Noise-induced switches in network systems of the genetic toggle switch

Background  

Bistability, the capacity to achieve two distinct stable steady states in response to a set of external stimuli, arises within biological systems ranging from the λ phage switch in bacteria to cellular signal transduction pathways in mammalian cells. On the other hand, more and more experimental evidence in the form of bimodal population distribution has indicated that noise plays a very important role in the switching of bistable systems. However, the physiological mechanism underling noise-induced switching behaviors remains to be fully understood.     

Dynamic bistable switches enhance robustness and accuracy of cell cycle transitions

Bistability is a common mechanism to ensure robust and irreversible cell cycle transitions. Whenever biological parameters or external conditions change such that a threshold is crossed, the system abruptly switches between different cell cycle states. Experimental studies have uncovered mechanisms that can make the shape of the bistable response curve change dynamically in time. Here, we show how such a dynamically changing bistable switch can provide a cell with better control over the timing of cell cycle transitions. Moreover, cell cycle oscillations built on bistable switches are more robust when the bistability is modulated in time. Our results are not specific to cell cycle models and may apply to other bistable systems in which the bistable response curve is time-dependent.     

Stochastic switching induced adaptation in a starved Escherichia coli population

Population adaptation can be determined by stochastic switching in living cells. To examine how stochastic switching contributes to the fate decision for a population under severe stress, we constructed an Escherichia coli strain crucially dependent on the expression of a rewired gene. The gene essential for tryptophan biosynthesis, trpC, was removed from the native regulatory unit, the Trp operon, and placed under the extraneous control of the lactose utilisation network. Bistability of the network provided the cells two discrete phenotypes: the induced and suppressed level of trpC. The two phenotypes permitted the cells to grow or not, respectively, under conditions of tryptophan depletion. We found that stochastic switching between the two states allowed the initially suppressed cells to form a new population with induced trpC in response to tryptophan starvation. However, the frequency of the transition from suppressed to induced state dropped off dramatically in the starved population, in comparison to that in the nourished population. This reduced switching rate was compensated by increasing the initial population size, which probably provided the cell population more chances to wait for the rarely appearing fit cells from the unfit cells. Taken together, adaptation of a starved bacterial population because of stochasticity in the gene rewired from the ancient regulon was experimentally confirmed, and the nutritional status and the population size played a great role in stochastic adaptation.     

Stochasticity,Bistability and the Wisdom of Crowds: A Model for Associative Learning in Genetic Regulatory Networks

It is generally believed that associative memory in the brain depends on multistable synaptic dynamics, which enable the synapses to maintain their value for extended periods of time. However, multistable dynamics are not restricted to synapses. In particular, the dynamics of some genetic regulatory networks are multistable, raising the possibility that even single cells, in the absence of a nervous system, are capable of learning associations. Here we study a standard genetic regulatory network model with bistable elements and stochastic dynamics. We demonstrate that such a genetic regulatory network model is capable of learning multiple, general, overlapping associations. The capacity of the network, defined as the number of associations that can be simultaneously stored and retrieved, is proportional to the square root of the number of bistable elements in the genetic regulatory network. Moreover, we compute the capacity of a clonal population of cells, such as in a colony of bacteria or a tissue, to store associations. We show that even if the cells do not interact, the capacity of the population to store associations substantially exceeds that of a single cell and is proportional to the number of bistable elements. Thus, we show that even single cells are endowed with the computational power to learn associations, a power that is substantially enhanced when these cells form a population.     

Bistable MAP kinase activity: a plausible mechanism contributing to maintenance of late long-term potentiation

Bistability of MAP kinase (MAPK) activity has been suggested to contribute to several cellular processes, including differentiation and long-term synaptic potentiation. A recent model (Markevich NI, Hoek JB, Kholodenko BN. J Cell Biol 164: 353–359, 2004) predicts bistability due to interactions of the kinases and phosphatases in the MAPK pathway, without feedback from MAPK to earlier reactions. Using this model and enzyme concentrations appropriate for neurons, we simulated bistable MAPK activity, but bistability was present only within a relatively narrow range of activity of Raf, the first pathway kinase. Stochastic fluctuations in molecule numbers eliminated bistability for small molecule numbers, such as are expected in the volume of a dendritic spine. However, positive-feedback loops have been posited from MAPK up to Raf activation. One proposed loop in which MAPK directly activates Raf was incorporated into the model. We found that such feedback greatly enhanced the robustness of both stable states of MAPK activity to stochastic fluctuations and to parameter variations. Bistability was robust for molecule numbers plausible for a dendritic spine volume. The upper state of MAPK activity was resistant to inhibition of MEK activation for >1 h, which suggests that inhibitor experiments have not sufficed to rule out a role for persistent MAPK activity in the maintenance of long-term potentiation (LTP). These simulations suggest that persistent MAPK activity and consequent upregulation of translation may contribute to LTP maintenance and to long-term memory. Experiments using a fluorescent MAPK substrate may further test this hypothesis. feedback; bistability; memory; model; stochastic     

Bistability in feedback circuits as a byproduct of evolution of evolvability

Noisy bistable dynamics in gene regulation can underlie stochastic switching and is demonstrated to be beneficial under fluctuating environments. It is not known, however, if fluctuating selection alone can result in bistable dynamics. Using a stochastic model of simple feedback networks, we apply fluctuating selection on gene expression and run in silico evolutionary simulations. We find that independent of the specific nature of the environment–fitness relationship, the main outcome of fluctuating selection is the evolution of increased evolvability in the network; system parameters evolve toward a nonlinear regime where phenotypic diversity is increased and small changes in genotype cause large changes in expression level. In the presence of noise, the evolution of increased nonlinearity results in the emergence and maintenance of bistability. Our results provide the first direct evidence that bistability and stochastic switching in a gene regulatory network can emerge as a mechanism to cope with fluctuating environments. They strongly suggest that such emergence occurs as a byproduct of evolution of evolvability and exploitation of noise by evolution.     

