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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.
The interplay between turnover or degradation and ribosome loading of messenger RNA (mRNA) is studied theoretically using a stochastic model that is motivated by recent experimental results. Random mRNA degradation affects the statistics of polysomes, i.e., the statistics of the number of ribosomes per mRNA as extracted from cells. Since ribosome loading of newly created mRNA chains requires some time to reach steady state, a fraction of the extracted mRNA/ ribosome complexes does not represent steady state conditions. As a consequence, the mean ribosome density obtained from the extracted complexes is found to be inversely proportional to the mRNA length. On the other hand, the ribosome density profile shows an exponential decrease along the mRNA for prokaryotes and becomes uniform in eukaryotic cells. Copyright (C) EPLA, 2010
Myoviruses, bacteriophages with T4-like architecture, must contract their tails prior to DNA release. However, quantitative kinetic data on myovirus particle opening are lacking, although they are promising tools in bacteriophage-based antimicrobial strategies directed against Gram-negative hosts. For the first time, we show time-resolved DNA ejection from a bacteriophage with a contractile tail, the multi-O-antigen-specific Salmonella myovirus Det7. DNA release from Det7 was triggered by lipopolysaccharide (LPS) O-antigen receptors and notably slower than in noncontractile-tailed siphoviruses. Det7 showed two individual kinetic steps for tail contraction and particle opening. Our in vitro studies showed that highly specialized tailspike proteins (TSPs) are necessary to attach the particle to LPS. A P22-like TSP confers specificity for the Salmonella Typhimurium O-antigen. Moreover, crystal structure analysis at 1.63 angstrom resolution confirmed that Det7 recognized the Salmonella Anatum O-antigen via an E15-like TSP, DettilonTSP. DNA ejection triggered by LPS from either host showed similar velocities, so particle opening is thus a process independent of O-antigen composition and the recognizing TSP. In Det7, at permissive temperatures TSPs mediate O-antigen cleavage and couple cell surface binding with DNA ejection, but no irreversible adsorption occurred at low temperatures. This finding was in contrast to short-tailed Salmonella podoviruses, illustrating that tailed phages use common particle-opening mechanisms but have specialized into different infection niches.
In Escherichia coli, two different systems that are important for the coordinate formation of Fe–S clusters have been identified, namely, the ISC and SUF systems. The ISC system is the housekeeping Fe–S machinery, which provides Fe–S clusters for numerous cellular proteins. The IscS protein of this system was additionally revealed to be the primary sulfur donor for several sulfur-containing molecules with important biological functions, among which are the molybdenum cofactor (Moco) and thiolated nucleosides in tRNA. Here, we show that deletion of central components of the ISC system in addition to IscS leads to an overall decrease in Fe–S cluster enzyme and molybdoenzyme activity in addition to a decrease in the number of Fe–S-dependent thiomodifications of tRNA, based on the fact that some proteins involved in Moco biosynthesis and tRNA thiolation are Fe–S-dependent. Complementation of the ISC deficient strains with the suf operon restored the activity of Fe–S-containing proteins, including the MoaA protein, which is involved in the conversion of 5′GTP to cyclic pyranopterin monophosphate in the fist step of Moco biosynthesis. While both systems share a high degree of similarity, we show that the function of their respective l-cysteine desulfurase IscS or SufS is specific for each cellular pathway. It is revealed that SufS cannot play the role of IscS in sulfur transfer for the formation of 2-thiouridine, 4-thiouridine, or the dithiolene group of molybdopterin, being unable to interact with TusA or ThiI. The results demonstrate that the role of the SUF system is exclusively restricted to Fe–S cluster assembly in the cell.
The interdisciplinary workshop STOCHASTIC PROCESSES WITH APPLICATIONS IN THE NATURAL SCIENCES was held in Bogotá, at Universidad de los Andes from December 5 to December 9, 2016. It brought together researchers from Colombia, Germany, France, Italy, Ukraine, who communicated recent progress in the mathematical research related to stochastic processes with application in biophysics.
The present volume collects three of the four courses held at this meeting by Angelo Valleriani, Sylvie Rœlly and Alexei Kulik.
A particular aim of this collection is to inspire young scientists in setting up research goals within the wide scope of fields represented in this volume.
Angelo Valleriani, PhD in high energy physics, is group leader of the team "Stochastic processes in complex and biological systems" from the Max-Planck-Institute of Colloids and Interfaces, Potsdam.
Sylvie Rœlly, Docteur en Mathématiques, is the head of the chair of Probability at the University of Potsdam.
Alexei Kulik, Doctor of Sciences, is a Leading researcher at the Institute of Mathematics of Ukrainian National Academy of Sciences.
In this work, we consider the reversible reaction between reactants of species A and B to form the product C. We consider this reaction as a prototype of many pseudobiomolecular reactions in biology, such as for instance molecular motors. We derive the exact probability density for the stochastic waiting time that a molecule of species A needs until the reaction with a molecule of species B takes place. We perform this computation taking fully into account the stochastic fluctuations in the number of molecules of species B. We show that at low numbers of participating molecules, the exact probability density differs from the exponential density derived by assuming the law of mass action. Finally, we discuss the condition of detailed balance in the exact stochastic and in the approximate treatment.
During life bones constantly adapt their structure to their mechanical environment via a mechanically controlled process called bone remodeling. For trabecular bone, this process modifies the thickness of each trabecula leading occasionally to full resorption. We describe the irreversible dynamics of the trabecular thickness distribution (TTD) by means of a Markov chain discrete in space and time. By using thickness data from adult patients, we derive the transition probabilities in the chain. This allows a quantification, in terms of geometrical quantities, of the control of bone remodeling and thus to determine the evolution of the TTD with age.
We say that (weak/strong) time duality holds for continuous time quasi-birth-and-death-processes if, starting from a fixed level, the first hitting time of the next upper level and the first hitting time of the next lower level have the same distribution. We present here a criterion for time duality in the case where transitions from one level to another have to pass through a given single state, the so-called bottleneck property. We also prove that a weaker form of reversibility called balanced under permutation is sufficient for the time duality to hold. We then discuss the general case.
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.
A simple measure for the efficiency of protein synthesis by ribosomes is provided by the steady state amount of protein per messenger RNA (mRNA), the so-called translational ratio, which is proportional to the translation rate. Taking the degradation of mRNA into account, we show theoretically that both the translation rate and the translational ratio decrease with increasing mRNA length, in agreement with available experimental data for the prokaryote Escherichia coli. We also show that, compared to prokaryotes, mRNA degradation in eukaryotes leads to a less rapid decrease of the translational ratio. This finding is consistent with the fact that, compared to prokaryotes, eukaryotes tend to have longer proteins.