A theory of measurement error and its implications for spatial and temporal gradient sensing during chemotaxis

Cells generally chemotax along a direction in which their receptor occupancy gradient—whether spatial or temporal—is maximum. Occupancy differentials are, however, often so small as to be masked by thermal noise; i.e., by fluctuations inherent in the stochastic nature of ligand binding. Such fluctuations therefore impose a fundamental limit on the sensitivity of a cell's ability to detect a chemoattractant gradient. In order to pursue the implications of this limit, fluctuation theories have been developed. The theories assume that the signal is some function of the receptor occupancy gradient, allow an estimate of the standard deviation abouts the mean signal, and permit an evaluation of, among other things, the extent to which a receptor defect can impair an effective response. Previous theories have assumed an equilibrated ligand-receptor interaction. In this paper we introduce a generalized definition of a signal caused by a receptor occupancy gradient that allows us to develop a non-equilibrium theory of thermal noise. We show that previous formulations are a special case of the current development. More specifically, we find the following.

1. Swimming cells subject to Brownian tumbling must generally average their signals over a very long time period to achieve a signal-to-noise ratio≤1. Spatial gradient detection is possible with ligand-receptor equilibrium constants<10³ M ^?1, but since such ligands are rare, theory predicts that tumbling cells will generally not detect gradients by measuring spatial occupancy differentials.These conclusions hold irrespective of whether chemical equilibrium is achieved.
2. For crawling cells not subject to Brownian tumbling, a range of affinities exists in which spatial or temporal gradient detection is possible. In general a spatial mechanism is more efficient for low affinity ligands (dissociation times <0.3s), whereas a temporal mechanism is more efficients for higherK. In this case the detection of gradients in slowly dissociating ligand will be facilitated if signal processing begins prior to chemical equilibration.
3. An important new parameter is indicated by the theory. The definitions of a temporal gradient signal is based on estimating and comparing average occupancy over two time intervals displaced by a timet ₁. The theory predicts an optimalt ₁, of order milliseconds, that leads to the shortest minimum averaging time.
4. Fort ₁ values at and longer than the optimum, and for all averaging times exceeding some minimum, the cell will detect a temporal signal.
5. For values oft ₁ at and near the optimum, if the averaging time becomes too long, the cell enters a region of insensitivity in which it can no longer respond.
6. Finally, as the interval between estimates of average occupancy decreases below the optimum, a critical value oft ₁ is reached at which the minimum averaging time undergoes an abrupt transition from a relatively short value to a value five orders of magnitude longer.

The molecular process(es) controllingt ₁ are at present unknown, nor has any attempt been made to identify them since the parameter has not been previously recognized. We speculate that the search for its molecular basis might uncover a highly sensitive control mechanism, with defects in this mechanism predicted to have a far more pronounced effect on the cells behavior than defects in receptor number or affinity.     

A theory of measurement error and its implications for spatial and temporal gradient sensing during chemotaxis

In order that cells respond to environmental cues, they must be able to measure ambient ligand concentration. Concentrations fluctuate, however, because of thermal noise, and one can readily show that estimates based on concentration values at a particular moment will be subject to substantial error. Cells are therefore expected to average their estimates over some limited time period. In this paper we assume that a cell uses fractional receptor occupancy as a measure of ambient ligand concentration and develop general expressions for the error a cell makes because the length of the averaging period is necessarily limited. Our analysis is general, relieving many of the assumptions underlying the seminal work of Berg and Purcell. The most important formal difference is our inclusion of occupancy-dependent dissociation--a phenomenon that has been well-documented for many systems. In addition, our formulation permits signal averaging to begin before chemical equilibrium has been established and it allows binding kinetics to be nonlinear (i.e., biomolecular rather than pseudo-first-order). The results are applied to spatial and temporal concentration gradients. In particular we estimate the minimum averaging times required for cells to detect such gradients under typical in vitro conditions. These estimates involve assigning numerical values to receptor ligand rate constants. If the rate constants are at their maximum possible values (limited only by center of mass diffusion), then either temporal or spatial gradients can be detected in minutes or less. If, however, as suggested by experiments, the rate constants are several orders of magnitude below their diffusion-limited values, then under typical constant gradient conditions the time required to detect a spatial gradient is prohibitively long, whereas temporal gradients can still be detected in reasonable lengths of time. This result was obtained for large cells such as lymphocytes, as well as for the smaller, bacterial cells. The ratio of averaging times for the two mechanisms--amounting to several orders of magnitude--is well beyond what could be reconciled by limitations of the calculation, and strongly suggests heavy reliance on temporal sensing mechanisms under typical in vitro conditions with constant spatial gradients.     

