance, and limited tumor accumulation. Here, we develop a multistage signal-interactive system on porous silicon particles through integrating the Self-peptide and Tyr-Ile-Gly-Ser-Arg (YIGSR) peptide into a hierarchical chimeric signaling interface with “don’t eat me” and “eat me” signals. This biochemical transceiver can act as both the signal receiver for amantadine to achieve NP transformation and signal conversion as well as the signal source to present different signals sequentially by reversible self-mimicking. Compared with the non-interactive controls, these signal-interactive NPs loaded with AS1411 and tanespimycin (17-AAG) as anticancer drugs improve tumor targeting 2.8-fold and tumor suppression 6.5-fold and showed only 51% accumulation in the liver with restricted hepatic injury.

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Constructing a signal-interactive NP system improves NP-cell communication efficiency

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Functional chimeric peptide design enables orderly integrating of multiple signal modules

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Signal-interactive NPs reduce liver accumulation and promote tumor targeting

PI3K Driver Mutations: A Biophysical Membrane-Centric Perspective

Ras activates its effectors at the membrane. Active PI3Kα and its associated kinases/phosphatases assemble at membrane regions enriched in signaling lipids. In contrast, the Raf kinase domain extends into the cytoplasm and its assembly is away from the crowded membrane surface. Our structural membrane-centric outlook underscores the spatiotemporal principles of membrane and signaling lipids, which helps clarify PI3Kα activation. Here we focus on mechanisms of activation driven by PI3Kα driver mutations, spotlighting the PI3Kα double (multiple) activating mutations. Single mutations can be potent, but double mutations are stronger: their combination is specific, a single strong driver cannot fully activate PI3K, and two weak drivers may or may not do so. In contrast, two strong drivers may successfully activate PI3K, where one, for example, H1047R, modulates membrane interactions facilitating substrate binding at the active site (km) and the other, for example, E542K and E545K, reduces the transition state barrier (ka), releasing autoinhibition by nSH2. Although mostly unidentified, weak drivers are expected to be common, so we ask here how common double mutations are likely to be and why PI3Kα with double mutations responds effectively to inhibitors. We provide a structural view of hotspot and weak driver mutations in PI3Kα activation, explain their mechanisms, compare these with mechanisms of Raf activation, and point to targeting cell-specific, chromatin-accessible, and parallel (or redundant) pathways to thwart the expected emergence of drug resistance. Collectively, our biophysical outlook delineates activation and highlights the challenges of drug resistance.

Controlling protein activity by dynamic recruitment on a supramolecular polymer platform

Nature uses dynamic molecular platforms for the recruitment of weakly associating proteins into higher-order assemblies to achieve spatiotemporal control of signal transduction. Nanostructures that emulate this dynamic behavior require features such as plasticity, specificity and reversibility. Here we introduce a synthetic protein recruitment platform that combines the dynamics of supramolecular polymers with the programmability offered by DNA-mediated protein recruitment. Assembly of benzene-1,3,5-tricarboxamide (BTA) derivatives functionalized with a 10-nucleotide receptor strand into µm-long supramolecular BTA polymers is remarkably robust, even with high contents of DNA-functionalized BTA monomers and associated proteins. Specific recruitment of DNA-conjugated proteins on the supramolecular polymer results in a 1000-fold increase in protein complex formation, while at the same time enabling their rapid exchange along the BTA polymer. Our results establish supramolecular BTA polymers as a generic protein recruitment platform and demonstrate how assembly of protein complexes along the supramolecular polymer allows efficient and dynamic control of protein activity.

DNA-origami allows the precise recruitment of DNA-protein conjugates but lacks the dynamics found in natural protein assemblies. Here the authors present a synthetic polymer platform that combines the dynamics of supramolecular polymers with the programmability of DNA-mediated protein recruitment.

Systems biology of cellular membranes: a convergence with biophysics

Systems biology and systems medicine have played an important role in the last two decades in shaping our understanding of biological processes. While systems biology is synonymous with network maps and '-omics' approaches, it is not often associated with mechanical processes. Here, we make the case for considering the mechanical and geometrical aspects of biological membranes as a key step in pushing the frontiers of systems biology of cellular membranes forward. We begin by introducing the basic components of cellular membranes, and highlight their dynamical aspects. We then survey the functions of the plasma membrane and the endomembrane system in signaling, and discuss the role and origin of membrane curvature in these diverse cellular processes. We further give an overview of the experimental and modeling approaches to study membrane phenomena. We close with a perspective on the converging futures of systems biology and membrane biophysics, invoking the need to include physical variables such as location and geometry in the study of cellular membranes. WIREs Syst Biol Med 2017, 9:e1386. doi: 10.1002/wsbm.1386 For further resources related to this article, please visit the WIREs website.

The Biological Function of the Prion Protein: A Cell Surface Scaffold of Signaling Modules

The prion glycoprotein (PrP^C) is mostly located at the cell surface, tethered to the plasma membrane through a glycosyl-phosphatydil inositol (GPI) anchor. Misfolding of PrP^C is associated with the transmissible spongiform encephalopathies (TSEs), whereas its normal conformer serves as a receptor for oligomers of the β-amyloid peptide, which play a major role in the pathogenesis of Alzheimer’s Disease (AD). PrP^C is highly expressed in both the nervous and immune systems, as well as in other organs, but its functions are controversial. Extensive experimental work disclosed multiple physiological roles of PrP^C at the molecular, cellular and systemic levels, affecting the homeostasis of copper, neuroprotection, stem cell renewal and memory mechanisms, among others. Often each such process has been heralded as the bona fide function of PrP^C, despite restricted attention paid to a selected phenotypic trait, associated with either modulation of gene expression or to the engagement of PrP^C with a single ligand. In contrast, the GPI-anchored prion protein was shown to bind several extracellular and transmembrane ligands, which are required to endow that protein with the ability to play various roles in transmembrane signal transduction. In addition, differing sets of those ligands are available in cell type- and context-dependent scenarios. To account for such properties, we proposed that PrP^C serves as a dynamic platform for the assembly of signaling modules at the cell surface, with widespread consequences for both physiology and behavior. The current review advances the hypothesis that the biological function of the prion protein is that of a cell surface scaffold protein, based on the striking similarities of its functional properties with those of scaffold proteins involved in the organization of intracellular signal transduction pathways. Those properties are: the ability to recruit spatially restricted sets of binding molecules involved in specific signaling; mediation of the crosstalk of signaling pathways; reciprocal allosteric regulation with binding partners; compartmentalized responses; dependence of signaling properties upon posttranslational modification; and stoichiometric requirements and/or oligomerization-dependent impact on signaling. The scaffold concept may contribute to novel approaches to the development of effective treatments to hitherto incurable neurodegenerative diseases, through informed modulation of prion protein-ligand interactions.

