Publications

Robustness of bidirectional microtubule network self-organization

A. Plochocka, A. Davie, N. Bulgakova, L. Chumakova

Robustness of biological systems is crucial for their survival, however, for many systems its origin is an open question. Here we analyze one sub-cellular level system, the microtubule cytoskeleton. Microtubules are highly dynamic polar polymers, which undergo periods of growth and shrinking and infrequently switch between them. In cells they self-organize into a network, along which cellular components are delivered to their biologically relevant locations. Here we consider bi-directional networks, which are present for example in epithelia, one of the four major tissue types found in all animals. While the dynamics of individual microtubules depends sensitively on the organism's environment and genetics, a similar sensitivity of the network would result in pathologies. Combining mathematical modeling with genetic manipulations in Drosophila fruit flies, we show that the microtubule self-organization indeed does not depend on the dynamics of individual microtubules, and is robust on the tissue level.

bioRxiv 825786

Cellular crowding guides and debundles the microtubule cytoskeleton

A. Plochocka, N. Bulgakova, L. Chumakova

Cytoplasm is densely packed with macromolecules causing cellular crowding, which alters interactions inside cells and differs between biological systems. Here we investigate the impact of crowding on microtubule cytoskeleton organization. Using mathematical modelling, we find that only anisotropic crowding affects the mean microtubule direction, but any crowding reduces the number of microtubules that form bundles. We validate these predictions in vivo using Drosophila follicular epithelium. Since cellular components are transported along microtubules, our results identify cellular crowding as a novel regulator of this transport and cell organization.

bioRxiv 830919

The walkoff effect: cargo distribution implies motor type in bidirectional microtubule bundles

G. Zhelezov, V. Alfred, N. Bulgakova, L. Chumakova

Cells rely on molecular motors moving along an ever-shifting network of polymers (microtubules) for the targeted delivery of cell organelles to biologically-relevant locations. We present a stochastic model for a molecular motor stepping along a bidirectional bundle of microtubules, as well as a tractable analytical model. Using these models, we investigate how the preferred stepping direction of the motor (parallel or antiparallel to the microtubule growth, corresponding to kinesin and dynein motor families) quantitatively and qualitatively affects the cargo delivery. We predict which motor type is responsible for which cargo type, given the experimental distribution of cargo in the cell, and report experimental findings which support this guideline for motor classification.

bioRxiv 831024

Inferring punctuated evolution in the learned songs of African sunbirds

Jay P. McEntee, Gleb Zhelezov, Chacha Werema, Nadje Najar, Joshua V. Peñalba, Elia Mulungu, Maneno Mbilinyi, Sylvester Karimi, Lyubov Chumakova, J. Gordon Burleigh, Rauri C.K. Bowie

Signals used in animal communication, especially those that are learned, are thought to be prone to rapid and/or regular evolution. It has been hypothesized that the evolution of song learning in birds has resulted in elevated diversification rates, as learned song may be subject to especially rapid evolution, and song is involved in mate choice. However, we know little about the evolutionary modes of learned song divergence over timescales relevant to speciation. Here we provide evidence that aspects of the territorial songs of Eastern Afromontane sky island sunbirds Cinnyris evolve in a punctuated fashion, with periods of stasis, on the order of hundreds of thousands of years or more, broken up by strong evolutionary pulses. Stasis in learned songs is inconsistent with learned traits being subject to constant or frequent change, as would be expected if selection does not constrain song phenotypes, or if novel phenotypes are frequently advantageous. Learned song may instead follow a process resembling peak shifts on adaptive landscapes. While much research has focused on the potential for rapid evolution in bird song, our results suggest that selection can tightly constrain the evolution of learned songs over fairly long timescales. More broadly, these results demonstrate that some aspects of highly variable, plastic traits can exhibit punctuated evolution, with stasis over fairly long time periods.

bioRxiv

1D group velocity for complex exponential waves and its application to atmospheric models with a leaky rigid lid

L. Chumakova, A. Rzeznik, E.G. Tabak, R.R. Rosales

In this paper we develop new techniques to work with leaky waves. These are dispersive waves that occur in problems, where the medium that supports waves undergoes a rapid change, leading to partial wave-trapping. This physical setup suggests considering instead the problem on the reduced compact domain, with an effective leaky radiation boundary condition, which ensures that radiating waves never come back. While the spectrum of the full problem is continuous, the spectrum of the reduced problem is often discrete. Furthermore, the standard approaches of using Fourier series to find the spectrum fail, due to poor convergence at the boundary. Instead, the natural basis for leaky problems on a compact domain are complex exponential waves, which have exponential envelops. However, working with them requires new mathematical tools, since the standard dispersive wave concept of group velocity is no longer valid.

Here we develop a mathematical framework to work with complex exponential waves, extend the classic concept of group velocity to them, and suggest a framework of how to find a complete basis set of complex exponential wave solutions. We demonstrate this approach on an example of dry hydrostatic non-rotating atmosphere, where the medium change is the jump of the buoyancy frequency at the tropopause. Finally, we show that the origin of the leaky waves is the natural boundary in the Laplace transform.

in preparation

Homoclinic chaos via Mobius orbits in a catalytic system with three time-scales

G. A. Chumakov, L. Chumakova, N. A. Chumakova

We study an kinetic model of a particular heterogeneous catalytic reaction with fast, intermediate and slow time-scales, which is represented by a system of three ODEs with two small parameters. In the route to chaos through the cascade of period-doubling bifurcations, we examine the topological invariants of the unstable periodic Mobius orbits -- the number of rotations of manifold around the unstable periodic orbit. The two parts of the unstable periodic orbits can be approximated by the limiting case of the one of the two 2D {\it degenerate} sub-systems, where one of the limiting sets includes the one-parameter canard families. Finally, we use the 1d Poincare map to find the transversal homoclinic orbit to the periodic solution, which starts the period doubling cascade to chaos.

in preparation

Microtubule organization is determined by the shape of epithelial cells

J.Gomez, L. Chumakova, N. Brown, N. Bulgakova

Interphase microtubule organization is critical for cell function and tissue architecture. In general, physical mechanisms are sufficient to drive microtubule organization in single cells, whereas cells within tissues are thought to utilize signalling mechanisms. By improving the imaging and quantitation of microtubule alignment within developing Drosophila embryos, here we demonstrate that microtubule alignment underneath the apical surface of epithelial cells follows cell shape. During development, epidermal cell elongation and microtubule alignment occur simultaneously, but by perturbing cell shape, we discover that microtubule organization responds to cell shape, rather than the converse. A simple set of microtubule behaviour rules is sufficient for a computer model to mimic the observed responses to changes in cell surface geometry. Moreover, we show that microtubules colliding with cell boundaries zip-up or depolymerize in an angle-dependent manner, as predicted by the model. Finally, we show microtubule alignment responds to cell shape in diverse epithelia.

Nature Communications, 7, 13172 (2016), doi