How robust are switches in intracellular signaling cascades?

Since all-or-none decisions of the cell are controlled by extracellular signals, cells have biochemical switches within their intracellular signaling networks. Central elements of these switches are multisite phosphorylation, enzymic saturation, and amplification by cascades. Moreover, positive feedback can contribute to switch-like behavior termed also ultrasensitivity. Here we analyse the robustness of these mechanisms exemplified by models of the three-molecule MAPK-cascade and the single-molecule Goldbeter-Koshland switch. We show that the ultrasensitivity in the MAPK-cascades is more robust against changes of the kinetic parameters than the Goldbeter-Koshland switch. If multiple parameters are changed randomly, the effects of parameter changes can compensate each other in the cascade leading to a remarkable robustness of the switch-like behavior. The different degrees of robustness can be traced back to the different mechanisms of generating ultrasensitivity. While in the Goldbeter-Koshland switch the saturation of the enzymes are crucial, in the MAPK-cascade the adjustment of working ranges determines the ultrasensitivity. Our results indicate that amplification of ultrasensitivity in cascades and multisite phosphorylation might be a design principle to achieve robust switches.     

On the distribution of the general irreversiblen-compartmental model having time-dependent transition probabilities

The cumulant generating function and first two moments are derived for the stochastic distribution of units in a general irreversiblen-compartment model with time-dependent transition probabilities. In this model, a unit in the first compartment can transfer to any one of the remainingn−1 compartments and a unit in the second compartment can transfer to any of the remainingn−2 compartments and so on. In addition, a unit can enter or leave the system through any compartment. The work is related to previous research and a numerical example is given.     

A computational method for the investigation of multistable systems and its application to genetic switches

Background

Genetic switches exhibit multistability, form the basis of epigenetic memory, and are found in natural decision making systems, such as cell fate determination in developmental pathways. Synthetic genetic switches can be used for recording the presence of different environmental signals, for changing phenotype using synthetic inputs and as building blocks for higher-level sequential logic circuits. Understanding how multistable switches can be constructed and how they function within larger biological systems is therefore key to synthetic biology.

Results

Here we present a new computational tool, called StabilityFinder, that takes advantage of sequential Monte Carlo methods to identify regions of parameter space capable of producing multistable behaviour, while handling uncertainty in biochemical rate constants and initial conditions. The algorithm works by clustering trajectories in phase space, and iteratively minimizing a distance metric. Here we examine a collection of models of genetic switches, ranging from the deterministic Gardner toggle switch to stochastic models containing different positive feedback connections. We uncover the design principles behind making bistable, tristable and quadristable switches, and find that rate of gene expression is a key parameter. We demonstrate the ability of the framework to examine more complex systems and examine the design principles of a three gene switch. Our framework allows us to relax the assumptions that are often used in genetic switch models and we show that more complex abstractions are still capable of multistable behaviour.

Conclusions

Our results suggest many ways in which genetic switches can be enhanced and offer designs for the construction of novel switches. Our analysis also highlights subtle changes in correlation of experimentally tunable parameters that can lead to bifurcations in deterministic and stochastic systems. Overall we demonstrate that StabilityFinder will be a valuable tool in the future design and construction of novel gene networks.

     

Motor pattern switching in the heartbeat pattern generator of the medicinal leech: membrane properties and lack of synaptic interaction in switch interneurons

The motor program for heartbeat in the medicinal leech is produced by a central pattern generator that regularly switches between two alternative coordination states. A pair of switch heart interneurons reciprocally alternate between rhythmically active and inactive states to effect these switches. During spontaneous switches in the activity state of switch interneurons, there was no correlation between the duration of a particular activity state and beat period, indicating that the timing networks for the switch cycle and the beat cycle are relatively independent. Simultaneous recordings from two switch heart interneurons showed that a perturbation in the electrical activity of one does not influence switching of the other and that there is no synaptic interaction between them. Using voltage clamp, we characterized an L-like Ca²⁺ current (measured as Ba²⁺ currents), inactivating and non-inactivating K⁺ currents, a persistent Na⁺ current, and a hyperpolarization-activated inward current in switch interneurons. Dynamic clamp experiments show that “subtraction” of an artificial switch leak conductance (described previously by Gramoll et al. 1994) from a switch interneuron when it is in the inactive state causes it to display activity associated with the active state. We discuss how the switch leak conductance may interact with the intrinsic currents of switch interneurons to control their activity state. Accepted: 1 December 1998     

Designing redox potential-controlled protein switches based on mutually exclusive proteins

Synthetic/artificial protein switches provide an efficient means of controlling protein functions using chemical signals and stimuli. Mutually exclusive proteins, in which only the host or guest domain can remain folded at a given time owing to conformational strain, have been used to engineer novel protein switches that can switch enzymatic functions on and off in response to ligand binding. To further explore the potential of mutually exclusive proteins as protein switches and sensors, we report here a new redox-based approach to engineer a mutually exclusive folding-based protein switch. By introducing a disulfide bond into the host domain of a mutually exclusive protein, we demonstrate that it is feasible to use redox potential to switch the host domain between its folded and unfolded conformations via the mutually exclusive folding mechanism, and thus switching the functionality of the host domain on and off. Our study opens a new and potentially general avenue that uses mutually exclusive proteins to design novel switches able to control the function of a variety of proteins.     