Mapping Cholesterol Interaction Sites on Serotonin Transporter through Coarse-Grained Molecular Dynamics

Serotonin transporter (SERT) modulates serotonergic signaling via re-uptake of serotonin in pre-synaptic cells. The inclusion in cholesterol-enriched membrane domains is crucial for SERT activity, suggesting a cross-talk between the protein and the sterol. Here, we develop a protocol to identify potential cholesterol interaction sites coupling statistical analysis to multi-microsecond coarse-grained molecular dynamics simulations of SERT in a previously validated raft-like membrane model. Six putative sites were found, including a putative CRAC motif on TM4 and a CARC motif on TM10. Among them, four hot-spots near regions related to ion binding, transport, and inhibition were detected. Our results encourage prospective studies to unravel mechanistic features of the transporter and related drug discovery implications.

SH2 Domains Serve as Lipid-Binding Modules for pTyr-Signaling Proteins

The Src-homology 2 (SH2) domain is a protein interaction domain that directs myriad phosphotyrosine (pY)-signaling pathways. Genome-wide screening of human SH2 domains reveals that ∼90% of SH2 domains bind plasma membrane lipids and many have high phosphoinositide specificity. They bind lipids using surface cationic patches separate from pY-binding pockets, thus binding lipids and the pY motif independently. The patches form grooves for specific lipid headgroup recognition or flat surfaces for non-specific membrane binding and both types of interaction are important for cellular function and regulation of SH2 domain-containing proteins. Cellular studies with ZAP70 showed that multiple lipids bind its C-terminal SH2 domain in a spatiotemporally specific manner and thereby exert exquisite spatiotemporal control over its protein binding and signaling activities in T cells. Collectively, this study reveals how lipids control SH2 domain-mediated cellular protein-protein interaction networks and suggest a new strategy for therapeutic modulation of pY-signaling pathways.

Oligomerization and nanocluster organization render specificity

Nanoclusters are anchored to membranes, either within them or in the cytoplasm latched onto the cytoskeleton, whose reorganization can regulate their activity. Nanoclusters have been viewed in terms of cooperativity and activation; here we perceive nanocluster organization from a conformational standpoint. This leads us to suggest that while single molecules encode activity, nanoclusters induce specificity, and that this is their main evolutionary aim. Distinct, isoform-specific nanocluster organization can drive the preferred effector (and ligand) interactions and thereby designate signalling pathways. The absence of detailed structural information across the nanocluster, due to size and dynamics, hinders an in-depth grasp of its mechanistic features; however, available data already capture some of the principles and their functional 'raison d'être'. Collectively, clustering lends stability and reduces the likelihood of proteolytic cleavage; it also increases the effective local concentration and enables efficient cooperative activation. However, clustering does not determine the ability of the single molecule to function. Drugs targeting nanoclusters can attenuate activity by hampering cooperativity; however, this may not perturb activation and signalling, which originate from the molecules themselves, and as such, are likely to endure. What then is the major role of nanoclustering? Assuming that single molecules evolved first, with a subsequent increase in cellular complexity and emergence of highly similar isoform variants, evolution faced the threat of signalling promiscuity. We reason that this potential risk was thwarted by oligomerization and clustering; clustering confers higher specificity, and a concomitant extra layer of cellular control. In our Ras example, signalling will be more accurate as a dimer than as a monomer, where its isomer specificity could be compromised.

Computational modeling reveals optimal strategy for kinase transport by microtubules to nerve terminals

Intracellular transport of proteins by motors along cytoskeletal filaments is crucial to the proper functioning of many eukaryotic cells. Since most proteins are synthesized at the cell body, mechanisms are required to deliver them to the growing periphery. In this article, we use computational modeling to study the strategies of protein transport in the context of JNK (c-JUN NH2-terminal kinase) transport along microtubules to the terminals of neuronal cells. One such strategy for protein transport is for the proteins of the JNK signaling cascade to bind to scaffolds, and to have the whole protein-scaffold cargo transported by kinesin motors along microtubules. We show how this strategy outperforms protein transport by diffusion alone, using metrics such as signaling rate and signal amplification. We find that there exists a range of scaffold concentrations for which JNK transport is optimal. Increase in scaffold concentration increases signaling rate and signal amplification but an excess of scaffolds results in the dilution of reactants. Similarly, there exists a range of kinesin motor speeds for which JNK transport is optimal. Signaling rate and signal amplification increases with kinesin motor speed until the speed of motor translocation becomes faster than kinase/scaffold-motor binding. Finally, we suggest experiments that can be performed to validate whether, in physiological conditions, neuronal cells do indeed adopt such an optimal strategy. Understanding cytoskeletal-assisted protein transport is crucial since axonal and cell body accumulation of organelles and proteins is a histological feature in many human neurodegenerative diseases. In this paper, we have shown that axonal transport performance changes with altered transport component concentrations and transport speeds wherein these aspects can be modulated to improve axonal efficiency and prevent or slowdown axonal deterioration.

