Stochastic models for regulatory networks of the genetic toggle switch

Bistability arises within a wide range of biological systems from the λ phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. In this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

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.

Stochastic models for regulatory networks of the genetic toggle switch

Bistability arises within a wide range of biological systems from the A phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. in this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

Design of double toggle switching mechanisms

Toggle mechanisms are ubiquitous in electrical switches. However, literature for their mechanical design is scarce. This paper defines and classifies the toggle phenomena observed during switching. The concept of double toggle introduced in this paper enables a systematic screening of kinematic structure for the suitability in high performance switches. Seven structural and three kinematic criteria are identified for this purpose. It is also demonstrated that each such feasible kinematic structure lends itself to multiple physical embodiments. Therefore, the theory and procedure presented in this work can be used for design of numerous kinematically distinct mechanisms. One representative mechanical embodiment for a novel double toggle switch, including mass and geometric shape of links has been included in the paper. The switching behavior of the design is validated using Pro/Mechanism (TM). (C) 2013 Elsevier Ltd. All rights reserved.

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.

Two Arginine-Glutamate Ionic Locks Near the Extracellular Surface of FFAR1 Gate Receptor Activation

Activation of a number of class A G protein-coupled receptors (GPCRs) is thought to involve two molecular switches, a rotamer toggle switch within the transmembrane domain and an ionic lock at the cytoplasmic surface of the receptor; however, the mechanism by which agonist binding changes these molecular interactions is not understood. Importantly, 80% of GPCRs including free fatty acid receptor 1 (FFAR1) lack the complement of amino acid residues implicated in either or both of these two switches; the mechanism of activation of these GPCRs is therefore less clear. By homology modeling, we identified two Glu residues (Glu-145 and Glu-172) in the second extracellular loop of FFAR1 that form putative interactions individually with two transmembrane Arg residues (Arg-183(5.39) and Arg-258(7.35)) to create two ionic locks. Molecular dynamics simulations showed that binding of agonists to FFAR1 leads to breakage of these Glu-Arg interactions. In mutagenesis experiments, breakage of these two putative interactions by substituting Ala for Glu-145 and Glu-172 caused constitutive receptor activation. Our results therefore reveal a molecular switch for receptor activation present on the extracellular surface of FFAR1 that is broken by agonist binding. Similar ionic locks between the transmembrane domains and the extracellular loops may constitute a mechanism common to other class A GPCRs also.

Symmetry in biology: from genetic code to stochastic gene regulation

Mathematical models, as instruments for understanding the workings of nature, are a traditional tool of physics, but they also play an ever increasing role in biology - in the description of fundamental processes as well as that of complex systems. In this review, the authors discuss two examples of the application of group theoretical methods, which constitute the mathematical discipline for a quantitative description of the idea of symmetry, to genetics. The first one appears, in the form of a pseudo-orthogonal (Lorentz like) symmetry, in the stochastic modelling of what may be regarded as the simplest possible example of a genetic network and, hopefully, a building block for more complicated ones: a single self-interacting or externally regulated gene with only two possible states: ` on` and ` off`. The second is the algebraic approach to the evolution of the genetic code, according to which the current code results from a dynamical symmetry breaking process, starting out from an initial state of complete symmetry and ending in the presently observed final state of low symmetry. In both cases, symmetry plays a decisive role: in the first, it is a characteristic feature of the dynamics of the gene switch and its decay to equilibrium, whereas in the second, it provides the guidelines for the evolution of the coding rules.

