Manifold curvature and Ehrenfest forces with a moving basis

Known force terms arising in the Ehrenfest dynamics of quantum electrons and classical nuclei, due to a moving basis set for the former, can be understood in terms of the curvature of the manifold hosting the quantum states of the electronic subsystem. Namely, the velocity-dependent terms appearing in the Ehrenfest forces on the nuclei acquire a geometrical meaning in terms of the intrinsic curvature of the manifold, while Pulay terms relate to its extrinsic curvature.

Regulation of 2D DNA Nanostructures by the Coupling of Intrinsic Tile Curvature and Arm Twist

The overwinding and underwinding of duplex segments between junctions have been used in designing both left-handed and right-handed DNA origami nanostructures. For a variety of DNA tubes obtained from self-assembled tiles, only a theoretical approach of the intrinsic curvature of the DNA tile (specified as the intrinsic tile curvature) has been previously used to explain their formation. Details regarding the quantitative and structural descriptions of the tile curvature and its evolution in DNA tubes by the coupling of the twist of the inter-tile arm (specified as the arm twist) have never been addressed. In this work, we designed three types of tile cores built around a circular 128 nucleotide scaffold by using longitudinal weaving (LW), bridged longitudinal weaving (bLW) and transverse weaving (TW). Joining the tiles with inter-tile arms having the length of an odd number of DNA half-turns (termed O-tiling) almost resulted into planar 2D lattices, whereas joining the tiles with the arms having the length of an even number of DNA half-turns (termed E-tiling) nearly generated tubes. Streptavidin bound to biotin was used as a labeling technique to characterize the inside and outside surfaces of the E-tiling tubes and thereby the conformations of their component tiles with addressable concave and convex curvatures. When the arms have the normal winding at the relaxed B-form of DNA, the intrinsic tile curvature deter-mines the chirality of the E-tiling tubes. By regulating the arm length and the sticky end length of the bLW-Ep/q (E-tiling of the bLW cores with the arm length of p-bp and the sticky end length of q-nt) assemblies, the arm can be overwound, resulting in a left-handed twist, and can also be underwound, resulting in a right-handed twist. Chiral bLW-Ep/q tubes with either a right-handed curvature or a left-handed curvature can also be formed by the coupling of the intrinsic tile curvature and the arm twist. We were able to assign the chiral indices (n,m) to each tube using high-resolution AFM images, and therefore were able to estimate the tile curvature using a regular polygon model that approximated the transverse section of the tube. A deeper understanding of the integrated actions of dif-ferent types of twisting forces on the DNA tubes will be extremely helpful in engineering more elaborate DNA nanostructures in the future.

Mammalian sperm hyperactivation regulates navigation via physical boundaries and promotes pseudo-chemotaxis

Mammalian sperm migration within the complex and dynamic environment of the female reproductive tract toward the fertilization site requires navigational mechanisms, through which sperm respond to the tract environment and maintain the appropriate swimming behavior. In the oviduct (fallopian tube), sperm undergo a process called “hyperactivation,” which involves switching from a nearly symmetrical, low-amplitude, and flagellar beating pattern to an asymmetrical, high-amplitude beating pattern that is required for fertilization in vivo. Here, exploring bovine sperm motion in high–aspect ratio microfluidic reservoirs as well as theoretical and computational modeling, we demonstrate that sperm hyperactivation, in response to pharmacological agonists, modulates sperm–sidewall interactions and thus navigation via physical boundaries. Prior to hyperactivation, sperm remained swimming along the sidewalls of the reservoirs; however, once hyperactivation caused the intrinsic curvature of sperm to exceed a critical value, swimming along the sidewalls was reduced. We further studied the effect of noise in the intrinsic curvature near the critical value and found that these nonthermal fluctuations yielded an interesting “Run–Stop” motion on the sidewall. Finally, we observed that hyperactivation produced a “pseudo-chemotaxis” behavior, in that sperm stayed longer within microfluidic chambers containing higher concentrations of hyperactivation agonists.