Adaptation is not required to explain the long-term response of axons to molecular gradients

It has been suggested that growth cones navigating through the developing nervous system might display adaptation, so that their response to gradient signals is conserved over wide variations in ligand concentration. Recently however, a new chemotaxis assay that allows the effect of gradient parameters on axonal trajectories to be finely varied has revealed a decline in gradient sensitivity on either side of an optimal concentration. We show that this behavior can be quantitatively reproduced with a computational model of axonal chemotaxis that does not employ explicit adaptation. Two crucial components of this model required to reproduce the observed sensitivity are spatial and temporal averaging. These can be interpreted as corresponding, respectively, to the spatial spread of signaling effects downstream from receptor binding, and to the finite time over which these signaling effects decay. For spatial averaging, the model predicts that an effective range of roughly one-third of the extent of the growth cone is optimal for detecting small gradient signals. For temporal decay, a timescale of about 3 minutes is required for the model to reproduce the experimentally observed sensitivity.     

Consequences of chemosensory phenomena for leukocyte chemotactic orientation

The stochastic nature of cell surface receptor-ligand binding is known to limit the accuracy of detection of chemoattractant gradients by leukocytes, thus limiting the orientation ability that is crucial to the chemotactic response in host defense. The probabilistic cell orientation model of Lauffenburger is extended here to assess the consequences of recently discovered receptor phenomena: "down-regulation" of total surface receptor number, spatial asymmetry of surface receptors, and existence of a higher-affinity receptor subpopulation. In general, a reduction in orientation accuracy is predicted by inclusion of these phenomena. An orientation signal based on a simple model of chemosensory adaptation (i.e., a spatial difference in relative receptor occupancy) is found to be functionally different from the signal suggested by an experimental correlation (i.e., a spatial difference in absolute receptor occupancy). However, in the context of receptor "signal noise," the signal based on adaptation yields predictions in better qualitative agreement with the experimental orientation data of Zigmond. From this cell orientation model we can estimate the effective time-averaging period required for noise diminution to a level allowing orientation predictions to match observed levels. This time-averaging period presumably reflects the time constant for receptor signal transduction and locomotory response.     

Detection of climate change‐driven trends in phytoplankton phenology

The timing of the annual phytoplankton spring bloom is likely to be altered in response to climate change. Quantifying that response has, however, been limited by the typically coarse temporal resolution (monthly) of global climate models. Here, we use higher resolution model output (maximum 5 days) to investigate how phytoplankton bloom timing changes in response to projected 21st century climate change, and how the temporal resolution of data influences the detection of long‐term trends. We find that bloom timing generally shifts later at mid‐latitudes and earlier at high and low latitudes by ~5 days per decade to 2100. The spatial patterns of bloom timing are similar in both low (monthly) and high (5 day) resolution data, although initiation dates are later at low resolution. The magnitude of the trends in bloom timing from 2006 to 2100 is very similar at high and low resolution, with the result that the number of years of data needed to detect a trend in phytoplankton phenology is relatively insensitive to data temporal resolution. We also investigate the influence of spatial scales on bloom timing and find that trends are generally more rapidly detectable after spatial averaging of data. Our results suggest that, if pinpointing the start date of the spring bloom is the priority, the highest possible temporal resolution data should be used. However, if the priority is detecting long‐term trends in bloom timing, data at a temporal resolution of 20 days are likely to be sufficient. Furthermore, our results suggest that data sources which allow for spatial averaging will promote more rapid trend detection.     

