Turning oscillations into opportunities: lessons from a bacterial decision gate

Agency as an Inherent Property of Living Organisms

A central characteristic of living organisms is their agency, that is, their intrinsic activity, both in terms of their basic life processes and their behavior in the environment. This aspect is currently a subject of debate and this article provides an overview of some of the relevant publications on this topic. We develop the argument that agency is immanent in living organisms. There is no life without agency. Even the basic life processes are an intrinsic activity, which we call the organismic level of agency. In addition to this we describe several further levels. These capture different qualities that occur or transform during evolution. In addition to the organismic level, we propose an ontogenetic level, a level of directed agency, directed agency with extended flexibility, and a level that includes the capacities to follow preconceived goals. A further property of organisms is their autonomy. It has been shown that the capacity for autonomy changed during evolution. Here we propose that the two organismic properties autonomy and agency are closely related. Enhanced physiological and behavioral autonomy extends the scope of self-generated, flexible actions and reactions. The increase in autonomy through the evolution of a widened scope of behavioral possibilities and versatility in organisms coincides with extended levels of agency. Especially the human organization, including the sophisticated brain, is the basis for an extended level of agency referring to the capacities to follow preconceived goals. However, it is important for the understanding of the phenomenon of agency not only to assume this latter form, but also to look at the different levels of agency.

Biology in the 21st century: Natural selection is cognitive selection

Natural selection has a formal definition as the natural process that results in the survival and reproductive success of individuals or groups best adjusted to their environment, leading to the perpetuation of those genetic qualities best suited to that organism's environmental niche. Within conventional Neo-Darwinism, the largest source of those variations that can be selected is presumed to be secondary to random genetic mutations. As these arise, natural selection sustains adaptive traits in the context of a 'struggle for existence'. Consequently, in the 20th century, natural selection was generally portrayed as the primary evolutionary driver. The 21st century offers a comprehensive alternative to Neo-Darwinian dogma within Cognition-Based Evolution. The substantial differences between these respective evolutionary frameworks have been most recently articulated in a revision of Crick's Central Dogma, a former centerpiece of Neo-Darwinism. The argument is now advanced that the concept of natural selection should also be comprehensively reappraised. Cognitive selection is presented as a more precise term better suited to 21st century biology. Since cognition began with life's origin, natural selection represents cognitive selection.

Theoretical study of the impact of adaptation on cell-fate heterogeneity and fractional killing

Fractional killing illustrates the cell propensity to display a heterogeneous fate response over a wide range of stimuli. The interplay between the nonlinear and stochastic dynamics of biochemical networks plays a fundamental role in shaping this probabilistic response and in reconciling requirements for heterogeneity and controllability of cell-fate decisions. The stress-induced fate choice between life and death depends on an early adaptation response which may contribute to fractional killing by amplifying small differences between cells. To test this hypothesis, we consider a stochastic modeling framework suited for comprehensive sensitivity analysis of dose response curve through the computation of a fractionality index. Combining bifurcation analysis and Langevin simulation, we show that adaptation dynamics enhances noise-induced cell-fate heterogeneity by shifting from a saddle-node to a saddle-collision transition scenario. The generality of this result is further assessed by a computational analysis of a detailed regulatory network model of apoptosis initiation and by a theoretical analysis of stochastic bifurcation mechanisms. Overall, the present study identifies a cooperative interplay between stochastic, adaptation and decision intracellular processes that could promote cell-fate heterogeneity in many contexts.

RNA Regulatory Networks as a Control of Stochasticity in Biological Systems

The discovery that the non-protein coding part of human genome, dismissed as "junk DNA," is actively transcripted and carries out crucial functions is probably one of the most important discoveries of the past decades. These transcripts are becoming the rising stars of modern biology. In this review, we have casted a new light on RNAs. We have placed these molecules in the context of life origins, evolution with a big emphasize on the "RNA networks" concept. We discuss how this view can help us to understand the global role of RNA networks in modern cells, and can change our perception of the cell biology and therapy. Finally, although high-throughput methods as well as traditional case-to-case studies have laid the groundwork for our current knowledge of transcriptomes, we would like to discuss new strategies that are better suited to uncover and tackle these integrated and complex RNA networks.

