Ultrasensitivity in the mitogen-activated protein kinase cascade.

The mitogen-activated protein kinase (MAPK) cascade is a highly conserved series of three protein kinases implicated in diverse biological processes. Here we demonstrate that the cascade arrangement has unexpected consequences for the dynamics of MAPK signaling. We solved the rate equations for the cascade numerically and found that MAPK is predicted to behave like a highly cooperative enzyme, even though it was not assumed that any of the enzymes in the cascade were regulated cooperatively. Measurements of MAPK activation in Xenopus oocyte extracts confirmed this prediction. The stimulus/response curve of the MAPK was found to be as steep as that of a cooperative enzyme with a Hill coefficient of 4-5, well in excess of that of the classical allosteric protein hemoglobin. The shape of the MAPK stimulus/ response curve may make the cascade particularly appropriate for mediating processes like mitogenesis, cell fate induction, and oocyte maturation, where a cell switches from one discrete state to another.

Mathematical modeling of the cancer cell’s control circuitry : paving the way to individualized therapeutic strategies

Cancer is a disease of signal transduction in which the dysregulation of the network of intracellular and extracellular signaling cascades is sufficient to thwart the cells finely-tuned biochemical control mechanisms. A keen interest in the mathematical modeling of cell signaling networks and the regulation of signal transduction has emerged in recent years, and has produced a glimmer of insight into the sophisticated feedback control and network regulation operating within cells. In this review, we present an overview of published theoretical studies on the control aspects of signal transduction, emphasizing the role and importance of mechanisms such as ‘ultrasensitivity’ and feedback loops. We emphasize that these exquisite and often subtle control strategies represent the key to orchestrating ‘simple’ signaling behaviors within the complex intracellular network, while regulating the trade-off between sensitivity and robustness to internal and external perturbations. Through a consideration of these apparent paradoxes, we explore how the basic homeostasis of the intracellular signaling network, in the face of carcinogenesis, can lead to neoplastic progression rather than cell death. A simple mathematical model is presented, furnishing a vivid illustration of how ‘control-oriented’ models of the deranged signaling networks in cancer cells may enucleate improved treatment strategies, including patient-tailored combination therapies, with the potential for reduced toxicity and more robust and potent antitumor activity.

Conformational Spread in the Flagellar Motor Switch: A Model Study

The reliable response to weak biological signals requires that they be amplified with fidelity. In E. coli, the flagellar motors that control swimming can switch direction in response to very small changes in the concentration of the signaling protein CheY-P, but how this works is not well understood. A recently proposed allosteric model based on cooperative conformational spread in a ring of identical protomers seems promising as it is able to qualitatively reproduce switching, locked state behavior and Hill coefficient values measured for the rotary motor. In this paper we undertook a comprehensive simulation study to analyze the behavior of this model in detail and made predictions on three experimentally observable quantities: switch time distribution, locked state interval distribution, Hill coefficient of the switch response. We parameterized the model using experimental measurements, finding excellent agreement with published data on motor behavior. Analysis of the simulated switching dynamics revealed a mechanism for chemotactic ultrasensitivity, in which cooperativity is indispensable for realizing both coherent switching and effective amplification. These results showed how cells can combine elements of analog and digital control to produce switches that are simultaneously sensitive and reliable. © 2012 Ma et al.

Robustness and dissipation of mitogen-activated protein kinases signal transduction network: Underlying funneled landscape against stochastic fluctuations

We uncovered the underlying energy landscape of the mitogen-activated protein kinases signal transduction cellular network by exploring the statistical natures of the Brownian dynamical trajectories. We introduce a dimensionless quantity: The robustness ratio of energy gap versus local roughness to measure the global topography of the underlying landscape. A high robustness ratio implies funneled landscape. The landscape is quite robust against environmental fluctuations and variants of the intrinsic chemical reaction rates.

Single molecule dynamics and statistical fluctuations of gene regulatory networks: A repressilator

The authors developed a time dependent method to study the single molecule dynamics of a simple gene regulatory network: a repressilator with three genes mutually repressing each other. They quantitatively characterize the time evolution dynamics of the repressilator. Furthermore, they study purely dynamical issues such as statistical fluctuations and noise evolution. They illustrated some important features of the biological network such as monostability, spirals, and limit cycle oscillation. Explicit time dependent Fano factors which describe noise evolution and show statistical fluctuations out of equilibrium can be significant and far from the Poisson distribution. They explore the phase space and the interrelationships among fluctuations, order, amplitude, and period of oscillations of the repressilators. The authors found that repressilators follow ordered limit cycle orbits and are more likely to appear in the lower fluctuating regions. The amplitude of the repressilators increases as the suppressing of the genes decreases and production of proteins increases. The oscillation period of the repressilators decreases as the suppressing of the genes decreases and production of proteins increases.

