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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

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.

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.

The most crucial step in data processing from high-throughput sequencing applications is the accurate and sensitive alignment of the sequencing reads to reference genomes or transcriptomes. The accurate detection of insertions and deletions (indels) and errors introduced by the sequencing platform or by misreading of modified nucleotides is essential for the quantitative processing of the RNA-based sequencing (RNA-Seq) datasets and for the identification of genetic variations and modification patterns. We developed a new, fast and accurate algorithm for nucleic acid sequence analysis, FANSe, with adjustable mismatch allowance settings and ability to handle indels to accurately and quantitatively map millions of reads to small or large reference genomes. It is a seed-based algorithm which uses the whole read information for mapping and high sensitivity and low ambiguity are achieved by using short and non-overlapping reads. Furthermore, FANSe uses hotspot score to prioritize the processing of highly possible matches and implements modified Smith-Watermann refinement with reduced scoring matrix to accelerate the calculation without compromising its sensitivity. The FANSe algorithm stably processes datasets from various sequencing platforms, masked or unmasked and small or large genomes. It shows a remarkable coverage of low-abundance mRNAs which is important for quantitative processing of RNA-Seq datasets.

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.

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. While moving along the rope the motor can also detach and is lost. 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.

Environmental stress is detrimental to cell viability and requires an adequate reprogramming of cellular activities to maximize cell survival. We present a global analysis of the response of Escherichia coli to acute heat and osmotic stress. We combine deep sequencing of total mRNA and ribosome-protected fragments to provide a genome-wide map of the stress response at transcriptional and translational levels. For each type of stress, we observe a unique subset of genes that shape the stress-specific response. Upon temperature upshift, mRNAs with reduced folding stability up-and downstream of the start codon, and thus with more accessible initiation regions, are translationally favoured. Conversely, osmotic upshift causes a global reduction of highly translated transcripts with high copy numbers, allowing reallocation of translation resources to not degraded and newly synthesized mRNAs.

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.