N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

http://web.mit.edu/biophysics/papers/CELL2008.pdf

Nature, Nurture, or Chance: Stochastic Gene Expression and Its Consequences

Protein and messenger RNA (mRNA) copy numbers vary from cell to cell in isogenic bacterial populations. However, these molecules often exist in low copy numbers and are difficult to detect in single cells. We carried out quantitative system-wide analyses of protein and mRNA expression in individual cells with single-molecule sensitivity using a newly constructed yellow fluorescent protein fusion library for Escherichia coli. We found that almost all protein number distributions can be described by the gamma distribution with two fitting parameters which, at low expression levels, have clear physical interpretations as the transcription rate and protein burst size. At high expression levels, the distributions are dominated by extrinsic noise. We found that a single cell's protein and mRNA copy numbers for any given gene are uncorrelated.

/pdf/quantifying-e-coli-proteome-and-transcriptome-with-single-1xqg8lgkev.pdf

Quantifying E. coli proteome and transcriptome with single-molecule sensitivity in single cells.

The text consists of two sections, one for those studying or practicing diagnostic radiology, nuclear medicine and radiation oncology; the other for those engaged in the study or clinical practice of radiation oncology--a new chapter, on radiologic terrorism, is specifically for those in the radiation sciences who would manage exposed individuals in the event of a terrorist event. The 17 chapters in Section I represent a general introduction to radiation biology and a complete, self-contained course especially for residents in diagnostic radiology and nuclear medicine that follows the Syllabus in Radiation Biology of the RSNA. The 11 chapters in Section II address more in-depth topics in radiation oncology, such as cancer biology, retreatment after radiotherapy, chemotherapeutic agents and hyperthermia.

Radiobiology for the Radiologist

In prokaryotes and eukaryotes, most genes appear to be transcribed during short periods called transcriptional bursts, interspersed by silent intervals. We describe how such bursts generate gene-specific temporal patterns of messenger RNA (mRNA) synthesis in mammalian cells. To monitor transcription at high temporal resolution, we established various gene trap cell lines and transgenic cell lines expressing a short-lived luciferase protein from an unstable mRNA, and recorded bioluminescence in real time in single cells. Mathematical modeling identified gene-specific on- and off-switching rates in transcriptional activity and mean numbers of mRNAs produced during the bursts. Transcriptional kinetics were markedly altered by cis-regulatory DNA elements. Our analysis demonstrated that bursting kinetics are highly gene-specific, reflecting refractory periods during which genes stay inactive for a certain time before switching on again.

https://science.sciencemag.org/content/sci/332/6028/472.full.pdf

Mammalian genes are transcribed with widely different bursting kinetics

Gene expression is significantly stochastic making modeling of genetic networks challenging. We present an approximation that allows the calculation of not only the mean and variance, but also the distribution of protein numbers. We assume that proteins decay substantially more slowly than their mRNA and confirm that many genes satisfy this relation by using high-throughput data from budding yeast. For a two-stage model of gene expression, with transcription and translation as first-order reactions, we calculate the protein distribution for all times greater than several mRNA lifetimes and thus qualitatively predict the distribution of times for protein levels to first cross an arbitrary threshold. If in addition the fluctuates between inactive and active states, we can find the steady-state protein distribution, which can be bimodal if fluctuations of the promoter are slow. We show that our assumptions imply that protein synthesis occurs in geometrically distributed bursts and allows mRNA to be eliminated from a master equation description. In general, we find that protein distributions are asymmetric and may be poorly characterized by their mean and variance. Through maximum likelihood methods, our expressions should therefore allow more quantitative comparisons with experimental data. More generally, we introduce a technique to derive a simpler, effective dynamics for a stochastic system by eliminating a fast variable.

https://www.pnas.org/content/pnas/105/45/17256.full.pdf

Analytical distributions for stochastic gene expression

Stochasticity is both exploited and controlled by cells. Although the intrinsic stochasticity inherent in biochemistry is relatively well understood, cellular variation, or ‘noise', is predominantly generated by interactions of the system of interest with other stochastic systems in the cell or its environment. Such extrinsic fluctuations are nonspecific, affecting many system components, and have a substantial lifetime, comparable to the cell cycle (they are ‘colored'). Here, we extend the standard stochastic simulation algorithm to include extrinsic fluctuations. We show that these fluctuations affect mean protein numbers and intrinsic noise, can speed up typical network response times, and can explain trends in high-throughput measurements of variation. If extrinsic fluctuations in two components of the network are correlated, they may combine constructively (amplifying each other) or destructively (attenuating each other). Consequently, we predict that incoherent feedforward loops attenuate stochasticity, while coherent feedforwards amplify it. Our results demonstrate that both the timescales of extrinsic fluctuations and their nonspecificity substantially affect the function and performance of biochemical networks.

/pdf/colored-extrinsic-fluctuations-and-stochastic-gene-2mdcr9awaa.pdf

Colored extrinsic fluctuations and stochastic gene expression.

https://swainlab.bio.ed.ac.uk/papers/curropinion08.pdf

The stochastic nature of biochemical networks.