Bistability and hysteresis of the 'Secteur' differentiation are controlled by a two-gene locus in <Emphasis Type="Italic">Nectria haematococca</Emphasis>

Background  

Bistability and hysteresis are increasingly recognized as major properties of regulatory networks governing numerous biological phenomena, such as differentiation and cell cycle progression. The full scope of the underlying molecular mechanisms leading to bistability and hysteresis remains elusive. Nectria haemaotcocca, a saprophytic or pathogenic fungus with sexual reproduction, exhibits a bistable morphological modification characterized by a reduced growth rate and an intense pigmentation. Bistability is triggered by the presence or absence of σ, a cytoplasmic determinant. This determinant spreads in an infectious manner in the hyphae of the growing margin, insuring hysteresis of the differentiation.     

Bistability explains threshold phenomena in protein aggregation both in vitro and in vivo

Neurodegenerative disease can originate from the misfolding and aggregation of proteins, such as Amyloid-beta, SOD1, or Huntingtin. Fortunately, all cells possess protein quality control machinery that sequesters misfolded proteins, either refolding or degrading them, before they can self-associate into proteotoxic oligomers and aggregates. This activity is largely performed by the stress response chaperones (i.e., Hsp70). However, the expression level of molecular chaperones varies widely among cell types. To understand the potential consequence of this variation, we studied the process of protein aggregation in the presence of molecular chaperones using mathematical modeling. We demonstrate that protein aggregation, in the presence of molecular chaperones, is a bistable process. Bistability in protein aggregation offers an explanation for threshold transitions to high aggregate concentration, which are observed both in vitro and in vivo. Additionally, we show that slight variations in chaperone concentration, due to natural fluctuations, have important consequences in a bistable system for the onset of protein aggregation. Therefore, our results offer a possible theoretical explanation for neuronal vulnerability observed in vivo and the onset of neurodegenerative phenotypes in neurons lacking an effective heat-shock response.     

Positive-feedback loops as a flexible biological module

BACKGROUND: Bistability in genetic networks allows cells to remember past events and to make discrete decisions in response to graded signals. Bistable behavior can result from positive feedback, but feedback loops can have other roles in signal transduction as well. RESULTS: We introduced positive feedback into the budding-yeast pheromone response to convert it into a bistable system. In the presence of feedback, transient induction with high pheromone levels caused persistent pathway activation, whereas at lower levels a fraction of cells became persistently active but the rest inactivated completely. We also generated mutations that quantitatively tuned the basal and induced expression levels of the feedback promoter and showed that they qualitatively changed the behavior of the system. Finally, we developed a simple stochastic model of our positive-feedback system and showed the agreement between our simulations and experimental results. CONCLUSIONS: The positive-feedback loop can display several different behaviors, including bistability, and can switch between them as a result of simple mutations.     

Bistability in the JNK cascade

BACKGROUND: Important signaling properties, like adaptation, oscillations, and bistability, can emerge at the level of relatively simple systems of signaling proteins. Here, we have examined the quantitative properties of one well-studied signaling system, the JNK cascade. We experimentally assessed the response of JNK to a physiological stimulus (progesterone) and a pathological stress (hyperosmolar sorbitol) in Xenopus laevis oocytes, a cell type that is well-suited to the quantitative analysis of cell signaling. Our aim was to determine whether JNK responses are graded (Michaelian) in character; ultrasensitive in character, resembling the responses of cooperative enzymes; or bistable and all-or-none in character. RESULTS: The responses of JNK to both progesterone and sorbitol were found to be essentially all-or-none. Individual oocytes had either very high or very low JNK activities, with few oocytes possessing intermediate levels of JNK activity. Moreover, JNK activation was autocatalytic, indicating that the JNK cascade is either embedded in or downstream of a positive feedback loop. JNK also exhibited hysteresis, a form of biochemical memory, in its response to sorbitol. These findings indicate that the JNK cascade is part of a bistable signaling system in oocytes. CONCLUSIONS: In Xenopus oocytes, JNK responds to physiological and pathological stimuli in an all-or-none manner. The JNK response shows all the hallmarks of a bistable response, including strong positive feedback and hysteresis. Bistability is a recurring theme in the biochemistry of oocyte maturation and early embryogenesis; the Mos/MEK/p42 MAPK cascade also exhibits bistable responses, and the Cdc2/cyclin B system is hypothesized to be bistable as well. However, the mechanisms underpinning the positive feedback and bistability in the three cases are different, suggesting that evolution has repeatedly converged upon bistability as a way of producing digital responses.     

Linear Population Allocation by Bistable Switches in Response to Transient Stimulation

Many cellular decision processes, including proliferation, differentiation, and phenotypic switching, are controlled by bistable signaling networks. In response to transient or intermediate input signals, these networks allocate a population fraction to each of two distinct states (e.g. OFF and ON). While extensive studies have been carried out to analyze various bistable networks, they are primarily focused on responses of bistable networks to sustained input signals. In this work, we investigate the response characteristics of bistable networks to transient signals, using both theoretical analysis and numerical simulation. We find that bistable systems exhibit a common property: for input signals with short durations, the fraction of switching cells increases linearly with the signal duration, allowing the population to integrate transient signals to tune its response. We propose that this allocation algorithm can be an optimal response strategy for certain cellular decisions in which excessive switching results in lower population fitness.