Efficient Estimation of the Robustness Region of Biological Models with Oscillatory Behavior

Robustness is an essential feature of biological systems, and any mathematical model that describes such a system should reflect this feature. Especially, persistence of oscillatory behavior is an important issue. A benchmark model for this phenomenon is the Laub-Loomis model, a nonlinear model for cAMP oscillations in Dictyostelium discoideum. This model captures the most important features of biomolecular networks oscillating at constant frequencies. Nevertheless, the robustness of its oscillatory behavior is not yet fully understood. Given a system that exhibits oscillating behavior for some set of parameters, the central question of robustness is how far the parameters may be changed, such that the qualitative behavior does not change. The determination of such a “robustness region” in parameter space is an intricate task. If the number of parameters is high, it may be also time consuming. In the literature, several methods are proposed that partially tackle this problem. For example, some methods only detect particular bifurcations, or only find a relatively small box-shaped estimate for an irregularly shaped robustness region. Here, we present an approach that is much more general, and is especially designed to be efficient for systems with a large number of parameters. As an illustration, we apply the method first to a well understood low-dimensional system, the Rosenzweig-MacArthur model. This is a predator-prey model featuring satiation of the predator. It has only two parameters and its bifurcation diagram is available in the literature. We find a good agreement with the existing knowledge about this model. When we apply the new method to the high dimensional Laub-Loomis model, we obtain a much larger robustness region than reported earlier in the literature. This clearly demonstrates the power of our method. From the results, we conclude that the biological system underlying is much more robust than was realized until now

Microtubule nucleation complex behavior is critical for cortical array homogeneity and xylem wall patterning

Plant cell walls are versatile materials that can adopt a wide range of mechanical properties through controlled deposition of cellulose fibrils. Wall integrity requires a sufficiently homogeneous fibril distribution to cope effectively with wall stresses. Additionally, specific conditions, such as the negative pressure in water transporting xylem vessels, may require more complex wall patterns, e.g., bands in protoxylem. The orientation and patterning of cellulose fibrils are guided by dynamic cortical microtubules. New microtubules are predominantly nucleated from parent microtubules causing positive feedback on local microtubule density with the potential to yield highly inhomogeneous patterns. Inhomogeneity indeed appears in all current cortical array simulations that include microtubule-based nucleation, suggesting that plant cells must possess an as-yet unknown balancing mechanism to prevent it. Here, in a combined simulation and experimental approach, we show that a limited local recruitment of nucleation complexes to microtubules can counter the positive feedback, whereas local tubulin depletion cannot. We observe that nucleation complexes preferentially appear at the plasma membrane near microtubules. By incorporating our experimental findings in stochastic simulations, we find that the spatial behavior of nucleation complexes delicately balances the positive feedback, such that differences in local microtubule dynamics—as in developing protoxylem—can quickly turn a homogeneous array into a banded one. Our results provide insight into how the plant cytoskeleton has evolved to meet diverse mechanical requirements and greatly increase the predictive power of computational cell biology studies

Більшовицькі амністії початку 1920-х рр. як засіб боротьби проти повстанського руху

У статті автор досліджував ефективність амністування як засобу боротьби проти повстанського руху.В статье автор исследовал эффективность амнистирования как средства борьбы с повстанческим движением.The author investigated the efficiency of amnesty as the means of struggle against the insurgent movement

Miller fisher anti-GQ1b antibodies:α-Latrotoxin - Like effects on motor end plates

In the Miller Fisher syndrome (MFS) variant of the Guillain-Barre syndrome, weakness is restricted to extraocular muscles and occasionally other craniobulbar muscles. Most MFS patients have serum antibodies against ganglioside type GQ1b of which the pathophysiological relevance is unclear. We examined the in vitro effects of MFS sera, MFS IgG, and a human monoclonal anti-GQ1b IgM antibody on mouse neuromuscular junctions (NMJs). It was found that anti-GQ1b antibodies bind at NMJs where they induce massive quantal release of acetylcholine from nerve terminals and eventually block neuromuscular transmission. This effect closely resembled the effect of the paralytic neurotoxin α-latrotoxin at the mouse NMJs, implying possible involvement of α-latrotoxin receptors or associated downstream pathways. By using complement-deficient sera, the effect of anti-GQ1b antibodies on NMJs was shown to be entirely dependent on activation of complement components. However, neither classical pathway activation nor the formation of membrane attack complex was required, indicating the effects could be due to involvement of the alternative pathway and intermediate complement cascade products. Our findings strongly suggest that anti-GQ1b antibodies in conjunction with activated complement components are the principal pathophysiological mediators of motor symptoms in MFS and that the NMJ is an important site of their action.</p

Simulation of Organ Patterning on the Floral Meristem Using a Polar Auxin Transport Model

An intriguing phenomenon in plant development is the timing and positioning of lateral organ initiation, which is a fundamental aspect of plant architecture. Although important progress has been made in elucidating the role of auxin transport in the vegetative shoot to explain the phyllotaxis of leaf formation in a spiral fashion, a model study of the role of auxin transport in whorled organ patterning in the expanding floral meristem is not available yet. We present an initial simulation approach to study the mechanisms that are expected to play an important role. Starting point is a confocal imaging study of Arabidopsis floral meristems at consecutive time points during flower development. These images reveal auxin accumulation patterns at the positions of the organs, which strongly suggests that the role of auxin in the floral meristem is similar to the role it plays in the shoot apical meristem. This is the basis for a simulation study of auxin transport through a growing floral meristem, which may answer the question whether auxin transport can in itself be responsible for the typical whorled floral pattern. We combined a cellular growth model for the meristem with a polar auxin transport model. The model predicts that sepals are initiated by auxin maxima arising early during meristem outgrowth. These form a pre-pattern relative to which a series of smaller auxin maxima are positioned, which partially overlap with the anlagen of petals, stamens, and carpels. We adjusted the model parameters corresponding to properties of floral mutants and found that the model predictions agree with the observed mutant patterns. The predicted timing of the primordia outgrowth and the timing and positioning of the sepal primordia show remarkable similarities with a developing flower in nature