Andreas Hilfinger

How molecular motors shape the flagellar beat

Cilia and eukaryotic flagella are slender cellular appendages whose regular beating propels cells and microorganisms through aqueous media. The beat is an oscillating pattern of propagating bends generated by dynein motor proteins. A key open question is how the activity of the motors is coordinated in space and time. To elucidate the nature of this coordination we inferred the mechanical properties of the motors by analyzing the shape of beating sperm: Steadily beating bull sperm were imaged and their shapes were measured with high precision using a Fourier averaging technique. Comparing our experimental data with wave forms calculated for different scenarios of motor coordination we found that only the scenario of interdoublet sliding regulating motor activity gives rise to satisfactory fits. We propose that the microscopic origin of such “sliding control” is the load dependent detachment rate of motors. Agreement between observed and calculated wave forms was obtained only if significant sliding between microtubules occurred at the base. This suggests a novel mechanism by which changes in basal compliance could reverse the direction of beat propagation. We conclude that the flagellar beat patterns are determined by an interplay of the basal properties of the axoneme and the mechanical feedback of dynein motors.

Separating intrinsic from extrinsic fluctuations in dynamic biological systems.

From molecules in cells to organisms in ecosystems, biological populations fluctuate due to the intrinsic randomness of individual events and the extrinsic influence of changing environments. The combined effect is often too complex for effective analysis, and many studies therefore make simplifying assumptions, for example ignoring either intrinsic or extrinsic effects to reduce the number of model assumptions. Here we mathematically demonstrate how two identical and independent reporters embedded in a shared fluctuating environment can be used to identify intrinsic and extrinsic noise terms, but also how these contributions are qualitatively and quantitatively different from what has been previously reported. Furthermore, we show for which classes of biological systems the noise contributions identified by dual-reporter methods correspond to the noise contributions predicted by correct stochastic models of either intrinsic or extrinsic mechanisms. We find that for broad classes of systems, the extrinsic noise from the dual-reporter method can be rigorously analyzed using models that ignore intrinsic stochasticity. In contrast, the intrinsic noise can be rigorously analyzed using models that ignore extrinsic stochasticity only under very special conditions that rarely hold in biology. Testing whether the conditions are met is rarely possible and the dual-reporter method may thus produce flawed conclusions about the properties of the system, particularly about the intrinsic noise. Our results contribute toward establishing a rigorous framework to analyze dynamically fluctuating biological systems.

The chirality of ciliary beats

Many eukaryotic cells possess cilia which are motile, whip-like appendages that can oscillate and thereby induce motion and fluid flows. These organelles contain a highly conserved structure called the axoneme, whose characteristic architecture is based on a cylindrical arrangement of nine doublets of microtubules. Complex bending waves emerge from the interplay of active internal forces generated by dynein motor proteins within the structure. These bending waves are typically chiral and often exhibit a sense of rotation. In order to study how the shape of the beat emerges from the axonemal structure, we present a three-dimensional description of ciliary dynamics based on the self-organization of dynein motors and microtubules. Taking into account both bending and twisting of the cilium, we determine self-organized beating patterns and find that modes with both a clockwise and anticlockwise sense of rotation exist. Because of the axonemal chirality, only one of these modes is selected dynamically for given parameter values and properties of dynein motors. This physical mechanism, which underlies the selection of a beating pattern with specific sense of rotation, triggers the breaking of the left-right symmetry of developing embryos which is induced by asymmetric fluid flows that are generated by rotating cilia.

Nonlinear dynamics of cilia and flagella

Cilia and flagella are hairlike extensions of eukaryotic cells which generate oscillatory beat patterns that can propel micro-organisms and create fluid flows near cellular surfaces. The evolutionary highly conserved core of cilia and flagella consists of a cylindrical arrangement of nine microtubule doublets, called the axoneme. The axoneme is an actively bending structure whose motility results from the action of dynein motor proteins cross-linking microtubule doublets and generating stresses that induce bending deformations. The periodic beat patterns are the result of a mechanical feedback that leads to self-organized bending waves along the axoneme. Using a theoretical framework to describe planar beating motion, we derive a nonlinear wave equation that describes the fundamental Fourier mode of the axonemal beat. We study the role of nonlinearities and investigate how the amplitude of oscillations increases in the vicinity of an oscillatory instability. We furthermore present numerical solutions of the nonlinear wave equation for different boundary conditions. We find that the nonlinear waves are well approximated by the linearly unstable modes for amplitudes of beat patterns similar to those observed experimentally.

Exploiting Natural Fluctuations to Identify Kinetic Mechanisms in Sparsely Characterized Systems

From biochemistry to ecology, many biological systems are stochastic, complex, and sparsely characterized. In such systems, each component may respond to changes in any directly or indirectly connected components, thus requiring knowledge of the whole to predict the dynamics of the parts. Here, we address this challenge by deriving relations between properties of fluctuations that only reflect local interactions between a subset of components but are invariant to all indirectly connected dynamics. This greatly reduces the number of assumptions when evaluating dynamic models experimentally. We illustrate the approach by revisiting systematic single-cell gene expression data, and we show that the observed fluctuations contradict the assumptions made in most published models of stochastic gene expression, even when accounting for the possibility of systematic experimental artifacts.

Systems biology: Defiant daughters and coordinated cousins.

Genetically identical cells can have many variable properties. A study of correlations between cells in a lineage explains paradoxical inheritance laws, in which mother and daughter cells seem less similar than cousins. See Letter p.468

How Molecular Motors Shape The Flagellar Beat

Cilia and eukaryotic flagella are slender cellular appendages whose regular beating propels cells and microorganisms through aqueous media. The beat is an oscillating pattern of propagating bends generated by dynein motor proteins. A key open question is how the activity of the motors is coordinated in space and time. To elucidate the nature of this coordination we inferred the mechanical properties of the motors by analyzing the shape of beating sperm: Steadily beating bull sperm were imaged and their shapes were measured with high precision using a Fourier averaging technique. Comparing our experimental data with wave forms calculated for different scenarios of motor coordination we found that only the scenario of interdoublet sliding regulating motor activity gives rise to satisfactory fits. We propose that the microscopic origin of such “sliding control” is the load dependent detachment rate of motors. Agreement between observed and calculated wave forms was obtained only if significant sliding between microtubules occurred at the base. This suggests a novel mechanism by which changes in basal compliance could reverse the direction of beat propagation. We conclude that the flagellar beat patterns are determined by an interplay of the basal properties of the axoneme and the mechanical feedback of dynein motors. [DOI: 10.2976/1.2773861]