Biological matter is driven far from thermodynamic equilibrium by active processes on the molecular scale. These processes are usually driven by the chemical reaction of a fuel and generate spontaneous movements and mechanical stresses in the system, even in the absence of external forces or torques. Moreover these active stresses effectively fluidify the material. The cell cytoskeleton, suspensions of swimming microorganisms or tissues are prominent examples of active fluids.
Active processes in biological systems often exhibit chiral asymmetries. Examples are the chirality of cytoskeletal filaments which interact with motor proteins, the chirality of the beat of cilia and flagella as well as the helical trajectories of many biological micro-swimmers. Moreover, large scale chiral flows have been observed in the cell cortex of C. elegans and Xenopus embryos.
Active force generation induces force and torque dipoles in the material. If all forces are internal the total force and torque vanish as required by the conservation of momentum and angular momentum. The density of force dipoles is an active stress in the material. In addition, active chiral processes allow for the existence of active torque dipoles which enter the conservation of angular momentum and generate an active antisymmetric stress and active angular momentum fluxes.
We developed a generic description of active fluids that takes into account active chiral processes and explicitly keeps track of spin and orbital angular momentum densities. We derived constitutive equations for an active chiral fluid based on identifying the entropy production rate from the rate of change of the free energy and linearly expanding thermodynamic fluxes in terms of thermodynamic forces.
We identified four elementary chiral motors that correspond to localized distributions of chiral force and torque dipoles that differ by their symmetry and produce different chiral fluid flows and intrinsic rotation fields.
We employ our theory to analyze different active chiral processes. We first show that chiral flows can occur spontaneously in an active fluid even in the absence of chiral processes. For this we investigate the Taylor-Couette motor, that is an active fluid confined between two concentric cylinders. For sufficiently high active stresses the fluid generates spontaneous rotations of the two cylinders with respect to each other thus breaking the chiral symmetry of the system spontaneously.
We then investigate cases where active chiral processes on the molecular scale break the chiral symmetry of the whole system. We show that chiral flows occur in films of chiral motors and derive a generic theory for thin films of active fluids. We discuss our results in the context of carpets of beating cilia or E. coli swimming close to a surface.
Finally, we discuss chiral flows that are observed in the cellular cortex of the nematode C. elegans at the one cell stage. Two distinct chiral flow events are observed. The first chiral flow event (i) is a screw like chiral rotation of the two cell halves with respect to each other and occurs around 15min after fertilization. This event coincides with the establishment of cortical cell polarity. The second chiral flow event (ii) is a chiral rotation of the entire cell cortex around the anterior posterior axis of the whole cell and occurs around 30min after fertilization. Measuring densities of molecular motors during episode (i) we fit the flow patterns observed using only two fit parameters: the hydrodynamic length and cortical chirality. The flows during (ii) can be understood assuming an increase of the hydrodynamic length. We hypothesize that the cell actively regulates the cortical viscosity and the friction of the cortex with the eggshell and cytosol.
We show that active chiral processes in soft biological matter give rise to interesting new physics and are essential to understand the material properties of many biological systems, such as the cell cortex.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:26082 |
| Date | 15 May 2012 |
| Creators | Fürthauer, Sebastian |
| Contributors | Jülicher, Frank, Stark, Holger, Technische Universität Dresden |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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