The spatial structure of cell signaling systems

The spatial structure of the cell is highly organized at all levels: from small complexes and assemblies, to local nano- and microclusters, to global, micrometer scales across and between cells. We suggest that this multiscale spatial cell organization also organizes signaling and coordinates cellular behavior. We propose a new view of the spatial structure of cell signaling systems. This new view describes cell signaling in terms of dynamic allosteric interactions within and among distinct, spatially organized transient clusters. The clusters vary over time and space and are on length scales from nanometers to micrometers. When considered across these length scales, primary factors in the spatial organization are cell membrane domains and the actin cytoskeleton, both also highly dynamic. A key challenge is to understand the interplay across these multiple scales, link it to the physicochemical basis of the conformational behavior of single molecules and ultimately relate it to cellular function. Overall, our premise is that at these scales, cell signaling should be thought of not primarily as a sequence of diffusion-controlled molecular collisions, but instead transient, allostery-driven cluster re-forming interactions.

Cholesterol modulates cell signaling and protein networking by specifically interacting with PDZ domain-containing scaffold proteins

Cholesterol is known to modulate the physical properties of cell membranes but its direct involvement in cellular signaling has not been thoroughly investigated. Here we show that cholesterol specifically binds many PDZ domains found in scaffold proteins, including the N-terminal PDZ domain of NHERF1/EBP50. This modular domain has a cholesterol-binding site topologically distinct from its canonical protein-binding site and serves as a dual specificity domain that bridges the membrane and juxta-membrane signaling complexes. Disruption of the cholesterol binding activity of NHERF1 largely abrogates its dynamic colocalization with and activation of cystic fibrosis transmembrane conductance regulator, one of its binding partners in the plasma membrane of mammalian cells. At least seven more PDZ domains from other scaffold proteins also bind cholesterol and have cholesterol-binding sites, suggesting that cholesterol modulates cell signaling through direct interactions with these scaffold proteins. This mechanism may provide an alternative explanation for the formation of signaling platforms in cholesterol-rich membrane domains.

Clustering and optimal arrangement of enzymes in reaction-diffusion systems

Enzymes within biochemical pathways are often colocalized, yet the consequences of specific spatial enzyme arrangements remain poorly understood. We study the impact of enzyme arrangement on reaction efficiency within a reaction-diffusion model. The optimal arrangement transitions from a cluster to a distributed profile as a single parameter, which controls the probability of reaction versus diffusive loss of pathway intermediates, is varied. We introduce the concept of enzyme exposure to explain how this transition arises from the stochastic nature of molecular reactions and diffusion.

Why Cells are Microscopic: A Transport-Time Perspective

Physical-chemical reasoning is used to demonstrate that the sizes of both prokaryotic and eukaryotic cells are such that they minimize the times needed for the macromolecules to migrate throughout the cells and interact/react with one another. This conclusion does not depend on a particular form of the crowded-medium diffusion model, as thus points toward a potential optimization principle of cellular organisms. In eukaryotes, size optimality renders the diffusive transport as efficient as active transport - in this way, the cells can conserve energetic resources that would otherwise be expended in active transport.

Protein logic: a statistical mechanical study of signal integration at the single-molecule level

Information processing and decision-making is based upon logic operations, which in cellular networks has been well characterized at the level of transcription. In recent years, however, both experimentalists and theorists have begun to appreciate that cellular decision-making can also be performed at the level of a single protein, giving rise to the notion of protein logic. Here we systematically explore protein logic using a well-known statistical mechanical model. As an example system, we focus on receptors that bind either one or two ligands, and their associated dimers. Notably, we find that a single heterodimer can realize any of the 16 possible logic gates, including the XOR gate, by variation of biochemical parameters. We then introduce what to our knowledge is a novel idea: that a set of receptors with fixed parameters can encode functionally unique logic gates simply by forming different dimeric combinations. An exhaustive search reveals that the simplest set of receptors (two single-ligand receptors and one double-ligand receptor) can realize several different groups of three unique gates, a result for which the parametric analysis of single receptors and dimers provides a clear interpretation. Both results underscore the surprising functional freedom readily available to cells at the single-protein level.

Receptor clustering affects signal transduction at the membrane level in the reaction-limited regime

Many types of membrane receptors are found to be organized as clusters on the cell surface. We investigate the potential effect of such receptor clustering on the intracellular signal transduction stage. We consider a canonical pathway with a membrane receptor (R) activating a membrane-bound intracellular relay protein (G). We use Monte Carlo simulations to recreate biochemical reactions using different receptor spatial distributions and explore the dynamics of the signal transduction. Results show that activation of G by R is severely impaired by R clustering, leading to an apparent blunted biological effect compared to control. Paradoxically, this clustering decreases the half maximal effective dose (ED50) of the transduction stage, increasing the apparent affinity. We study an example of inter-receptor interaction in order to account for possible compensatory effects of clustering and observe the parameter range in which such interactions slightly counterbalance the loss of activation of G. The membrane receptors' spatial distribution affects the internal stages of signal amplification, suggesting a functional role for membrane domains and receptor clustering independently of proximity-induced receptor-receptor interactions.

Time-resolved, confocal single-molecule tracking of individual organic dyes and fluorescent proteins in three dimensions

We demonstrate following individual fluorescent protein constructs and individual organic dyes as they diffuse in 3-D in solution at rates up to 1 μm(2)/s over distances of several micrometers in X, Y, and Z. Our 3-D tracking method is essentially a stage scanning confocal microscope that uses a unique spatial filter geometry and active feedback 200 times/s to follow fast 3-D motion. Here we detail simulations used to find optimal feedback parameters for following individual fluorescent proteins in 3-D and show that a wide range of parameters are capable of following individual proteins diffusing at 1 μm(2)/s rates. In addition, we experimentally show that through 3-D single-molecule tracking of a protein oligomer series (monomer, dimer, and tetramer) of the fluorescent protein Azami Green one can determine the protein oligomerization state. We also perform time-resolved spectroscopy (photon pair correlation measurements) during the measured 3-D trajectories. The photon pair correlation measurements show clear fluorescence photon antibunching, demonstrating that the trajectories are of single fluorescent molecules. We note that the rates of single-molecule diffusive motion we follow (approximately 1 μm(2)/s) are comparable to or faster than many intracellular transport processes.

