Energetics of optimal undulatory swimming organisms.

Energy consumption is one of the primary considerations in animal locomotion. In swimming locomotion, a number of questions related to swimming energetics of an organism and how the energetic quantities scale with body size remain open, largely due to the difficulties with modeling and measuring the power production and consumption. Based on a comprehensive theoretical framework that incorporates cyclic muscle behavior, structural dynamics and swimming hydrodynamics, we perform extensive computational simulations and show that many of the outstanding problems in swimming energetics can be explained by considering the coupling between hydrodynamics and muscle contraction characteristics, as well as the trade-offs between the conflicting performance goals of sustained swimming speed U and cost of transport COT. Our results lead to three main conclusions: (1) in contrast to previous hypotheses, achieving optimal values of U and COT is independent of producing maximal power or efficiency; (2) muscle efficiency in swimming, in contrast to that in flying or running, decreases with increasing body size, consistent with muscle contraction characteristics; (3) the long-standing problem of two disparate patterns of longitudinal power output distributions in swimming fish can be reconciled by relating the two patterns to U-optimal or COT-optimal swimmers, respectively. We also provide further evidence that the use of tendons in caudal regions is beneficial from an energetic perspective. Our conclusions explain and unify many existing observations and are supported by computational data covering nine orders of magnitude in body size.

Modeling variation coefficient of wave-induced underwater irradiance for clear ocean and its application to find the optimal detector size.

In measuring the coefficient of variation (CV) of underwater wave-induced sunlight irradiance, the spatial integration of irradiance signals due to the finite aperture size of an irradiance detector usually causes underestimation of the measured variance. Because this spatial integration effect is strongly coupled with ocean wave features, inherent optical properties (IOPs) of water, and atmospheric radiance conditions, direct deconvolution techniques from measured irradiance signals can lead to serious signal-to-noise degradation in a noisy upper ocean. On the other hand, choosing a small detector to guarantee CV accuracy is expensive. We address the intrinsic dependence of the CV on the detector size and choice of optimal detector size for measuring irradiance variability in a turbid ocean environment. We present a new theoretical model to directly obtain the form of the CV of the wave-induced scalar irradiance as the function of the detector size, ocean surface wave parameters, and IOPs of ocean water. The model is derived under the small-angle scattering approximation and the first-order assumption of Snell's law and Fresnel transmission coefficient. We demonstrate the validity and efficacy of the model for weakly roughened Gaussian ocean surface conditions, by comparison with Monte Carlo radiative transfer simulations. The model shows that the CV of wave-induced irradiance reaches an asymptotic with decreasing the detector size, thereby providing an optimal or maximum detector size for given IOP and environmental conditions.

Interplay between motility and cell-substratum adhesion in amoeboid cells.

The effective migration of amoeboid cells requires a fine regulation of cell-substratum adhesion. These entwined processes have been shown to be regulated by a host of biophysical and biochemical cues. Here, we reveal the pivotal role played by calcium-based mechanosensation in the active regulation of adhesion resulting in a high migratory adaptability. Using mechanotactically driven Dictyostelium discoideum amoebae, we uncover the existence of optimal mechanosensitive conditions-corresponding to specific levels of extracellular calcium-for persistent directional migration over physicochemically different substrates. When these optimal mechanosensitive conditions are met, noticeable enhancement in cell migration directionality and speed is achieved, yet with significant differences among the different substrates. In the same narrow range of calcium concentrations that yields optimal cellular mechanosensory activity, we uncovered an absolute minimum in cell-substratum adhesion activity, for all considered substrates, with differences in adhesion strength among them amplified. The blocking of the mechanosensitive ion channels with gadolinium-i.e., the inhibition of the primary mechanosensory apparatus-hampers the active reduction in substrate adhesion, thereby leading to the same undifferentiated and drastically reduced directed migratory response. The adaptive behavioral responses of Dictyostelium cells sensitive to substrates with varying physicochemical properties suggest the possibility of novel surface analyses based on the mechanobiological ability of mechanosensitive and guidable cells to probe substrates at the nanometer-to-micrometer level.

Analytical solution of beam spread function for ocean light radiative transfer.

