Using Computational and Mechanical Models to Study Animal Locomotion

Recent advances in computational methods have made realistic large-scale simulations of animal locomotion possible. This has resulted in numerous mathematical and computational studies of animal movement through fluids and over substrates with the purpose of better understanding organisms’ performance and improving the design of vehicles moving through air and water and on land. This work has also motivated the development of improved numerical methods and modeling techniques for animal locomotion that is characterized by the interactions of fluids, substrates, and structures. Despite the large body of recent work in this area, the application of mathematical and numerical methods to improve our understanding of organisms in the context of their environment and physiology has remained relatively unexplored. Nature has evolved a wide variety of fascinating mechanisms of locomotion that exploit the properties of complex materials and fluids, but only recently are the mathematical, computational, and robotic tools available to rigorously compare the relative advantages and disadvantages of different methods of locomotion in variable environments. Similarly, advances in computational physiology have only recently allowed investigators to explore how changes at the molecular, cellular, and tissue levels might lead to changes in performance at the organismal level. In this article, we highlight recent examples of how computational, mathematical, and experimental tools can be combined to ultimately answer the questions posed in one of the grand challenges in organismal biology: “Integrating living and physical systems.

Somersault of Paramecium in extremely confined environments

We investigate various swimming modes of Paramecium in geometric confinements and a non-swimming self-bending behavior like a somersault, which is quite different from the previously reported behaviors. We observe that Paramecia execute directional sinusoidal trajectories in thick fluid films, whereas Paramecia meander around a localized region and execute frequent turns due to collisions with adjacent walls in thin fluid films. When Paramecia are further constrained in rectangular channels narrower than the length of the cell body, a fraction of meandering Paramecia buckle their body by pushing on the channel walls. The bucking (self-bending) of the cell body allows the Paramecium to reorient its anterior end and explore a completely new direction in extremely confined spaces. Using force deflection method, we quantify the Young’s modulus of the cell and estimate the swimming and bending powers exerted by Paramecium. The analysis shows that Paramecia can utilize a fraction of its swimming power to execute the self-bending maneuver within the confined channel and no extra power may be required for this new kind of self-bending behavior. This investigation sheds light on how micro-organisms can use the flexibility of the body to actively navigate within confined spaces

Roles for the Conserved Spc105p/Kre28p Complex in Kinetochore-Microtubule Binding and the Spindle Assembly Checkpoint

Kinetochores attach sister chromatids to microtubules of the mitotic spindle and orchestrate chromosome disjunction at anaphase. Although S. cerevisiae has the simplest known kinetochores, they nonetheless contain approximately 70 subunits that assemble on centromeric DNA in a hierarchical manner. Developing an accurate picture of the DNA-binding, linker and microtubule-binding layers of kinetochores, including the functions of individual proteins in these layers, is a key challenge in the field of yeast chromosome segregation. Moreover, comparison of orthologous proteins in yeast and humans promises to extend insight obtained from the study of simple fungal kinetochores to complex animal cell kinetochores.We show that S. cerevisiae Spc105p forms a heterotrimeric complex with Kre28p, the likely orthologue of the metazoan kinetochore protein Zwint-1. Through systematic analysis of interdependencies among kinetochore complexes, focused on Spc105p/Kre28p, we develop a comprehensive picture of the assembly hierarchy of budding yeast kinetochores. We find Spc105p/Kre28p to comprise the third linker complex that, along with the Ndc80 and MIND linker complexes, is responsible for bridging between centromeric heterochromatin and kinetochore MAPs and motors. Like the Ndc80 complex, Spc105p/Kre28p is also essential for kinetochore binding by components of the spindle assembly checkpoint. Moreover, these functions are conserved in human cells.Spc105p/Kre28p is the last of the core linker complexes to be analyzed in yeast and we show it to be required for kinetochore binding by a discrete subset of kMAPs (Bim1p, Bik1p, Slk19p) and motors (Cin8p, Kar3p), all of which are nonessential. Strikingly, dissociation of these proteins from kinetochores prevents bipolar attachment, even though the Ndc80 and DASH complexes, the two best-studied kMAPs, are still present. The failure of Spc105 deficient kinetochores to bind correctly to spindle microtubules and to recruit checkpoint proteins in yeast and human cells explains the observed severity of missegregation phenotypes