Potential energy landscape and robustness of a gene regulatory network: Toggle switch

Finding a multidimensional potential landscape is the key for addressing important global issues, such as the robustness of cellular networks. We have uncovered the underlying potential energy landscape of a simple gene regulatory network: a toggle switch. This was realized by explicitly constructing the steady state probability of the gene switch in the protein concentration space in the presence of the intrinsic statistical fluctuations due to the small number of proteins in the cell. We explored the global phase space for the system. We found that the protein synthesis rate and the unbinding rate of proteins to the gene were small relative to the protein degradation rate; the gene switch is monostable with only one stable basin of attraction. When both the protein synthesis rate and the unbinding rate of proteins to the gene are large compared with the protein degradation rate, two global basins of attraction emerge for a toggle switch. These basins correspond to the biologically stable functional states. The potential energy barrier between the two basins determines the time scale of conversion from one to the other. We found as the protein synthesis rate and protein unbinding rate to the gene relative to the protein degradation rate became larger, the potential energy barrier became larger. This also corresponded to systems with less noise or the fluctuations on the protein numbers.

Dynamics and intrinsic statistical fluctuations of a gene switch

We studied a simple gene regulatory network, the toggle switch. Specifically, we examined the means and statistical fluctuations in numbers of proteins. We found that when omega, the ratio of rates of protein-gene unbinding to protein degradation, was between similar to 10(-3) and similar to 10, the fluctuations were much larger than those we would have expected from Poisson statistics. In addition, we examined characteristic time values for system relaxation and found both that they increased with omega and that they have significant phase transition effects, with a secondary time scale appearing near the boundary between bistable and other phases. Last, we discuss the bistability of the toggle switch.

Quantifying robustness and dissipation cost of yeast cell cycle network: The funneled energy landscape perspectives

We study the origin of robustness of yeast cell cycle cellular network through uncovering its underlying energy landscape. This is realized from the information of the steady-state probabilities by solving a discrete set of kinetic master equations for the network. We discovered that the potential landscape of yeast cell cycle network is funneled toward the global minimum, G1 state. The ratio of the energy gap between G1 and average versus roughness of the landscape termed as robustness ratio ( RR) becomes a quantitative measure of the robustness and stability for the network. The funneled landscape is quite robust against random perturbations from the inherent wiring or connections of the network. There exists a global phase transition between the more sensitive response or less self-degradation phase leading to underlying funneled global landscape with large RR, and insensitive response or more self-degradation phase leading to shallower underlying landscape of the network with small RR. Furthermore, we show that the more robust landscape also leads to less dissipation cost of the network. Least dissipation and robust landscape might be a realization of Darwinian principle of natural selection at cellular network level. It may provide an optimal criterion for network wiring connections and design.

Funneled landscape leads to robustness of cellular networks: MAPK signal transduction

We uncover the underlying potential energy landscape for a cellular network. We find that the potential energy landscape of the mitogen-activated protein-kinase signal transduction network is funneled toward the global minimum. The funneled landscape is quite robust against random perturbations. This naturally explains robustness from a physical point of view. The ratio of slope versus roughness of the landscape becomes a quantitative measure of robustness of the network. Funneled landscape is a realization of the Darwinian principle of natural selection at the cellular network level. It provides an optimal criterion for network connections and design. Our approach is general and can be applied to other cellular networks.

Role of DNA binding sites and slow unbinding kinetics in titration-based oscillators.

Genetic oscillators, such as circadian clocks, are constantly perturbed by molecular noise arising from the small number of molecules involved in gene regulation. One of the strongest sources of stochasticity is the binary noise that arises from the binding of a regulatory protein to a promoter in the chromosomal DNA. In this study, we focus on two minimal oscillators based on activator titration and repressor titration to understand the key parameters that are important for oscillations and for overcoming binary noise. We show that the rate of unbinding from the DNA, despite traditionally being considered a fast parameter, needs to be slow to broaden the space of oscillatory solutions. The addition of multiple, independent DNA binding sites further expands the oscillatory parameter space for the repressor-titration oscillator and lengthens the period of both oscillators. This effect is a combination of increased effective delay of the unbinding kinetics due to multiple binding sites and increased promoter ultrasensitivity that is specific for repression. We then use stochastic simulation to show that multiple binding sites increase the coherence of oscillations by mitigating the binary noise. Slow values of DNA unbinding rate are also effective in alleviating molecular noise due to the increased distance from the bifurcation point. Our work demonstrates how the number of DNA binding sites and slow unbinding kinetics, which are often omitted in biophysical models of gene circuits, can have a significant impact on the temporal and stochastic dynamics of genetic oscillators.