Use of classical bird census transects as spatial replicates for hierarchical modeling of an avian community

New monitoring programs are often designed with some form of temporal replication to deal with imperfect detection by means of occupancy models. However, classical bird census data from earlier times often lack temporal replication, precluding detection‐corrected inferences about occupancy. Historical data have a key role in many ecological studies intended to document range shifts, and so need to be made comparable with present‐day data by accounting for detection probability. We analyze a classical bird census conducted in the region of Murcia (SE Spain) in 1991 and 1992 and propose a solution to estimating detection probability for such historical data when used in a community occupancy model: the spatial replication of subplots nested within larger plots allows estimation of detection probability. In our study, the basic sample units were 1‐km transects, which were considered spatial replicates in two aggregation schemes. We fit two Bayesian multispecies occupancy models, one for each aggregation scheme, and evaluated the linear and quadratic effect of forest cover and temperature, and a linear effect of precipitation on species occupancy probabilities. Using spatial rather than temporal replicates allowed us to obtain individual species occupancy probabilities and species richness accounting for imperfect detection. Species‐specific occupancy and community size decreased with increasing annual mean temperature. Both aggregation schemes yielded estimates of occupancy and detectability that were highly correlated for each species, so in the design of future surveys ecological reasons and cost‐effective sampling designs should be considered to select the most suitable aggregation scheme. In conclusion, the use of spatial replication may often allow historical survey data to be applied formally hierarchical occupancy models and be compared with modern‐day data of the species community to analyze global change process.     

Receptor specificity of the fibroblast growth factor family. The complete mammalian FGF family

In mammals, fibroblast growth factors (FGFs) are encoded by 22 genes. FGFs bind and activate alternatively spliced forms of four tyrosine kinase FGF receptors (FGFRs 1-4). The spatial and temporal expression patterns of FGFs and FGFRs and the ability of specific ligand-receptor pairs to actively signal are important factors regulating FGF activity in a variety of biological processes. FGF signaling activity is regulated by the binding specificity of ligands and receptors and is modulated by extrinsic cofactors such as heparan sulfate proteoglycans. In previous studies, we have engineered BaF3 cell lines to express the seven principal FGFRs and used these cell lines to determine the receptor binding specificity of FGFs 1-9 by using relative mitogenic activity as the readout. Here we have extended these semiquantitative studies to assess the receptor binding specificity of the remaining FGFs 10-23. This study completes the mitogenesis-based comparison of receptor specificity of the entire FGF family under standard conditions and should help in interpreting and predicting in vivo biological activity.     

Spatial dynamics of an invasive bird species assessed using robust design occupancy analysis: the case of the Eurasian collared dove (Streptopelia decaocto) in France

Aim The study of the spatial dynamics of invasive species is a key issue in invasion ecology. While mathematical models are useful for predicting the extent of population expansions, they are not suitable for measuring and characterizing spatial patterns of invasion unless the probability of detection is homogeneous across the distribution range. Here, we apply recently developed statistical approaches incorporating detection uncertainty to characterize the spatial dynamics of an invasive bird species, the Eurasian collared dove (Streptopelia decaocto). Location France. Methods Data on presence/absence of doves were recorded from 1996 to 2004 over 1045 grid cells (28 × 20 km) covering the entire country. Each grid cell included five point counts spaced along a route, which was visited twice a year, allowing for an estimation of detection probability. Each route was assigned to one of six geographical regions. We used robust design occupancy analysis to assess spatial and temporal variation in parameters related to the spatial dynamics of the species. These parameters included occupancy rate, colonization and local extinction probabilities. Our inference approach was based on the selection of the most parsimonious model among competitive models parametrized with conditional probabilities. Results The probability of detecting the presence of doves on a given route was high. However, we found evidence to incorporate detection uncertainty in inference processes about spatial dynamics, since detection probability was neither perfect (i.e. it was < 1), nor constant over space and time. Results showed a clear positive trend in occupancy rate over the study period, increasing from 55% in 1996 to 76% in 2004. In addition, occupancy rate differed among regions (range: 37–79%) and further analysis showed that colonization probability by region was positively related to occupancy rate. Finally, local extinction probability was lower than colonization probability and showed a tendency to decrease over the study period. Main conclusions Our results emphasize the importance of estimating detection probabilities in order to draw proper inferences about the spatial and temporal dynamics of the invasion pattern of the collared dove. In contrast to the perceived spatial dynamics from national atlas surveys, we provide evidence that the range of this species is currently increasing in France. Other results, such as regional specificity in colonization probabilities and time variation in local extinction are consistent with expectations from invasion and metapopulation theory.     