Dynamic Modeling of Streptococcus pneumoniae Competence Provides Regulatory Mechanistic Insights Into Its Tight Temporal Regulation

In the human pathogen Streptococcus pneumoniae, the gene regulatory circuit leading to the transient state of competence for natural transformation is based on production of an auto-inducer that activates a positive feedback loop. About 100 genes are activated in two successive waves linked by a central alternative sigma factor ComX. This mechanism appears to be fundamental to the biological fitness of S. pneumoniae. We have developed a knowledge-based model of the competence cycle that describes average cell behavior. It reveals that the expression rates of the two competence operons, comAB and comCDE, involved in the positive feedback loop must be coordinated to elicit spontaneous competence. Simulations revealed the requirement for an unknown late com gene product that shuts of competence by impairing ComX activity. Further simulations led to the predictions that the membrane protein ComD bound to CSP reacts directly to pH change of the medium and that blindness to CSP during the post-competence phase is controlled by late DprA protein. Both predictions were confirmed experimentally.

Cell fate in antiviral response arises in the crosstalk of IRF, NF-κB and JAK/STAT pathways

The innate immune system processes pathogen-induced signals into cell fate decisions. How information is turned to decision remains unknown. By combining stochastic mathematical modelling and experimentation, we demonstrate that feedback interactions between the IRF3, NF-κB and STAT pathways lead to switch-like responses to a viral analogue, poly(I:C), in contrast to pulse-like responses to bacterial LPS. Poly(I:C) activates both IRF3 and NF-κB, a requirement for induction of IFNβ expression. Autocrine IFNβ initiates a JAK/STAT-mediated positive-feedback stabilising nuclear IRF3 and NF-κB in first responder cells. Paracrine IFNβ, in turn, sensitises second responder cells through a JAK/STAT-mediated positive feedforward pathway that upregulates the positive-feedback components: RIG-I, PKR and OAS1A. In these sensitised cells, the 'live-or-die' decision phase following poly(I:C) exposure is shorter-they rapidly produce antiviral responses and commit to apoptosis. The interlinked positive feedback and feedforward signalling is key for coordinating cell fate decisions in cellular populations restricting pathogen spread.

Biophysical clocks face a trade-off between internal and external noise resistance

Many organisms use free running circadian clocks to anticipate the day night cycle. However, others organisms use simple stimulus-response strategies ('hourglass clocks') and it is not clear when such strategies are sufficient or even preferable to free running clocks. Here, we find that free running clocks, such as those found in the cyanobacterium Synechococcus elongatus and humans, can efficiently project out light intensity fluctuations due to weather patterns ('external noise') by exploiting their limit cycle attractor. However, such limit cycles are necessarily vulnerable to 'internal noise'. Hence, at sufficiently high internal noise, point attractor-based 'hourglass' clocks, such as those found in a smaller cyanobacterium with low protein copy number, Prochlorococcus marinus, can outperform free running clocks. By interpolating between these two regimes in a diverse range of oscillators drawn from across biology, we demonstrate biochemical clock architectures that are best suited to different relative strengths of external and internal noise.

Reduction of multiscale stochastic biochemical reaction networks using exact moment derivation

Biochemical reaction networks (BRNs) in a cell frequently consist of reactions with disparate timescales. The stochastic simulations of such multiscale BRNs are prohibitively slow due to high computational cost for the simulations of fast reactions. One way to resolve this problem uses the fact that fast species regulated by fast reactions quickly equilibrate to their stationary distribution while slow species are unlikely to be changed. Thus, on a slow timescale, fast species can be replaced by their quasi-steady state (QSS): their stationary conditional expectation values for given slow species. As the QSS are determined solely by the state of slow species, such replacement leads to a reduced model, where fast species are eliminated. However, it is challenging to derive the QSS in the presence of nonlinear reactions. While various approximation schemes for the QSS have been developed, they often lead to considerable errors. Here, we propose two classes of multiscale BRNs which can be reduced by deriving an exact QSS rather than approximations. Specifically, if fast species constitute either a feedforward network or a complex balanced network, the reduced model based on the exact QSS can be derived. Such BRNs are frequently observed in a cell as the feedforward network is one of fundamental motifs of gene or protein regulatory networks. Furthermore, complex balanced networks also include various types of fast reversible bindings such as bindings between transcriptional factors and gene regulatory sites. The reduced models based on exact QSS, which can be calculated by the computational packages provided in this work, accurately approximate the slow scale dynamics of the original full model with much lower computational cost.