Before mating, a Saccharomyces cerevisiae yeast cell must detect a partner cell in the vicinity that is expressing large amounts of a sex pheromone. The pheromone detection system involves the MAP kinase signal transduction cascade, and the potential partner that secretes the highest pheromone levels is the one chosen. A study combining experiment and mathematical modelling shows that the mating decision is an all-or-none 'switch-like' response: for mating to initiate the pheromone must be at a critical concentration around the yeast cell and if this level is not reached, the yeast cell continues to reproduce asexually. The decision is taken quickly, within 2 minutes of initial contact with the pheromone. The scaffold protein Ste5, which binds MAPK cascade components in an active complex, is the direct modulator of the pheromone's action. If similar ultrasensitive mechanisms occur in mammalian signalling pathways, they may be particularly vulnerable to mutations that lead to disease and could thus prove to be important therapeutic targets. Before mating, a yeast cell must detect a partner cell that is close enough and expresses sufficiently large amounts of a sex pheromone. The mating decision is an all-or-none, switch-like response to pheromone concentration. It is now shown that this decision involves the competition of one kinase and one phosphatase enzyme for multiple phosphorylation sites on a 'scaffold' protein. The results should prompt a re-evaluation of the role of related signalling molecules that have been implicated in cancer. Evolution has resulted in numerous innovations that allow organisms to increase their fitness by choosing particular mating partners, including secondary sexual characteristics, behavioural patterns, chemical attractants and corresponding sensory mechanisms1. The haploid yeast Saccharomyces cerevisiae selects mating partners by interpreting the concentration gradient of pheromone secreted by potential mates through a network of mitogen-activated protein kinase (MAPK) signalling proteins2,3. The mating decision in yeast is an all-or-none, or switch-like, response that allows cells to filter weak pheromone signals, thus avoiding inappropriate commitment to mating by responding only at or above critical concentrations when a mate is sufficiently close4. The molecular mechanisms that govern the switch-like mating decision are poorly understood. Here we show that the switching mechanism arises from competition between the MAPK Fus3 and a phosphatase Ptc1 for control of the phosphorylation state of four sites on the scaffold protein Ste5. This competition results in a switch-like dissociation of Fus3 from Ste5 that is necessary to generate the switch-like mating response. Thus, the decision to mate is made at an early stage in the pheromone pathway and occurs rapidly, perhaps to prevent the loss of the potential mate to competitors. We argue that the architecture of the Fus3–Ste5–Ptc1 circuit generates a novel ultrasensitivity mechanism, which is robust to variations in the concentrations of these proteins. This robustness helps assure that mating can occur despite stochastic or genetic variation between individuals. The role of Ste5 as a direct modulator of a cell-fate decision expands the functional repertoire of scaffold proteins beyond providing specificity and efficiency of information processing5,6. Similar mechanisms may govern cellular decisions in higher organisms and be disrupted in cancer.

/pdf/the-scaffold-protein-ste5-directly-controls-a-switch-like-2jpca8nllk.pdf

The scaffold protein Ste5 directly controls a switch-like mating decision in yeast

Developing hippocampal neurons in microisland culture undergo rapid and extensive transmitter release-dependent depression of evoked (phasic) excitatory synaptic activity in response to 1 sec trains of 20 Hz stimulation. Although evoked phasic release was attenuated by repeated stimuli, asynchronous (miniature like) release continued at a high rate equivalent to approximately 2.8 readily releasable pools (RRPs) of quanta/sec. Asynchronous release reflected the recovery and immediate release of quanta because it was resistant to sucrose-induced depletion of the RRP. Asynchronous and phasic release appeared to compete for a common limited supply of release-ready quanta because agents that block asynchronous release, such as EGTA-AM, led to enhanced steady-state phasic release, whereas prolongation of the asynchronous release time course by LiCl delayed recovery of phasic release from depression. Modeling suggested that the resistance of asynchronous release to depression was associated with its ability to out-compete phasic release for recovered quanta attributable to its relatively low release rate (up to 0.04/msec per vesicle) stimulated by bulk intracellular Ca2+ concentration ([Ca2+]i) that could function over prolonged intervals between successive stimuli. Although phasic release was associated with a considerably higher peak rate of release (0.4/msec per vesicle), the [Ca2+]i microdomains that trigger it are brief (1 msec), and with asynchronous release present, relatively few quanta can accumulate within the RRP to be available for phasic release. We conclude that despite depression of phasic release during train stimulation, transmission can be maintained at a near-maximal rate by switching to an asynchronous mode that takes advantage of a bulk presynaptic [Ca2+]i.

https://www.jneurosci.org/content/jneuro/24/2/420.full.pdf

Vahid Shahrezaei

Papers

Analytical distributions for stochastic gene expression

Colored extrinsic fluctuations and stochastic gene expression.

The stochastic nature of biochemical networks.

The scaffold protein Ste5 directly controls a switch-like mating decision in yeast

Competition between Phasic and Asynchronous Release for Recovered Synaptic Vesicles at Developing Hippocampal Autaptic Synapses