Necessary Noise

Developmental noise, entropy, and biological system condition

Developmental noise is considered as a permissible level of entropy, as a compromise between the cost and needed precision of the realization of genetic information. In terms of entropy, noise is a measure of acceptable level of disorder to ensure a reliable system operation. Developmental noise plays a role in the observed phenotypic diversity and is associated with other indicators of the biological system condition. The thermodynamic characteristic of entropy by the energy metabolism also turns out to be related to the developmental noise. Phenotypic variability is largely determined by developmental homeostasis, including both canalization (an ability to form a similar phenotype under different conditions) and developmental stability (a capability for perfect development measured by noise level). It is shown that the change in the noise level, as an expression of the certain entropy level, unlike other forms of phenotypic variability, is a reflection of a change in the system condition. Although the entropy indices of ontogeny and community under certain conditions can change simultaneously, the entropy index at the level of developmental noise proves to be a more unambiguous and universal measure of the disorder of a biological system, compared to biodiversity indices at the community level.

An Approximate Method of System Entropy in Discrete-Time Nonlinear Biological Networks

This study discusses the calculation of entropy of discrete-time stochastic biological systems. First, measurement methods of the system entropy of discrete-time linear stochastic networks are introduced. The system entropy is found to be characterized by system matrices of the discrete-time biological systems. Secondly, the system entropy of nonlinear discrete-time stochastic biological systems is discussed and is calculated based on a global linearization method. The approximation of the values of system entropy of nonlinear stochastic systems needs to solve an optimization problem that is constrained by a kind of linear matrix inequality (LMI). Finally, a practical biochemical system is provided to verify the effectiveness of the proposed calculation method.

Active Degradation Explains the Distribution of Nuclear Proteins during Cellular Senescence

The amount of cellular proteins is a crucial parameter that is known to vary between cells as a function of the replicative passages, and can be important during physiological aging. The process of protein degradation is known to be performed by a series of enzymatic reactions, ranging from an initial step of protein ubiquitination to their final fragmentation by the proteasome. In this paper we propose a stochastic dynamical model of nuclear proteins concentration resulting from a balance between a constant production of proteins and their degradation by a cooperative enzymatic reaction. The predictions of this model are compared with experimental data obtained by fluorescence measurements of the amount of nuclear proteins in murine tail fibroblast (MTF) undergoing cellular senescence. Our model provides a three-parameter stationary distribution that is in good agreement with the experimental data even during the transition to the senescent state, where the nuclear protein concentration changes abruptly. The estimation of three parameters (cooperativity, saturation threshold, and maximal velocity of the reaction), and their evolution during replicative passages shows that only the maximal velocity varies significantly. Based on our modeling we speculate the reduction of functionality of the protein degradation mechanism as a possible competitive inhibition of the proteasome.

Quantifying the contribution of chromatin dynamics to stochastic gene expression reveals long, locus-dependent periods between transcriptional bursts

BACKGROUND

A number of studies have established that stochasticity in gene expression may play an important role in many biological phenomena. This therefore calls for further investigations to identify the molecular mechanisms at stake, in order to understand and manipulate cell-to-cell variability. In this work, we explored the role played by chromatin dynamics in the regulation of stochastic gene expression in higher eukaryotic cells.

RESULTS

For this purpose, we generated isogenic chicken-cell populations expressing a fluorescent reporter integrated in one copy per clone. Although the clones differed only in the genetic locus at which the reporter was inserted, they showed markedly different fluorescence distributions, revealing different levels of stochastic gene expression. Use of chromatin-modifying agents showed that direct manipulation of chromatin dynamics had a marked effect on the extent of stochastic gene expression. To better understand the molecular mechanism involved in these phenomena, we fitted these data to a two-state model describing the opening/closing process of the chromatin. We found that the differences between clones seemed to be due mainly to the duration of the closed state, and that the agents we used mainly seem to act on the opening probability.

CONCLUSIONS

In this study, we report biological experiments combined with computational modeling, highlighting the importance of chromatin dynamics in stochastic gene expression. This work sheds a new light on the mechanisms of gene expression in higher eukaryotic cells, and argues in favor of relatively slow dynamics with long (hours to days) periods of quiet state.

Embracing noise to improve cross-batch prediction accuracy

One important application of microarray in clinical settings is for constructing a diagnosis or prognosis model. Batch effects are a well-known obstacle in this type of applications. Recently, a prominent study was published on how batch effects removal techniques could potentially improve microarray prediction performance. However, the results were not very encouraging, as prediction performance did not always improve. In fact, in up to 20% of the cases, prediction accuracy was reduced. Furthermore, it was stated in the paper that the techniques studied require sufficiently large sample sizes in both batches (train and test) to be effective, which is not a realistic situation especially in clinical settings. In this paper, we propose a different approach, which is able to overcome limitations faced by conventional methods. Our approach uses ranking value of microarray data and a bagging ensemble classifier with sequential hypothesis testing to dynamically determine the number of classifiers required in the ensemble. Using similar datasets to those in the original study, we showed that in only one case (<2%) is our performance reduced (by more than -0.05 AUC) and, in >60% of cases, it is improved (by more than 0.05 AUC). In addition, our approach works even on much smaller training data sets and is independent of the sample size of the test data, making it feasible to be applied on clinical studies.

