Orientation by helical motion—III. Microorganisms can orient to stimuli by changing the direction of their rotational velocity

Organisms that move along helical trajectories change their net direction of motion largely by changing the direction, with respect to the body of the organism, of their rotational velocity (Crenshaw and Edelstein-Keshet, 1993,Bull. math. Biol. 55, 213–230). This paper demonstrates that an organism orients to a stimulus field, such as a chemical concentration gradient or a ray of light, if the components of its rotational velocity, with respect to the, body of the organism, are simple functions of the stimulus intensity encountered by the organism. For example, an organism can orient to a chemical concentration gradient if the rate at which it rotates around its anterior-posterior axis is proportional to the chemical concentration it encounters. Such an orientation can be either positive or negative. Furthermore, it is true taxis—orientation of the axis of helical motion is direct. It is neither a kinesis nor a phobic response—there is no random component to this mechanism of orientation.     

Modelling of the activation of G-protein coupled receptors: drug free constitutive receptor activity

G-protein coupled receptors (GPCRs) form a crucial component of approximately 80% of hormone pathways. In this paper, the most popular mechanism for activation of GPCRs—the shuttling mechanism—is modelled mathematically. An asymptotic analysis of this model clarifies the dynamics of the system in the absence of drug, in particular which reactions dominate during the different timescales. Equilibrium analysis of the model demonstrates the model’s ability to predict constitutive receptor activity.     

Helical nature of sperm swimming affects the fit of fertilization-kinetics models to empirical data

Models of fertilization kinetics rely upon estimates of the swimming velocity of sperm to predict collision rates between egg and sperm. Most investigators measure sperm swimming velocity without accounting for the helical motion of sperm, thereby obtaining an inflated estimate of the velocity with which sperm approach eggs. In turn, models of fertilization predict inflated rates of sperm/egg collision. I observed sea urchin sperm colliding with eggs, quantified the rate of sperm/egg collision, and measured sperm velocity as a component of the helix through which they swim. I also adjusted the "target size" of eggs to reflect the diameter of the helix. My estimate of sperm swimming velocity is an order of magnitude lower than other estimates for the same species. By using helical parameters in fertilization kinetics models and accounting for dead sperm in laboratory trials, I was able to accurately predict lower rates of sperm/egg collision. Moreover, making these adjustments in the model increased the estimated proportion of sperm that initiate fertilization by 6- to 7-fold, suggesting that a better understanding of sperm swimming might lead to a more complete understanding of fertilization biology and natural selection on gamete traits.     

Sociability leads to instability

We present a general stochastic model showing that colonial breeding can lead to complex multi-colony population dynamics when combined with nothing more than (inevitably) imperfect decision-making by individuals. In particular, frequent “switching cascades”—mass movement of individuals between locations from one breeding season to the next—arise naturally from our model, bringing into question the need to invoke a separate, fitness-based explanation for this commonly observed real-world phenomenon. A key component of the model is the development, at the beginning of each breeding season, of a set of colonies, based on sequential choices by individuals about where to breed. Individuals favor the colony they bred in previously, but are also attracted to colonies that are rapidly establishing, and may switch locations. This provides a positive feedback that leads to switching cascades. We examine the effect on the dynamics of individuals’ access to (and ability to act on) information, as well as the overall size of the colony system and of individual colonies. We compare the model’s dynamics to the observed population dynamics of a set of heron and egret breeding colonies in New York Harbor.     

A 3D Motile Rod-Shaped Monotrichous Bacterial Model

We introduce a 3D model for a motile rod-shaped bacterial cell with a single polar flagellum which is based on the configuration of a monotrichous type of bacteria such as Pseudomonas aeruginosa. The structure of the model bacterial cell consists of a cylindrical body together with the flagellar forces produced by the rotation of a helical flagellum. The rod-shaped cell body is composed of a set of immersed boundary points and elastic links. The helical flagellum is assumed to be rigid and modeled as a set of discrete points along the helical flagellum and flagellar hook. A set of flagellar forces are applied along this helical curve as the flagellum rotates. An additional set of torque balance forces are applied on the cell body to induce counter-rotation of the body and provide torque balance. The three-dimensional Navier–Stokes equations for incompressible fluid are used to describe the fluid dynamics of the coupled fluid–microorganism system using Peskin’s immersed boundary method. A study of numerical convergence is presented along with simulations of a single swimming cell, the hydrodynamic interaction of two cells, and the interaction of a small cluster of cells.     