We develop a new method to analytically obtain the beam spread function (BSF) for light radiative transfer in oceanic environments. The BSF, which is defined as the lateral distribution of the (scalar) irradiance with increasing depth in response to a uni-directional beam emanating from a point source in an infinite ocean, must in general be obtained by solving the three-dimensional (3D) radiative transfer equation (RTE). By taking advantage of the highly forward-peaked scattering property of the ocean particles, we assume, for a narrow beam source, the dependence of radiance on polar angle and azimuthal angle is deliberately separated; only single scattering takes place in the azimuthal direction while multiple scattering still occurs in the polar direction. This assumption enables us to reduce the five-variable 3D RTE to a three-variable two-dimensional (2D) RTE. With this simplification, we apply Fourier spectral method to both spatial and angular variables so that we are able to analytically solve the 2D RTE and obtain the 2D BSF accordingly. Using the relations between 2D and 3D solutions acquired during the process of simplification, we are able to obtain the 3D BSF in explicit form. The 2D and 3D analytical solutions are validated by comparing with Monte Carlo radiative transfer simulations. The 2D analytical BSF agrees excellently with the Monte Carlo result. Despite assumptions of axial symmetry and spike-like azimuthal profile of the radiance in deriving the 3D BSF, the comparisons to numerical simulations are very satisfactory especially for limited optical depths (< O(5)) for single scattering albedo values typical in the ocean. The explicit form of the analytical BSF and the significant gain in computational efficiency (several orders higher) relative to RTE simulations make many forward and inverse problems in ocean optics practical for routine applications.

Persistent cellular motion control and trapping using mechanotactic signaling.

Chemotactic signaling and the associated directed cell migration have been extensively studied owing to their importance in emergent processes of cellular aggregation. In contrast, mechanotactic signaling has been relatively overlooked despite its potential for unique ways to artificially signal cells with the aim to effectively gain control over their motile behavior. The possibility of mimicking cellular mechanotactic signals offers a fascinating novel strategy to achieve targeted cell delivery for in vitro tissue growth if proven to be effective with mammalian cells. Using (i) optimal level of extracellular calcium ([Ca(2+)]ext = 3 mM) we found, (ii) controllable fluid shear stress of low magnitude (σ < 0.5 Pa), and (iii) the ability to swiftly reverse flow direction (within one second), we are able to successfully signal Dictyostelium discoideum amoebae and trigger migratory responses with heretofore unreported control and precision. Specifically, we are able to systematically determine the mechanical input signal required to achieve any predetermined sequences of steps including straightforward motion, reversal and trapping. The mechanotactic cellular trapping is achieved for the first time and is associated with a stalling frequency of 0.06 ~ 0.1 Hz for a reversing direction mechanostimulus, above which the cells are effectively trapped while maintaining a high level of directional sensing. The value of this frequency is very close to the stalling frequency recently reported for chemotactic cell trapping [Meier B, et al. (2011) Proc Natl Acad Sci USA 108:11417-11422], suggesting that the limiting factor may be the slowness of the internal chemically-based motility apparatus.

Direct numerical investigation of turbulence of capillary waves.

We consider the inertial range spectrum of capillary wave turbulence. Under the assumptions of weak turbulence, the theoretical surface elevation spectrum scales with wave number k as Iη∼k(α), where α=α0=-19/4, energy (density) flux P as P(1/2). The proportional factor C, known as the Kolmogorov constant, has a theoretical value of C=C0=9.85 (we show that this value holds only after a formulation in the original derivation is corrected). The k(-19/4) scaling has been extensively, but not conclusively, tested; the P(1/2) scaling has been investigated experimentally, but until recently remains controversial, while direct confirmation of the value of C0 remains elusive. We conduct a direct numerical investigation implementing the primitive Euler equations. For sufficiently high nonlinearity, the theoretical k^{-19/4} and P(1/2) scalings as well as value of C0 are well recovered by our numerical results. For a given number of numerical modes N, as nonlinearity decreases, the long-time spectra deviate from theoretical predictions with respect to scaling with P, with calculated values of α<α0 and C>C0, all due to finite box effect.