Does Dormancy Increase Fitness of Bacterial Populations in Time-Varying Environments?

A simple family of models of a bacterial population in a time varying environment in which cells can transit between dormant and active states is constructed. It consists of a linear system of ordinary differential equations for active and dormant cells with time-dependent coefficients reflecting an environment which may be periodic or random, with alternate periods of low and high resource levels. The focus is on computing/estimating the dominant Lyapunov exponent, the fitness, and determining its dependence on various parameters and the two strategies—responsive and stochastic—by which organisms switch between dormant and active states. A responsive switcher responds to good and bad times by making timely and appropriate transitions while a stochastic switcher switches continuously without regard to the environmental state. The fitness of a responsive switcher is examined and compared with fitness of a stochastic switcher, and with the fitness of a dormancy-incapable organism. Analytical methods show that both switching strategists have higher fitness than a dormancy-incapable organism when good times are rare and that responsive switcher has higher fitness than stochastic switcher when good times are either rare or common. Numerical calculations show that stochastic switcher can be most fit when good times are neither too rare or too common. This research was supported by NSF Grant DMS 0414270, Department of Mathematics, Arizona State University, Tempe, AZ.     

Outlook for the use of microsecond plasma opening switches to generate high-power nanosecond current pulses

An analysis is made of the current break process in microsecond plasma opening switches and their possible application in high-current generators. Necessary conditions are determined for generating megavolt pulses in the erosion mode of a plasma opening switch with the gap insulated by an external magnetic field. Under these conditions, efficient sharpening of high-power submegampere current pulses can be achieved. The possibility of using plasma opening switches operating at voltages of 5–6 MV to generate X-ray and gamma emission is discussed. The main operating and design parameters of a six-module plasma opening switch with a current pulse amplitude of 3.7 MA and voltage of 4–6 MV for use in the MOL generator, which is the prototype of one of the 24 modules of the projected Baikal multimegajoule generator, are estimated by using the available scalings.     

Self-consistent proteomic field theory of stochastic gene switches

We present a self-consistent field approximation approach to the problem of the genetic switch composed of two mutually repressing/activating genes. The protein and DNA state dynamics are treated stochastically and on an equal footing. In this approach the mean influence of the proteomic cloud created by one gene on the action of another is self-consistently computed. Within this approximation a broad range of stochastic genetic switches may be solved exactly in terms of finding the probability distribution and its moments. A much larger class of problems, such as genetic networks and cascades, also remain exactly solvable with this approximation. We discuss, in depth, certain specific types of basic switches used by biological systems and compare their behavior to the expectation for a deterministic switch.     

Modeling genetic switches with positive feedback loops

In this paper, we develop a new methodology to design synthetic genetic switch networks with multiple genes and time delays, by using monotone dynamical systems. We show that the networks with only positive feedback loops have no stable oscillation but stable equilibria whose stability is independent of the time delays. In other words, such systems have ideal properties for switch networks and can be designed without consideration of time delays, because the systems can be reduced from functional spaces to Euclidian spaces. Therefore, we can ensure that the designed switches function correctly even with uncertain delays. We first prove the basic properties of the genetic networks composed of only positive feedback loops, and then propose a procedure to design the switches, which drastically simplifies analysis of the switches and makes theoretical analysis and design tractable even for large-scaled systems. Finally, to demonstrate our theoretical results, we show biologically plausible examples by designing a synthetic genetic switch with experimentally well investigated lacI, tetR, and cI genes for numerical simulation.     

Stochasticity,spikes and decoding: sufficiency and utility of order statistics

For over 75 years it has been clear that the number of spikes in a neural response is an important part of the neuronal code. Starting as early as the 1950’s with MacKay and McCullough, there has been speculation over whether each spike and its exact time of occurrence carry information. Although it is obvious that the firing rate carries information it has been less clear as to whether there is information in exactly timed patterns, when they arise from the dynamics of the neurons and networks, as opposed to when they represent some strong external drive that entrains them. One strong null hypothesis that can be applied is that spike trains arise from stochastic sampling of an underlying deterministic temporally modulated rate function, that is, there is a time-varying rate function. In this view, order statistics seem to provide a sufficient theoretical construct to both generate simulated spike trains that are indistinguishable from those observed experimentally, and to evaluate (decode) the data recovered from experiments. It remains to learn whether there are physiologically important signals that are not described by such a null hypothesis. This article is part of a special issue on Neuronal Dynamics of Sensory Coding.     

