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.     

The Sensory Histidine Kinases TorS and EvgS Tend to Form Clusters in Escherichia coli Cells

Microorganisms use multiple two-component sensory systems to detect changes in their environment and elicit physiological responses. Despite their wide spread and importance, the intracellular organization of two-component sensory proteins in bacteria remains little investigated. A notable exception is the well-studied clustering of the chemoreceptor-kinase complexes that mediate chemotaxis behaviour. However, these chemosensory complexes differ fundamentally from other systems, both structurally and functionally. Therefore, studying the organization of typical sensory kinases in bacteria is essential for understanding the general role of receptor clustering in bacterial sensory signalling. Here, by studying mYFP-tagged sensory kinases in Escherichia coli, we show that the tagged TorS and EvgS sensors have a clear tendency for self-association and clustering. These sensors clustered even when expressed at a level of a few hundred copies per cell. Moreover, the mYFP-tagged response regulator TorR showed clear TorS-dependent clustering, indicating that untagged TorS sensors also tend to form clusters. We also provide evidence for the functionality of these tagged sensors. Experiments with truncated TorS or EvgS proteins suggested that clustering of EvgS sensors depends on the cytoplasmic part of the protein, whereas clustering of TorS sensors can be potentially mediated by the periplasmic/transmembrane domain. Overall, these findings support the notion that sensor clustering plays a role in bacterial sensory signalling beyond chemotaxis.     

ODE,RDE and SDE models of cell cycle dynamics and clustering in yeast

Biologists have long observed periodic-like oxygen consumption oscillations in yeast populations under certain conditions, and several unsatisfactory explanations for this phenomenon have been proposed. These ‘autonomous oscillations’ have often appeared with periods that are nearly integer divisors of the calculated doubling time of the culture. We hypothesize that these oscillations could be caused by a form of cell cycle synchronization that we call clustering. We develop some novel ordinary differential equation models of the cell cycle. For these models, and for random and stochastic perturbations, we give both rigorous proofs and simulations showing that both positive and negative growth rate feedback within the cell cycle are possible agents that can cause clustering of populations within the cell cycle. It occurs for a variety of models and for a broad selection of parameter values. These results suggest that the clustering phenomenon is robust and is likely to be observed in nature. Since there are necessarily an integer number of clusters, clustering would lead to periodic-like behaviour with periods that are nearly integer divisors of the period of the cell cycle. Related experiments have shown conclusively that cell cycle clustering occurs in some oscillating yeast cultures.     

Clustering requires modified methyl-accepting sites in low-abundance but not high-abundance chemoreceptors of Escherichia coli

Chemotaxis signalling complexes of Escherichia coli, composed of chemoreceptors, CheA and CheW, form clusters located predominantly at cell poles. As the only kind of receptor in a cell, high-abundance receptors are polar and clustered whereas low-abundance chemoreceptors are polar but largely unclustered. We found that clustering was a function of the cytoplasmic, carboxyl-terminal domain and that effective clustering was conferred on low-abundance receptors by addition of the approximately 20-residue sequence from the carboxyl terminus of either high-abundance receptor. These sequences are different but share a carboxyl-terminal pentapeptide that enhances adaptational covalent modification and allows a physiological balance between modified and unmodified methyl-accepting sites, implying that receptor modification might influence clustering. Thus we investigated directly effects of modification state on chemoreceptor clustering. As the sole receptor type in a cell, low-abundance receptors were clustered only if modified, but high-abundance receptors were clustered independent of extent of modification. This difference could mean that the two receptor types are fundamentally different or that they are poised at different positions in the same conformational equilibrium. Notably, no receptor perturbation we tested altered a predominant location at cell poles, emphasizing a distinction between determinants of clustering and polar localization.     

