Studies of bacterial chemotaxis in defined concentration gradients. A model for chemotaxis toward L-serine

The details of the chemotactic response of Salmonella typhimurium to gradients of L-serine have been examined in some detail. Two relatively macroscopic techniques have been employed to measure the bacterial response. These include measurements of the average velocity as the bacterial population moves toward attractants, and measurement of the upward-to-downward flux ratio, R, in the stable preformed attractant gradients. The dependence of the average velocity on gradient appears to be hyperbolic in nature, while the flux ratio depends linearly on the gradient. These data suggest a microscopic model for the dependence of bacterial behavior on the serine gradient. The model involves a linear dependence of the mean lifetime of a bacterial trajectory on the gradient for those bacteria moving toward higher attractant concentration. Those moving toward low concentrations of attractant do not change the mean duration of their trajectories, or the speed at which a given bacterium swims through the solution. This model generates the observed dependences of the average velocity and flux ratio on gradient. Interpretation of the experimental data suggests that a gradient which increases serine concentration by a factor of 2 in 10 mm is sufficient to double the average duration of a trajectory for a bacterium moving directly up the gradient. The concentration dependence of the chemotactic response to serine is more complicated. It suggests that more than one receptor of serine may be involved in determining chemotactic behavior to this attractant.     

Different Migration Patterns of Sea Urchin and Mouse Sperm Revealed by a Microfluidic Chemotaxis Device

Chemotaxis refers to a process whereby cells move up or down a chemical gradient. Sperm chemotaxis is known to be a strategy exploited by marine invertebrates such as sea urchins to reach eggs efficiently in moving water. Less is understood about how or whether chemotaxis is used by mammalian sperm to reach eggs, where fertilization takes place within the confinement of a reproductive tract. In this report, we quantitatively assessed sea urchin and mouse sperm chemotaxis using a recently developed microfluidic model and high-speed imaging. Results demonstrated that sea urchin Arbacia punctulata sperm were chemotactic toward the peptide resact with high chemotactic sensitivity, with an average velocity V_x up the chemical gradient as high as 20% of its average speed (238 μm/s), while mouse sperm displayed no statistically significant chemotactic behavior in progesterone gradients, which had been proposed to guide mammalian sperm toward eggs. This work demonstrates the validity of a microfluidic model for quantitative sperm chemotaxis studies, and reveals a biological insight that chemotaxis up a progesterone gradient may not be a universal strategy for mammalian sperm to reach eggs.     

Collective cell migration guided by dynamically maintained gradients

How cell collectives move and deposit subunits within a developing embryo is a question of outstanding interest. In many cases, a chemotactic mechanism is employed, where cells move up or down a previously generated attractive or repulsive gradient of signalling molecules. Recent studies revealed the existence of systems with isotropic chemoattractant expression in the lateral line primordium of zebrafish. Here we propose a mechanism for a cell collective, which actively modulates an isotropically expressed ligand and encodes an initial symmetry breaking in its velocity. We derive a closed solution for the velocity and identify an optimal length that maximizes the tissues' velocity. A length dependent polar gradient is identified, its use for pro-neuromast deposition is shown by simulations and a critical time for cell deposition is derived. Experiments to verify this model are suggested.     

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.     

The aggregation characteristics of column-purified rabbit skeletal myosin in the presence and absence of C-protein at pH 7.0.

