Idan Tuval

Microfluidics of cytoplasmic streaming and its implications for intracellular transport

Found in many large eukaryotic cells, particularly in plants, cytoplasmic streaming is the circulation of their contents driven by fluid entrainment from particles carried by molecular motors at the cell periphery. In the more than two centuries since its discovery, streaming has frequently been conjectured to aid in transport and mixing of molecular species in the cytoplasm and, by implication, in cellular homeostasis, yet no theoretical analysis has been presented to quantify these processes. We show by a solution to the coupled dynamics of fluid flow and diffusion appropriate to the archetypal “rotational streaming” of algal species such as Chara and Nitella that internal mixing and the transient dynamical response to changing external conditions can indeed be enhanced by streaming, but to an extent that depends strongly on the pitch of the helical flow. The possibility that this may have a developmental consequence is illustrated by the coincidence of the exponential growth phase of Nitella and the point of maximum enhancement of those processes.

Fidelity of adaptive phototaxis

Along the evolutionary path from single cells to multicellular organisms with a central nervous system are species of intermediate complexity that move in ways suggesting high-level coordination, yet have none. Instead, organisms of this type possess many autonomous cells endowed with programs that have evolved to achieve concerted responses to environmental stimuli. Here experiment and theory are used to develop a quantitative understanding of how cells of such organisms coordinate to achieve phototaxis, by using the colonial alga Volvox carteri as a model. It is shown that the surface somatic cells act as individuals but are orchestrated by their relative position in the spherical extracellular matrix and their common photoresponse function to achieve colony-level coordination. Analysis of models that range from the minimal to the biologically faithful shows that, because the flagellar beating displays an adaptive down-regulation in response to light, the colony needs to spin around its swimming direction and that the response kinetics and natural spinning frequency of the colony appear to be mutually tuned to give the maximum photoresponse. These models further predict that the phototactic ability decreases dramatically when the colony does not spin at its natural frequency, a result confirmed by phototaxis assays in which colony rotation was slowed by increasing the fluid viscosity.

Embryonic nodal flow and the dynamics of nodal vesicular parcels

We address with fluid-dynamical simulations using direct numerical techniques three important and fundamental questions with respect to fluid flow within the mouse node and left–right development. First, we consider the differences between what is experimentally observed when assessing cilium-induced fluid flow in the mouse node in vitro and what is to be expected in vivo. The distinction is that in vivo, the leftward fluid flow across the mouse node takes place within a closed system and is consequently confined, while this is no longer the case on removing the covering membrane and immersing the embryo in a fluid-filled volume to perform in vitro experiments. Although there is a central leftward flow in both instances, we elucidate some important distinctions about the closed in vivo situation. Second, we model the movement of the newly discovered nodal vesicular parcels (NVPs) across the node and demonstrate that the flow should indeed cause them to accumulate on the left side of the node, as required for symmetry breaking. Third, we discuss the rupture of NVPs. Based on the biophysical properties of these vesicles, we argue that the morphogens they contain are likely not delivered to the surrounding cells by their mechanical rupture either by the cilia or the flow, and rupture must instead be induced by an as yet undiscovered biochemical mechanism.

Fluid dynamics in developmental biology: moving fluids that shape ontogeny.

Human conception, indeed fertilization in general, takes place in a fluid, but what role does fluid dynamics have during the subsequent development of an organism? It is becoming increasingly clear that the number of genes in the genome of a typical organism is not sufficient to specify the minutiae of all features of its ontogeny. Instead, genetics often acts as a choreographer, guiding development but leaving some aspects to be controlled by physical and chemical means. Fluids are ubiquitous in biological systems, so it is not surprising that fluid dynamics should play an important role in the physical and chemical processes shaping ontogeny. However, only in a few cases have the strands been teased apart to see exactly how fluid forces operate to guide development. Here, we review instances in which the hand of fluid dynamics in developmental biology is acknowledged, both in human development and within a wider biological context, together with some in which fluid dynamics is notable but whose workings have yet to be understood, and we provide a fluid dynamicists perspective on possible avenues for future research.