Coordination of cell decisions and promotion of phenotypic diversity in B. subtilis via pulsed behavior of the phosphorelay

The phosphorelay of Bacillus subtilis, a kinase cascade that activates master regulator Spo0A ~ P in response to starvation signals, is the core of a large network controlling the cell's decision to differentiate into sporulation and other phenotypes. This article reviews recent advances in understanding the origins and purposes of the complex dynamical behavior of the phosphorelay, which pulses with peaks of activity coordinated with the cell cycle. The transient imbalance in the expression of two critical genes caused by their strategic placement at opposing ends of the chromosome proved to be the key for this pulsed behavior. Feedback control loops in the phosphorelay use these pulses to implement a timer mechanism, which creates several windows of opportunity for phenotypic transitions over multiple generations. This strategy allows the cell to coordinate multiple differentiation programs in a decision process that fosters phenotypic diversity and adapts to current conditions.

Feedbacks, Bifurcations, and Cell Fate Decision-Making in the p53 System

The p53 transcription factor is a regulator of key cellular processes including DNA repair, cell cycle arrest, and apoptosis. In this theoretical study, we investigate how the complex circuitry of the p53 network allows for stochastic yet unambiguous cell fate decision-making. The proposed Markov chain model consists of the regulatory core and two subordinated bistable modules responsible for cell cycle arrest and apoptosis. The regulatory core is controlled by two negative feedback loops (regulated by Mdm2 and Wip1) responsible for oscillations, and two antagonistic positive feedback loops (regulated by phosphatases Wip1 and PTEN) responsible for bistability. By means of bifurcation analysis of the deterministic approximation we capture the recurrent solutions (i.e., steady states and limit cycles) that delineate temporal responses of the stochastic system. Direct switching from the limit-cycle oscillations to the “apoptotic” steady state is enabled by the existence of a subcritical Neimark—Sacker bifurcation in which the limit cycle loses its stability by merging with an unstable invariant torus. Our analysis provides an explanation why cancer cell lines known to have vastly diverse expression levels of Wip1 and PTEN exhibit a broad spectrum of responses to DNA damage: from a fast transition to a high level of p53 killer (a p53 phosphoform which promotes commitment to apoptosis) in cells characterized by high PTEN and low Wip1 levels to long-lasting p53 level oscillations in cells having PTEN promoter methylated (as in, e.g., MCF-7 cell line).

Cancers are diseases of signaling networks. Transcription factor p53 is a pivotal node of a network that integrates a variety of stress signals and governs critical processes of DNA repair, cell cycle arrest, and apoptosis. Somewhat paradoxically, despite the fact that carcinogenesis is prevalently caused by p53 network malfunction, most of our knowledge about p53 signaling is based on cancer or immortalized cell lines. In this paper, we construct a mathematical model of intact p53 network to understand dynamics of non-cancerous cells and then dynamics of cancerous cells by introducing perturbations to the regulatory system. Cell fate decisions are enabled by the presence of interlinked feedback loops which give rise to a rich repertoire of behaviors. We explain and analyze by means of numerical simulations how the dynamical structure of the regulatory system allows for generating unambiguous single-cell fate decisions, also in the case when the cell population splits into an apoptotic and a surviving subpopulation. Perturbation analysis provides an explanation why cancer cell lines known to have vastly diverse expression levels of p53 regulators can exhibit a broad spectrum of responses to DNA damage.

Periodic, Quasi-periodic and Chaotic Dynamics in Simple Gene Elements with Time Delays

Regulatory gene circuit motifs play crucial roles in performing and maintaining vital cellular functions. Frequently, theoretical studies of gene circuits focus on steady-state behaviors and do not include time delays. In this study, the inclusion of time delays is shown to entirely change the time-dependent dynamics for even the simplest possible circuits with one and two gene elements with self and cross regulations. These elements can give rise to rich behaviors including periodic, quasi-periodic, weak chaotic, strong chaotic and intermittent dynamics. We introduce a special power-spectrum-based method to characterize and discriminate these dynamical modes quantitatively. Our simulation results suggest that, while a single negative feedback loop of either one- or two-gene element can only have periodic dynamics, the elements with two positive/negative feedback loops are the minimalist elements to have chaotic dynamics. These elements typically have one negative feedback loop that generates oscillations, and another unit that allows frequent switches among multiple steady states or between oscillatory and non-oscillatory dynamics. Possible dynamical features of several simple one- and two-gene elements are presented in details. Discussion is presented for possible roles of the chaotic behavior in the robustness of cellular functions and diseases, for example, in the context of cancer.