Molecular mechanisms for a switch-like mating decision in Saccharomyces cerevisiae

Les changements évolutifs nous instruisent sur les nombreuses innovations permettant à chaque organisme de maximiser ses aptitudes en choisissant le partenaire approprié, telles que les caractéristiques sexuelles secondaires, les patrons comportementaux, les attractifs chimiques et les mécanismes sensoriels y répondant. L'haploïde de la levure Saccharomyces cerevisiae distingue son partenaire en interprétant le gradient de la concentration d'une phéromone sécrétée par les partenaires potentiels grâce à un réseau de protéines signalétiques de type kinase activées par la mitose (MAPK). La décision de la liaison sexuelle chez la levure est un événement en "tout–ourien", à la manière d'un interrupteur. Les cellules haploïdes choisissent leur partenaire sexuel en fonction de la concentration de phéromones qu’il produit. Seul le partenaire à proximité sécrétant des concentrations de phéromones égales ou supérieures à une concentration critique est retenu. Les faibles signaux de phéromones sont attribués à des partenaires pouvant mener à des accouplements infructueux. Notre compréhension du mécanisme moléculaire contrôlant cet interrupteur de la décision d'accouplement reste encore mince. Dans le cadre de la présente thèse, je démontre que le mécanisme de décision de la liaison sexuelle provient de la compétition pour le contrôle de l'état de phosphorylation de quatre sites sur la protéine d'échafaudage Ste5, entre la MAPK, Fus3, et la phosphatase,Ptc1. Cette compétition résulte en la dissociation de type « intérupteur » entre Fus3 et Ste5, nécessaire à la prise de décision d'accouplement en "tout-ou-rien". Ainsi, la décision de la liaison sexuelle s'effectue à une étape précoce de la voie de réponse aux phéromones et se produit rapidement, peut-être dans le but de prévenir la perte d’un partenaire potentiel. Nous argumentons que l'architecture du circuit Fus3-Ste5-Ptc1 génère un mécanisme inédit d'ultrasensibilité, ressemblant à "l'ultrasensibilité d'ordre zéro", qui résiste aux variations de concentration de ces protéines. Cette robustesse assure que l'accouplement puisse se produire en dépit de la stochasticité cellulaire ou de variations génétiques entre individus.Je démontre, par la suite, qu'un évènement précoce en réponse aux signaux extracellulaires recrutant Ste5 à la membrane plasmique est également ultrasensible à l'augmentation de la concentration de phéromones et que cette ultrasensibilité est engendrée par la déphosphorylation de huit phosphosites en N-terminal sur Ste5 par la phosphatase Ptc1 lorsqu'elle est associée à Ste5 via la protéine polarisante, Bem1. L'interférence dans ce mécanisme provoque une perte de l'ultrasensibilité et réduit, du même coup, l'amplitude et la fidélité de la voie de réponse aux phéromones à la stimulation. Ces changements se reflètent en une réduction de la fidélité et de la précision de la morphologie attribuable à la réponse d'accouplement. La polarisation dans l'assemblage du complexe protéique à la surface de la membrane plasmique est un thème général persistant dans tous les organismes, de la bactérie à l'humain. Un tel complexe est en mesure d'accroître l'efficacité, la fidélité et la spécificité de la transmission du signal. L'ensemble de nos découvertes démontre que l'ultrasensibilité, la précision et la robustesse de la réponse aux phéromones découlent de la régulation de la phosphorylation stoichiométrique de deux groupes de phosphosites sur Ste5, par la phosphatase Ptc1, un groupe effectuant le recrutement ultrasensible de Ste5 à la membrane et un autre incitant la dissociation et l'activation ultrasensible de la MAPK terminal Fus3. Le rôle modulateur de Ste5 dans la décision de la destinée cellulaire étend le répertoire fonctionnel des protéines d'échafaudage bien au-delà de l'accessoire dans la spécificité et l'efficacité des traitements de l'information. La régulation de la dynamique des caractères signal-réponse à travers une telle régulation modulaire des groupes de phosphosites sur des protéines d'échafaudage combinées à l'assemblage à la membrane peut être un moyen général par lequel la polarisation du destin cellulaire est obtenue. Des mécanismes similaires peuvent contrôler les décisions cellulaires dans les organismes complexes et peuvent être compromis dans des dérèglements cellulaires, tel que le cancer. Finalement, sur un thème relié, je présente la découverte d'un nouveau mécanisme où le seuil de la concentration de phéromones est contrôlé par une voie sensorielle de nutriments, ajustant, de cette manière, le point prédéterminé dans lequel la quantité et la qualité des nutriments accessibles dans l'environnement déterminent le seuil à partir duquel la levure s'accouple. La sous-unité régulatrice de la kinase à protéine A (PKA),Bcy1, une composante clé du réseau signalétique du senseur aux nutriments, interagit directement avec la sous-unité α des petites protéines G, Gpa1, le premier effecteur dans le réseau de réponse aux phéromones. L'interaction Bcy1-Gpa1 est accrue lorsque la cellule croit en présence d'un sucre idéal, le glucose, diminuant la concentration seuil auquel la décision d'accouplement est activée. Compromettre l'interaction Bcy1-Gpa1 ou inactiver Bcy1 accroît la concentration seuil nécessaire à une réponse aux phéromones. Nous argumentons qu'en ajustant leur sensibilité, les levures peuvent intégrer le stimulus provenant des phéromones au niveau du glucose extracellulaire, priorisant la décision de survie dans un milieu pauvre ou continuer leur cycle sexuel en choisissant un accouplement.