The ligand-receptor-G-protein ternary complex as a GTP-synthase. steady-state proton pumping and dose-response relationships for beta -adrenoceptors

Steady-state solutions are developed for the rate of G alpha.GTP production in a synthase model of the ligand-receptor-G-protein ternary complex activated by a ligand-receptor proton pumping mechanism. The effective rate, k(31), defining the proton transfer, phosphorylation and G alpha.GTP release is a controlling rate of the synthase in the presence of a ligand with an efficient mode of signal activation, the ligand-receptor interaction taking place under effectively equilibrium conditions. The composite rate, however, becomes an amplifying factor in any dose-response relationship. The amplification is a triple product of the rate, k(31), the equilibrium constant associated with the activation of the proton signal, K(act)and the fraction of agonist conformer transmitting the signal, f(*). Where the rate of activation of the proton signal becomes critically inefficient, the rate of activation, k(act 1)replaces k(31)K(act). A correlation between beta(1)-adrenergic receptor-stimulated GDP release and adenylate cyclase activation shows that this correlation is not unique to an exchange reaction. Within the initiating Tyr-Arg-Tyr receptor proton shuttle mechanism, the position of Arg(r156) paralleldictates the high-(R(p)) and low-(R(u)) ligand-binding affinities. These states are close to R(*)and R(0)of the equilibrium model (De Lean et al., 1980, J. Biol. Chem.255, 7108-7117). An increased rate of hydrogen ion diffusion into a receptor mutant can give rise to constitutive activity while increased rates of G-protein release and changes in receptor state balance can contribute to the resultant level of action. Constitutive action will arise from a faster rate of G-protein release alone if proton diffusion in the wild-type receptor contributes to a basal level of G-protein activation. Competitive ligand-receptor occupancy for constitutive mutants shows that, where the rate of G-protein activation from the proportion of ligand-occupied receptors is less than the equivalent rate that would be generated from this fraction by proton diffusion, inverse agonism will occur. Rate-dependent dose-responses developed for the proposed synthase mechanism give explicit definition to the operational model for partial agonism (Black & Leff, 1983, Proc. Roy. Soc. Lond. B220, 141-162). When comparable ligands have effectively identical conformational states at the transition state for signal activation, the antagonist component of the binding "in vitro" can be derived by multiplying the apparent binding constant by (1-e) where e is the maximum stimulatory response. This component should be consistent throughout the tissues.     

Consequences of chemosensory phenomena for leukocyte chemotactic orientation

The stochastic nature of cell surface receptor-ligand binding is known to limit the accuracy of detection of chemoattractant gradients by leukocytes (11, 12), thus limiting the orientation ability that is crucial to the chemotactic response in host defense. The probabilistic cell orientation model of Lauffenburger (11) is extended here to assess the consequences of recently discovered receptor phenomena: “down-regulation” of total surface receptor number, spatial asymmetry of surface receptors, and existence of a higher-affinity receptor subpopulation. In general, a reduction in orientation accuracy is predicted by inclusion of these phenomena. An orientation signal based on a simple model of chemosensory adaptation (i.e., a spatial difference inrelative receptor occupancy) is found to be functionally different from the signal suggested by an experimental correlation (i.e., a spatial difference inabsolute receptor occupancy). However, in the context of receptor “signal noise,” the signal based on adaptation yields predictions in better qualitative agreement with the experimental orientation data of Zigmond (10). From this cell orientation model we can estimate the effective timeaveraging period required for noise diminution to a level allowing orientation predictions to match observed levels. This time-averaging period presumably reflects the time constant for receptor signal transduction and locomotory response.     