Mathematical modelling of juxtacrine patterning

Spatial pattern formation is one of the key issues in developmental biology. Some patterns arising in early development have a very small spatial scale and a natural explanation is that they arise by direct cell—cell signalling in epithelia. This necessitates the use of a spatially discrete model, in contrast to the continuum-based approach of the widely studied Turing and mechanochemical models. In this work, we consider the pattern-forming potential of a model for juxtacrine communication, in which signalling molecules anchored in the cell membrane bind to and activate receptors on the surface of immediately neighbouring cells. The key assumption is that ligand and receptor production are both up-regulated by binding. By linear analysis, we show that conditions for pattern formation are dependent on the feedback functions of the model. We investigate the form of the pattern: specifically, we look at how the range of unstable wavenumbers varies with the parameter regime and find an estimate for the wavenumber associated with the fastest growing mode. A previous juxtacrine model for Delta-Notch signalling studied by Collier et al. (1996, J. Theor. Biol. 183, 429–446) only gives rise to patterning with a length scale of one or two cells, consistent with the fine-grained patterns seen in a number of developmental processes. However, there is evidence of longer range patterns in early development of the fruit fly Drosophila. The analysis we carry out predicts that patterns longer than one or two cell lengths are possible with our positive feedback mechanism, and numerical simulations confirm this. Our work shows that juxtacrine signalling provides a novel and robust mechanism for the generation of spatial patterns.     

Attractant binding induces distinct structural changes to the polar and lateral signaling clusters in Bacillus subtilis chemotaxis

Bacteria employ a modified two-component system for chemotaxis, where the receptors form ternary complexes with CheA histidine kinases and CheW adaptor proteins. These complexes are arranged in semi-ordered arrays clustered predominantly at the cell poles. The prevailing models assume that these arrays are static and reorganize only locally in response to attractant binding. Recent studies have shown, however, that these structures may in fact be much more fluid. We investigated the localization of the chemotaxis signaling arrays in Bacillus subtilis using immunofluorescence and live cell fluorescence microscopy. We found that the receptors were localized in clusters at the poles in most cells. However, when the cells were exposed to attractant, the number exhibiting polar clusters was reduced roughly 2-fold, whereas the number exhibiting lateral clusters distinct from the poles increased significantly. These changes in receptor clustering were reversible as polar localization was reestablished in adapted cells. We also investigated the dynamic localization of CheV, a hybrid protein consisting of an N-terminal CheW-like adaptor domain and a C-terminal response regulator domain that is known to be phosphorylated by CheA, using immunofluorescence. Interestingly, we found that CheV was localized predominantly at lateral clusters in unstimulated cells. However, upon exposure to attractant, CheV was found to be predominantly localized to the cell poles. Moreover, changes in CheV localization are phosphorylation-dependent. Collectively, these results suggest that the chemotaxis signaling arrays in B. subtilis are dynamic structures and that feedback loops involving phosphorylation may regulate the positioning of individual proteins.     

On periodic cohort solutions of a size-structured population model

 We consider a size-structured population model with discontinuous reproduction and feedback through the environmental variable ‘substrate’. The model admits solutions with finitely many cohorts and in that case the problem is described by a system of ODEs involving a bifurcation parameter β. Existence of nontrivial periodic n-cohort solutions is investigated. Moreover, we discuss the question whether n cohorts (n≧2) with small size differences will tend to a periodic one-cohort solution as t→∞. Received 16 March 1995; received in revised form 7 January 1997     

Receptive field properties of near neighbor orientation selective neurons in the visual cortex: a modeling study

The primary visual cortex is organized into clusters of cells having similar receptive fields (RFs). A purely feedforward model has been shown to produce realistic simple cell receptive fields. The modeled cells capture a wide range of receptive field properties of orientation selective cortical cells. We have analyzed the responses of 78 nearby cell pairs to study which RF properties are clustered. Orientation preference shows strongest clustering. Orientation tuning width (hwhh) and tuning height (spikes/sec) at the preferred orientation are not as tightly clustered. Spatial frequency is also not as tightly clustered and RF phase has the least clustering. Clustering property of orientation preference, orientation tuning height and width depend on the location of cells in the orientation map. No such location dependence is observed for spatial frequency and RF phase. Our results agree well with experimental data.     

A Highlights from MBoC Selection: Slk19 clusters kinetochores and facilitates chromosome bipolar attachment

In all eukaryotic cells, DNA is packaged into multiple chromosomes that are linked to microtubules through a large protein complex called a kinetochore. Previous data show that the kinetochores are clustered together during most of the cell cycle, but the mechanism and the biological significance of kinetochore clustering are unknown. As a kinetochore protein in budding yeast, the role of Slk19 in the stability of the anaphase spindle has been well studied, but its function in chromosome segregation has remained elusive. Here we show that Slk19 is required for kinetochore clustering when yeast cells are treated with the microtubule-depolymerizing agent nocodazole. We further find that slk19Δ mutant cells exhibit delayed kinetochore capture and chromosome bipolar attachment after the disruption of the kinetochore–microtubule interaction by nocodazole, which is likely attributed to defective kinetochore clustering. In addition, we show that Slk19 interacts with itself, suggesting that the dimerization of Slk19 may mediate the interaction between kinetochores for clustering. Therefore Slk19 likely acts as kinetochore glue that clusters kinetochores to facilitate efficient and faithful chromosome segregation.     