Spatial simulations in systems biology: from molecules to cells

Cells are highly organized objects containing millions of molecules. Each biomolecule has a specific shape in order to interact with others in the complex machinery. Spatial dynamics emerge in this system on length and time scales which can not yet be modeled with full atomic detail. This review gives an overview of methods which can be used to simulate the complete cell at least with molecular detail, especially Brownian dynamics simulations. Such simulations require correct implementation of the diffusion-controlled reaction scheme occurring on this level. Implementations and applications of spatial simulations are presented, and finally it is discussed how the atomic level can be included for instance in multi-scale simulation methods.

Genome-wide functional annotation of dual-specificity protein- and lipid-binding modules that regulate protein interactions

Emerging evidence indicates that membrane lipids regulate protein networking by directly interacting with protein-interaction domains (PIDs). As a pilot study to identify and functionally annodate lipid-binding PIDs on a genomic scale, we performed experimental and computational studies of PDZ domains. Characterization of 70 PDZ domains showed that ~40% had submicromolar membrane affinity. Using a computational model built from these data, we predicted the membrane-binding properties of 2,000 PDZ domains from 20 species. The accuracy of the prediction was experimentally validated for 26 PDZ domains. We also subdivided lipid-binding PDZ domains into three classes based on the interplay between membrane- and protein-binding sites. For different classes of PDZ domains, lipid binding regulates their protein interactions by different mechanisms. Functional studies of a PDZ domain protein, rhophilin 2, suggest that all classes of lipid-binding PDZ domains serve as genuine dual-specificity modules regulating protein interactions at the membrane under physiological conditions.

Structural determinants of the specificity of a membrane binding domain of the scaffold protein Ste5 of budding yeast: implications in signaling by the scaffold protein in MAPK pathway

In the mitogen activated protein kinase (MAPK) cascades of budding yeast, the scaffold protein Ste5 is recruited to the plasma membrane to transmit pheromone induced signal. A region or domain of Ste5 i.e. residues P44-R67, referred here as Ste5PM24, has been known to be involved in direct interactions with the membrane. In order to gain structural insights into membrane interactions of Ste5, here, we have investigated structures and interactions of two synthetic peptide fragments of Ste5, Ste5PM24, and a hyperactive mutant, Ste5PM24LM, by NMR, ITC, and fluorescence spectroscopy, with lipid membranes. We observed that Ste5PM24 predominantly interacted only with the anionic lipid vesicles. By contrast, Ste5PM24LM exhibited binding with negatively charged as well as zwitterionic or mixed lipid vesicles. Binding of Ste5 peptides with the negatively charged lipid vesicles were primarily driven by hydrophobic interactions. NMR studies revealed that Ste5PM24 assumes dynamic or transient conformations in zwitterionic dodecylphosphocholine (DPC) micelles. By contrast, NMR structure, obtained in anionic sodium dodecyl sulphate (SDS), demonstrated amphipathic helical conformations for the central segment of Ste5PM24. The hydrophobic surface of the helix was found to be buried inside the micelles. Taken together, these results provide important insights toward the structure and specificity determinants of the scaffold protein interactions with the plasma membrane.

Advanced imaging of cellular signaling events

Cells continuously communicate with the surrounding environment employing variety of signaling molecules and pathways to integrate and transport the information in the cell. An example of signaling initiation is binding of extracellular ligand to its receptor at the plasma membrane. This initializes enzymatic reactions leading to the formation of bi- or multimolecular signaling complexes responsible for the regulation or progress of signal transduction. Here, we describe three imaging techniques enabling detection of individual signaling molecules, their complexes, and clusters in human cells. Described imaging techniques require only basic microscopy systems available in the majority of current biomedical research centers but apply advanced data processing. First, total internal reflection fluorescence microscopy (TIRFM) variant of wide-field fluorescence microscopy for imaging highly dynamic clusters is described. Second, superresolution localization microscopy techniques-photoactivated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM)-recently enabled to achieve higher resolution with precision limit of about 20 nm in fixed samples. The developments toward live cell superresolution imaging are indicated. Third, raster image correlation spectroscopy (RICS) employed for molecular diffusion and binding analysis explains the advantages and hurdles of this novel method. Presented techniques provide a new level of detail one can learn about higher organization of signaling events in human cells.

From water and ions to crowded biomacromolecules: in vivo structuring of a prokaryotic cell

The interactions and processes which structure prokaryotic cytoplasm (water, ions, metabolites, and biomacromolecules) and ensure the fidelity of the cell cycle are reviewed from a physicochemical perspective. Recent spectroscopic and biological evidence shows that water has no active structuring role in the cytoplasm, an unnecessary notion still entertained in the literature; water acts only as a normal solvent and biochemical reactant. Subcellular structuring arises from localizations and interactions of biomacromolecules and from the growth and modifications of their surfaces by catalytic reactions. Biomacromolecular crowding is a fundamental physicochemical characteristic of cells in vivo. Though some biochemical and physiological effects of crowding (excluded volume effect) have been documented, crowding assays with polyglycols, dextrans, etc., do not properly mimic the compositional variety of biomacromolecules in vivo. In vitro crowding assays are now being designed with proteins, which better reflect biomacromolecular environments in vivo, allowing for hydrophobic bonding and screened electrostatic interactions. I elaborate further the concept of complex vectorial biochemistry, where crowded biomacromolecules structure the cytosol into electrolyte pathways and nanopools that electrochemically "wire" the cell. Noncovalent attractions between biomacromolecules transiently supercrowd biomacromolecules into vectorial, semiconducting multiplexes with a high (35 to 95%)-volume fraction of biomacromolecules; consequently, reservoirs of less crowded cytosol appear in order to maintain the experimental average crowding of ∼25% volume fraction. This nonuniform crowding model allows for fast diffusion of biomacromolecules in the uncrowded cytosolic reservoirs, while the supercrowded vectorial multiplexes conserve the remarkable repeatability of the cell cycle by preventing confusing cross talk of concurrent biochemical reactions.