The aggregation properties of column-purified rabbit skeletal myosin at pH 7.0 were investigated as functions of ionic strength, protein concentration, and time. Filaments prepared by dialysis exhibited the same average length and population distribution at 0.10 and 0.15 M KCl at protein concentrations greater than 0.10 mg/ml; similar results were obtained at .0.20 M KCl, although average filament length was approximately 0.5 micrometer shorter. Once formed, these length distributions remained virtually unchanged over an 8-d period. At and below 0.10 mg/ml, average filament length decreased as a function of protein concentration; filaments prepared from an initial concentration of 0.02 mg/ml were half the length of those prepared at 0.2 mg/ml. Filaments prepared by dilution exhibited a sharp increase in average length as the time-course increased up to 40 s, then altered only slightly over a further period of 4 min. Addition of C-protein in a molar ratio of 1-3.3 myosin molecules affected most of these results. Average filament length was affected neither by ionic strength nor by initial protein concentration down to 0.04 mg/ml or over an 8-d period. Filaments formed by dilution in the presence of C-protein exhibited a constant average length and hypersharp length distribution over variable time courses up to 7 min. It is possible that C-protein acts to stabilize the antiparallel intermediate during filamentogenesis, and may also affect subunit addition to this nucleus.     

人体坐下站起过程中平衡功能评估及训练系统软件的设计与实现

本研究针对脑卒中偏瘫患者的平衡功能定量评估的需求,设计一种针对坐下站起过程中各阶段平衡功能评估及训练的系统软件,该软件配合坐位站起平衡功能训练仪使用。软件采用面向对象编程技术,应用VS2010(Microsoft Visual Studio2010)开发平台编写,可实时获得人体在坐下站起过程中的各评估参数,包括左右臀前后最大压力、左右足底平均压力、伸展期时间、伸展前期时间、左右侧最大和平均压力及站起时的最大加速度等。结合图形和数字实时显示及虚拟现实技术,对人体坐下站起的各阶段进行平衡功能评估和训练,通过视觉、听觉反馈,使训练更具趣味性。经过测试应用,结果表明,该系统软件运行稳定可靠,具有针对性的评估并结合实时可观测的压力曲线及大量的评估参数,可使评估结果更快速更有效。     

Growth cones turn and migrate up an immobilized gradient of the laminin IKVAV peptide

Growth cone navigation is guided by extrinsic environmental proteins, called guidance cues. Many in vitro studies have characterized growth cone turning up and down gradients of soluble guidance cues. Although previous studies have shown that axonal elongation rates can be regulated by gradients of surface-bound molecules, there are no convincing demonstrations of growth cones turning to migrate up a surface-bound gradient of an adhesive ligand or guidance cue. In order to test this mode of axonal guidance, we used a photo-immobilization technique to create grids and gradients of an adhesive laminin peptide on polystyrene culture dish surfaces. Chick embryo dorsal root ganglia (DRGs) were placed on peptide grid patterns containing surface-bound gradients of the IKVAV-containing peptide. DRG growth cones followed a path of surface-bound peptide to the middle of a perpendicularly oriented gradient with a 25% concentration difference across 30 microm. The majority of growth cones turned and migrated up the gradient, turning until they were oriented directly up the gradient. Growth cones slowed their migration when they encountered the gradient, but growth cone velocity returned to the previous rate after turning up or down the gradient. This resembles in vivo situations where growth cones slow at a choice point before changing the direction of axonal extension. Thus, these results support the hypothesis that mechanisms of axonal guidance include growth cone orientation by gradients of surface-bound adhesive molecules and guidance cues.     

Run and Tumble Chemotaxis in a Shear Flow: The Effect of Temporal Comparisons,Persistence, Rotational Diffusion,and Cell Shape

Escherichia coli is a motile bacterium that moves up a chemoattractant gradient by performing a biased random walk composed of alternating runs and tumbles. This paper presents calculations of the chemotactic drift velocity v _d (the mean velocity up the chemoattractant gradient) of an E. coli cell performing chemotaxis in a uniform, steady shear flow, with a weak chemoattractant gradient at right angles to the flow. Extending earlier models, a combined analytic and numerical approach is used to assess the effect of several complications, namely (i) a cell cannot detect a chemoattractant gradient directly but rather makes temporal comparisons of chemoattractant concentration, (ii) the tumbles exhibit persistence of direction, meaning that the swimming directions before and after a tumble are correlated, (iii) the cell suffers random re-orientations due to rotational Brownian motion, and (iv) the non-spherical shape of the cell affects the way that it is rotated by the shear flow. These complications influence the dependence of v _d on the shear rate γ. When they are all included, it is found that (a) shear disrupts chemotaxis and shear rates beyond γ≈2 s⁻¹ render chemotaxis ineffective, (b) in terms of maximizing drift velocity, persistence of direction is advantageous in a quiescent fluid but disadvantageous in a shear flow, and (c) a more elongated body shape is advantageous in performing chemotaxis in a shear flow. J.T. Locsei is supported by an Oliver Gatty Studentship from the University of Cambridge.     

