Future Tail Tales: A Forward-Looking, Integrative Perspective on Tail Research.

Synopsis Tails are a defining characteristic of chordates and show enormous diversity in function and shape. Although chordate tails share a common evolutionary and genetic-developmental origin, tails are extremely versatile in morphology and function. For example, tails can be short or long, thin or thick, and feathered or spiked, and they can be used for propulsion, communication, or balancing, and they mediate in predator-prey outcomes. Depending on the species of animal the tail is attached to, it can have extraordinarily multi-functional purposes. Despite its morphological diversity and broad functional roles, tails have not received similar scientific attention as, for example, the paired appendages such as legs or fins. This forward-looking review article is a first step toward interdisciplinary scientific synthesis in tail research. We discuss the importance of tail research in relation to five topics: (1) evolution and development, (2) regeneration, (3) functional morphology, (4) sensorimotor control, and (5) computational and physical models. Within each of these areas, we highlight areas of research and combinations of long-standing and new experimental approaches to move the field of tail research forward. To best advance a holistic understanding of tail evolution and function, it is imperative to embrace an interdisciplinary approach, re-integrating traditionally siloed fields around discussions on tail-related research.

Fish-like aquatic propulsion studied using a pneumatically-actuated soft-robotic model.

Fish locomotion is characterized by waves of muscle electrical activity that proceed from head to tail, and result in an undulatory pattern of body bending that generates thrust during locomotion. Isolating the effects of parameters like body stiffness, co-activation between the right and left sides of the body, and frequency on thrust generation has proven to be difficult in live fishes. We use a pneumatically-actuated fish-like model to investigate how these parameters affect locomotor force generation. We measure thrust as well as side forces and torques generated during propulsion. Using a statistical linear model we examine the effects of input parameter combinations on thrust generation. We show that both stiffness and frequency substantially affect swimming kinematics, and that there are complex interactive effects of these two parameters on thrust. The stiffer the backbone the more impact that increasing frequency has on thrust production. For stiffer models, increasing frequency resulted in higher values for both thrust and lateral forces. Large side forces reduce swimming efficiency but this effect could be mitigated by decreasing undulatory wavelength and allowing appropriate phasing of left and right body movements to reduce amplitudes of side force.

Righting and turning in mid-air using appendage inertia: reptile tails, analytical models and bio-inspired robots.

Unlike the falling cat, lizards can right themselves in mid-air by a swing of their large tails in one direction causing the body to rotate in the other. Here, we developed a new three-dimensional analytical model to investigate the effectiveness of tails as inertial appendages that change body orientation. We anchored our model using the morphological parameters of the flat-tailed house gecko Hemidactylus platyurus. The degree of roll in air righting and the amount of yaw in mid-air turning directly measured in house geckos matched the model's results. Our model predicted an increase in body roll and turning as tails increase in length relative to the body. Tails that swung from a near orthogonal plane relative to the body (i.e. 0-30° from vertical) were the most effective at generating body roll, whereas tails operating at steeper angles (i.e. 45-60°) produced only half the rotation. To further test our analytical model's predictions, we built a bio-inspired robot prototype. The robot reinforced how effective attitude control can be attained with simple movements of an inertial appendage.

Surface potential of spherical polyelectrolyte brushes in the presence of trivalent counterions.

We consider the zeta-potential and the effective charge of spherical polyelectrolyte brushes (SPBs) in aqueous solution in the presence of trivalent europium ions. The SPB consists of a polystyrene core of ca. 250 nm diameter onto which long chains of the strong polyelectrolyte poly(styrene sulfonate) are grafted (contour length: 82 nm). At low concentration of EuCl3 the chains are stretched to nearly full length. If the concentration of the trivalent ions is raised, the surface layer of the polyelectrolyte chains collapses. The zeta-potential of the SPB is calculated from the electrophoretic mobilities measured at different concentrations of EuCl3. At the collapse, zeta decreases by the partial neutralization of the charges by the trivalent ions. The experimental zeta-potential thus obtained agrees with the theoretical surface potential Psi(theo) calculated for the effective shear plane by a variational free energy model of the SPB.

Anomalous small-angle X-ray scattering: analyzing correlations and fluctuations in polyelectrolytes.

We review recent structural investigations done by anomalous small-angle X-ray scattering (ASAXS). ASAXS uses the dependence of the scattering length of a given element if the energy of the incident X-ray beam is near the absorption edge of this element. The analysis of the ASAXS data leads to three partial intensities. We show that the comparison of these three partial intensities leads to valuable information in fluctuating systems. This has been demonstrated from data derived from recent molecular dynamics simulations of charged colloidal spheres. Moreover, it is shown that the three partial intensities can be obtained from experimental ASAXS data indeed. As an example for this analysis, we discuss recent ASAXS data referring to rod-like polyelectrolytes. These polyelectrolytes consist of a stiff poly(p-phenylene) backbone with attached charged groups that are balanced by bromine counterions. The three partial intensities can be determined experimentally and compared to the prediction of the Poisson-Boltzmann cell model. Quantitative agreement is found demonstrating the strong correlation of the counterions to the rod-like macroion. ASAXS is thus shown to furnish information not available by the conventional small-angle scattering experiment.

Bulk and interfacial properties in colloid-polymer mixtures.

Large-scale Monte Carlo simulations of a phase-separating colloid-polymer mixture are performed and compared to recent experiments. The approach is based on effective interaction potentials in which the central monomers of self-avoiding polymer chains are used as effective coordinates. By incorporating polymer nonideality together with soft colloid-polymer repulsion, the predicted binodal is in excellent agreement with recent experiments. In addition, the interfacial tension as well as the capillary length are in quantitative agreement with experimental results obtained at a number of points in the phase-coexistence region, without the use of any fit parameters.

Conformations and interactions of star-branched polyelectrolytes.

Combining monomer-resolved molecular dynamics simulations with a theory based on a variational free energy, we calculate the conformational properties and the effective interactions of star-branched polyelectrolytes for a large variety of arm numbers, degrees of polymerization, and charge fractions, with and without added salt. We find quantitative agreement between theory and simulation and put forward analytical expressions that allow the calculation of the interaction between such macromolecules.

Phase separation in star-polymer-colloid mixtures.

We examine the demixing transition in star-polymer-colloid mixtures for star arm numbers f=2,6,16,32 and different star-polymer-colloid size ratios 0.18< or =q< or =0.50. Theoretically, we solve the thermodynamically self-consistent Rogers-Young integral equations for binary mixtures using three effective pair potentials obtained from direct molecular computer simulations. The numerical results show a spinodal instability. The demixing binodals are approximately calculated and found to be consistent with experimental observations.

Polydisperse star polymer solutions

We analyze the effect of polydispersity in the arm number on the effective interactions, structural correlations, and phase behavior of star polymers in a good solvent. The effective interaction potential between two star polymers with different arm numbers is derived using scaling theory. The resulting expression is tested against monomer-resolved molecular dynamics simulations. We find that the theoretical pair potential is in agreement with the simulation data in a much wider polydispersity range than other proposed potentials. We then use this pair potential as an input in a many-body theory to investigate polydispersity effects on the structural correlations and the phase diagram of dense star polymer solutions. In particular, we find that a polydispersity of 10%, which is typical in experimental samples, does not significantly alter previous findings for the phase diagram of monodisperse solutions.