Reduction of calcium release site models via moment fitting of phase-type distributions

Models of calcium (Ca(2 +)) release sites derived from continuous-time Markov chain (CTMC) models of intracellular Ca(2 +) channels exhibit collective gating reminiscent of the experimentally observed phenomenon of Ca(2 +) puffs and sparks. In order to overcome the state-space explosion that occurs in compositionally defined Ca(2 +) release site models, we have implemented an automated procedure for model reduction that replaces aggregated states of the full release site model with much simpler CTMCs that have similar within-group phase-type sojourn times and inter-group transitions. Error analysis based on comparison of full and reduced models validates the method when applied to release site models composed of 20 three-state channels that are both activated and inactivated by Ca(2 +). Although inspired by existing techniques for fitting moments of phase-type distributions, the automated reduction method for compositional Ca(2 +) release site models is unique in several respects and novel in this biophysical context.

Modeling cholesterol metabolism by gene expression profiling in the hippocampus

An important part of the challenge of building models of biochemical reactions is determining reaction rate constants that transform substrates into products. We present a method to derive enzymatic kinetic values from mRNA expression levels for modeling biological networks without requiring further tuning. The core metabolic reactions of cholesterol in the brain, particularly in the hippocampus, were simulated. To build the model the baseline mRNA expression levels of genes involved in cholesterol metabolism were obtained from the Allen Mouse Brain Atlas. The model is capable of replicating the trends of relative cholesterol levels in Alzheimer's and Huntington's diseases; and reliably simulated SLOS, desmosterolosis, and Dhcr14/Lbr knockout studies. A sensitivity analysis correctly uncovers the Hmgcr, Idi2 and Fdft1 sites that regulate cholesterol homeostasis. Overall, our model and methodology can be used to pinpoint key reactions, which, upon manipulation, may predict altered cholesterol levels and reveal insights into potential drug therapy targets under diseased conditions.

Model of cell signal transduction in a three-dimensional domain

Intracellular signalling molecules form pathways inside the cell. These pathways carry a signal to target proteins which results in cellular responses. We consider a spherical cell with two internal compartments containing localized activating enzymes where as deactivating enzymes are spread uniformly through out the cytosol. Two diffusible signalling molecules are activated at the compartments and later deactivated in the cytosol due to deactivating enzymes. The two signalling molecules are a single link in a cascade reaction and form a self regulated dynamical system involving positive and negative feedback. Using matched asymptotic expansions we obtain approximate solutions of the steady state diffusion equation with a linear decay rate. We obtain three-dimensional concentration profiles for the signalling molecules. We also investigate an extension of the above system which has multiple cascade reactions occurring between multiple signalling molecules. Numerically, we show that the speed of the signal is an increasing function of the number of links in the cascade.

Multiparticle diffusion limited [Formula: see text] reaction in small volumes

A multiparticle reaction model in which particles A annihilate in clusters of size k as [Formula: see text] is investigated analytically. The system is studied for arbitrary reaction order k > 2, dimension d, and size L. Particles diffuse with diffusion constant D, and annihilate with rate σ which depends on the positions of kA particles in the cluster prior to a reaction. The particles are assumed to be spatially extended objects with radius a. Exclusion effects are not taken into account since A particles are allowed to overlap. The master equation is rephrased in the language of a field theory which, in turn, is used to derive the equations of motion for many-point densities. An approximate form of the equations of motion was solved analytically in the diffusion-controlled limit (infinite reaction rate). An explicit expression for the effective reaction rate has been found in the form of the Laplace transform. It was shown that the number of particles saturates to a constant value for large times. The value is approached through an exponential decay. The exponential decay constant is the non-algebraic function of particle size a and system size L.

Caveolin-1 assembles type 1 inositol 1,4,5-trisphosphate receptors and canonical transient receptor potential 3 channels into a functional signaling complex in arterial smooth muscle cells

Physical coupling of sarcoplasmic reticulum (SR) type 1 inositol 1,4,5-trisphosphate receptors (IP(3)R1) to plasma membrane canonical transient receptor potential 3 (TRPC3) channels activates a cation current (I(Cat)) in arterial smooth muscle cells that induces vasoconstriction. However, structural components that enable IP(3)R1 and TRPC3 channels to communicate locally are unclear. Caveolae are plasma membrane microdomains that can compartmentalize proteins. Here, we tested the hypothesis that caveolae and specifically caveolin-1 (cav-1), a caveolae scaffolding protein, facilitate functional IP(3)R1 to TRPC3 coupling in smooth muscle cells of resistance-size cerebral arteries. Methyl-β-cyclodextrin (MβCD), which disassembles caveolae, reduced IP(3)-induced I(Cat) activation in smooth muscle cells and vasoconstriction in pressurized arteries. Cholesterol replenishment reversed these effects. Cav-1 knockdown using shRNA attenuated IP(3)-induced vasoconstriction, but did not alter TRPC3 and IP(3)R1 expression. A synthetic peptide corresponding to the cav-1 scaffolding domain (CSD) sequence (amino acids 82-101) also attenuated IP(3)-induced I(Cat) activation and vasoconstriction. A cav-1 antibody co-immunoprecipitated cav-1, TRPC3, and IP(3)R1 from cerebral artery lysate. ImmunoFRET indicated that cav-1, TRPC3 channels and IP(3)R1 are spatially co-localized in arterial smooth muscle cells. IP(3)R1 and TRPC3 channel spatial localization was disrupted by MβCD and a CSD peptide. Cholesterol replenishment re-established IP(3)R1 and TRPC3 channel close spatial proximity. Taken together, these data indicate that in arterial smooth muscle cells, cav-1 co-localizes SR IP(3)R1 and plasma membrane TRPC3 channels in close spatial proximity thereby enabling IP(3)-induced physical coupling of these proteins, leading to I(Cat) generation and vasoconstriction.