Incidental sounds of locomotion in animal cognition

The highly synchronized formations that characterize schooling in fish and the flight of certain bird groups have frequently been explained as reducing energy expenditure. I present an alternative, or complimentary, hypothesis that synchronization of group movements may improve hearing perception. Although incidental sounds produced as a by-product of locomotion (ISOL) will be an almost constant presence to most animals, the impact on perception and cognition has been little discussed. A consequence of ISOL may be masking of critical sound signals in the surroundings. Birds in flight may generate significant noise; some produce wing beats that are readily heard on the ground at some distance from the source. Synchronization of group movements might reduce auditory masking through periods of relative silence and facilitate auditory grouping processes. Respiratory locomotor coupling and intermittent flight may be other means of reducing masking and improving hearing perception. A distinct border between ISOL and communicative signals is difficult to delineate. ISOL seems to be used by schooling fish as an aid to staying in formation and avoiding collisions. Bird and bat flocks may use ISOL in an analogous way. ISOL and interaction with animal perception, cognition, and synchronized behavior provide an interesting area for future study

Hydrodynamics of the bluegill sunfish C-start escape response: three-dimensional simulations and comparison with experimental data

In this work we study the hydrodynamics of a bluegill sunfish performing a C-start maneuver in unprecedented detail using 3-D numerical simulations guided by previous laboratory experiments with live fish. The 3-D fish body geometry and kinematics are reconstructed from the experiments using high-speed video and prescribed as input to the numerical simulation. The calculated instantaneous flow fields at various stages of the C-start maneuver are compared with the two-dimensional particle image velocimetry measurements, and are shown to capture essentially all flow features observed in the measurements with good quantitative accuracy; the simulations reveal the experimentally observed three primary jet flow patterns whose momentum time series are in very good agreement with the measured flow field. The simulations elucidate for the first time the complex 3-D structure of the wake during C-starts, revealing an intricate vortical structure consisting of multiple connected vortex loops at the end of the C-start. We also find that the force calculated based on the 3-D flow field has higher magnitudes than that implied by the jet momentum on the midplane, and it exhibits large and rapid fluctuations during the two stages of the C-start. These fluctuations are physical and are related to the change in the direction of the acceleration of the fish body, which changes the location of the high and low pressure pockets around the fish.Organismic and Evolutionary Biolog

Disentangling the Functional Roles of Morphology and Motion in the Swimming of Fish

In fishes the shape of the body and the swimming mode generally are correlated. Slender-bodied fishes such as eels, lampreys, and many sharks tend to swim in the anguilliform mode, in which much of the body undulates at high amplitude. Fishes with broad tails and a narrow caudal peduncle, in contrast, tend to swim in the carangiform mode, in which the tail undulates at high amplitude. Such fishes also tend to have different wake structures. Carangiform swimmers generally produce two staggered vortices per tail beat and a strong downstream jet, while anguilliform swimmers produce a more complex wake, containing at least two pairs of vortices per tail beat and relatively little downstream flow. Are these differences a result of the different swimming modes or of the different body shapes, or both? Disentangling the functional roles requires a multipronged approach, using experiments on live fishes as well as computational simulations and physical models. We present experimental results from swimming eels (anguilliform), bluegill sunfish (carangiform), and rainbow trout (subcarangiform) that demonstrate differences in the wakes and in swimming performance. The swimming of mackerel and lamprey was also simulated computationally with realistic body shapes and both swimming modes: the normal carangiform mackerel and anguilliform lamprey, then an anguilliform mackerel and carangiform lamprey. The gross structure of simulated wakes (single versus double vortex row) depended strongly on Strouhal number, while body shape influenced the complexity of the vortex row, and the swimming mode had the weakest effect. Performance was affected even by small differences in the wakes: both experimental and computational results indicate that anguilliform swimmers are more efficient at lower swimming speeds, while carangiform swimmers are more efficient at high speed. At high Reynolds number, the lamprey-shaped swimmer produced a more complex wake than the mackerel-shaped swimmer, similar to the experimental results. Finally, we show results from a simple physical model of a flapping fin, using fins of different flexural stiffness. When actuated in the same way, fins of different stiffnesses propel themselves at different speeds with different kinematics. Future experimental and computational work will need to consider the mechanisms underlying production of the anguilliform and carangiform swimming modes, because anguilliform swimmers tend to be less stiff, in general, than are carangiform swimmers