Half-width scaling of electric field autocorrelation functions of light scattered from bull spermatozoa.

The half-width scaling of experimental and model electric field autocorrelation functions of light scattered from normally swimming, defectively swimming, and immotile bull spermatozoa is examined. It is found that a scatter of size 9.0 x 2.3 x 0.45 micrometers is most appropriate for this Rayleigh-Gans-Debye ellipsoid model. In the case of the immotile cells, this model correctly predicts the features seen in the scaling data as well as the absolute value of the data. For the normally swimming and defective populations the model proves to predict correctly the features seen in experimental scaling curves, but not the absolute value of the data. This discrepancy appears to be related to a lack of detail in the model, since the agreement is poorest at large scattering angles.     

Quasi-elastic light-scattering spectra of swimming spermatozoa. Rotational and translational effects.

The electric field autocorrelation functions of light scattered from normal swimming bull spermatozoa are shown to be dependent on the mean head rotation frequency and not on the translational speed of the cells, as previously believed. This result was obtained from numerical generation of functions in which spermatozoa were modeled as Rayleigh-Gans-Debye ellipsoids having semiaxes a = 0.5 micrometer, b = 2.3 micrometer, and c = 9.0 micrometer. The magnitude of c required to achieve agreement with the experimental data is larger than the half-length of the head region of the cell. This implies that the midpiece, which also lies along c, contributes to the scattering power. Details regarding swimming trajectory and head orientation are included in the model. Analyses of the calculated functions and comparisons with experimentally determined ones suggest that at a scattering angle of 15 degrees the electric field autocorrelation function can be fit a simple Lorentzian whose half-width is inversely proportional to the scattering vector and the mean head rotational frequency.     

Flow Loading Induces Oscillatory Trajectories in a Bloodstream Parasite

The dynamics of isolated microswimmers are studied in bounded flow using the African trypanosome, a unicellular parasite, as the model organism. With the help of a microfluidics platform, cells are subjected to flow and found to follow an oscillatory path that is well fit by a sine wave. The frequency and amplitudes of the oscillatory trajectories are dependent on the flow velocity and cell orientation. When traveling in such a manner, trypanosomes orient upstream while downstream-facing cells tumble within the same streamline. A comparison with immotile trypanosomes demonstrates that self-propulsion is essential to the trajectories of trypanosomes even at flow velocities up to ～40 times higher than their own swimming speed. These studies reveal important swimming dynamics that may be generally pertinent to the transport of microswimmers in flow and may be relevant to microbial pathogenesis.     

From lamprey to salamander: an exploratory modeling study on the architecture of the spinal locomotor networks in the salamander

The evolutionary transition from water to land required new locomotor modes and corresponding adjustments of the spinal “central pattern generators” for locomotion. Salamanders resemble the first terrestrial tetrapods and represent a key animal for the study of these changes. Based on recent physiological data from salamanders, and previous work on the swimming, limbless lamprey, we present a model of the basic oscillatory network in the salamander spinal cord, the spinal segment. Model neurons are of the Hodgkin–Huxley type. Spinal hemisegments contain sparsely connected excitatory and inhibitory neuron populations, and are coupled to a contralateral hemisegment. The model yields a large range of experimental findings, especially the NMDA-induced oscillations observed in isolated axial hemisegments and segments of the salamander Pleurodeles waltlii. The model reproduces most of the effects of the blockade of AMPA synapses, glycinergic synapses, calcium-activated potassium current, persistent sodium current, and $h$ -current. Driving segments with a population of brainstem neurons yields fast oscillations in the in vivo swimming frequency range. A minimal modification to the conductances involved in burst-termination yields the slower stepping frequency range. Slow oscillators can impose their frequency on fast oscillators, as is likely the case during gait transitions from swimming to stepping. Our study shows that a lamprey-like network can potentially serve as a building block of axial and limb oscillators for swimming and stepping in salamanders.     