The "acrosomal synapse": Subcellular organization by lipid rafts and scaffolding proteins exhibits high similarities in neurons and mammalian spermatozoa

Mammalian spermatozoa are highly polarized cells composed of two morphological and functional units, each optimized for a special task. Although the apparent division into head and tail may as such represent the anatomical basis to avoid random diffusion of their special sets of signaling proteins and lipids, recent findings demonstrate the presence of lipid raft-derived membrane platforms and specific scaffolding proteins, thus indicating that smaller sub-domains exist in the two functional units of male germ cells. The aim of this review is to summarize new insights into the principles of subcellular organization in mammalian spermatozoa. Special emphasis is placed on recent observations indicating that an "acrosomal synapse" is formed by lipid raft-derived membrane micro-environments and multidomain scaffolding proteins. Both mechanisms appear to be responsible for ensuring the attachment of the huge acrosomal vesicle to the overlaying plasma membrane, as well as for preventing an accidental spontaneous loss of the single acrosome.

A modular gradient-sensing network for chemotaxis in Escherichia coli revealed by responses to time-varying stimuli

Combining in vivo FRET with time-varying stimuli, such as steps, ramps, and sinusoids allowed deduction of the molecular mechanisms underlying cellular signal processing.

The bacterial chemotaxis pathway can be described as a two-module feedback circuit, the transfer functions of which we have characterized quantitatively by experiment. Model-driven experimental design allowed the use of a single FRET pair for measurements of both transfer functions of the pathway.

The adaptation module's transfer function revealed that feedback near steady state is weak, consistent with high sensitivity to shallow gradients, but also strong steady-state fluctuations in pathway output.

The measured response to oscillatory stimuli defines the frequency band over which the chemotaxis system can compute time derivatives.

In searching for better environments, bacteria sample their surroundings by random motility, and make temporal comparisons of experienced sensory cues to bias their movement toward favorable directions (Berg and Brown, 1972). Thus, the problem of sensing spatial gradients is reduced to time-derivative computations, carried out by a signaling pathway that is well characterized at the molecular level in Escherichia coli. Here, we study the physiology of this signal processing system in vivo by fluorescence resonance energy transfer (FRET) experiments in which live cells are stimulated by time-varying chemoeffector signals. By measuring FRET between the active response regulator of the pathway CheY-P and its phosphatase CheZ, each labeled with GFP variants, we obtain a readout that is directly proportional to pathway activity (Sourjik et al, 2007). We analyze the measured response functions in terms of mechanistic models of signaling, and discuss functional consequences of the observed quantitative characteristics.

Experiments are guided by a coarse-grained modular model (Tu et al, 2008) of the sensory network (Figure 1), in which we identify two important ‘transfer functions': one corresponding to the receptor–kinase complex, which responds to changes in input ligand concentration on a fast time scale, and another corresponding to the adaptation system, which provides negative feedback, opposing the effect of ligand on a slower time scale. For the receptor module, we calibrate an allosteric MWC-type model of the receptor–kinase complex by FRET measurements of the ‘open-loop' transfer function G([L],m) using step stimuli. This calibration provides a basis for using the same FRET readout (between CheY-P and CheZ) to further study properties of the adaptation module.

It is well known that adaptation in E. coli's chemotaxis system uses integral feedback, which guarantees exact restoration of the baseline activity after transient responses to step stimuli (Barkai and Leibler, 1997; Yi et al, 2000). However, the output of time-derivative computations during smoothly varying stimuli depends not only on the presence of integral feedback, but also on what is being integrated. As this integrand can in general be any function of the output, we represent it by a black-box function F(a) in our model, and set out to determine its shape by experiments with time-varying stimuli.

We first apply exponential ramp stimuli—waveforms in which the logarithm of the stimulus level varies linearly with time, at a fixed rate r. It was shown many years ago that during such a stimulus, the kinase output of the pathway changes to a new constant value, a_c that is dependent on the applied ramp rate, r (Block et al, 1983). A plot of a_c versus r (Figure 5A) can thus be considered as an output of time-derivative computations by the network, and could also be used to study the ‘gradient sensitivity' of bacteria traveling at constant speeds.

To obtain the feedback transfer function, F(a), we apply a simple coordinate transformation, identified using our model, to the same ramp-response data (Figure 5B). This function reveals how the temporal rate of change of the feedback signal m depends on the current output signal a. The shape of this function is analyzed using a biochemical reaction scheme, from which in vivo kinetic parameters of the feedback enzymes, CheR and CheB, are extracted. The fitted Michaelis constants for these enzymatic reactions are small compared with the steady-state abundance of their substrates, thus indicating that these enzymes operate close to saturation in vivo. The slope of the function near steady state can be used to assess the strength of feedback, and to compute the relaxation time of the system, τ_m. Relaxation is found to be slow (i.e. large τ_m), consistent with large fluctuations about the steady-state activity caused by the near-saturation kinetics of the feedback enzymes (Emonet and Cluzel, 2008).

Finally, exponential sine-wave stimuli are used to map out the system's frequency response (Figure 5C). The measured data points for both the amplitude and phase of the response are found to be in excellent agreement with model predictions based on parameters from the independently measured step and ramp responses. No curve fitting was required to obtain this agreement. Although the amplitude response as a function of frequency resembles a first-order high-pass filter with a well-defined cutoff frequency, ν_m, we point out that the chemotaxis pathway is actually a low-pass filter if the time derivative of the input is viewed as the input signal. In this latter perspective, ν_m defines an upper bound for the frequency band over which time-derivative computations can be carried out.

The two types of measurements yield complementary information regarding time-derivative computations by E. coli. The ramp-responses characterize the asymptotically constant output when a temporal gradient is held fixed over extended periods. Interestingly, the ramp responses do not depend on receptor cooperativity, but only on properties of the adaptation system, and thus can be used to reveal the in vivo adaptation kinetics, even outside the linear regime of the kinase response. The frequency response is highly relevant in considering spatial searches in the real world, in which experienced gradients are not held fixed in time. The characteristic cutoff frequency ν_m is found by working within the linear regime of the kinase response, and depends on parameters from both modules (it increases with both cooperativity in the receptor module, and the strength of feedback in the adaptation module).