Effects of modeling and lineage on fishing behavior in the small-eared bushbaby (otolemur garnettii)

Thirty-eight bushbabies(Otolemur garnettii)were subjects in an observational learning study. We exposed them to one of three modeling conditions: (1) fishing model—one that actually performed fishing behavior; (2) nonfishing model—one that performed as a model in every way except performance of fishing behavior; and (3) no model. We assessed them with regard to latency to approach the fishbowl, latency to make an initial fishing attempt, duration of time spent in the vicinity of the fishbowls, and number of actual fishing attempts. Results indicate that subjects that were exposed to either fishing or nonfishing models were faster to approach the fishbowls and spent more time in the vicinity of the fishbowls than animals in the no-model condition Lineage, i.e., whether or not the animals’ parents fished, rather than modeling condition, was the best predictor of the latency to initial fishing attempt and the number of attempts made.     

On the mysterious propulsion of Synechococcus

We propose a model for the self-propulsion of the marine bacterium Synechococcus utilizing a continuous looped helical track analogous to that found in Myxobacteria [1]. In our model cargo-carrying protein motors, driven by proton-motive force, move along a continuous looped helical track. The movement of the cargo creates surface distortions in the form of small amplitude traveling ridges along the S-layer above the helical track. The resulting fluid motion adjacent to the helical ribbon provides the propulsive thrust. A variation on the helical rotor model of [1] allows the motors to be anchored to the peptidoglycan layer, where they drive rotation of the track creating traveling helical waves along the S-layer. We derive expressions relating the swimming speed to the amplitude, wavelength, and velocity of the surface waves induced by the helical rotor, and show that they fall in reasonable ranges to explain the velocity and rotation rate of swimming Synechococcus.     

Theory predicts a rapid transition from niche-structured to neutral biodiversity patterns across a speciation-rate gradient

A central challenge in community ecology is to predict patterns of biodiversity with mechanistic models. The neutral model of biodiversity is a simple model that appears to provide parsimonious and accurate predictions of biodiversity patterns in some ecosystems, even though it ignores processes such as species interactions and niche structure. In a recent paper, we used analytical techniques to reveal why the mean predictions of the neutral model are robust to niche structure in high diversity but not low-diversity ecosystems. In the present paper, we explore this phenomenon further by generating stochastic simulated data from a spatially implicit hybrid niche-neutral model across different speciation rates. We compare the resulting patterns of species richness and abundance with the patterns expected from a pure neutral and a pure niche model. As the speciation rate in the hybrid model increases, we observe a surprisingly rapid transition from an ecosystem in which diversity is almost entirely governed by niche structure to one in which diversity is statistically indistinguishable from that of the neutral model. Because the transition is rapid, one prediction of our abstract model is that high-diversity ecosystems such as tropical forests can be approximated by one simple model—the neutral model—whereas low-diversity ecosystems such as temperate forests can be approximated by another simple model—the niche model. Ecosystems that require the hybrid model are predicted to be rare, occurring only over a narrow range of speciation rates.     

Effects of Geometric Parameters on Swimming of Micro Organisms with Single Helical Flagellum in Circular Channels

We present a computational fluid dynamics (CFD) model for the swimming of micro organisms with a single helical flagellum in circular channels. The CFD model is developed to obtain numerical solutions of Stokes equations in three dimensions, validated with experiments reported in literature, and used to analyze the effects of geometric parameters, such as the helical radius, wavelength, radii of the channel and the tail and the tail length on forward and lateral swimming velocities, rotation rates, and the efficiency of the swimmer. Optimal shapes for the speed and the power efficiency are reported. Effects of Brownian motion and electrostatic interactions are excluded to emphasize the role of hydrodynamic forces on lateral velocities and rotations on the trajectory of swimmers. For thin flagella, as the channel radius decreases, forward velocity and the power efficiency of the swimmer decreases as well; however, for thick flagella, there is an optimal radius of the channel that maximizes the velocity and the efficiency depending on other geometric parameters. Lateral motion of the swimmer is suppressed as the channel is constricted below a critical radius, for which the magnitude of the lateral velocity reaches a maximum. Results contribute significantly to the understanding of the swimming of bacteria in micro channels and capillary tubes.     

