Strategies for cellular decision‐making

Stochasticity pervades life at the cellular level. Cells receive stochastic signals, perform detection and transduction with stochastic biochemistry, and grow and die in stochastic environments. Here we review progress in going from the molecular details to the information‐processing strategies cells use in their decision‐making. Such strategies are fundamentally influenced by stochasticity. We argue that the cellular decision‐making can only be probabilistic and occurs at three levels. First, cells must infer from noisy signals the probable current and anticipated future state of their environment. Second, they must weigh the costs and benefits of each potential response, given that future. Third, cells must decide in the presence of other, potentially competitive, decision‐makers. In this context, we discuss cooperative responses where some individuals can appear to sacrifice for the common good. We believe that decision‐making strategies will be conserved, with comparatively few strategies being implemented by different biochemical mechanisms in many organisms. Determining the strategy of a decision‐making network provides a potentially powerful coarse‐graining that links systems and evolutionary biology to understand biological design.     

Stochastic Responses May Allow Genetically Diverse Cell Populations to Optimize Performance with Simpler Signaling Networks

Two theories have emerged for the role that stochasticity plays in biological responses: first, that it degrades biological responses, so the performance of biological signaling machinery could be improved by increasing molecular copy numbers of key proteins; second, that it enhances biological performance, by enabling diversification of population-level responses. Using T cell biology as an example, we demonstrate that these roles for stochastic responses are not sufficient to understand experimental observations of stochastic response in complex biological systems that utilize environmental and genetic diversity to make cooperative responses. We propose a new role for stochastic responses in biology: they enable populations to make complex responses with simpler biochemical signaling machinery than would be required in the absence of stochasticity. Thus, the evolution of stochastic responses may be linked to the evolvability of different signaling machineries.     

Colored extrinsic fluctuations and 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.     

种群统计随机性和环境随机性对种群绝灭的影响

影响种群绝灭的随机干扰可分为种群统计随机性、环境随机性和随机灾害三大类。在相对稳定的环境条件下和相对较短的时间内,以前两类随机干扰对种群绝灭的影响为生态学家关注的焦点。但是,由于自然种群动态及其影响因子的复杂特征,进一步深入研究随机干扰对种群绝灭的作用在理论上和实践上都必须发展新的技术手段。本文回顾了种群统计随机性与环境随机性的概念起源与发展,系统阐述了其分析方法。归纳了两类随机性在种群绝灭研究中的应用范围、作用方式和特点的异同和区别方法。各类随机作用与种群动态之间关系的理论研究与对种群绝灭机理的实践研究紧密相关。根据理论模型模拟和自然种群实际分析两方面的研究现状,作者提出了进一步深入研究随机作用与种群非线性动态方法的策略。指出了随机干扰影响种群绝灭过程的研究的方向：更多的研究将从单纯的定性分析随机干扰对种群动力学简单性质的作用,转向结合特定的种群非线性动态特征和各类随机力作用特点具体分析绝灭极端动态的成因,以期做出精确的预测。     

Analysing dynamical behavior of cellular networks via stochastic bifurcations

The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types.     

Multi-cellular logistics of collective cell migration

During development, the formation of biological networks (such as organs and neuronal networks) is controlled by multicellular transportation phenomena based on cell migration. In multi-cellular systems, cellular locomotion is restricted by physical interactions with other cells in a crowded space, similar to passengers pushing others out of their way on a packed train. The motion of individual cells is intrinsically stochastic and may be viewed as a type of random walk. However, this walk takes place in a noisy environment because the cell interacts with its randomly moving neighbors. Despite this randomness and complexity, development is highly orchestrated and precisely regulated, following genetic (and even epigenetic) blueprints. Although individual cell migration has long been studied, the manner in which stochasticity affects multi-cellular transportation within the precisely controlled process of development remains largely unknown. To explore the general principles underlying multicellular migration, we focus on the migration of neural crest cells, which migrate collectively and form streams. We introduce a mechanical model of multi-cellular migration. Simulations based on the model show that the migration mode depends on the relative strengths of the noise from migratory and non-migratory cells. Strong noise from migratory cells and weak noise from surrounding cells causes "collective migration," whereas strong noise from non-migratory cells causes "dispersive migration." Moreover, our theoretical analyses reveal that migratory cells attract each other over long distances, even without direct mechanical contacts. This effective interaction depends on the stochasticity of the migratory and non-migratory cells. On the basis of these findings, we propose that stochastic behavior at the single-cell level works effectively and precisely to achieve collective migration in multi-cellular systems.     

Gene correction by RNA-DNA oligonucleotides

An oligonucleotide composed of a contiguous stretch of RNA and DNA residues has been developed to facilitate the correction of single-base mutations of episomal and chromosomal targets in mammalian cells. The design of the oligonucleotide exploited the highly recombinogenic RNA-DNA hybrids and featured hairpin capped ends avoiding destruction by cellular helicases or exonucleases. The RNA-DNA oligonucleotide (RDO) was designed to correct a point mutation in the tyrosinase gene and caused a permanent gene correction in mouse albino melanocytes, determined by clonal analysis at the level of genomic sequence, protein and phenotypic change. Recently, we demonstrated correction of the tyrosinase gene using the same RDO in vivo, as detected by dark pigmentation of several hairs and DOPA staining of hair follicles in the treated skin of albino mice. Such RDOs might hold a promise as a therapeutic method for the treatment of skin diseases. However, the frequency of gene correction varies among different cells, indicating that cellular activities, such as recombination and repair, may be important for gene conversion by RDOs. As this technology becomes more widely utilized in the scientific community, it will be important to understand the mechanism and to optimize the design of RDOs to improve their efficiency and general applicability.     