Both ramp responses and sine-wave responses were measured at two different temperatures (22 and 32°C), and found to differ significantly. Both the slope of F(a) near steady state, from ramp experiments, and the characteristic cutoff frequency, from sine-wave experiments, were higher by a factor of ∼3 at 32°C. Fits of the enzymatic model to F(a) suggest that temperature affects the maximal velocity (V_max) more strongly than the Michaelis constants (K_m) for CheR and CheB.

Successful application of inter-molecular FRET in live cells using GFP variants always requires some degree of serendipity. Genetic fusions to these bulky fluorophores can impair the function of the original proteins, and even when fusions are functional, efficient FRET still requires the fused fluorophores to come within the small (<10 nm) Förster radius on interactions between the labeled proteins. Thus, when a successful FRET pair is identified, it is desirable to make the most of it. We have shown here that combined with careful temporal control of input stimuli, and appropriately calibrated models, a single FRET pair can be used to study the structure of multiple transfer functions within a signaling network.

The Escherichia coli chemotaxis-signaling pathway computes time derivatives of chemoeffector concentrations. This network features modules for signal reception/amplification and robust adaptation, with sensing of chemoeffector gradients determined by the way in which these modules are coupled in vivo. We characterized these modules and their coupling by using fluorescence resonance energy transfer to measure intracellular responses to time-varying stimuli. Receptor sensitivity was characterized by step stimuli, the gradient sensitivity by exponential ramp stimuli, and the frequency response by exponential sine-wave stimuli. Analysis of these data revealed the structure of the feedback transfer function linking the amplification and adaptation modules. Feedback near steady state was found to be weak, consistent with strong fluctuations and slow recovery from small perturbations. Gradient sensitivity and frequency response both depended strongly on temperature. We found that time derivatives can be computed by the chemotaxis system for input frequencies below 0.006 Hz at 22°C and below 0.018 Hz at 32°C. Our results show how dynamic input–output measurements, time honored in physiology, can serve as powerful tools in deciphering cell-signaling mechanisms.

Exact equilibrium-state solution of an intracellular complex formation model: kA↔P reaction in a small volume

A generic model of complex formation in small volumes was studied under the assumption of perfect mixing. Particles A react in clusters, and each reaction converts k A particles into a P particle. The back reaction is also allowed. The equilibrium state of the model is solved exactly. Fluctuations in product particle number are reduced by increasing the degree of cooperativity k. Three qualitatively distinct reactant fluctuation characteristics emerge.

Rule-based spatial modeling with diffusing, geometrically constrained molecules

Background

We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined.

For our implementation (based on LAMMPS), we have chosen an already existing formalism (BioNetGen) for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided.

Results

Our simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules). When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa.

Conclusions

We conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial simulation systems like those for DNA or virus capsid self-assembly.

Quantifying the effects of elastic collisions and non-covalent binding on glutamate receptor trafficking in the post-synaptic density

One mechanism of information storage in neurons is believed to be determined by the strength of synaptic contacts. The strength of an excitatory synapse is partially due to the concentration of a particular type of ionotropic glutamate receptor (AMPAR) in the post-synaptic density (PSD). AMPAR concentration in the PSD has to be plastic, to allow the storage of new memories; but it also has to be stable to preserve important information. Although much is known about the molecular identity of synapses, the biophysical mechanisms by which AMPAR can enter, leave and remain in the synapse are unclear. We used Monte Carlo simulations to determine the influence of PSD structure and activity in maintaining homeostatic concentrations of AMPARs in the synapse. We found that, the high concentration and excluded volume caused by PSD molecules result in molecular crowding. Diffusion of AMPAR in the PSD under such conditions is anomalous. Anomalous diffusion of AMPAR results in retention of these receptors inside the PSD for periods ranging from minutes to several hours in the absence of strong binding of receptors to PSD molecules. Trapping of receptors in the PSD by crowding effects was very sensitive to the concentration of PSD molecules, showing a switch-like behavior for retention of receptors. Non-covalent binding of AMPAR to anchored PSD molecules allowed the synapse to become well-mixed, resulting in normal diffusion of AMPAR. Binding also allowed the exchange of receptors in and out of the PSD. We propose that molecular crowding is an important biophysical mechanism to maintain homeostatic synaptic concentrations of AMPARs in the PSD without the need of energetically expensive biochemical reactions. In this context, binding of AMPAR with PSD molecules could collaborate with crowding to maintain synaptic homeostasis but could also allow synaptic plasticity by increasing the exchange of these receptors with the surrounding extra-synaptic membrane.

One of the most accepted theories of information storage in neurons is that it is partially localized in the strength of synaptic contacts. Evidence suggests that at the cellular level, in combination with other cellular mechanisms, this is implemented by increasing or decreasing the concentration of a particular type of membrane molecules. Two opposing mechanisms have to coexist in synapses to allow them to store information. On one hand, synapses have to be flexible, to allow the storage of new memories. On the other hand, synapses have to be stable to preserve previously learned information. Although much is known about the molecular identity of synapses, the biophysical mechanisms by which molecules can enter, leave and remain in the synapse are unclear. Our modeling work uses fundamental biophysical principles to quantify the effects of molecular collisions and biochemical reactions. Our results show that molecular collisions alone, between the diffusing proteins with anchored molecules in the synapse, can replicate known experimental results. Molecular collision in combination with biochemical binding can be fundamental biophysical principles used by synapses for the formation and preservation of memories.