Molds on house walls and the effect of their chloroform-extractable metabolites on the respiratory cilia movement of one-day-old chicksin vitro

The ciliostatic activity of the chloroform-extractable endo- and exometabolites of 5 strains of filamentous fungi—Alternaria sp.,Aspergillus glaucus group,Aspergillus versicolor, Cladosporium sphœrospermum, Penicillium sp. andUlocladium sp.—isolated from molded walls of a dwelling—on tracheal cilia from 1-d-old chicksin vitro was evaluated. Endometabolites ofAlternaria sp. andA. versicolor and exometabolites ofUlocladium sp. were the most active, these extracts stopped the ciliary movement within 1 d. The results are discussed in relation to the health status of people living in “moldy” dwellings.     

Transient Responses to Spatial Perturbations in Advective Systems

We study the transient dynamics, following a spatially-extended perturbation of models describing populations residing in advective media such as streams and rivers. Our analyses emphasize metrics that are independent of initial perturbations—resilience, reactivity, and the amplification envelope—and relate them to component spatial wavelengths of the perturbation using spatial Fourier transforms of the state variables. This approach offers a powerful way of understanding the influence of spatial scale on the initial dynamics of a population following a spatially variable environmental perturbation, an important property in determining the ecological implications of transient dynamics in advective systems. We find that asymptotically stable systems may exhibit transient amplification of perturbations (i.e., have positive reactivity) for some spatial wavelengths and not others. Furthermore, the degree and duration of amplification varies strongly with spatial wavelength. For two single-population models, there is a relationship between transient dynamics and the response length that characterizes the steady state response to spatial perturbations: a long response length implies that peak amplification of perturbations is small and occurs fast. This relationship holds less generally in a specialist consumer-resource model, likely due to the model’s tendency for flow-induced instabilities at an alternative characteristic spatial scale.     

Extinction dynamics in mainland-island metapopulations: an N-patch stochastic model

A generalization of the well-known Levins’ model of metapopulations is studied. The generalization consists of (i) the introduction of immigration from a mainland, and (ii) assuming the dynamics is stochastic, rather than deterministic. A master equation, for the probability that n of the patches are occupied, is derived and the stationary probability P _s (n), together with the mean and higher moments in the stationary state, determined. The time-dependence of the probability distribution is also studied: through a Gaussian approximation for general n when the boundary at n = 0 has little effect, and by calculating P(0, t), the probability that no patches are occupied at time t, by using a linearization procedure. These analytic calculations are supplemented by carrying out numerical solutions of the master equation and simulations of the stochastic process. The various approaches are in very good agreement with each other. This allows us to use the forms for P _s 0) and P(0, t) in the linearization approximation as a basis for calculating the mean time for a metapopulation to become extinct. We give an analytical expression for the mean time to extinction derived within a mean field approach. We devise a simple method to apply our mean field approach even to complex patch networks in realistic model metapopulations. After studying two spatially extended versions of this nonspatial metapopulation model—a lattice metapopulation model and a spatially realistic model—we conclude that our analytical formula for the mean extinction time is generally applicable to those metapopulations which are really endangered, where extinction dynamics dominates over local colonization processes. The time evolution and, in particular, the scope of our analytical results, are studied by comparing these different models with the analytical approach for various values of the parameters: the rates of immigration from the mainland, the rates of colonization and extinction, and the number of patches making up the metapopulation.     

The Measurement of Swimming Velocity of Vibrio cholerae and Pseudomonas aeruginosa Using the Video Tracking Method

The swimming velocities of two monotrichous flagellated bacteria were measured by a computer-assisted video tracking method. Tracing the moving path of the individual bacterium revealed that the bacterial cell did not swim continuously in a straight direction, but frequently changed swimming direction and velocity. The average swimming velocities calculated from the 3-sec path were 75.4 ±9.4 μm/sec in four strains of Vibrio cholerae and 513 ±8.4 μm/sec in five strains of Pseudomonas aeruginosa. These results suggest that V. cholerae swim faster than P. aeruginosa at 30 C in nutrient broth. This method is useful for a detailed analysis of bacterial movement and moving patterns in different environmental conditions.     