Modeling of the ComRS Signaling Pathway Reveals the Limiting Factors Controlling Competence in Streptococcus thermophilus

In streptococci, entry in competence is dictated by ComX abundance. In Streptococcus thermophilus, production of ComX is transient and tightly regulated during growth: it is positively regulated by the cell-cell communication system ComRS during the activation phase and negatively regulated during the shut-off phase by unidentified late competence gene(s). Interestingly, most S. thermophilus strains are not or weakly transformable in permissive growth conditions (i.e., chemically defined medium, CDM), suggesting that some players of the ComRS regulatory pathway are limiting. Here, we combined mathematical modeling and experimental approaches to identify the components of the ComRS system which are critical for both dynamics and amplitude of ComX production in S. thermophilus. We built a deterministic, population-scaled model of the time-course regulation of specific ComX production in CDM growth conditions. Strains LMD-9 and LMG18311 were respectively selected as representative of highly and weakly transformable strains. Results from in silico simulations and in vivo luciferase activities show that ComR concentration is the main limiting factor for the level of comX expression and controls the kinetics of spontaneous competence induction in strain LMD-9. In addition, the model predicts that the poor transformability of strain LMG18311 results from a 10-fold lower comR expression level compared to strain LMD-9. In agreement, comR overexpression in both strains was shown to induce higher competence levels with deregulated kinetics patterns during growth. In conclusion, we propose that the level of ComR production is one important factor that could explain competence heterogeneity among S. thermophilus strains.

The relationship between stochastic and deterministic quasi-steady state approximations

Background

The quasi steady-state approximation (QSSA) is frequently used to reduce deterministic models of biochemical networks. The resulting equations provide a simplified description of the network in terms of non-elementary reaction functions (e.g. Hill functions). Such deterministic reductions are frequently a basis for heuristic stochastic models in which non-elementary reaction functions are used to define reaction propensities. Despite their popularity, it remains unclear when such stochastic reductions are valid. It is frequently assumed that the stochastic reduction can be trusted whenever its deterministic counterpart is accurate. However, a number of recent examples show that this is not necessarily the case.

Results

Here we explain the origin of these discrepancies, and demonstrate a clear relationship between the accuracy of the deterministic and the stochastic QSSA for examples widely used in biological systems. With an analysis of a two-state promoter model, and numerical simulations for a variety of other models, we find that the stochastic QSSA is accurate whenever its deterministic counterpart provides an accurate approximation over a range of initial conditions which cover the likely fluctuations from the quasi steady-state (QSS). We conjecture that this relationship provides a simple and computationally inexpensive way to test the accuracy of reduced stochastic models using deterministic simulations.

Conclusions

The stochastic QSSA is one of the most popular multi-scale stochastic simulation methods. While the use of QSSA, and the resulting non-elementary functions has been justified in the deterministic case, it is not clear when their stochastic counterparts are accurate. In this study, we show how the accuracy of the stochastic QSSA can be tested using their deterministic counterparts providing a concrete method to test when non-elementary rate functions can be used in stochastic simulations.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0218-3) contains supplementary material, which is available to authorized users.

A computational model for the coordination of neural progenitor self-renewal and differentiation through Hes1 dynamics

Proper tissue development requires that stem/progenitor cells precisely coordinate cell division and differentiation in space and time. Notch-Hes1 intercellular signaling, which affects both differentiation and cell cycle progression and directs cell fate decisions at various developmental stages in many cell types, is central to this process. This study explored whether the pattern of connections among the cell cycle regulatory module, the Notch effector Hes1 and the proneural factor Ngn2 could explain salient aspects of cell fate determination in neural progenitors. A mathematical model that includes mutual interactions between Hes1, Ngn2 and G1-phase regulators was constructed and simulated at the single- and two-cell levels. By differentially regulating G1-phase progression, Hes1 and Ngn2 are shown to induce two contrasting cell cycle arrest states in early and late G1, respectively. Indeed, steady Hes1 overexpression promotes reversible quiescence by downregulating activators of G0/G1 exit and Ngn2. Ngn2 also downregulates activators of G0/G1 exit, but cooperates with Cip/Kip proteins to prevent G1/S transit, whereby it promotes G1-phase lengthening and, ultimately, contributes to reinforcing an irreversible late G1 arrest coincident with terminal differentiation. In this scheme, Hes1 oscillation in single cells is able to maintain a labile proliferation state in dynamic balance with two competing cell fate outputs associated with Hes1-mediated and Ngn2-mediated cell cycle arrest states. In Delta/Notch-connected cells, Hes1 oscillations and a lateral inhibition mechanism combine to establish heterogeneous Hes1, Ngn2 and cell cycle dynamics between proliferating neural progenitors, thereby increasing the chances of asymmetric cell fate decisions and improving the reliability of commitment to differentiation.