Analysis of bifurcations in continuous fermentation using recombinant microorganisms with delayed responses

When the feed rate to a fermenter is varied periodically in order to favor the growth of plasmid-containing cells, a transition may occur from the starting stationary state to another state. The resulting state may be constant or oscillatory. A generalised model based on the adaption times of plasmid-free and plasmid-harboring cells has been used. Analytical conditions have been derived for bifurcation from one nonoscillatory state to another or to an oscillatory state (Hopf bifurcation). The frequency of oscillation is shown to have an upper bound, which can be controlled by manipulating certain process parameters. The production of tryptophan synthetase by the plasmid pPLc23trpAl in E. coli is used as an example to determine the nature of the Hopf bifurcations.     

High-Throughput Phenotyping of Chlamydomonas Swimming Mutants Based on Nanoscale Video Analysis

Studies on biflagellated algae Chlamydomonas reinhardtii mutants have resulted in significant contributions to our understanding of the functions of cilia/flagella components. However, visual inspection conducted under a microscope to screen and classify Chlamydomonas swimming requires considerable time, effort, and experience. In addition, it is likely that identification of mutants by this screening is biased toward individual cells with severe swimming defects, and mutants that swim slightly more slowly than wild-type cells may be missed by these screening methods. To systematically screen Chlamydomonas swimming mutants, we have here developed the cell-locating-with-nanoscale-accuracy (CLONA) method to identify the cell position to within 10-nm precision through the analysis of high-speed video images. Instead of analyzing the shape of the flagella, which is not always visible in images, we determine the position of Chlamydomonas cell bodies by determining the cross-correlation between a reference image and the image of the cell. From these positions, various parameters related to swimming, such as velocity and beat frequency, can be accurately estimated for each beat cycle. In the examination of wild-type and seven dynein arm mutants of Chlamydomonas, we found characteristic clustering on scatter plots of beat frequency versus swimming velocity. Using the CLONA method, we have screened 38 Chlamydomonas strains and detected believed-novel motility-deficient mutants that would be missed by visual screening. This CLONA method can automate the screening for mutants of Chlamydomonas and contribute to the elucidation of the functions of motility-associated proteins.     

High-Throughput Phenotyping of Chlamydomonas Swimming Mutants Based on Nanoscale Video Analysis

Studies on biflagellated algae Chlamydomonas reinhardtii mutants have resulted in significant contributions to our understanding of the functions of cilia/flagella components. However, visual inspection conducted under a microscope to screen and classify Chlamydomonas swimming requires considerable time, effort, and experience. In addition, it is likely that identification of mutants by this screening is biased toward individual cells with severe swimming defects, and mutants that swim slightly more slowly than wild-type cells may be missed by these screening methods. To systematically screen Chlamydomonas swimming mutants, we have here developed the cell-locating-with-nanoscale-accuracy (CLONA) method to identify the cell position to within 10-nm precision through the analysis of high-speed video images. Instead of analyzing the shape of the flagella, which is not always visible in images, we determine the position of Chlamydomonas cell bodies by determining the cross-correlation between a reference image and the image of the cell. From these positions, various parameters related to swimming, such as velocity and beat frequency, can be accurately estimated for each beat cycle. In the examination of wild-type and seven dynein arm mutants of Chlamydomonas, we found characteristic clustering on scatter plots of beat frequency versus swimming velocity. Using the CLONA method, we have screened 38 Chlamydomonas strains and detected believed-novel motility-deficient mutants that would be missed by visual screening. This CLONA method can automate the screening for mutants of Chlamydomonas and contribute to the elucidation of the functions of motility-associated proteins.     

Graviresponses of gliding and swimming Loxodes using step transition to weightlessness