Computation of aortic pulse wave velocity and aortic pulse wave velocity and aortic extensibility from pressure gradient measurements.

This study is concerned with the computation of aortic pulse wave velocity based on simultaneous recordings of the aortic pressure gradient and first-time derivative of aortic pressure. These variables were recorded by means of a double-lumen catheter introduced in the aorta of four anesthetized closed chest dogs, and connected to critically damped manometer systems. Results of aortic pulse wave velocity were then compared: (i) to the true phase velocity obtained from spectra of apparent phase velocity, and (ii) to the pulse wave velocity computed from the time shift between maximum slopes of the pressure wave. From the aortic valves to 37 cm down the aortic trunk, pulse wave velocity increased from 410-460 cm/s to approximately 600-800 cm/s. Based on the wave propagation equation presented of Bramwell and Hill (Bramwell, J.C., and Hill, A. V. 1922. Proc. R. Soc. 93, 298-306), volumetric extensibility coefficients were computed from pulse wave velocity data. Results indicated that, from the aortic valves to 37 cm down to the aorta, the mean volumetric extensibility decreased from 0.43-0.56% deltaV/cm H2O to 0.16-0.25% deltaV/cm H2O (1 cm H2O = 94.1 N/m2).     

Precision and Variability in Bacterial Temperature Sensing

In Escherichia coli, the ratio of the two most abundant chemoreceptors, Tar/Tsr, has become the focus of much attention in bacterial taxis studies. This ratio has been shown to change under various growth conditions and to determine the response of the bacteria to the environment. Here, we present a study that makes a quantitative link between the ratio Tar/Tsr and the favored temperature of the cell in a temperature gradient and in various chemical environments. From the steady-state density-profile of bacteria with one dominant thermo-sensor, Tar or Tsr, we deduce the response function of each receptor to temperature changes. Using the response functions of both receptors, we determine the relationship between the favored temperature of wild-type bacteria with mixed clusters of receptors and the receptor ratio. Our model is based on the assumption that the behavior of a wild-type bacterium in a temperature gradient is determined by a linear combination of the independent responses of the two receptors, factored by the receptor’s relative abundance in the bacterium. This is confirmed by comparing our model predictions with measurements of the steady-state density-profile of several bacterial populations in a temperature gradient. Our results reveal that the density-profile of wild-type bacteria can be accurately described by measuring the distribution of the ratio Tar/Tsr in the population, which is then used to divide the population into groups with distinct Tar/Tsr values, whose behavior can be described in terms of independent Gaussian distributions. Each of these Gaussians is centered about the favored temperature of the subpopulation, which is determined by the receptor ratio, and has a width defined by the temperature-dependent speed and persistence time.     

A stochastic model for leukocyte random motility and chemotaxis based on receptor binding fluctuations