The physics of bacterial decision making

The choice that bacteria make between sporulation and competence when subjected to stress provides a prototypical example of collective cell fate determination that is stochastic on the individual cell level, yet predictable (deterministic) on the population level. This collective decision is performed by an elaborated gene network. Considerable effort has been devoted to simplify its complexity by taking physics approaches to untangle the basic functional modules that are integrated to form the complete network: (1) A stochastic switch whose transition probability is controlled by two order parameters-population density and internal/external stress. (2) An adaptable timer whose clock rate is normalized by the same two previous order parameters. (3) Sensing units which measure population density and external stress. (4) A communication module that exchanges information about the cells' internal stress levels. (5) An oscillating gate of the stochastic switch which is regulated by the timer. The unique circuit architecture of the gate allows special dynamics and noise management features. The gate opens a window of opportunity in time for competence transitions, during which the circuit generates oscillations that are translated into a chain of short intervals with high transition probability. In addition, the unique architecture of the gate allows filtering of external noise and robustness against variations in circuit parameters and internal noise. We illustrate that a physics approach can be very valuable in investigating the decision process and in identifying its general principles. We also show that both cell-cell variability and noise have important functional roles in the collectively controlled individual decisions.

Construction of an effective landscape for multistate genetic switches

Multistate genetic switches play a crucial role during embryonic development and tumorigenesis. An archetypical example is the three-way switch regulating epithelial-hybrid-mesenchymal transitions. We devise a special WKB-based approach to investigate white Gaussian and shot noise effects on three-way switches, and construct an effective landscape in good quantitative agreement with stochastic simulations. This approach allows efficient analytical or numerical calculation of the landscape contours, the optimal path, and the state relative stability for general multicomponent multistate switches.

Reliable binary cell-fate decisions based on oscillations

Biological systems have often to perform binary decisions under highly dynamic and noisy environments, such as during cell-fate determination. These decisions can be implemented by two main bifurcation mechanisms based on the transitions from either monostability or oscillation to bistability. We compare these two mechanisms by using stochastic models with time-varying fields and by establishing asymptotic formulas for the choice probabilities. Different scaling laws for decision sensitivity with respect to noise strength and signal timescale are obtained, supporting a role for oscillatory dynamics in performing noise-robust and temporally tunable binary decision-making. This result provides a rationale for recent experimental evidences showing that oscillatory expression of proteins often precedes binary cell-fate decisions.

Noise in biology

Noise permeates biology on all levels, from the most basic molecular, sub-cellular processes to the dynamics of tissues, organs, organisms and populations. The functional roles of noise in biological processes can vary greatly. Along with standard, entropy-increasing effects of producing random mutations, diversifying phenotypes in isogenic populations, limiting information capacity of signaling relays, it occasionally plays more surprising constructive roles by accelerating the pace of evolution, providing selective advantage in dynamic environments, enhancing intracellular transport of biomolecules and increasing information capacity of signaling pathways. This short review covers the recent progress in understanding mechanisms and effects of fluctuations in biological systems of different scales and the basic approaches to their mathematical modeling.

MicroRNA-based regulation of epithelial-hybrid-mesenchymal fate determination

Forward and backward transitions between epithelial and mesenchymal phenotypes play crucial roles in embryonic development and tissue repair. Aberrantly regulated transitions are also a hallmark of cancer metastasis. The genetic network that regulates these transitions appears to allow for the existence of a hybrid phenotype (epithelial/mesenchymal). Hybrid cells are endowed with mixed epithelial and mesenchymal characteristics, enabling specialized capabilities such as collective cell migration. Cell-fate determination between the three phenotypes is in fact regulated by a circuit composed of two highly interconnected chimeric modules--the miR-34/SNAIL and the miR-200/ZEB mutual-inhibition feedback circuits. Here, we used detailed modeling of microRNA-based regulation to study this core unit. More specifically, we investigated the functions of the two isolated modules and subsequently of the combined unit when the two modules are integrated into the full regulatory circuit. We found that miR-200/ZEB forms a tristable circuit that acts as a ternary switch, driven by miR-34/SNAIL, that is a monostable module that acts as a noise-buffering integrator of internal and external signals. We propose to associate the three stable states--(1,0), (high miR-200)/(low ZEB); (0,1), (low miR-200)/(high ZEB); and (1/2,1/2), (medium miR-200)/(medium ZEB)--with the epithelial, mesenchymal, and hybrid phenotypes, respectively. Our (1/2,1/2) state hypothesis is consistent with recent experimental studies (e.g., ZEB expression measurements in collectively migrating cells) and explains the lack of observed mesenchymal-to-hybrid transitions in metastatic cells and in induced pluripotent stem cells. Testable predictions of dynamic gene expression during complete and partial transitions are presented.