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Register a new userNonlinear dynamics and fluctuations in biological systems (Habilitation thesis)
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Benjamin M. Friedrich
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The present habilitation thesis in theoretical biological physics addresses two central dynamical processes in cells and organisms: (i) active motility and motility control and (ii) self-organized pattern formation. The unifying theme is the nonlinear dynamics of biological function and its robustness in the presence of strong fluctuations, structural variations, and external perturbations. We theoretically investigate motility control at the cellular scale, using cilia and flagella as ideal model system. Cilia and flagella are highly conserved slender cell appendages that exhibit spontaneous bending waves. This flagellar beat represents a prime example of a chemo-mechanical oscillator, which is driven by the collective dynamics of molecular motors inside the flagellar axoneme. We study the nonlinear dynamics of flagellar swimming, steering, and synchronization, which encompasses shape control of the flagellar beat by chemical signals and mechanical forces. Mechanical forces can synchronize collections of flagella to beat at a common frequency, despite active motor noise that tends to randomize flagellar synchrony. In Chapter 2, we present a new physical mechanism for flagellar synchronization by mechanical self-stabilization that applies to free-swimming flagellated cells. This new mechanism is independent of direct hydrodynamic interactions between flagella. Comparison with experimental data provided by experimental collaboration partners in the laboratory of J. Howard (Yale, New Haven) confirmed our new mechanism in the model organism of the unicellular green alga Chlamydomonas. Further, we characterize the beating flagellum as a noisy oscillator. Using a minimal model of collective motor dynamics, we argue that measured non-equilibrium fluctuations of the flagellar beat result from stochastic motor dynamics at the molecular scale. Noise and mechanical coupling are antagonists ...
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The formation of new bone involves both the deposition of bone matrix, and the formation of a network of cells embedded within the bone matrix, called osteocytes. Osteocytes derive from bone-synthesising cells (osteoblasts) that become buried in bone matrix during bone deposition. The generation of osteocytes is a complex process that remains incompletely understood. Whilst osteoblast burial determines the density of osteocytes, the expanding network of osteocytes regulates in turn osteoblast activity and osteoblast burial. In this paper, a spatiotemporal continuous model is proposed to investigate the osteoblast-to-osteocyte transition. The aims of the model are (i) to link dynamic properties of osteocyte generation with properties of the osteocyte network imprinted in bone, and (ii) to investigate Marottis hypothesis that osteocytes prompt the burial of osteoblasts when they become covered with sufficient bone matrix. Osteocyte density is assumed in the model to be generated at the moving bone surface by a combination of osteoblast density, matrix secretory rate, rate of entrapment, and curvature of the bone substrate, but is found to be determined solely by the ratio of the instantaneous burial rate and matrix secretory rate. Osteocyte density does not explicitly depend on osteoblast density nor curvature. Osteocyte apoptosis is also included to distinguish between the density of osteocyte lacuna and the density of live osteocytes. Experimental measurements of osteocyte lacuna densities are used to estimate the rate of burial of osteoblasts in bone matrix. These results suggest that: (i) burial rate decreases during osteonal infilling, and (ii) the control of osteoblast burial by osteocytes is likely to emanate as a collective signal from a large group of osteocytes, rather than from the osteocytes closest to the bone deposition front.
We analyse the effects of environmental noise in three different biological systems: (i) mating behaviour of individuals of emph{Nezara viridula} (L.) (Heteroptera Pentatomidae); (ii) polymer translocation in crowded solution; (iii) an ecosystem described by a Verhulst model with a multiplicative L{e}vy noise.
Information transmission in biological signaling circuits has often been described using the metaphor of a noise filter. Cellular systems need accurate, real-time data about their environmental conditions, but the biochemical reaction networks that propagate, amplify, and process signals work with noisy representations of that data. Biology must implement strategies that not only filter the noise, but also predict the current state of the environment based on information delayed due to the finite speed of chemical signaling. The idea of a biochemical noise filter is actually more than just a metaphor: we describe recent work that has made an explicit mathematical connection between signaling fidelity in cellular circuits and the classic theories of optimal noise filtering and prediction that began with Wiener, Kolmogorov, Shannon, and Bode. This theoretical framework provides a versatile tool, allowing us to derive analytical bounds on the maximum mutual information between the environmental signal and the real-time estimate constructed by the system. It helps us understand how the structure of a biological network, and the response times of its components, influences the accuracy of that estimate. The theory also provides insights into how evolution may have tuned enzyme kinetic parameters and populations to optimize information transfer.
Nematode species are well-known for their invariant cell lineage pattern during development. Combining knowledge about the fate specification induced by asymmetric division and the anti-correlation between cell cycle length and cell volume in Caenorhabditis elegans, we propose a model to simulate lineage initiation by altering cell volume segregation ratio in each division, and quantify the derived patterns performance in proliferation speed, fate diversity and space robustness. The stereotypic pattern in C. elegans embryo is found to be one of the most optimal solutions taking minimum time to achieve the cell number before gastrulation, by programming asymmetric division as a strategy.
In this paper a quantum mechanical description of the assembly/disassembly process for microtubules is proposed. We introduce creation and annihilation operators that raise or lower the microtubule length by a tubulin layer. Following that, the Hamiltonian and corresponding equations of motion are derived that describe the dynamics of microtubules. These Heisenberg-type equations are then transformed to semi-classical equations using the method of coherent structures. The latter equations are very similar to the phenomenological equations that describe dynamic instability of microtubules in a tubulin solution.
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