Anomalous propulsion regime in axonemal-propelled cargoes

Bio-actuated micro-swimmers provide a platform to understand physical principles related to the motion of micro-organisms at low Reynolds numbers. Here, we used isolated and demembranated flagella from green algae Chlamydomonas reinhardtii as an ATP-fueled bio-actuator for propulsion of micron-sized beads. Chlamydomonas flagella have an asymmetric waveform, which can be accurately described as a superposition of a static component corresponding to an arc-shaped intrinsic curvature, a mode describing the global oscillations of the axonemal curvature, and a main base- to-tip traveling wave component. By decomposing experimental beat patterns in Fourier modes, and applying resistive force theory, we performed numerical simulations and obtained analytical approximations for the mean rotational and translational velocities of a flagellum-propelled bead. Our analysis reveals the existence of a counter- intuitive anomalous propulsion regime where the speed of the flagellum-driven cargo increases with increasing the cargo size. Further, it demonstrates that in addition to the intrinsic curvature and even harmonics, asymmetric bead-flagellum attachment also contributes in the rotational velocity of the micro-swimmer. This turning mechanism induced by sideways cargo attachment has potential applications in fabrication of bio- actuated medical micro-robots in the subject of targeted drug delivery and synthetic micro-swimmers.

Time-reversal symmetric component of the flagellar beat enhances the translational and rotational velocities of isolated Chlamydomonas flagella

The beating of cilia and flagella is essential to perform many important biological functions, including generating fluid flows on the cell surface or propulsion of micro-organisms. In this work, we analyze the motion of isolated and demembranated flagella from green algae Chlamydomonas reinhardtii, which act as ATP-driven micro-swimmers. The waveform of the Chlamydomonas beating flagella has an asymmetric waveform that is known to involve the superposition of a static component, corresponding to a fixed, intrinsic curvature, and a dynamic wave component traveling in the base-to-tip direction at the fundamental beat frequency, plus higher harmonics. Here, we demonstrate that these modes are not sufficient to reproduce the observed flagella waveforms. We find that two extra modes play an essential role to describe the motion: first, a time-symmetric mode, which corresponds to a global oscillation of the axonemal curvature, and second, a secondary tip-to-base wave component at the fundamental frequency that propagates opposite to the dominant base-to-tip wave, albeit with a smaller amplitude. Although the time-symmetric mode cannot, by itself, contribute to propulsion (scallop theorem), it does enhance the translational and rotational velocities of the flagellum by approximately a factor of 2. This mode highlights a long-range coupled on/off activity of force-generating dynein motors and can provide further insight into the underling biology of the ciliary beat.

Intrinsic lipid curvatures of mammalian plasma membrane outer leaflet lipids and ceramides

We developed a global X-ray data analysis method to determine the intrinsic curvatures of lipids hosted in inverted hexagonal phases. In particular, we combined compositional modelling with molecular shape-based arguments to account for non-linear mixing effects of guest-in-host lipids on intrinsic curvature. The technique was verified by all-atom molecular dynamics simulations and applied to sphingomyelin and a series of phosphatidylcholines and ceramides with differing composition of the hydrocarbon chains. We report positive lipid curvatures for sphingomyelin and all phosphatidylcholines with disaturated and monounsaturated hydrocarbons. Substitution of the second saturated hydrocarbon with an unsaturated acyl chain in turn shifted the intrinsic lipid curvatures to negative values. All ceramides, with chain lengths varying between C2:0 and C24:0, displayed significant negative lipid curvature values. Moreover, we report non-additive mixing for C2:0 ceramide and sphingomyelin. Our findings manifest the high and manifold potential of lipids to modulate physiological membrane function.

Stochastic vs. deterministic magnetic coding in designed cylindrical nanowires for 3D magnetic networks

Advances in cylindrical nanowires for 3D information technologies profit from intrinsic curvature that introduces significant differences with regards to planar systems. A model is proposed to control the stochastic and...

Chiral self-sorting of active semiflexible filaments with intrinsic curvature

Many-body interactions in systems of active matter can cause particles to move collectively and self-organize into dynamic structures with long-range order. In cells, the self-assembly of cy- toskeletal filaments is...

The hook shape of growing leaves results from an active regulatory process

The rachis of most growing compound leaves observed in nature exhibits a stereotypical hook shape. In this study, we focus on the canonical case of Averrhoa carambola. Combining kinematics and mechanical investigation, we characterize this hook shape and shed light on its establishment and maintenance. We show quantitatively that the hook shape is a conserved bent zone propagating at constant velocity and constant distance from the apex throughout development. A simple mechanical test reveals non-zero intrinsic curvature profiles for the rachis during its growth, indicating that the hook shape is actively regulated. We show a robust spatial organization of growth, curvature, rigidity, and lignification, and their interplay. Regulatory processes appear to be specifically localized: in particular, differential growth occurs where the elongation rate drops. Finally, impairing the graviception of the leaf on a clinostat led to reduced hook curvature but not to its loss. Altogether, our results suggest a role for proprioception in the regulation of the leaf hook shape, likely mediated via mechanical strain.