Physical limits on cellular directional mechanosensing.

Many eukaryotic cells are able to perform directional mechanosensing by directly measuring minute spatial differences in the mechanical stress on their membranes. Here, we explore the limits of a single mechanosensitive channel activation using a two-state double-well model for the gating mechanism. We then focus on the physical limits of directional mechanosensing by a single cell having multiple mechanosensors and subjected to a shear flow inducing a nonuniform membrane tension. Our results demonstrate that the accuracy in sensing the mechanostimulus direction not only increases with cell size and exposure to a signal, but also grows for cells with a near-critical membrane prestress. Finally, the existence of a nonlinear threshold effect, fundamentally limiting the cell's ability to effectively perform directional mechanosensing at a low signal-to-noise ratio, is uncovered.

Optimal shape and motion of undulatory swimming organisms.

Undulatory swimming animals exhibit diverse ranges of body shapes and motion patterns and are often considered as having superior locomotory performance. The extent to which morphological traits of swimming animals have evolved owing to primarily locomotion considerations is, however, not clear. To shed some light on that question, we present here the optimal shape and motion of undulatory swimming organisms obtained by optimizing locomotive performance measures within the framework of a combined hydrodynamical, structural and novel muscular model. We develop a muscular model for periodic muscle contraction which provides relevant kinematic and energetic quantities required to describe swimming. Using an evolutionary algorithm, we performed a multi-objective optimization for achieving maximum sustained swimming speed U and minimum cost of transport (COT)--two conflicting locomotive performance measures that have been conjectured as likely to increase fitness for survival. Starting from an initial population of random characteristics, our results show that, for a range of size scales, fish-like body shapes and motion indeed emerge when U and COT are optimized. Inherent boundary-layer-dependent allometric scaling between body mass and kinematic and energetic quantities of the optimal populations is observed. The trade-off between U and COT affects the geometry, kinematics and energetics of swimming organisms. Our results are corroborated by empirical data from swimming animals over nine orders of magnitude in size, supporting the notion that optimizing U and COT could be the driving force of evolution in many species.

A model for the probability density function of downwelling irradiance under ocean waves.

We present a statistical model that analytically quantifies the probability density function (PDF) of the downwelling light irradiance under random ocean waves modeling the surface as independent and identically distributed flat facets. The model can incorporate the separate effects of surface short waves and volume light scattering. The theoretical model captures the characteristics of the PDF, from skewed to near-Gaussian shape as the depth increases from shallow to deep water. The model obtains a closed-form asymptotic for the probability that diminishes at a rate between exponential and Gaussian with increasing extreme values. The model is validated by comparisons with existing field measurements and Monte Carlo simulation.

Hydrodynamics of cell-cell mechanical signaling in the initial stages of aggregation.

Mechanotactic cell motility has recently been shown to be a key player in the initial aggregation of crawling cells such as leukocytes and amoebae. The effects of mechanotactic signaling in the early aggregation of amoeboid cells are here investigated using a general mathematical model based on known biological evidence. We elucidate the hydrodynamic fundamentals of the direct guiding of a cell through mechanotaxis in the case where one cell transmits a mechanotactic signal through the fluid flow by changing its shape. It is found that any mechanosensing cells placed in the stimulus field of mechanical stress are able to determine the signal transmission direction with a certain angular dispersion which does not preclude the aggregation from happening. The ubiquitous presence of noise is accounted for by the model. Finally, the mesoscopic pattern of aggregation is obtained which constitutes the bridge between, on one hand, the microscopic world where the changes in the cell shape occur and, on the other hand, the cooperative behavior of the cells at the mesoscopic scale.

Evidence of holes in the Arnold tongues of flow past two oscillating cylinders.

The wake of two oscillating cylinders in a tandem arrangement is a nonlinear system that displays Arnold tongues. We show by numerical simulations that their geometry depends on the phase difference theta between the two oscillating cylinders. At theta = 0 there may be holes inside these intraresonance regions unlike the solid Arnold tongues encountered in single-cylinder oscillations. This implies that, surprisingly, self-excitation of the system may be suppressed inside these holes, at conditions close to its natural frequency.