Microfluidics of cytoplasmic streaming and its implications for intracellular transport

Abstract

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. Since Bonaventura Corti's discovery (1) in 1774 of the persistent circulation of the cytoplasm of plant cells, the phenomenon now known as cytoplasmic streaming or cyclosis has been conjectured to play an important role in metabolism (2). It occurs in organisms as diverse as amoebae (3), algae and terrestrial plants (4,5), and fungi (6). In plants (4, 5, 7) it is driven by multitudes of the motor protein myosin moving along bundled actin at the boundary of the cytoplasm, carrying microscopic particles or organelles (8, 9), and entraining fluid. The motion of protoplasmic granules entrained in the flow includes unidirectional streaming, ''fountain streaming'' (in which the motion near the central axis of the cell is opposite to that near the periphery), and spiral ''rotational streaming.'' Plant myosins can move at tens of micrometers per second (10-13), considerably faster than most animal myosins (although some can reach Ϸ30 m/s), and the speed U of cyclosis can reach Ϸ100 m/s in cells whose radius R can reach 0.5 mm. These speeds greatly outpace diffusion, as measured by the Péclet number Pe ϭ UR/D, where D is a molecular diffusion constant. For the smallest molecules, with D ϳ 10 Ϫ5 cm 2 /s, we see that Pe ϳ 50, and it can easily reach 500-1,000 for larger proteins. The fact that transport by fluid motion becomes necessary to outrun the slow pace of diffusion in larger organisms, as emphasized in the celebrated essay by Haldane on size in biology (14), has been a theme in discussions of cytoplasmic streaming for many years. Yet, there has been little theoretical work and fewer experiments that have quantified the full implications of cytoplasmic streaming for transport and mixing. Only recently has it been recognized (2, 15) that the large Péclet numbers found in vivo could enhance metabolite exchange with organelles such as chloroplasts. Still, a range of basic questions has remained unanswered (16): What is the role of cytoplasmic streaming in homeostasis? Ho...

Running Faster Together: Huge Speed up of Thermal Ratchets due to Hydrodynamic Coupling

“…In this case the fluid-like membrane [11] will sustain the hydrodynamic coupling while the proximity of the cargo to the filament will enhance the binding rate of non-processive motors. Finally we speculate that the strong velocity enhancement that we observe may play a role in the very fast cytoplasmic streaming that has been observed in some plant cells [8]. …”

“…Physical realizations of such ratchet motors, to which we will refer generically as steppers, can be created in colloidal systems [6] and may be found in molecular motors [7] that move along polar biofilaments, such as microtubules or actin. Hence, the effect of hydrodynamic coupling on stepping particles is likely to be relevant for the understanding of the physical mechanisms underlying intracellular transport processes such as cytoplasmic streaming [8], axonal transport [9, 10] and membrane-embedded cargo pulling [11].In order to study the behavior of many steppers moving along the same filament, we employ a simple model that accounts both for the essential features of steppers and for the time-dependent hydrodynamics of the embedding fluid. The moving particles are described using the two-state ratchet model [7], a standard, simplified model that accounts for the mechanochemical coupling underlying molecular motor mechanics.…”

“…Physical realizations of such ratchet motors, to which we will refer generically as steppers, can be created in colloidal systems [6] and may be found in molecular motors [7] that move along polar biofilaments, such as microtubules or actin. Hence, the effect of hydrodynamic coupling on stepping particles is likely to be relevant for the understanding of the physical mechanisms underlying intracellular transport processes such as cytoplasmic streaming [8], axonal transport [9,10] and membrane-embedded cargo pulling [11].…”

Nanoscale hydrodynamics in the cell: Balancing motorized transport with diffusion

“…I was stunned: how could something so small ͑20 µm͒ be so complex, and how did all the parts communicate with each other? The recent paper by Goldstein (Goldstein et al, 2008) gives an intriguing answer to some of the physics of this process.…”

“…I have a couple of memories from graduate school at the University of Illinois that have some relevance to this paper by Goldstein et al (2008) I knew some smart fellow grad students at the University of Illinois, smarter than me by a long shot, one of them was Larry Nodulman. One day, as we were leaving Loomis Labs, Larry looked at a typically Urbana summer sky with scattered puffy clouds and wondered: why are the clouds so distinct and sharp against the atmosphere; why isn't the water vapor just all blurred out into a haze?…”