Cells of Loxodes striatus were adjusted to defined culturing, experimental solution O2-supply, temperature, and state of equilibration to be subjected to step type transition of acceleration from normal gravity, (1 g) to the weightless condition (microgravity) during free fall in a 500 m drop shaft. Cellular locomotion inside a vertical experimental chamber was recorded preceding transition and during 10 s of microgravity. Cell tracks from video records were used to separate cells gliding along a solid surface from free swimmers, and to determine gravitaxis and gravikenesis of gliding and swimming cells. With O2 concentrations > or = 40% air saturation gliders and swimmers showed a positive gravitaxis. In microgravity gravitaxis of gliders relaxed within 5 s whereas gravitaxis relaxation of swimmers was not completed even after 10 s. Rates of horizontal gliders (319 micrometers/s) exceeded those, of horizontal swimmers (275 micrometers/s). Relaxation of gravikinesis was incomplete after 10 s of microgravity. Analysis of the locomotion rates during the g-step transition revealed that gliders sediment more slowly, than swimmers (14 versus 45 micrometers/s). The gravikinesis of gliders cancelled sedimentation effects during upward and downward locomotion tending to maintain cells at a predetermined level inside sediments of a freshwater habitat. At > or = 40% air saturation, gravikinesis of swimmers augmented the speed of the majority of cells during gravitaxis, which favours fast vertical migrations of Loxodes.     

On the localization of the origin of DNA replication in E. coli.

A theory is presented to describe the behavior of micro-organisms, bacteria and protozoa. Individual cells are regarded as particles having internal state variables. The change of each variable with time depends on the environmental condition. The velocity and the frequency of direction change of swimming cells are determined by the values of these variables. With this framework, the theory gives a method to connect the behaviour in a spatial gradient of the environment and the behaviour upon a change of the environment with time. Observed behaviors of bacteria and protozoa are understandable on the basis of simple rate equations for internal state variables and the product expressions for the velocity and the frequency of direction change as functions of these variables. Experimental data on the thermotaxis of paramecium are shown for comparison with the theoretical results.     

Estimating the active metabolic rate (AMR) in fish based on tail beat frequency (TBF) and body mass

Tail beat frequency (TBF) was measured for carp (Cyprinus carpio) and roach (Rutilus rutilus), during steady swimming at five different speeds and for fish of various body masses. A multiple stepwise linear regression analysis resulted in models for the prediction of TBFs depending on swimming speed as an independent variable. Speed explained 72 and 86% of the variance in TBF for carp and roach, respectively. By using these data to predict TBF from speed and substituting values into a model from a previous study that predicts active metabolic rates (AMR) from body mass and swimming speed, we can calculate AMR from only fish mass and TBF. Thus, the derived models can be used to estimate the AMR in fish by measuring TBFs in the field using biotelemetry. The approach presented here is a useful and relatively simple tool for estimating the activity metabolism in free-swimming fish. In future studies this method should be applied to a larger and more representative sample size to test the applicability and the validity for a broader range of species.     

Swimming speed distributions of bull spermatozoa as determined by quasi-elastic light scattering.

88 semen samples from 39 bulls have been investigated by the quasi-elastic light scattering technique. Normal, defective, and dead cells each yielded characteristic autocorrelation functions. The form of these functions indicates that the swimming speed distribution of normal cells is a gamma distribution with two degrees of freedom while that for defective or circular swimmers is a gamma distribution with one degree of freedom. The resulting analysis of the experimental autocorrelation functions yields the fraction of the sample that is normal, the fraction that is defective, and the average speed of each group. The average helical swimming speed of normal cells was found to be 384 micron/s, while the average trajectory speed of the circular swimmers was found to be 103 micron/s. The overall quality of the semen samples as determined by light scattering is compared to quality determination on the same samples by technicians from the artificial insemination industry.     

Synchronization of olfactory bulb mitral cells by precisely timed inhibitory inputs

Synchronized oscillatory activity at the gamma frequency (30-70 Hz) is thought to be important for information processing in many sensory systems. Here, I used patch-clamp recordings in neuron pairs in rat olfactory bulb slices to assess the mechanisms underlying such "gamma" activity in the olfactory system. Patterned electrical stimulation of afferents that mimicked a natural odor stimulus elicited rapidly synchronized spikes (lag < or = 5 ms) in mitral cells, along with oscillatory activity at the gamma (approximately 50 Hz) frequency. Analysis of coupling potentials, combined with dendritic sectioning, indicated that mitral cell synchrony was mainly driven by inhibitory postsynaptic potentials (IPSPs) imposed by GABAergic granule cells. Recordings in granule cell pairs indicated that granule cells were themselves synchronized by their excitatory inputs from mitral cells, providing a means to coordinate GABA release. These results demonstrate that rapid synchrony can emerge in a network through the precise back-and-forth interplay between neuronal populations.     