The TACE zymogen

The tumor necrosis factor-α-converting enzyme (TACE) is a member of the disintegrin family of metallopro-teinases (ADAMs) that plays a central role in the regulated shedding of a host of cell surface proteins. TACE is biosynthesized as a precursor protein with latent proteolytic activity (zymogen). TACE’s zymogen inhibition is mediated by its Pro domain, a 197-amino acid region that serves this function as well as aiding in the secretion of this enzyme through the secretory pathway. We have discovered that a conserved “cysteine switch” consensus motif within TACE’s Pro domain is, contrary to expectations, not required for maintenance of the inactive precursor state or for the secretion of this metalloproteinase in its functional form. The only role for this motif seems to be in decreasing TACE’s susceptibility to proteolytic degradation during its biogenesis and maturation within the secretory pathway. Interestingly, the Pro domain of TACE seems to carry both its inhibitory and secretory functions through the same mechanism: it seems to prevent the Catalytic domain from accessing its native, functional state, resembling the function of true molecular chaperones. Recent evidence suggests that TACE may also be switched out of the active conformation even by small, drug-like molecules such as the synthetic compound SB-3CT. These findings point at the possibility of developing, in the near future, a new generation of anti-inflammatory, noncompetitive TACE inhibitors that would exert negative allosteric modulation over the activity of this key enzyme, mediating several inflammatory diseases and certain cancers.     

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.     

About a possible role of parasomnias as a factor of stabilization of sleep cycles

Cyclical organization of sleep is one of necessary conditions of normal human and animal life activity and one of basic manifestations of the circadian cycle. Transition from the slowwave to the paradoxical sleep is often accompanied by brief, sometimes rhythmical motor and autonomic reactions that do not cause awakening, but seem to promote activation of the mechanisms providing the “switch” of the sleep phases. Immaturity (or a lesion) of the neurophysiologic mechanisms responsible for the “switch” of the sleep stages leads to hindering of alternation of the sleep phases, which disturbs their normal sequence and leads to deficit of reparative and homeostatic processes. This is manifested as deterioration of the neuropsychical state during wakefulness. The data are presented which allow suggesting that the stereotypical motor or autonomic reactionspathological parasomnias, for instance enuresis, can appear as a compensatory mechanism promoting the sleep phase switch. Episodes of the pathological parasomnias promote normalization of the sleep stage alternation and thereby affect positively recovery of its cyclical organization.     

Effects of immigration on some stochastic logistic models: a cumulant truncation analysis.

This paper uses a new cumulant truncation methodology to investigate the stochastic power law logistic model with immigration, and illustrates the model with parameter values used to describe the growth of muskrat populations in the Netherlands. This model has a stable equilibrium distribution. The incorporation of immigration into the model, therefore, simplifies the qualitative nature of the stochastic solution. The (unconditional) cumulant functions for the transient and the equilibrium population size distributions are obtained, from which the distributions are shown to be near-normal at all times for the parameter values of interest. Approximating cumulant functions, which are relatively easy to find in practice, are derived and shown to be quite accurate, except for the case of massive immigration. As the level of immigration increases, the mean value rises more rapidly initially, as expected; however, the variance and the skewness of both the transient and the equilibrium distributions are reduced.     

Effects of six-day maternal separation on tonkean macaque infants

Maternal separation may induce a depressive state in infant macaques. However, this does not occur in all macaque species. From present hypotheses, it may be predicted that infants belonging to a species characterized by open and tolerant social relationships should not develop severe depressive symptoms. Tonkean macaques (Macaca tonkeana) stand as such a species. The goal of the study was to verify that the infant’s reaction to mother loss is related to the social environment. The mothers of eight 5- to 9-month-old infants were removed during 6-day experimental periods. Infants’ behavior was characterized by a mild initial protest stage, followed by a slight decrease in activity during later maternal separation, and quick recovery after the mother’s return. No despair stage occurred. During separation, group members compensated for mother’s absence by cradling the infants. That social networks determine the intensity of the infant’s response to separation has far-reaching implications with regard to the meaning of depression occurrence within social networks.     

Evolving cell models for systems and synthetic biology

This paper proposes a new methodology for the automated design of cell models for systems and synthetic biology. Our modelling framework is based on P systems, a discrete, stochastic and modular formal modelling language. The automated design of biological models comprising the optimization of the model structure and its stochastic kinetic constants is performed using an evolutionary algorithm. The evolutionary algorithm evolves model structures by combining different modules taken from a predefined module library and then it fine-tunes the associated stochastic kinetic constants. We investigate four alternative objective functions for the fitness calculation within the evolutionary algorithm: (1) equally weighted sum method, (2) normalization method, (3) randomly weighted sum method, and (4) equally weighted product method. The effectiveness of the methodology is tested on four case studies of increasing complexity including negative and positive autoregulation as well as two gene networks implementing a pulse generator and a bandwidth detector. We provide a systematic analysis of the evolutionary algorithm’s results as well as of the resulting evolved cell models.