Biomedical subjects
Charles J Brokaw
Publications and source records attributed to Charles J Brokaw.
Computer simulation of flagellar movement IX. Oscillation and symmetry breaking in a model for short flagella and nodal cilia.
A computer model of flagella in which oscillation results from regulation of active sliding force by sliding velocity can simulate the movements of very short flagella and cilia. Of particular interest are the movements of the short (2-3 microm) nodal cilia of the mammalian embryo, which determine the development of the asymmetry of the internal organs. These cilia must generate a counterclockwise (viewed from base to tip) circling motion. A three-dimensional computer model, with active force generated by a simple mathematical formulation and regulated by sliding velocity, can generate this circling motion if a time delay process is included in the control specification. Without the introduction of a symmetry-breaking mechanism, the computer models start randomly in either direction, and maintain either clockwise or counterclockwise circling. Symmetry can be broken by at least two mechanisms: (1) control of dynein activity on one outer doublet by sliding velocity can be influenced by the sliding velocity experienced on an adjacent outer doublet, or (2) a constant twist of the axoneme caused by an off-axis component of dynein force. This second mechanism appears more reasonable, but its effectiveness is highly dependent upon specifications for the elastic resistances of the model. These symmetry-breaking mechanisms need to be present only at the beginning of circling. With these models, once a circling direction is established, it remains stable even if the symmetry-breaking mechanism is removed.
Computer simulation of flagellar movement VIII: coordination of dynein by local curvature control can generate helical bending waves.
Computer simulations have been carried out with a model flagellum that can bend in three dimensions. A pattern of dynein activation in which regions of dynein activity propagate along each doublet, with a phase shift of approximately 1/9 wavelength between adjacent doublets, will produce a helical bending wave. This pattern can be termed "doublet metachronism." The simulations show that doublet metachronism can arise spontaneously in a model axoneme in which activation of dyneins is controlled locally by the curvature of each outer doublet microtubule. In this model, dyneins operate both as sensors of curvature and as motors. Doublet metachronism and the chirality of the resulting helical bending pattern are regulated by the angular difference between the direction of the moment and sliding produced by dyneins on a doublet and the direction of the controlling curvature for that doublet. A flagellum that is generating a helical bending wave experiences twisting moments when it moves against external viscous resistance. At high viscosities, helical bending will be significantly modified by twist unless the twist resistance is greater than previously estimated. Spontaneous doublet metachronism must be modified or overridden in order for a flagellum to generate the planar bending waves that are required for efficient propulsion of spermatozoa. Planar bending can be achieved with the three-dimensional flagellar model by appropriate specification of the direction of the controlling curvature for each doublet. However, experimental observations indicate that this "hard-wired" solution is not appropriate for real flagella.