Chemosensory and thermosensory excitation in adaptation-deficient mutants of Escherichia coli

Methyl-accepting chemotaxis protein-methyltransferase-deficient mutants, cheR mutants, of Escherichia coli showed a tumble response to repellents only at low temperatures, and the resultant tumbling lasted unless the condition was changed. The swimming pattern of the repellent-treated cells was different at different temperatures, indicating that the absolute temperature is a determinant of the tumbling frequency of those cells. The tumbling of those cells was also suppressed by the addition of attractants. Under a suitable repellent concentration, the tumbling frequency of the cells was found to be simply determined by the ligand occupancy of chemoreceptors for many attractants. In a methyl-accepting chemotaxis protein-methylesterase-deficient mutant, a cheB deletion mutant, the tumbling frequency was also determined by receptor occupancy of some attractants. These results indicate that in the adaptation-deficient mutants, sensory signals are produced in proportion to the amount of ligand-bound or of thermally altered receptors and transmitted to the flagellar motors without any modification. Thus, it is concluded that the adaptation system, namely, the methylation-demethylation system of methyl-accepting chemotaxis proteins, is not concerned with the step of chemosensory or thermosensory excitation. A simple model is proposed to explain how the swimming pattern of the adaptation-deficient mutants is determined.     

At what spatial scale(s) do mammals respond to urbanization?

Spatial scale is fundamental in understanding species–landscape relationships because species’ responses to landscape characteristics typically vary across scales. Nonetheless, such scales are often unidentified or unreliably predicted by theory. Many landscapes worldwide are urbanizing, yet the spatial scaling of species’ responses to urbanization is poorly understood. We investigated the spatial scaling of urbanization effects on a community of 15 mammal species using ~60 000 wildlife detections collected from a constellation of 207 camera traps across an extensive urban park system. We embedded a bivariate Gaussian kernel in hierarchical multi-species models to determine two scales of effect (a scale of maximal effect and a broader scale of cumulative landscape effect) for two biological responses (occupancy and site visit frequency) across two seasons (winter and summer) for each species. We then assessed whether scales of effect varied according to theoretical predictions associated with biological responses and species traits (body size and mobility). Scales of effect ranged from < 50 m to > 9000 m and varied among species, but not as predicted by theory. Species’ occupancy generally showed a weak response to urbanization and the scale of this effect was both highly uncertain and consistent across species. We did not detect any relationship between scales of effect and species’ body size or mobility, nor was there any evident pattern of scaling across biological response or seasons. These results imply that 1) urbanization effects on mammals manifest across a very broad spectrum of spatial scales, and 2) current theories that a priori predict the scale at which urbanization affects mammals may be of limited use within a given system. Overall, this study suggests that developing general theory regarding the scaling of species–landscape relationships requires additional empirical work conducted across multiple species, systems and timescales.     

Concentration sensing in crowded environments

Signal transduction within crowded cellular compartments is essential for the physiological function of cells. Although the accuracy with which receptors can probe the concentration of ligands has been thoroughly investigated in dilute systems, the effect of macromolecular crowding on the inference of concentration remains unclear. In this work, we develop an algorithm to simulate reversible reactions between reacting Brownian particles. Our algorithm facilitates the calculation of reaction rates and correlation times for ligand-receptor systems in the presence of macromolecular crowding. Using this method, we show that it is possible for crowding to increase the accuracy of estimated ligand concentration based on receptor occupancy. In particular, we find that crowding can enhance the effective association rates between small ligands and receptors to a degree sufficient to overcome the increased chance of rebinding due to caging by crowding molecules. For larger ligands, crowding decreases the accuracy of the receptor’s estimate primarily by decreasing the microscopic association and dissociation rates.     