A biased random walk model for the trajectories of swimming micro-organisms

The motion of swimming micro-organisms that have a preferred direction of travel, such as single-celled algae moving upwards (gravitaxis) or towards a light source (phototaxis), is modelled as the continuous limit of a correlated and biased random walk as the time step tends to zero. This model leads to a Fokker-Planck equation for the probability distribution function of the orientation of the cells, from which macroscopic parameters such as the mean cell swimming direction and the diffusion coefficient due to cell swimming can be calculated. The model is tested on experimental data for gravitaxis and phototaxis and used to derive values for the macroscopic parameters for future use in theories of bioconvection, for example.     

Effect of weight and frontal area of external telemetry packages on the kinematics,activity levels and swimming performance of small‐bodied sharks

This study sought to observe the effects of submerged weight and frontal cross‐sectional area of external telemetry packages on the kinematics, activity levels and swimming performance of small‐bodied juvenile sharks, using lemon sharks Negaprion brevirostris (60–80 cm total length, L_T) as a model species. Juveniles were observed free‐swimming in a mesocosm untagged and with small and large external accelerometer packages that increased frontal cross‐sectional area of the animals and their submerged weight. Despite adhering to widely used standards for tag mass, the presence of an external telemetry package altered swimming kinematics, activity levels and swimming performance of juvenile N. brevirostris relative to untagged individuals, suggesting that tag mass is not a suitable standalone metric of device suitability. Changes in swimming performance could not be detected from tail‐beat frequency, which suggests that tail‐beat frequency is an unsuitable standalone metric of swimming performance for small N. brevirostris. Lastly, sharks experienced treatment‐specific changes in activity level and swimming kinematics from morning to afternoon observation. Therefore, the presence of external telemetry packages altered the kinematics, activity levels and swimming performance of small young‐of‐the‐year N. brevirostris and these data may therefore be relevant to other similar‐sized juveniles of other shark species.     

Oscillatory neural networks in the rabbit hippocampus

A model is described to account for damped oscillatory activity of two interacting neural populations, pyramidal cells and interneurons. This network in the hippocampus is treated as a lumped system with tine delays between elements. The physiological mechanism underlying the oscillatory activity appears to involve neural population interaction and cannot be described in terms of a network composed of but two neurons, a single pyramidal cell and a single interneuron. An unusual aspect of the model is the explicit incorporation of an ongoing background input to raise the mean level of activity of the pyramidal cell population. This model has evolved from a series of studies previously performed on cats. To test the model experiments were performed on rabbits. The data showing oscillatory activity following fornix stimulation in the rabbit indicate that the model can be applied not only to the cat but also to the rabbit. In additions, for commissural stimulation oscillatory potentials of neural populations and individual pyramidal cells were evoked as predicted by the model.     

Oscillations in plant membrane transport: model predictions, experimental validation, and physiological implications

Although oscillations in membrane-transport activity are ubiquitous in plants, the ionic mechanisms of ultradian oscillations in plant cells remain largely unknown, despite much phenomenological data. The physiological role of such oscillations is also the subject of much speculation. Over the last decade, much experimental evidence showing oscillations in net ion fluxes across the plasma membrane of plant cells has been accumulated using the non-invasive MIFE technique. In this study, a recently proposed feedback-controlled oscillatory model was used. The model adequately describes the observed ion flux oscillations within the minute range of periods and predicts: (i) strong dependence of the period of oscillations on the rate constants for the H+ pump; (ii) a substantial phase shift between oscillations in net H+ and K+ fluxes; (iii) cessation of oscillations when H+ pump activity is suppressed; (iv) the existence of some 'window' of external temperatures and ionic concentrations, where non-damped oscillations are observed: outside this range, even small changes in external parameters lead to progressive damping and aperiodic behaviour; (v) frequency encoding of environmental information by oscillatory patterns; and (vi) strong dependence of oscillatory characteristics on cell size. All these predictions were successfully confirmed by direct experimental observations, when net ion fluxes were measured from root and leaf tissues of various plant species, or from single cells. Because oscillatory behaviour is inherent in feedback control systems having phase shifts, it is argued from this model that suitable conditions will allow oscillations in any cell or tissue. The possible physiological role of such oscillations is discussed in the context of plant adaptive responses to salinity, temperature, osmotic, hypoxia, and pH stresses.     

