Geometric phase predicts locomotion performance in undulating living systems across scales.

Self-propelling organisms locomote via generation of patterns of self-deformation. Despite the diversity of body plans, internal actuation schemes and environments in limbless vertebrates and invertebrates, such organisms often use similar traveling waves of axial body bending for movement. Delineating how self-deformation parameters lead to locomotor performance (e.g. speed, energy, turning capabilities) remains challenging. We show that a geometric framework, replacing laborious calculation with a diagrammatic scheme, is well-suited to discovery and comparison of effective patterns of wave dynamics in diverse living systems. We focus on a regime of undulatory locomotion, that of highly damped environments, which is applicable not only to small organisms in viscous fluids, but also larger animals in frictional fluids (sand) and on frictional ground. We find that the traveling wave dynamics used by mm-scale nematode worms and cm-scale desert dwelling snakes and lizards can be described by time series of weights associated with two principal modes. The approximately circular closed path trajectories of mode weights in a self-deformation space enclose near-maximal surface integral (geometric phase) for organisms spanning two decades in body length. We hypothesize that such trajectories are targets of control (which we refer to as "serpenoid templates"). Further, the geometric approach reveals how seemingly complex behaviors such as turning in worms and sidewinding snakes can be described as modulations of templates. Thus, the use of differential geometry in the locomotion of living systems generates a common description of locomotion across taxa and provides hypotheses for neuromechanical control schemes at lower levels of organization.

Thrust and Power Output of the Bacterial Flagellar Motor: A Micromagnetic Tweezers Approach.

One of the most common swimming strategies employed by microorganisms is based on the use of rotating helical filaments, called flagella, that are powered by molecular motors. Determining the physical properties of this propulsive system is crucial to understanding the behavior of these organisms. Furthermore, the ability to dynamically monitor the activity of the flagellar motor is a valuable indicator of the overall energetics of the cell. In this work, inherently magnetic bacteria confined in micromagnetic CoFe traps are used to directly and noninvasively determine the flagellar thrust force and swimming speed of motile cells. The technique permits determination of the ratio of propulsive force/swimming speed (the hydrodynamic resistance) and the power output of the flagellar motor for individual cells over extended time periods. Cells subjected to ultraviolet radiation are observed to experience exponential decays in power output as a function of exposure time. By noninvasively measuring thrust, velocity, and power output over time at a single-cell level, this technique can serve as the foundation for fundamental studies of bacterial hydrodynamics and also provides a novel, to our knowledge, tether-free probe of single-cell energetics over time.

Dispersion Relations for Active Undulators in Overdamped Environments.

Organisms that locomote by propagating waves of body bending can maintain performance across heterogeneous environments by modifying their gait frequency $\omega$ or wavenumber $k$. We identify a unifying relationship between these parameters for overdamped undulatory swimmers (including nematodes, spermatozoa, and mm-scale fish) moving in diverse environmental rheologies, in the form of an active `dispersion relation' $\omega\propto k^{\pm2}$. A model treating the organisms as actively driven viscoelastic beams reproduces the experimentally observed scaling. The relative strength of rate-dependent dissipation in the body and the environment determines whether $k^2$ or $k^{-2}$ scaling is observed. The existence of these scaling regimes reflects the $k$ and $\omega$ dependence of the various underlying force terms and how their relative importance changes with the external environment and the neuronally commanded gait.

Highly selective quantum sieving of D2 from H2 by a metal-organic framework as determined by gas manometry and infrared spectroscopy.

The quantum sieving effect between D2 and H2 is examined for a series of metal-organic frameworks (MOFs) over the temperature range 77-150 K. Isothermal adsorption measurements demonstrate a consistently larger isosteric heat of adsorption for D2 vs H2, with the largest difference being 1.4 kJ/mol in the case of Ni-MOF-74. This leads to a low-pressure selectivity for this material that increases from 1.5 at 150 K to 5.0 at 77 K. Idealized adsorption solution theory indicates that the selectivity decreases with increasing pressure, but remains well above unity at ambient pressure. Infrared measurements on different MOF materials show a strong correlation between selectivity and the frequency of the adsorbed H2 translational band. This confirms that the separation is predominantly due to the difference in the zero-point energies of the adsorbed isotopologues.

Metal-specific interactions of H2 adsorbed within isostructural metal-organic frameworks.

Diffuse reflectance infrared (IR) spectroscopy performed over a wide temperature range (35-298 K) is used to study the dynamics of H(2) adsorbed within the isostructural metal-organic frameworks M(2)L (M = Mg, Mn, Co, Ni and Zn; L = 2,5-dioxidobenzene-1,4-dicarboxylate) referred to as MOF-74 and CPO-27. Spectra collected at H(2) concentrations ranging from 0.1 to 3.0 H(2) per metal cation reveal that strongly red-shifted vibrational modes arise from isolated H(2) bound to the available metal coordination site. The red shift of the bands associated with this site correlate with reported isosteric enthalpies of adsorption (at small surface coverage), which in turn depend on the identity of M. In contrast, the bands assigned to H(2) adsorbed at positions >3 Å from the metal site exhibit only minor differences among the five materials. Our results are consistent with previous models based on neutron diffraction data and independent IR studies, but they do not support a recently proposed adsorption mechanism that invokes strong H(2)···H(2) interactions (Nijem et al. J. Am. Chem. Soc.2010, 132, 14834-14848). Room temperature IR spectra comparable to those on which the recently proposed adsorption mechanism was based were only reproduced after contaminating the adsorbent with ambient air. Our interpretation that the uncontaminated spectral features result from stepwise adsorption at discrete framework sites is reinforced by systematic red shifts of adsorbed H(2) isotopologues and consistencies among overtone bands that are well-described by the Buckingham model of molecular interactions in vibrational spectroscopy.