Displacement,velocity preference,and substrate use of three native California stream fishes in simulated pulsed flows

We studied whether juvenile fishes were able to maintain swimming speed and position during simulated river pulsed flows in a laboratory flume. We used a glass flume (15.24 × 0.6 m) with river-rock substrate to determine the longitudinal displacement, movement distances and frequencies, velocity selection, and substrate use of juvenile (SL range: 6.1 ± 0.2 cm) hardhead Mylopharodon conocephalus (n = 13), rainbow trout Oncorhynchus mykiss (n = 11), and Sacramento sucker Catostomus occidentalis (n = 12) during a 100-min flow pulse, as velocity changed from slow to medium, fast, medium, and slow. Fish were capable of maintaining swimming speed and position up to the maximum flume velocity of 0.46 m·s⁻¹, except for one hardhead that impinged on the rear fish screen. Fish swam faster in the flume during the medium and fast intervals than the slow intervals, but fish speeds were similar among the medium and faster intervals, when some fish took cover behind the rock substrate. In comparison with a Brett-type swim-tunnel, fish showed less increase in mean swimming speed as the flume velocity increased. Fish in the flume were able to use the rock substrate as hydraulic cover, decreasing the encountered water velocity, and, presumably, conserving energy.     

Effects of Geometric Parameters on Swimming of Micro Organisms with Single Helical Flagellum in Circular Channels

We present a computational fluid dynamics (CFD) model for the swimming of micro organisms with a single helical flagellum in circular channels. The CFD model is developed to obtain numerical solutions of Stokes equations in three dimensions, validated with experiments reported in literature, and used to analyze the effects of geometric parameters, such as the helical radius, wavelength, radii of the channel and the tail and the tail length on forward and lateral swimming velocities, rotation rates, and the efficiency of the swimmer. Optimal shapes for the speed and the power efficiency are reported. Effects of Brownian motion and electrostatic interactions are excluded to emphasize the role of hydrodynamic forces on lateral velocities and rotations on the trajectory of swimmers. For thin flagella, as the channel radius decreases, forward velocity and the power efficiency of the swimmer decreases as well; however, for thick flagella, there is an optimal radius of the channel that maximizes the velocity and the efficiency depending on other geometric parameters. Lateral motion of the swimmer is suppressed as the channel is constricted below a critical radius, for which the magnitude of the lateral velocity reaches a maximum. Results contribute significantly to the understanding of the swimming of bacteria in micro channels and capillary tubes.     

Diurnal variations of potassium content in lucerne plants

Diurnal changes in K content in leaf blades, petioles, stems and roots of eleven lucerne genotypes were followed. Significant positive correlations between changes in K content in petioles and upper half of stems and significant negative correlations between changes of K content in leaf blades and lower half of stems reflected rapid K movement. The velocity — up to 60 μmol g−1 (f.m.)h−1 — of changes in K content from leaf blades to lower part of stems and the other way round showed that long distance phloem transport occurred. Only moderate increase of K content contemporarily took place in roots. When total K amount in the whole plant was calculated then K uptake alternatively with K release were noticed during the day. Average K release reached 1.48 μmol g−1 (f.m.) h−1. The rate of K movement correlated with irradiance and physiological activity of plants. The time course of K movement was uniform in plants of the same strain and it differed partially in different strains.     