Interplay between Intrinsic Noise and the Stochasticity of the Cell Cycle in Bacterial Colonies

Herein we report on the effects that different stochastic contributions induce in bacterial colonies in terms of protein concentration and production. In particular, we consider for what we believe to be the first time cell-to-cell diversity due to the unavoidable randomness of the cell-cycle duration and its interplay with other noise sources. To that end, we model a recent experimental setup that implements a protein dilution protocol by means of division events to characterize the gene regulatory function at the single cell level. This approach allows us to investigate the effect of different stochastic terms upon the total randomness experimentally reported for the gene regulatory function. In addition, we show that the interplay between intrinsic fluctuations and the stochasticity of the cell-cycle duration leads to different constructive roles. On the one hand, we show that there is an optimal value of protein concentration (alternatively an optimal value of the cell cycle phase) such that the noise in protein concentration attains a minimum. On the other hand, we reveal that there is an optimal value of the stochasticity of the cell cycle duration such that the coherence of the protein production with respect to the colony average production is maximized. The latter can be considered as a novel example of the recently reported phenomenon of diversity induced resonance.     

How does stochasticity in colonization accelerate the speed of invasion in a cellular automaton model?

We investigate the speed of invasion waves for a single species generated by stochastic short- and/or long-distance colonizations in a time-continuous cellular automaton (CA) model on a two-dimensional homogenous landscape. By simulating the CA models, we demonstrate that stochasticity can dramatically increase the speed of invasion compared to the corresponding deterministic CA model or the corresponding one-dimensional stochastic CA model. To explain this phenomenon, we first develop a mathematical model for the invasion involving only short-distance colonization (i.e., colonization only occurs from the eight adjacent cells), and present several approximation methods for solving the model. Our analyses show that the increased wave speed in the stochastic model is due to irregularity in the shape of the wavefront. Further extension of this model to include long-distance colonization demonstrates that stochasticity influences speeds to even greater extents in this case. Using dimension analysis, we deduced a semi-empirical formula for the speed as a function of three parameters intrinsic to short- and long-distance colonization, which agrees well with simulation results. Based on these results, we discuss how important stochasticity in colonization and spatial dimensionality are in the acceleration of invasion speed.     

Stochastic Fluctuations and Distributed Control of Gene Expression Impact Cellular Memory

Despite the stochastic noise that characterizes all cellular processes the cells are able to maintain and transmit to their daughter cells the stable level of gene expression. In order to better understand this phenomenon, we investigated the temporal dynamics of gene expression variation using a double reporter gene model. We compared cell clones with transgenes coding for highly stable mRNA and fluorescent proteins with clones expressing destabilized mRNA-s and proteins. Both types of clones displayed strong heterogeneity of reporter gene expression levels. However, cells expressing stable gene products produced daughter cells with similar level of reporter proteins, while in cell clones with short mRNA and protein half-lives the epigenetic memory of the gene expression level was completely suppressed. Computer simulations also confirmed the role of mRNA and protein stability in the conservation of constant gene expression levels over several cell generations. These data indicate that the conservation of a stable phenotype in a cellular lineage may largely depend on the slow turnover of mRNA-s and proteins.     

Gene Correction by RNA‐DNA Oligonucleotides

An oligonucleotide composed of a contiguous stretch of RNA and DNA residues has been developed to facilitate the correction of single‐base mutations of episomal and chromosomal targets in mammalian cells. The design of the oligonucleotide exploited the highly recombinogenic RNA‐DNA hybrids and featured hairpin capped ends avoiding destruction by cellular helicases or exonucleases. The RNA‐DNA oligonucleotide (RDO) was designed to correct a point mutation in the tyrosinase gene and caused a permanent gene correction in mouse albino melanocytes, determined by clonal analysis at the level of genomic sequence, protein and phenotypic change. Recently, we demonstrated correction of the tyrosinase gene using the same RDO in vivo, as detected by dark pigmentation of several hairs and DOPA staining of hair follicles in the treated skin of albino mice. Such RDOs might hold a promise as a therapeutic method for the treatment of skin diseases. However, the frequency of gene correction varies among different cells, indicating that cellular activities, such as recombination and repair, may be important for gene conversion by RDOs. As this technology becomes more widely utilized in the scientific community, it will be important to understand the mechanism and to optimize the design of RDOs to improve their efficiency and general applicability.     

Role of Intracellular Stochasticity in Biofilm Growth. Insights from Population Balance Modeling

There is increasing recognition that stochasticity involved in gene regulatory processes may help cells enhance the signal or synchronize expression for a group of genes. Thus the validity of the traditional deterministic approach to modeling the foregoing processes cannot be without exception. In this study, we identify a frequently encountered situation, i.e., the biofilm, which has in the past been persistently investigated with intracellular deterministic models in the literature. We show in this paper circumstances in which use of the intracellular deterministic model appears distinctly inappropriate. In Enterococcus faecalis, the horizontal gene transfer of plasmid spreads drug resistance. The induction of conjugation in planktonic and biofilm circumstances is examined here with stochastic as well as deterministic models. The stochastic model is formulated with the Chemical Master Equation (CME) for planktonic cells and Reaction-Diffusion Master Equation (RDME) for biofilm. The results show that although the deterministic model works well for the perfectly-mixed planktonic circumstance, it fails to predict the averaged behavior in the biofilm, a behavior that has come to be known as stochastic focusing. A notable finding from this work is that the interception of antagonistic feedback loops to signaling, accentuates stochastic focusing. Moreover, interestingly, increasing particle number of a control variable could lead to an even larger deviation. Intracellular stochasticity plays an important role in biofilm and we surmise by implications from the model, that cell populations may use it to minimize the influence from environmental fluctuation.