Bistability in the chemical master equation for dual phosphorylation cycles

Dual phospho/dephosphorylation cycles, as well as covalent enzymatic-catalyzed modifications of substrates are widely diffused within cellular systems and are crucial for the control of complex responses such as learning, memory, and cellular fate determination. Despite the large body of deterministic studies and the increasing work aimed at elucidating the effect of noise in such systems, some aspects remain unclear. Here we study the stationary distribution provided by the two-dimensional chemical master equation for a well-known model of a two step phospho/dephosphorylation cycle using the quasi-steady state approximation of enzymatic kinetics. Our aim is to analyze the role of fluctuations and the molecules distribution properties in the transition to a bistable regime. When detailed balance conditions are satisfied it is possible to compute equilibrium distributions in a closed and explicit form. When detailed balance is not satisfied, the stationary non-equilibrium state is strongly influenced by the chemical fluxes. In the last case, we show how the external field derived from the generation and recombination transition rates, can be decomposed by the Helmholtz theorem, into a conservative and a rotational (irreversible) part. Moreover, this decomposition allows to compute the stationary distribution via a perturbative approach. For a finite number of molecules there exists diffusion dynamics in a macroscopic region of the state space where a relevant transition rate between the two critical points is observed. Further, the stationary distribution function can be approximated by the solution of a Fokker-Planck equation. We illustrate the theoretical results using several numerical simulations.

Design and connection of robust genetic circuits

Phenotypic robustness is a highly sought after goal for synthetic biology. There are many well-studied examples of robust systems in biology, and for the advancement of synthetic biology, particularly in performance-critical applications, fundamental understanding of how robustness is both achieved and maintained is very important. A synthetic circuit may fail to behave as expected for a multitude of reasons, and since many of these failures are difficult to predict a priori, a better understanding of a circuit's behavior as well as its possible failures are needed. In this chapter, we outline work that has been done in developing design principles for robust synthetic circuits, as well as sharing our experiences designing and constructing gene circuits.

Functional models for large-scale gene regulation networks: realism and fiction

High-throughput experiments are shedding light on the topology of large regulatory networks and at the same time their functional states, namely the states of activation of the nodes (for example transcript or protein levels) in different conditions, times, environments. We now possess a certain amount of information about these two levels of description, stored in libraries, databases and ontologies. A current challenge is to bridge the gap between topology and function, i.e. developing quantitative models aimed at characterizing the expression patterns of large sets of genes. However, approaches that work well for small networks become impossible to master at large scales, mainly because parameters proliferate. In this review we discuss the state of the art of large-scale functional network models, addressing the issue of what can be considered as "realistic" and what the main limitations may be. We also show some directions for future work, trying to set the goals that future models should try to achieve. Finally, we will emphasize the possible benefits in the understanding of biological mechanisms underlying complex multifactorial diseases, and in the development of novel strategies for the description and the treatment of such pathologies.

Of cardiovascular illness and diversity of biological response

Noise in gene expression (stochastic variation in the composition of the transcriptome in response to stimuli) may play an important role in maintaining robustness and flexibility, which ensure the stability of normal physiology and provide adaptability to environmental changes for the living system. Broad-based technologies have allowed us to study with unprecedented accuracy the molecular profiles of various states of health and cardiovascular disease. In doing so, we have observed a correlation between the degree of variation in gene expression and the state of health. Specifically, the stochastic variation in gene expression in response to environmental and physiological factors is found in healthy mice, and tends to disappear in mice with advanced disease states. Although further evidence is needed to draw a solid conclusion with respect to the significance of decreased transcriptional noise in the disease state as a whole, it is tantalizing to introduce the concept that stochasticity may be linked to the organism's adaptability to a changing environment, and the "quiet" states of gene expression may indicate the loss of diversity in the organism's response.

From DNA nanotechnology to synthetic biology

Attempts to construct artificial systems from biological molecules such as DNA and RNA by self-assembly are compatible with the recent development of synthetic biology. Genetic mechanisms can be used to produce or control artificial structures made from DNA and RNA, and these structures can in turn be used as artificial gene regulatory elements, in vitro as well as in vivo. Artificial biochemical circuits can be incorporated into cell-like reaction compartments, which opens up the possibility to operate them permanently out of equilibrium. In small systems, stochastic effects become noticeable and will have to be accounted for in the design of future systems.