Two central features of polymorphonuclear leukocyte chemosensory movement behavior demand fundamental theoretical understanding. In uniform concentrations of chemoattractant, these cells exhibit a persistent random walk, with a characteristic "persistence time" between significant changes in direction. In chemoattractant concentration gradients, they demonstrate a biased random walk, with an "orientation bias" characterizing the fraction of cells moving up the gradient. A coherent picture of cell movement responses to chemoattractant requires that both the persistence time and the orientation bias be explained within a unifying framework. In this paper, we offer the possibility that "noise" in the cellular signal perception/response mechanism can simultaneously account for these two key phenomena. In particular, we develop a stochastic mathematical model for cell locomotion based on kinetic fluctuations in chemoattractant/receptor binding. This model can simulate cell paths similar to those observed experimentally, under conditions of uniform chemoattractant concentrations as well as chemoattractant concentration gradients. Furthermore, this model can quantitatively predict both cell persistence time and dependence of orientation bias on gradient size. Thus, the concept of signal "noise" can quantitatively unify the major characteristics of leukocyte random motility and chemotaxis. The same level of noise large enough to account for the observed frequency of turning in uniform environments is simultaneously small enough to allow for the observed degree of directional bias in gradients.     

Accuracy of circadian entrainment under fluctuating light conditions: contributions of phase and period responses.

The accuracy with which a circadian pacemaker can entrain to an environmental 24-h zeitgeber signal depends on (a) characteristics of the entraining signal and (b) response characteristics and intrinsic stability of the pacemaker itself. Position of the sun, weather conditions, shades, and behavioral variations (eye closure, burrowing) all modulate the light signal reaching the pacemaker. A simple model of a circadian pacemaker allows researchers to explore the impact of these factors on pacemaker accuracy. Accuracy is operationally defined as the reciprocal value of the day-to-day standard deviation of the clock times at which a reference phase (0) is reached. For the purpose of this exploration, the authors used a model pacemaker characterized solely by its momentary phase and momentary velocity. The average velocity determines the time needed to complete one pacemaker cycle and, therefore, is inversely proportional to pacemaker period. The model pacemaker responds to light by shifting phase and/or changing its velocity. The authors assumed further that phase and velocity show small random fluctuations and that the velocity is subject to aftereffects. Aftereffects were incorporated mathematically in a term allowing period to contract exponentially to a stable steady-state value, with a time constant of 69 d in the absence of light. The simulations demonstrate that a pacemaker reaches highest accuracy when it responds to light by simultaneous phase shifts and changes of its velocity. Phase delays need to coincide with slowing down and advances with speeding up; otherwise, no synchronization to the zeitgeber occurs. At maximal accuracy, the changes in velocity are such that the average period of the pacemaker under entrained conditions equals 24 h. The results suggest that during entrainment, the pacemaker adjusts its period to 24 h, after which daily phase shifts to compensate for differences between the periods of the zeitgeber and the clock are no longer necessary. On average, phase shifts compensate for maladjustments of phase and velocity changes compensate for maladjustments of period.     

Optimal setups for forced-choice staircases with fixed step sizes

Forced-choice staircases with fixed step sizes are used in a variety of formats whose relative merits have never been studied. This paper presents a comparative study aimed at determining their optimal format. Factors included in the study were the up/down rule, the length (number of reversals), and the size of the steps. The study also addressed the issue of whether a protocol involving three staircases running for N reversals each (with a subsequent average of the estimates provided by each individual staircase) has better statistical properties than an alternative protocol involving a single staircase running for 3N reversals. In all cases the size of a step up was different from that of a step down, in the appropriate ratio determined by García-Pérez (Vision Research, 1998, 38, 1861 - 1881). The results of a simulation study indicate that a) there are no conditions in which the 1-down/1-up rule is advisable; b) different combinations of up/down rule and number of reversals appear equivalent in terms of precision and cost: c) using a single long staircase with 3N reversals is more efficient than running three staircases with N reversals each: d) to avoid bias and attain sufficient accuracy, threshold estimates should be based on at least 30 reversals: and e) to avoid excessive cost and imprecision, the size of the step up should be between 2/3 and 3/3 the (known or presumed) spread of the psychometric function. An empirical study with human subjects confirmed the major characteristics revealed by the simulations.     

