“Coarse” stability and bifurcation analysis using time-steppers: A reaction-diffusion example

Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099–1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective (“coarse”) bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice–Boltzmann model.

A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectrical-transduction channels

Amplification of auditory stimuli by hair cells augments the sensitivity of the vertebrate inner ear. Cell-body contractions of outer hair cells are thought to mediate amplification in the mammalian cochlea. In vertebrates that lack these cells, and perhaps in mammals as well, active movements of hair bundles may underlie amplification. We have evaluated a mathematical model in which amplification stems from the activity of mechanoelectrical-transduction channels. The intracellular binding of Ca2+ to channels is posited to promote their closure, which increases the tension in gating springs and exerts a negative force on the hair bundle. By enhancing bundle motion, this force partially compensates for viscous damping by cochlear fluids. Linear stability analysis of a six-state kinetic model reveals Hopf bifurcations for parameter values in the physiological range. These bifurcations signal conditions under which the system’s behavior changes from a damped oscillatory response to spontaneous limit-cycle oscillation. By varying the number of stereocilia in a bundle and the rate constant for Ca2+ binding, we calculate bifurcation frequencies spanning the observed range of auditory sensitivity for a representative receptor organ, the chicken’s cochlea. Simulations using prebifurcation parameter values demonstrate frequency-selective amplification with a striking compressive nonlinearity. Because transduction channels occur universally in hair cells, this active-channel model describes a mechanism of auditory amplification potentially applicable across species and hair-cell types.

The reversible condensation and expansion of the rotavirus genome

Understanding the structural organization of the genome is particularly relevant in segmented double-stranded RNA viruses, which exhibit endogenous transcription activity. These viruses are molecular machines capable of repeated cycles of transcription within the intact capsid. Rotavirus, a major cause of infantile gastroenteritis, is a prototypical segmented double-stranded RNA virus. From our three-dimensional structural analyses of rotavirus examined under various chemical conditions using electron cryomicroscopy, we show here that the viral genome exhibits a remarkable conformational flexibility by reversibly changing its packaging density. In the presence of ammonium ions at high pH, the genome condenses to a radius of ≈180 Å from ≈220 Å. Upon returning to physiological conditions, the genome re-expands and fully maintains its transcriptional properties. These studies provide further insights into the genome organization and suggest that the observed isometric and concentric nature of the condensation is due to strong interactions between the genome core and the transcription enzymes anchored to the capsid inner surface. The ability of the genome to condense beyond what is normally observed in the native virus indicates that the negative charges on the RNA in the native state may be only partially neutralized. Partial neutralization may be required to maintain appropriate interstrand spacing for templates to move around the enzyme complexes during transcription. Genome condensation was not observed either with increased cation concentrations at normal pH or at high pH without ammonium ions. This finding indicates that the observed genome condensation is a synergistic effect of hydroxyl and ammonium ions involving disruption of protein–RNA interactions that perhaps facilitate further charge neutralization and consequent reduction in the interstrand spacing.

Delivery of proteins into living cells by reversible membrane permeabilization with streptolysin-O

The pore-forming toxin streptolysin O (SLO) can be used to reversibly permeabilize adherent and nonadherent cells, allowing delivery of molecules with up to 100 kDa mass to the cytosol. Using FITC-labeled albumin, 105–106 molecules were estimated to be entrapped per cell. Repair of toxin lesions depended on Ca2+-calmodulin and on intact microtubules, but was not sensitive to actin disruption or to inhibition of protein synthesis. Resealed cells were viable for days and retained the capacity to endocytose and to proliferate. The active domains of large clostridial toxins were introduced into three different cell lines. The domains were derived from Clostridium difficile B-toxin and Clostridium sordelli lethal toxin, which glycosylate small G-proteins, and from Clostridium botulinum C2 toxin, which ADP-ribosylates actin. After delivery with SLO, all three toxins disrupted the actin cytoskeleton to cause rounding up of the cells. Glucosylation assays demonstrated that G-proteins Rho and Ras were retained in the permeabilized cells and were modified by the respective toxins. Inactivation of these G-proteins resulted in reduced stimulus-dependent granule secretion, whereas ADP-ribosylation of actin by the C. botulinum C2-toxin resulted in enhanced secretion in cells. The presented method for introducing proteins into living cells should find multifaceted application in cell biology.