Resonance tuning in a neuro-musculo-skeletal model of the forearm

In rhythmic movements, humans activate their muscles in a robust and energy efficient way. These activation patterns are oscillatory and seem to originate from neural networks in the spinal cord, called central pattern generators (CPGs). Evidence for the existence of CPGs was found for instance in lampreys, cats and rats. There are indications that CPGs exist in humans as well, but this is not proven yet. Energy efficiency is achieved by resonance tuning: the central nervous system is able to tune into the resonance frequency of the limb, which is determined by the local reflex gains. The goal of this study is to investigate if the existence of a CPG in the human spine can explain the resonance tuning behavior, observed in human rhythmic limb movement. A neuro-musculo-skeletal model of the forearm is proposed, in which a CPG is organized in parallel to the local reflexloop. The afferent and efferent connections to the CPG are based on clues about the organization of the CPG, found in literature. The model is kept as simple as possible (i.e., lumped muscle models, groups of neurons are lumped into half-centers, simple reflex model), but incorporates enough of the essential dynamics to explain behavior—such as resonance tuning—in a qualitative way. Resonance tuning is achieved above, at and below the endogenous frequency of the CPG in a highly non-linear neuro- musculo-skeletal model. Afferent feedback of muscle lengthening to the CPG is necessary to accomplish resonance tuning above the endogenous frequency of the CPG, while feedback of muscle velocity is necessary to compensate for the phase lag, caused by the time delay in the loop coupling the limb to the CPG. This afferent feedback of muscle lengthening and velocity represents the Ia and II fibers, which—according to literature—is the input to the CPG. An internal process of the CPG, which integrates the delayed muscle lengthening and feeds it to the half-center model, provides resonance tuning below the endogenous frequency. Increased co-contraction makes higher movement frequencies possible. This agrees with studies of rhythmic forearm movements, which have shown that co-contraction increases with movement frequency. Robustness against force perturbations originates mainly from the CPG and the local reflex loop. The CPG delivers an increasing part of the necessary muscle activation for increasing perturbation size. As far as we know, the proposed neuro-musculo-skeletal model is the first that explains the observed resonance tuning in human rhythmic limb movement.     

DNA amounts in the nuclei ofParamecium aurelia andTetrahymena pyriformis

DNA amounts have been determined in the micronuclei and macronuclei of 8 strains ofParamecium aurelia and 6 strains ofTetrahymena pyriformis. In the case ofTetrahymena a distribution of values for the amount of DNA in the macronuclei of all the strains was observed but the lowest values were approximately the same, viz. 1.17×10⁻¹¹ g. There are two groups of strains in relation to micronuclear DNA values ofTetrahymena, one giving an average of 0.36×10⁻¹² g and the other 0.815×10⁻¹² g. The ratio of MIC/MAC DNA varies in the two groups.Paramecium again has a range of macronuclear values within each stock—lowest value 2.51×10⁻¹⁰ g—and the micronuclear values are similar in all stocks—approximately 0.613×10⁻¹² g. The ratio of MIC/MAC DNA is similar in each stock.—The haploid genome values calculated from these data show excellent agreement with the values obtained by DNA renaturation studies. Supported by a Research Grant B/SR/8276 from the Science Research Council. The Vickers densitometer was purchased with a grant from the Medical Research Council.     

Simulating harvesting scenarios towards the sustainable use of mangrove forest plantations

Mangrove forests appear among the most productive ecosystems on earth and provide important goods and services to tropical coastal populations. Thirty-five percent of mangrove forest areas have been lost worldwide in the last two decades. Management measures could be an option to combine human use and conservation of mangroves. These measures can be improved if their impacts are assessed before they are performed. By doing so, the best management option out of a set of all potential options can be selected in advance. The mangrove model—KiWi—has been proven to be suitable for analyzing mangrove forest dynamics in the neotropics. Here, the model was applied to mangrove management scenarios. For this, the model was parameterized to Rhizophora apiculata, one of the most common mangrove species planted in Asia for timber production. It is thus the first simulation model describing Asian mangrove plantations. The recently developed Pattern Oriented Modelling approach was used to find those parameters fitting best density patterns and dbh (diameter at breast height) size classes reported in literature. The results demonstrated that the KiWi model was able to: (1) reproduce the growth patterns of a mono-specific plantation of R. apiculata in terms of forest density and size class distribution and (2) can provide criteria for the selection of a thinning strategy within a harvesting cycle.     

Characteristic spatial and temporal scales unify models of animal movement

Animal movements have been modeled with diffusion at large scales and with more detailed movement models at smaller scales. We argue that the biologically relevant behavior of a wide class of movement models can be efficiently summarized with two parameters: the characteristic temporal and spatial scales of movement. We define these scales so that they describe movement behavior both at short scales (through the velocity autocorrelation function) and at long scales (through the diffusion coefficient). We derive these scales for two types of commonly used movement models: the discrete-step correlated random walk, with either constant or random step intervals, and the continuous-time correlated velocity model. For a given set of characteristic scales, the models produce very similar trajectories and encounter rates between moving searchers and stationary targets. Thus, we argue that characteristic scales provide a unifying currency that can be used to parameterize a wide range of ecological phenomena related to movement.