Lipid raft proteins have a random distribution during localized activation of the T-cell receptor

The extent to which lipid raft proteins are organized in functional clusters within the plasma membrane is central to the debate on structure and function of rafts. Glycosylphosphatidylinositol (GPI)-linked proteins are characteristic components of biochemically defined rafts. Several studies report a function for rafts in T-cell stimulation, but it is unclear whether molecules involved in T-cell receptor (TCR) signalling are recruited to (or excluded from) T-cell synapses through asymmetric distribution of raft microdomains or through specific protein-protein interactions. Here we used FRET analysis in live cells to determine whether GPI-linked proteins are clustered in the plasma membrane of unstimulated cells, and at regions where TCR signalling has been activated using antibody-coated beads. Multiple criteria suggested that FRET between different GPI-linked fluorescent proteins in COS-7 or unstimulated Jurkat T-cells is generated by a random, un-clustered distribution. Stimulation of TCR signalling in Jurkat cells resulted in localized increases in fluorescence of GPI-linked fluorescent proteins and cholera toxin B-subunit (CTB). However, measurements of FRET and ratio imaging showed that there was no detectable clustering and no overall enrichment of GPI-linked proteins or CTB in these regions.     

Spatial organization in bacterial chemotaxis

Spatial organization of signalling is not an exclusive property of eukaryotic cells. Despite the fact that bacterial signalling pathways are generally simpler than those in eukaryotes, there are several well‐documented examples of higher‐order intracellular signalling structures in bacteria. One of the most prominent and best‐characterized structures is formed by proteins that control bacterial chemotaxis. Signals in chemotaxis are processed by ordered arrays, or clusters, of receptors and associated proteins, which amplify and integrate chemotactic stimuli in a highly cooperative manner. Receptor clusters further serve to scaffold protein interactions, enhancing the efficiency and specificity of the pathway reactions and preventing the formation of signalling gradients through the cell body. Moreover, clustering can also ensure spatial separation of multiple chemotaxis systems in one bacterium. Assembly of receptor clusters appears to be a stochastic process, but bacteria evolved mechanisms to ensure optimal cluster distribution along the cell body for partitioning to daughter cells at division.     

A density-dependent switch drives stochastic clustering and polarization of signaling molecules

Positive feedback plays a key role in the ability of signaling molecules to form highly localized clusters in the membrane or cytosol of cells. Such clustering can occur in the absence of localizing mechanisms such as pre-existing spatial cues, diffusional barriers, or molecular cross-linking. What prevents positive feedback from amplifying inevitable biological noise when an un-clustered “off” state is desired? And, what limits the spread of clusters when an “on” state is desired? Here, we show that a minimal positive feedback circuit provides the general principle for both suppressing and amplifying noise: below a critical density of signaling molecules, clustering switches off; above this threshold, highly localized clusters are recurrently generated. Clustering occurs only in the stochastic regime, suggesting that finite sizes of molecular populations cannot be ignored in signal transduction networks. The emergence of a dominant cluster for finite numbers of molecules is partly a phenomenon of random sampling, analogous to the fixation or loss of neutral mutations in finite populations. We refer to our model as the “neutral drift polarity model.” Regulating the density of signaling molecules provides a simple mechanism for a positive feedback circuit to robustly switch between clustered and un-clustered states. The intrinsic ability of positive feedback both to create and suppress clustering is a general mechanism that could operate within diverse biological networks to create dynamic spatial organization.     

Yeast Nuclei Display Prominent Centromere Clustering That Is Reduced in Nondividing Cells and in Meiotic Prophase

Chromosome arrangement in spread nuclei of the budding yeast, Saccharomyces cerevisiae was studied by fluorescence in situ hybridization with probes to centromeres and telomeric chromosome regions. We found that during interphase centromeres are tightly clustered in a peripheral region of the nucleus, whereas telomeres tend to occupy the area outside the centromeric domain. In vigorously growing cultures, centromere clustering occurred in ~90% of cells and it appeared to be maintained throughout interphase. It was reduced when cells were kept under stationary conditions for an extended period. In meiosis, centromere clusters disintegrated before the emergence of the earliest precursors of the synaptonemal complex. Evidence for the contribution of centromere clustering to other aspects of suprachromosomal nuclear order, in particular the vegetative association of homologous chromosomes, is provided, and a possible supporting role in meiotic homology searching is discussed.     