Frontiers of chaotic advection

This work reviews the present position of and surveys future perspectives in the physics of chaotic advection: the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear dynamics, which encompasses a range of applications with length scales ranging from micrometers to hundreds of kilometers, including systems as diverse as mixing and thermal processing of viscous fluids, microfluidics, biological flows, and oceanographic and atmospheric flows.

Antiphase Synchronization in a Flagellar-Dominance Mutant of Chlamydomonas

Groups of beating flagella or cilia often synchronize so that neighboring filaments have identical frequencies and phases. A prime example is provided by the unicellular biflagellate Chlamydomonas reinhardtii, which typically displays synchronous in-phase beating in a low-Reynolds number version of breaststroke swimming. We report the discovery that ptx1, a flagellar-dominance mutant of C. reinhardtii, can exhibit synchronization in precise antiphase, as in the freestyle swimming stroke. High-speed imaging shows that ptx1 flagella switch stochastically between in-phase and antiphase states, and that the latter has a distinct waveform and significantly higher frequency, both of which are strikingly similar to those found during phase slips that stochastically interrupt in-phase beating of the wild-type. Possible mechanisms underlying these observations are discussed.

Brinicles as a case of inverse chemical gardens

Brinicles are hollow tubes of ice from centimeters to meters in length that form under floating sea ice in the polar oceans when dense, cold brine drains downward from sea ice to seawater close to its freezing point. When this extremely cold brine leaves the ice, it freezes the water it comes into contact with: a hollow tube of ice-a brinicle-growing downward around the plume of descending brine. We show that brinicles can be understood as a form of the self-assembled tubular precipitation structures termed chemical gardens, which are plantlike structures formed on placing together a soluble metal salt, often in the form of a seed crystal, and an aqueous solution of one of many anions, often silicate. On one hand, in the case of classical chemical gardens, an osmotic pressure difference across a semipermeable precipitation membrane that filters solutions by rejecting the solute leads to an inflow of water and to its rupture. The internal solution, generally being lighter than the external solution, flows up through the break, and as it does so, a tube grows upward by precipitation around the jet of internal solution. Such chemical-garden tubes can grow to many centimeters in length. In the case of brinicles, on the other hand, in floating sea ice we have porous ice in a mushy layer that filters out water, by freezing it, and allows concentrated brine through. Again there is an osmotic pressure difference leading to a continuing ingress of seawater in a siphon pump mechanism that is sustained as long as the ice continues to freeze. Because the brine that is pumped out is denser than the seawater and descends rather than rises, a brinicle is a downward-growing tube of ice, an inverse chemical garden.

Bailout Embeddings and Neutrally Buoyant Particles in Three-Dimensional Flows

We use the bailout embeddings of three-dimensional volume-preserving maps to study qualitatively the dynamics of small spherical neutrally buoyant impurities suspended in a time-periodic incompressible fluid flow. The accumulation of impurities in tubular vortical structures, the detachment of particles from fluid trajectories near hyperbolic invariant lines, and the formation of nontrivial three-dimensional structures in the distribution of particles are predicted.

Microalgae Scatter off Solid Surfaces by Hydrodynamic and Contact Forces

Interactions between microorganisms and solid boundaries play an important role in biological processes, such as egg fertilization, biofilm formation, and soil colonization, where microswimmers move within a structured environment. Despite recent efforts to understand their origin, it is not clear whether these interactions can be understood as being fundamentally of hydrodynamic origin or hinging on the swimmers direct contact with the obstacle. Using a combination of experiments and simulations, here we study in detail the interaction of the biflagellate green alga Chlamydomonas reinhardtii, widely used as a model puller microorganism, with convex obstacles, a geometry ideally suited to highlight the different roles of steric and hydrodynamic effects. Our results reveal that both kinds of forces are crucial for the correct description of the interaction of this class of flagellated microorganisms with boundaries.

Fluid dynamics of establishing left-right patterning in development

How does the clockwise motion of tens of monocilia drive a leftward flow in the node? And, as the observed flow is leftward, how is the fluid recirculating within the node, as it must, because the node is a closed structure? How does the nodal flow lead to left-right symmetry breaking in the embryo? These questions are within the realm of fluid physics, whose application to the problem of left-right symmetry breaking in vertebrates has led to important advances in the field.