Extreme streams: species persistence and genomic change in montane insect populations across a flooding gradient

The ecological and evolutionary consequences of extreme events are poorly understood. Here, we tested predictions about species persistence and population genomic change in aquatic insects in 14 Colorado mountain streams across a hydrological disturbance gradient caused by a one in 500‐year rainfall event. Taxa persistence ranged from 39 to 77% across sites and declined with increasing disturbance in relation to species' resistance and resilience traits. For taxa with mobile larvae and terrestrial adult stages present at the time of the flood, average persistence was 84% compared to 25% for immobile taxa that lacked terrestrial adults. For two of six species analysed, genomic diversity (allelic richness) declined after the event. For one species it greatly expanded, suggesting resilience via re‐colonisation from upstream populations. Thus, while resistance and resilience traits can explain species persistence to extreme disturbance, population genomic change varies among species, challenging generalisations about evolutionary responses to extreme events at landscape scales.     

Niche specialization of reef-building corals in the mesophotic zone: metabolic trade-offs between divergent Symbiodinium types

The photobiology of two reef corals and the distribution of associated symbiont types were investigated over a depth gradient of 0-60 m at Scott Reef, Western Australia. Pachyseris speciosa hosted mainly the same Symbiodinium C type similar to C3 irrespective of sampling depth. By contrast, Seriatopora hystrix hosted predominantly Symbiodinium type D1a or D1a-like at shallow depths while those in deeper water were dominated by a Symbiodinium C type closely related to C1. The photosynthesis/respiration (P/R) ratio increased consistently with depth at the two sampling times (November 2008 and April 2009) for P. speciosa and in November 2008 only for S. hystrix, suggesting a reduction in metabolic energy expended for every unit of energy obtained from photosynthesis. However, in April 2009, shallow colonies of S. hystrix exhibited decreased P/R ratios down to depths of approximately 23 m, below which the ratio increased towards the maximum depth sampled. This pattern was mirrored by changes in tissue biomass determined as total protein content. The depth of change in the direction of the P/R ratio correlated with a shift from Symbiodinium D to C-dominated colonies. We conclude that while photobiological flexibility is vital for persistence in contrasting light regimes, a shift in Symbiodinium type may also confer a functional advantage albeit at a metabolic cost with increased depth.     

Patterns of structural and defense investments in fine roots of Scots pine (Pinus sylvestris L.) across a strong temperature and latitudinal gradient in Europe

Plant functional traits may be altered as plants adapt to various environmental constraints. Cold, low fertility growing conditions are often associated with root adjustments to increase acquisition of limiting nutrient resources, but they may also result in construction of roots with reduced uptake potential but higher tissue persistence. It is ultimately unclear whether plants produce fine roots of different structure in response to decreasing temperatures and whether these changes represent a trade‐off between root function or potential root persistence. We assessed patterns of root construction based on various root morphological, biochemical and defense traits including root diameter, specific root length (SRL), root tissue density (RTD), C:N ratio, phenolic compounds, and number of phellem layers across up to 10 root orders in diverse populations of Scots pine along a 2000‐km climatic gradient in Europe. Our results showed that different root traits are related to mean annual temperature (MAT) and expressed a pattern of higher root diameter and lower SRL and RTD in northern sites with lower MAT. Among absorptive roots, we observed a gradual decline in chemical defenses (phenolic compounds) with decreasing MAT. In contrast, decreasing MAT resulted in an increase of structural protection (number of phellem layers) in transport fine roots. This indicated that absorptive roots with high capacity for nutrient uptake, and transport roots with low uptake capacity, were characterized by distinct and contrasting trade‐offs. Our observations suggest that diminishing structural and chemical investments into the more distal, absorptive roots in colder climates is consistent with building roots of higher absorptive capacity. At the same time, roots that play a more prominent role in transport of nutrients and water within the root system saw an increase in structural investment, which can increase persistence and reduce long‐term costs associated with their frequent replacement.     