The chemotaxis defect of Shwachman-Diamond Syndrome leukocytes

Shwachman-Diamond Syndrome (SDS) is a rare autosomal recessive, multisystem disorder presenting in childhood with intermittent neutropenia and pancreatic insufficiency. It is characterized by recurrent infections independent of neutropenia, suggesting a functional neutrophil defect. While mutations at a single gene locus (SBDS) appear to be responsible for SDS in a majority of patients, the function of that gene and a specific defect in SDS neutrophil behavior have not been elucidated. Therefore, employing 2D and 3D computer-assisted motion analysis systems, we have analyzed the basic motile behavior and chemotactic responsiveness of individual polymorphonuclear leukocytes (PMNs) of 14 clinically diagnosed SDS patients. It is demonstrated that the basic motile behavior of SDS PMNs is normal in the absence of chemoattractant, that SDS PMNs respond normally to increasing and decreasing temporal gradients of the chemoattractant fMLP, and that SDS PMNs exhibit a normal chemokinetic response to a spatial gradient of fMLP. fMLP receptors were also distributed uniformly through the plasma membrane of SDS PMNs as in control PMNs. SDS PMNs, however, were incapable of orienting in and chemotaxing up a spatial gradient of fMLP. This unique defect in orientation was manifested by the PMNs of every SDS patient tested. The PMNs of an SDS patient who had received an allogenic hematopoietic stem cell transplant, as well as PMNs from a cystic fibrosis patient, oriented normally. These results suggest that the defect in SDS PMNs is in a specific pathway emanating from the fMLP receptor that is involved exclusively in regulating orientation in response to a spatial gradient of fMLP. This pathway must function in parallel with additional pathways, intact in SDS patients, that emanate from the fMLP receptor and regulate responses to temporal rather than spatial changes in receptor occupancy.     

Dynamic receptor team formation can explain the high signal transduction gain in Escherichia coli

Evolution has provided many organisms with sophisticated sensory systems that enable them to respond to signals in their environment. The response frequently involves alteration in the pattern of movement, either by directed movement, a process called taxis, or by altering the speed or frequency of turning, which is called kinesis. Chemokinesis has been most thoroughly studied in the peritrichous bacterium Escherichia coli, which has four helical flagella distributed over the cell surface, and swims by rotating them. When rotated counterclockwise the flagella coalesce into a propulsive bundle, producing a relatively straight "run," and when rotated clockwise they fly apart, resulting in a "tumble" which reorients the cell with little translocation. A stochastic process generates the runs and tumbles, and in a chemoeffector gradient, runs that carry the cell in a favorable direction are extended. The cell senses spatial gradients as temporal changes in receptor occupancy and changes the probability of counterclockwise rotation (the bias) on a fast timescale, but adaptation returns the bias to baseline on a slow timescale, enabling the cell to detect and respond to further concentration changes. The overall structure of the signal transduction pathways is well characterized in E. coli, but important details are still not understood. Only recently has a source of gain in the signal transduction network been identified experimentally, and here we present a mathematical model based on dynamic assembly of receptor teams that can explain this observation.     

Cytoplasmic pH mediates pH taxis and weak-acid repellent taxis of bacteria.

Bacteria migrate away from an acid pH and from a number of chemicals, including organic acids such as acetate; the basis for detection of these environmental cues has not been demonstrated. Membrane-permeant weak acids caused prolonged tumbling when added to Salmonella sp. or Escherichia coli cells at pH 5.5. Tethered Salmonella cells went from a prestimulus behavior of 14% clockwise rotation to 80% clockwise rotation when 40 mM acetate was added and remained this way for more than 30 min. A low external pH in the absence of weak acid did not markedly affect steady-state tumbling frequency. Among the weak acids tested, the rank for acidity (salicylate greater than benzoate greater than acetate greater than 5,5-dimethyl-2,4-oxazolidinedione) was the same as the rank for the ability to collapse the transmembrane pH gradient and to cause tumbling. At pH 7.0, the tumbling responses caused by the weak acids were much briefer. Indole, a non-weak-acid repellent, did not cause prolonged tumbling at low pH. Two chemotaxis mutants (a Salmonella mutant defective in the chemotaxis methylesterase and an E. coli mutant defective in the methyl-accepting protein in MCP I) showed inverse responses of enhanced counterclockwise rotation in the first 1 min after acetate addition. The latter mutant had been found previously to be defective in the sensing of gradients of extracellular pH and (at neutral pH) of acetate. We conclude (i) that taxes away from acid pH and membrane-permeant weak acids are both mediated by a pH-sensitive component located either in the cytoplasm or on the cytoplasmic side of the membrane, rather than by an external receptor (as in the case of the attractants), and (ii) that both of these taxes involve components of the chemotaxis methylation system, at least in the early phase of the response.     

Spatial sensing of stimulus gradients can be superior to temporal sensing for free-swimming bacteria.