Crowding-induced anisotropic transport modulates reaction kinetics in nanoscale porous media

We quantify the emergence of persistent anisotropy in the diffusion of spherical tracer particles through a nanoscale porous medium composed of a uniform distribution of purely symmetric crowding particles. We focus on the interior of a biological cell as an example of such a medium and find that diffusion is highly directional for distances comparable to the size of some organelles. We use a geometrical procedure that avoids the standard orientational averaging to quantify the anisotropy of diffusive paths and show that the point source distributions are predominantly of prolate ellipsoidal shape as a result of local volume exclusion. This geometrical symmetry breaking strongly skews the distribution of kinetic rates of diffusion-limited reactions toward small values, leading to the result that, for short to intermediate times, almost 80% of the rates measured in an ensemble of heterogeneous media are smaller than the expected rate in an ideal homogeneous medium of similar excluded volume fraction. This crowding-induced modulation may have implications for our understanding and measurement of diffusion-controlled intracellular reaction kinetics and for experimental nanotechnology applications, such as nanoparticle-based bioimaging and drug delivery, where diffusion plays an important role.

Signalling complexes and clusters: functional advantages and methodological hurdles

Signalling molecules integrate, codify and transport information in cells. Organisation of these molecules in complexes and clusters improves the efficiency, fidelity and robustness of cellular signalling. Here, we summarise current views on how signalling molecules assemble into macromolecular complexes and clusters and how they use their physical properties to transduce environmental information into a variety of cellular processes. In addition, we discuss recent innovations in live-cell imaging at the sub-micrometer scale and the challenges of object (particle) tracking, both of which help us to observe signalling complexes and clusters and to examine their dynamic character.

A mechanism for the polarity formation of chemoreceptors at the growth cone membrane for gradient amplification during directional sensing

Accurate response to external directional signals is essential for many physiological functions such as chemotaxis or axonal guidance. It relies on the detection and amplification of gradients of chemical cues, which, in eukaryotic cells, involves the asymmetric relocalization of signaling molecules. How molecular events coordinate to induce a polarity at the cell level remains however poorly understood, particularly for nerve chemotaxis. Here, we propose a model, inspired by single-molecule experiments, for the membrane dynamics of GABA chemoreceptors in nerve growth cones (GCs) during directional sensing. In our model, transient interactions between the receptors and the microtubules, coupled to GABA-induced signaling, provide a positive-feedback loop that leads to redistribution of the receptors towards the gradient source. Using numerical simulations with parameters derived from experiments, we find that the kinetics of polarization and the steady-state polarized distribution of GABA receptors are in remarkable agreement with experimental observations. Furthermore, we make predictions on the properties of the GC seen as a sensing, amplification and filtering module. In particular, the growth cone acts as a low-pass filter with a time constant ∼10 minutes determined by the Brownian diffusion of chemoreceptors in the membrane. This filtering makes the gradient amplification resistent to rapid fluctuations of the external signals, a beneficial feature to enhance the accuracy of neuronal wiring. Since the model is based on minimal assumptions on the receptor/cytoskeleton interactions, its validity extends to polarity formation beyond the case of GABA gradient sensing. Altogether, it constitutes an original positive-feedback mechanism by which cells can dynamically adapt their internal organization to external signals.

Effects of macromolecular crowding on intracellular diffusion from a single particle perspective

Compared to biochemical reactions taking place in relatively well-defined aqueous solutions in vitro, the corresponding reactions happening in vivo occur in extremely complex environments containing only 60-70% water by volume, with the remainder consisting of an undefined array of bio-molecules. In a biological setting, such extremely complex and volume-occupied solution environments are termed 'crowded'. Through a range of intermolecular forces and pseudo-forces, this complex background environment may cause biochemical reactions to behave differently to their in vitro counterparts. In this review, we seek to highlight how the complex background environment of the cell can affect the diffusion of substances within it. Engaging the subject from the perspective of a single particle's motion, we place the focus of our review on two areas: (1) experimental procedures for conducting single particle tracking experiments within cells along with methods for extracting information from these experiments; (2) theoretical factors affecting the translational diffusion of single molecules within crowded two-dimensional membrane and three-dimensional solution environments. We conclude by discussing a number of recent publications relating to intracellular diffusion in light of the reviewed material.

Analysis of reaction-diffusion systems with anomalous subdiffusion

Reaction-diffusion equations are the cornerstone of modeling biochemical systems with spatial gradients, which are relevant to biological processes such as signal transduction. Implicit in the formulation of these equations is the assumption of Fick's law, which states that the local diffusive flux of species i is proportional to its concentration gradient; however, in the context of complex fluids such as cytoplasm and cell membranes, the use of Fick's law is based on empiricism, whereas evidence has been mounting that such media foster anomalous subdiffusion (with mean-squared displacement increasing less than linearly with time) over certain length scales. Particularly when modeling diffusion-controlled reactions and other systems where the spatial domain is considered semi-infinite, assuming Fickian diffusion might not be appropriate. In this article, two simple, conceptually extreme models of anomalous subdiffusion are used in the framework of Green's functions to demonstrate the solution of four reaction-diffusion problems that are well known in the biophysical context of signal transduction: fluorescence recovery after photobleaching, the Smolochowski limit for diffusion-controlled reactions in solution, the spatial range of a diffusing molecule with finite lifetime, and the collision coupling mechanism of diffusion-controlled reactions in two dimensions. In each case, there are only subtle differences between the two subdiffusion models, suggesting how measurements of mean-squared displacement versus time might generally inform models of reactive systems with partial diffusion control.

From molecules to systems: the importance of looking both ways

Although molecular biology has meant different things at different times, the term is often associated with a tendency to view cellular causation as conforming to simple linear schemas in which macro-scale effects are specified by micro-scale structures. The early achievements of molecular biologists were important for the formation of such an outlook, one to which the discovery of recombinant DNA techniques, and a number of other findings, gave new life even after the complexity of genotype-phenotype relations had become apparent. Against this background we outline how a range of scientific developments and conceptual considerations can be regarded as enabling and perhaps necessitating contemporary systems approaches. We suggest that philosophical ideas have a valuable part to play in making sense of complex scientific and disciplinary issues.