Local control of globally competing patterns in coupled Swift-Hohenberg equations.

We present analytical and numerical investigations of two anti-symmetrically coupled 1D Swift-Hohenberg equations (SHEs) with cubic nonlinearities. The SHE provides a generic formulation for pattern formation at a characteristic length scale. A linear stability analysis of the homogeneous state reveals a wave instability in addition to the usual Turing instability of uncoupled SHEs. We performed weakly nonlinear analysis in the vicinity of the codimension-two point of the Turing-wave instability, resulting in a set of coupled amplitude equations for the Turing pattern as well as left- and right-traveling waves. In particular, these complex Ginzburg-Landau-type equations predict two major things: there exists a parameter regime where multiple different patterns are stable with respect to each other and that the amplitudes of different patterns interact by local mutual suppression. In consequence, different patterns can coexist in distinct spatial regions, separated by localized interfaces. We identified specific mechanisms for controlling the position of these interfaces, which distinguish what kinds of patterns the interface connects and thus allow for global pattern selection. Extensive simulations of the original SHEs confirm our results.

Control of electrical turbulence by periodic excitation of cardiac tissue.

Electrical turbulence in cardiac tissue is associated with arrhythmias such as life-threatening ventricular fibrillation. Recent experimental studies have shown that a sequence of low-energy electrical far-field pulses is able to terminate fibrillation more gently than a single high-energy pulse which causes severe side effects. During this low-energy antifibrillation pacing (LEAP), only tissue near sufficiently large conduction heterogeneities, such as large coronary arteries, is activated. In order to optimize LEAP, we performed extensive simulations of cardiac tissue perforated by blood vessels, employing two alternative cellular models that exhibit electrical turbulence at a similar length scale. Moreover, the scale of blood vessels in our two-dimensional simulations was chosen such that the threshold for single pulse defibrillation matches experimental values. For each of the 100 initial conditions, we tested different electrical field strengths, pulse shapes, numbers of pulses, and periods between the pulses. LEAP is successful for both models, albeit with substantial differences. One model exhibits a spectrum of chaotic activity featuring a narrow peak around a dominant frequency. In this case, the optimal period between low-energy pulses matches this frequency and LEAP greatly reduces the required energy for successful defibrillation. For pulses with larger energies, the system is perturbed such that underdrive pacing becomes advantageous. The spectrum of the second model features a broader peak, resulting in a less pronounced optimal pacing period and a decreased energy reduction. In both cases, pacing with five or six pulses which are separated by the dominant period maximizes the energy reduction.

Association-dissociation process with aging subunits: Recursive solution.

The coupling of stochastic growth and shrinkage of one-dimensional structures to random aging of the constituting subunits defines the simple association-dissociation-aging process which captures the essential features of the nonequilibrium assembly of cytoskeletal filaments. Because of correlations, previously employed mean-field methods fail to correctly describe filament growth. We study an alternative formulation of the full master equation of the stochastic process. An ansatz for the steady-state solution leads to a recursion relation which allows for the calculation of all emergent quantities with increasing accuracy and in excellent agreement with stochastic simulations.

Intermittent depolymerization of actin filaments is caused by photo-induced dimerization of actin protomers.

Actin, one of the most abundant proteins within eukaryotic cells, assembles into long filaments that form intricate cytoskeletal networks and are continuously remodelled via cycles of actin polymerization and depolymerization. These cycles are driven by ATP hydrolysis, a process that also acts to destabilize the filaments as they grow older. Recently, abrupt dynamical changes during the depolymerization of single filaments have been observed and seemed to imply that old filaments are more stable than young ones [Kueh HY, et al. (2008) Proc Natl Acad Sci USA 105:16531-16536]. Using improved experimental setups and quantitative theoretical analysis, we show that these abrupt changes represent actual pauses in depolymerization, unexpectedly caused by the photo-induced formation of actin dimers within the filaments. The stochastic dimerization process is triggered by random transitions of single, fluorescently labeled protomers. Each pause represents the delayed dissociation of a single actin dimer, and the statistics of these single molecule events can be determined by optical microscopy. Unlabeled actin filaments do not exhibit pauses in depolymerization, which implies that, in vivo, older filaments become destabilized by ATP hydrolysis, unless this aging effect is overcompensated by actin-binding proteins. The latter antagonism can now be systematically studied for single filaments using our combined experimental and theoretical method. Furthermore, the dimerization process discovered here provides a molecular switch, by which one can control the length of actin filaments via changes in illumination. This process could also be used to locally "freeze" the dynamics within networks of filaments.

Individual actin filaments in a microfluidic flow reveal the mechanism of ATP hydrolysis and give insight into the properties of profilin.

The hydrolysis of ATP associated with actin and profilin-actin polymerization is pivotal in cell motility. It is at the origin of treadmilling of actin filaments and controls their dynamics and mechanical properties, as well as their interactions with regulatory proteins. The slow release of inorganic phosphate (Pi) that follows rapid cleavage of ATP gamma phosphate is linked to an increase in the rate of filament disassembly. The mechanism of Pi release in actin filaments has remained elusive for over 20 years. Here, we developed a microfluidic setup to accurately monitor the depolymerization of individual filaments and determine their local ADP-Pi content. We demonstrate that Pi release in the filament is not a vectorial but a random process with a half-time of 102 seconds, irrespective of whether the filament is assembled from actin or profilin-actin. Pi release from the depolymerizing barbed end is faster (half-time of 0.39 seconds) and further accelerated by profilin. Profilin accelerates the depolymerization of both ADP- and ADP-Pi-F-actin. Altogether, our data show that during elongation from profilin-actin, the dissociation of profilin from the growing barbed end is not coupled to Pi release or to ATP cleavage on the terminal subunit. These results emphasize the potential of microfluidics in elucidating actin regulation at the scale of individual filaments.

Fragmentation is crucial for the steady-state dynamics of actin filaments.

Despite the recognition that actin filaments are important for numerous cellular processes, and decades of investigation, the dynamics of in vitro actin filaments are still not completely understood. Here, we follow the time evolution of the length distribution of labeled actin reporter filaments in an unlabeled F-actin solution via fluorescence microscopy. Whereas treadmilling and diffusive length fluctuations cannot account for the observed dynamics, our results suggest that at low salt conditions, spontaneous fragmentation is crucial.

Synchronization, phase locking, and metachronal wave formation in ciliary chains.

Synchronization and wave formation in one-dimensional ciliary arrays are studied analytically and numerically. We develop a simple model for ciliary motion that is complex enough to describe well the behavior of beating cilia but simple enough to study collective effects analytically. Beating cilia are described as phase oscillators moving on circular trajectories with a variable radius. This radial degree of freedom turns out to be essential for the occurrence of hydrodynamically induced synchronization of ciliary beating between neighboring cilia. The transitions to the synchronized and phase-locked state of two cilia and the formation of metachronal waves in ciliary chains with different boundary conditions are discussed.