Predictions of the minimal size an organism must have to swim along stimulus gradients were used to compare the relative advantages of sensory systems employing spatial (simultaneous) and temporal (sequential) gradient detection mechanisms for small free-swimming bacteria, leading to the following conclusions: 1) there are environmental conditions where spatial detection mechanisms can function for smaller organisms than can temporal mechanisms, 2) temporal mechanisms are superior (have a smaller size limit) for the difficult conditions of low concentration and shallow gradients, but 3) observed bacterial chemotaxis occurs mostly under conditions where spatial mechanisms have a smaller size limit, and 4) relevant conditions in the natural environment favor temporal mechanisms in some cases and spatial mechanisms in others. Thus, sensory ecology considerations do not preclude free-swimming bacteria from employing spatial detection mechanisms, as has been thought, and microbiologists should be on the lookout for them. If spatial mechanisms do not occur, the explanation should be sought elsewhere.     

Persistence of direction increases the drift velocity of run and tumble chemotaxis

Escherichia coli is a motile bacterium that moves up a chemoattractant gradient by performing a biased random walk composed of alternating runs and tumbles. Previous models of run and tumble chemotaxis neglect one or more features of the motion, namely (a) a cell cannot directly detect a chemoattractant gradient but rather makes temporal comparisons of chemoattractant concentration, (b) rather than being entirely random, tumbles exhibit persistence of direction, meaning that the new direction after a tumble is more likely to be in the forward hemisphere, and (c) rotational Brownian motion makes it impossible for an E. coli cell to swim in a straight line during a run. This paper presents an analytic calculation of the chemotactic drift velocity taking account of (a), (b) and (c), for weak chemotaxis. The analytic results are verified by Monte Carlo simulation. The results reveal a synergy between temporal comparisons and persistence that enhances the drift velocity, while rotational Brownian motion reduces the drift velocity. This work was supported by an Oliver Gatty Studentship from the University of Cambridge.     

Theoretical analysis of gradient detection by growth cones.

Gradients of diffusible and substrate-bound molecules play an important role in guiding axons to appropriate targets in the developing nervous system. Although some of the molecules involved have recently been identified, little is known about the physical mechanisms by which growth cones sense gradients. This article applies the seminal Berg and Purcell (1977) model of gradient sensing to this problem. The model provides estimates for the statistical fluctuations in the measurement of concentration by a small sensing device. By assuming that gradient detection consists of the comparison of concentrations at two spatially or temporally separated points, the model therefore provides an estimate for the steepness of gradient that can be detected as a function of physiological parameters. The model makes the following specific predictions. (a) It is more likely that growth cones use a spatial rather than temporal sensing strategy. (b) Growth cone sensitivity increases with the concentration of ligand, the speed of ligand diffusion, the size of the growth cone, and the time over which it averages the gradient signal. (c) The minimum detectable gradient steepness for growth cones is roughly in the range 1-10%. (d) This value varies depending on whether a bound or freely diffusing ligand is being sensed, and on whether the sensing occurs in three or two dimensions. The model also makes predictions concerning the role of filopodia in gradient detection.     

Roles of cheY and cheZ gene products in controlling flagellar rotation in bacterial chemotaxis of Escherichia coli.

To understand output control in bacterial chemotaxis, we varied the levels of expression of cellular cheY and cheZ genes and found that the overproduction of the corresponding proteins affected Escherichia coli swimming behavior. In the absence of other signal-transducing gene products, CheY overproduction made free-swimming cells tumble more frequently. A plot of the fraction of the population that are tumbling versus the CheY concentration was hyperbolic, with half of the population tumbling at 30 microM (25,000 copies per cell) CheY monomers in the cytosol. Overproduction of aspartate receptor (Tar) by 30-fold had a negligible effect on CheY-induced tumbling, so Tar does not sequester CheY. CheZ overproduction decreased tumbling in all tumbling mutants except certain flaAII(cheC) mutants. In the absence of other chemotaxis gene products, CheZ overproduction inhibited CheY-induced tumbling. Models for CheY as a tumbling signal and CheZ as a smooth-swimming signal to control flagellar rotation are discussed.