TY - JOUR A1 - Rading, M. Michael A1 - Sandmann, Michael A1 - Steup, Martin A1 - Chiarugi, Davide A1 - Valleriani, Angelo T1 - Weak correlation of starch and volume in synchronized photosynthetic cells JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - In cultures of unicellular algae, features of single cells, such as cellular volume and starch content, are thought to be the result of carefully balanced growth and division processes. Single-cell analyses of synchronized photoautotrophic cultures of the unicellular alga Chlamydomonas reinhardtii reveal, however, that the cellular volume and starch content are only weakly correlated. Likewise, other cell parameters, e.g., the chlorophyll content per cell, are only weakly correlated with cell size. We derive the cell size distributions at the beginning of each synchronization cycle considering growth, timing of cell division and daughter cell release, and the uneven division of cell volume. Furthermore, we investigate the link between cell volume growth and starch accumulation. This work presents evidence that, under the experimental conditions of light-dark synchronized cultures, the weak correlation between both cell features is a result of a cumulative process rather than due to asymmetric partition of biomolecules during cell division. This cumulative process necessarily limits cellular similarities within a synchronized cell population. Y1 - 2015 U6 - https://doi.org/10.1103/PhysRevE.91.012711 SN - 1539-3755 SN - 1550-2376 VL - 91 IS - 1 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Keller, Peter A1 - Roelly, Sylvie A1 - Valleriani, Angelo T1 - On time duality for Markov Chains JF - Stochastic models N2 - For an irreducible continuous time Markov chain, we derive the distribution of the first passage time from a given state i to another given state j and the reversed passage time from j to i, each under the condition of no return to the starting point. When these two distributions are identical, we say that i and j are in time duality. We introduce a new condition called permuted balance that generalizes the concept of reversibility and provides sufficient criteria, based on the structure of the transition graph of the Markov chain. Illustrative examples are provided. KW - Time duality KW - Detailed balance KW - First passage time KW - Reversibility KW - Permuted balance KW - Markov chain Y1 - 2015 U6 - https://doi.org/10.1080/15326349.2014.969736 SN - 1532-6349 SN - 1532-4214 VL - 31 IS - 1 SP - 98 EP - 118 PB - Taylor & Francis Group CY - Philadelphia ER - TY - JOUR A1 - Keller, Peter A1 - Roelly, Sylvie A1 - Valleriani, Angelo T1 - A Quasi Random Walk to Model a Biological Transport Process JF - Methodology and computing in applied probability N2 - Transport molecules play a crucial role for cell viability. Amongst others, linear motors transport cargos along rope-like structures from one location of the cell to another in a stochastic fashion. Thereby each step of the motor, either forwards or backwards, bridges a fixed distance and requires several biochemical transformations, which are modeled as internal states of the motor. While moving along the rope, the motor can also detach and the walk is interrupted. We give here a mathematical formalization of such dynamics as a random process which is an extension of Random Walks, to which we add an absorbing state to model the detachment of the motor from the rope. We derive particular properties of such processes that have not been available before. Our results include description of the maximal distance reached from the starting point and the position from which detachment takes place. Finally, we apply our theoretical results to a concrete established model of the transport molecule Kinesin V. KW - Molecular motor KW - Kinesin V KW - Birth-and-death process KW - Markov Chain KW - Quasi Random Walk Y1 - 2015 U6 - https://doi.org/10.1007/s11009-013-9372-5 SN - 1387-5841 SN - 1573-7713 VL - 17 IS - 1 SP - 125 EP - 137 PB - Springer CY - Dordrecht ER -