Fiber alignment directs cell motility over chemotactic gradients

The ability of tissue engineered scaffolds to direct cell behavior is paramount for scaffold design. Cell migration can be directed by various methods including chemical, adhesive, mechanical, and topographical cues. Electrospinning has emerged as a popular method to control topography and create fibrous scaffolds similar to that found in extracellular matrix. One major hurdle is limited cell infiltration and several studies have explored methods to alter electrospun materials to increase scaffold porosity; however, uniform cell distributions within scaffolds is still limited. Towards this, we investigated the motility of HUVECs on a model system of electrospun hyaluronic acid fibers under a gradient of VEGF and found that topographical cues dominate cell motility direction. Using time‐lapse microscopy, cell aspect ratio, and migration angle were measured; cells were directed in a chemical gradient and/or on aligned electrospun fibers. Measurements of the persistence time demonstrated an additive effect of the chemical gradient and fiber alignment. However, when fibers were aligned perpendicular to a chemical gradient, cells were directed by fiber alignment and there was no effect of the chemical gradient. These results suggest that topographical cues may be more influential than chemical cues in directing cell motility and should be considered in material design. Biotechnol. Bioeng. 2013; 110: 1249–1254. © 2012 Wiley Periodicals, Inc.     

Steady-state running rate sets the speed and accuracy of accumulation of swimming bacteria

We study the chemotaxis of a population of genetically identical swimming bacteria undergoing run and tumble dynamics driven by stochastic switching between clockwise and counterclockwise rotation of the flagellar rotary system, where the steady-state rate of the switching changes in different environments. Understanding chemotaxis quantitatively requires that one links the measured steady-state switching rates of the rotary system, as well as the directional changes of individual swimming bacteria in a gradient of chemoattractant/repellant, to the efficiency of a population of bacteria in moving up/down the gradient. Here we achieve this by using a probabilistic model, parametrized with our experimental data, and show that the response of a population to the gradient is complex. We find the changes to the steady-state switching rate in the absence of gradients affect the average speed of the swimming bacterial population response as well as the width of the distribution. Both must be taken into account when optimizing the overall response of the population in complex environments.     

Evidence for solution flow in the phloem of willow

Sucrose specific mass transfer measurements were made in a translocating willow shoot (Salix viminalis L.) by a steady state labelling technique and the translocate sucrose specific activity, concentration and velocity monitored by analysis of the honeydew from two colonies of the willow aphid Tuberolachnus salignus Gmelin. The values of sucrose SMT obtained were related to the simultaneous measurements of translocate concentration and velocity and to the gradients of sucrose concentration within the stem transport path to determine if transport was a bulk flow or a diffusional analogue. Estimates of potassium ion concentration in the sieve tubes were made, using aphid honeydew, and related to the sucrose SMT measured simultaneously. Correlations were found between translocate concentration, velocity and SMT which suggested that solution flow was occurring rather than a process analogous to diffusion. Evidence was obtained that velocity of flow was a valid concept and that the measured velocity was being lowered by leakage of tracer from the sieve tubes. The analysis of potassium concentration suggested that if solution flow was occurring then potassium must be very exchangeable down the transport path. A good correlation was observed between the SMT of sucrose and the combined gradient of sucrose and potassium concentration, though this gradient was in the opposite direction to transport in some cases.Abbreviations SMT Sucrose specific mass transfer rate - SAR Specific activity ratio - OP Osmotic pressure     

The flow linear dichroism of DNA: comparison with the bead-spring theory

The flow linear dichroism if T7 bacteriophage DNA has been obtained as a function of velocity gradient in neutral aqueous solutions containing 0.15M Na⁺ or K⁺. The data are compared with the hydrodynamic bead-spring theory of Rouse and Zimm using currently available spectroscopy, structural, and hydrodynamic parameters. Good agreement between theoretical and experimental isocline angle behavior is found. The magnitude of the measured linear dichroism is not in exact agreement with theory when presently accepted stiffness and optical parameters are used. Agreement is improved either by assuming a shorter persistence length or a less negative value for the limiting dichroism of DNA.