Dynamics and stability of a three-dimensional model of cell signal transduction

In this paper, we consider a three-dimensional model of cell signal transduction. In this model, the deactivation of signalling proteins occur throughout the cytosol and activation is localized to specific sites in the cell. We use matched asymptotic expansions to construct the dynamic solutions of signalling protein concentrations. The result of the asymptotic analysis is a system of ordinary differential equations. This reduced system is compared to numerical simulations of the full three-dimensional system. As well, we consider the stability of equilibrium solutions. We find that the systems under consideration may undergo sustained oscillations, hysteresis and other complex behaviors. The simulations of the full three-dimensional system agree with simulations of the reduced ordinary differential equations.     

Regulation of cell size and Wee1 kinase by elevated levels of the cell cycle regulatory protein kinase Cdr2

Many cell cycle regulatory proteins catalyze cell cycle progression in a concentration-dependent manner. In the fission yeast Schizosaccharomyces pombe, the protein kinase Cdr2 promotes mitotic entry by organizing cortical oligomeric nodes that lead to inhibition of Wee1, which itself inhibits the cyclin-dependent kinase Cdk1. cdr2Δ cells lack nodes and divide at increased size due to overactive Wee1, but it has not been known how increased Cdr2 levels might impact Wee1 and cell size. It also has not been clear if and how Cdr2 might regulate Wee1 in the absence of the related kinase Cdr1/Nim1. Using a tetracycline-inducible expression system, we found that a 6× increase in Cdr2 expression caused hyperphosphorylation of Wee1 and reduction in cell size even in the absence of Cdr1/Nim1. This overexpressed Cdr2 formed clusters that sequestered Wee1 adjacent to the nuclear envelope. Cdr2 mutants that disrupt either kinase activity or clustering ability failed to sequester Wee1 and to reduce cell size. We propose that Cdr2 acts as a dosage-dependent regulator of cell size by sequestering its substrate Wee1 in cytoplasmic clusters, away from Cdk1 in the nucleus. This mechanism has implications for other clustered kinases, which may act similarly by sequestering substrates.     

TlpC,a novel chemotaxis protein in Rhodobacter sphaeroides,localizes to a discrete region in the cytoplasm

TlpC is encoded in the second chemotaxis operon of Rhodobacter sphaeroides. This protein shows some homology to membrane-spanning chemoreceptors of many bacterial species but, unlike these, is essential for R. sphaeroides chemotaxis to all compounds tested. Genomic replacement of tlpC with a C-terminal gfp fusion demonstrated that TlpC localized to a discrete cluster within the cytoplasm. Immunogold electron microscopy also showed that TlpC localized to a cytoplasmic electron-dense region. Correct TlpC-GFP localization depended on the downstream signalling proteins, CheW3, CheW4 and CheA2, and was tightly linked to cell division. Newly divided cells contained a single cluster but, as the cell cycle progressed, a second cluster appeared close to the initial cluster. As elongation continued, these clusters moved apart so that, on septation, each daughter cell contained a single TlpC cluster. The data presented suggest that TlpC is either a cytoplasmic chemoreceptor responding to or integrating global signals of metabolic state or a novel and essential component of the chemotaxis signalling pathway. These data also suggest that clustering is essential for signalling and that a mechanism may exist for targeting and localizing proteins within the bacterial cytoplasm.     

The importance of an inter-compartmental delay in a model for human gastric acid secretion

In this work we re-examine an existing model of gastric acid secretion. The model is a 2-compartment model of the human stomach accounting for regions where relevant cells (D, G, ECL and parietal cells) and proteins and acid they secrete (somatostatin, gastrin, histamine, and gastric acid, respectively) are found. These proteins compose a positive and negative feedback system that controls the secretion of gastric acid by parietal cells. The original model consists of 18 ordinary differential equations and yields a stable 3-period limit cycle solution. We modify the existing model by introducing a delay into the system and assuming that the cell populations are in steady state over a short-time window (<300 h) and are able to reduce the system to an 8-equation delay differential equation model. In addition to demonstrating congruency between the two models, we also show that a similar stability is only reproducible when the delay in gastrin transport is approximately 30 min. This suggests that gastric acid secretion homeostasis likely depends strongly on the delay in gastrin transport from the antrum to the corpus. Equal contribution.