Modeling pollen tube growth: Feeling the pressure to deliver testifiable predictions

The frequency and amplitude of oscillatory pollen tube growth can be altered by changing the osmotic value of the surrounding medium. This has motivated the proposition that the periodic change in growth velocity is caused by changes in turgor pressure. Using mathematical modeling we recently demonstrated that the oscillatory pollen tube growth does not require turgor to change but that this behavior can be explained with a mechanism that relies on changes in the mechanical properties of the cell wall which in turn are caused by temporal variations in the secretion of cell wall precursors. The model also explains why turgor and growth rate are correlated for oscillatory growth with long growth cycles while they seem uncorrelated for oscillatory growth with short growth cycles. The predictions made by the model are testifiable by experimental data and therefore represent an important step towards understanding the dynamics of the growth behavior in walled cells.     

Cardiorespiratory performance during prolonged swimming tests with salmonids: a perspective on temperature effects and potential analytical pitfalls

A prolonged swimming trial is the most common approach in studying steady-state changes in oxygen uptake, cardiac output and tissue oxygen extraction as a function of swimming speed in salmonids. The data generated by these sorts of studies are used here to support the idea that a maximum oxygen uptake is reached during a critical swimming speed test. Maximum oxygen uptake has a temperature optimum. Potential explanations are advanced to explain why maximum aerobic performance falls off at high temperature. The valuable information provided by critical swimming tests can be confounded by non-steady-state swimming behaviours, which typically occur with increasing frequency as salmonids approach fatigue. Two major concerns are noted. Foremost, measurements of oxygen uptake during swimming can considerably underestimate the true cost of transport near critical swimming speed, apparently in a temperature-dependent manner. Second, based on a comparison with voluntary swimming ascents in a raceway, forced swimming trials in a swim tunnel respirometer may underestimate critical swimming speed, possibly because fish in a swim tunnel respirometer are unable to sustain a ground speed.     

A simple kinetic model for dynein oscillatory activity

A kinetic model for dynein, a molecular motor, complexed with microtubule fragments, is considered. The model explains the experimental observations of oscillatory movements in surprisingly simple axonemal fragments perfused by the ATP solution. The model explains at first time the oscillatory dynein activity as a phenomenon induced by two dynein heads cooperative interaction in the axoneme. The oscillation form, frequency, and amplitude, observed for the model, are close to these experimental characteristics. Kinetic parameters, used in the model, are close to the known experimental parameters.     

On the Inference of Functional Circadian Networks Using Granger Causality

Being able to infer one way direct connections in an oscillatory network such as the suprachiastmatic nucleus (SCN) of the mammalian brain using time series data is difficult but crucial to understanding network dynamics. Although techniques have been developed for inferring networks from time series data, there have been no attempts to adapt these techniques to infer directional connections in oscillatory time series, while accurately distinguishing between direct and indirect connections. In this paper an adaptation of Granger Causality is proposed that allows for inference of circadian networks and oscillatory networks in general called Adaptive Frequency Granger Causality (AFGC). Additionally, an extension of this method is proposed to infer networks with large numbers of cells called LASSO AFGC. The method was validated using simulated data from several different networks. For the smaller networks the method was able to identify all one way direct connections without identifying connections that were not present. For larger networks of up to twenty cells the method shows excellent performance in identifying true and false connections; this is quantified by an area-under-the-curve (AUC) 96.88%. We note that this method like other Granger Causality-based methods, is based on the detection of high frequency signals propagating between cell traces. Thus it requires a relatively high sampling rate and a network that can propagate high frequency signals.