Mechanical power limitations emerge from the physical trade-off between force and velocity. Many biological systems incorporate power-enhancing mechanisms enabling extraordinary accelerations at small sizes. We establish how power enhancement emerges through the dynamic coupling of motors, springs, and latches and reveal how each displays its own force-velocity behavior. We mathematically demonstrate a tunable performance space for spring-actuated movement that is applicable to biological and synthetic systems. Incorporating nonideal spring behavior and parameterizing latch dynamics allows the identification of critical transitions in mass and trade-offs in spring scaling, both of which offer explanations for long-observed scaling patterns in biological systems. This analysis defines the cascading challenges of power enhancement, explores their emergent effects in biological and engineered systems, and charts a pathway for higher-level analysis and synthesis of power-amplified systems.

Highlights d Lacrymaria is a unicellular predator that hunts using extreme morphology dynamics d Computer vision digitizes millions of real-time sub-cellular postures during hunts d Morphology dynamics result in dense stochastic sampling of the local environment d Behavior emerges from fast and slow response of helical cytoskeleton to cyclic stress

Recent experiments have shown that suspensions of swimming micro-organisms are characterized by complex dynamics involving enhanced swimming speeds, large-scale correlated motions and enhanced diffusivities of embedded tracer particles. Understanding this dynamics is of fundamental interest and also has relevance to biological systems. The observed collective dynamics has been interpreted as the onset of a hydrodynamic instability, of the quiescent isotropic state of pushers, swimmers with extensile force dipoles, above a critical threshold proportional to the swimmer concentration. In this work, we develop a particle-based model to simulate a suspension of hydrodynamically interacting rod-like swimmers to estimate this threshold. Unlike earlier simulations, the velocity disturbance field due to each swimmer is specified in terms of the intrinsic swimmer stress alone, as per viscous slender-body theory. This allows for a computationally efficient kinematic simulation where the interaction law between swimmers is known a priori. The neglect of induced stresses is of secondary importance since the aforementioned instability arises solely due to the intrinsic swimmer force dipoles.Our kinematic simulations include, for the first time, intrinsic decorrelation mechanisms found in bacteria, such as tumbling and rotary diffusion. To begin with, we simulate so-called straight swimmers that lack intrinsic orientation decorrelation mechanisms, and a comparison with earlier results serves as a proof of principle. Next, we simulate suspensions of swimmers that tumble and undergo rotary diffusion, as a function of the swimmer number density (n), and the intrinsic decorrelation time (the average duration between tumbles, τ , for tumblers, and the inverse of the rotary diffusivity, D −1 r , for rotary diffusers). The simulations, as a function of the decorrelation time, are carried out with hydrodynamic interactions (between swimmers) turned off and on, and for both pushers and pullers (swimmers with contractile force dipoles). The 'interactions-off' simulations allow for a validation based on analytical expressions for the tracer diffusivity in the stable regime, and reveal a non-trivial box size dependence that arises with varying strength of the hydrodynamic interactions. The 'interactions-on' simulations lead us to our main finding: the existence of a box-size-independent parameter that characterizes the onset of instability in a pusher suspension, and is given by nUL 2 τ for tumblers and † Email address for correspondence: sganesh@jncasr.ac.in ‡ Present address:Collective motion in micro-swimmer suspensions 423 nUL 2 /D r for rotary diffusers; here, U and L are the swimming speed and swimmer length, respectively. The instability manifests as a bifurcation of the tracer diffusivity curves, in pusher and puller suspensions, for values of the above dimensionless parameters exceeding a critical threshold.

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