Master Equation: Biological Applications and Thermodynamic Description

It is well known that many realistic mathematical models of biological systems, such as cell growth, cellular development and differentiation, gene expression, gene regulatory networks, enzyme cascades, synaptic plasticity, aging and population growth need to include stochasticity. These systems are not isolated, but rather subject to intrinsic and extrinsic fluctuations, which leads to a quasi equilibrium state (homeostasis). The natural framework is provided by Markov processes and the Master equation (ME) describes the temporal evolution of the probability of each state, specified by the number of units of each species. The ME is a relevant tool for modeling realistic biological systems and allow also to explore the behavior of open systems. These systems may exhibit not only the classical thermodynamic equilibrium states but also the nonequilibrium steady states (NESS). This thesis deals with biological problems that can be treat with the Master equation and also with its thermodynamic consequences. It is organized into six chapters with four new scientific works, which are grouped in two parts: (1) Biological applications of the Master equation: deals with the stochastic properties of a toggle switch, involving a protein compound and a miRNA cluster, known to control the eukaryotic cell cycle and possibly involved in oncogenesis and with the propose of a one parameter family of master equations for the evolution of a population having the logistic equation as mean field limit. (2) Nonequilibrium thermodynamics in terms of the Master equation: where we study the dynamical role of chemical fluxes that characterize the NESS of a chemical network and we propose a one parameter parametrization of BCM learning, that was originally proposed to describe plasticity processes, to study the differences between systems in DB and NESS.

A novel high voltage pulsed power supply based on low voltage switch-capacitor units

This paper presents a high voltage pulsed power system based on low voltage switch-capacitor units connected to a current source for several applications such as plasma systems. A buck-boost converter topology is used to utilize the current source and a series of low voltage switch-capacitor units is connected to the current source in order to provide high voltage with high voltage stress (dv/dt) as demanded by loads. This pulsed power converter is flexible in terms of energy control, in that the stored energy in the current source can be adjusted by changing the current magnitude to significantly improve the efficiency of various systems with different requirements. Output voltage magnitude and stress (dv/dt) can be controlled by a proper selection of components and control algorithm to turn on and off switching devices.

A novel high voltage pulsed power supply based on low voltage switch-capacitor units

This paper presents a high voltage pulsed power system based on low voltage switch-capacitor units connected to a current source for several applications such as plasma systems. A modified positive buck-boost converter topology is used to utilize the current source concept and a series of low voltage switch-capacitor units is connected to the current source in order to provide high voltage with high voltage stress (dv/dt) as demanded by loads. This pulsed power converter is flexible in terms of energy control, in that the stored energy in the current source can be adjusted by changing the current magnitude to significantly improve the efficiency of various systems with different requirements. Output voltage magnitude and stress (dv/dt) can be controlled by a proper selection of components and control algorithm to turn on and off switching devices.

An improved genetic algorithm and graph theory based method for optimal sectionalizer switch placement in distribution networks with DG

In this paper a new graph-theory and improved genetic algorithm based practical method is employed to solve the optimal sectionalizer switch placement problem. The proposed method determines the best locations of sectionalizer switching devices in distribution networks considering the effects of presence of distributed generation (DG) in fitness functions and other optimization constraints, providing the maximum number of costumers to be supplied by distributed generation sources in islanded distribution systems after possible faults. The proposed method is simulated and tested on several distribution test systems in both cases of with DG and non DG situations. The results of the simulations validate the proposed method for switch placement of the distribution network in the presence of distributed generation.

The switch

In this video, text types across the screen one line at a time set to an emotive stock music soundtrack. The text combines two teen film plot descriptions into one story. This work engages with the language of Hollywood narratives. By emphasizing the potentially abstract and convoluted qualities of linguistic communication, it challenges our capacity to assimilate information into conventional narratives. It draws specific attention to the conventions of Hollywood plot development, and questions the mechanisms by which they construct and communicate meaning.

A class B switch-mode assisted linear amplifier

A switch-mode assisted linear amplifier (SMALA) combining a linear (Class B) and a switch-mode (Class D) amplifier is presented. The usual single hysteretic controlled half-bridge current dumping stage is replaced by two parallel buck converter stages, in a parallel voltage controlled topology. These operate independently: one buck converter sources current to assist the upper Class B output device, and a complementary converter sinks current to assist the lower device. This topology lends itself to a novel control approach of a dead-band at low power levels where neither class D amplifier assists, allowing the class B amplifier to supply the load without interference, ensuring high fidelity. A 20 W implementation demonstrates 85% efficiency, with distortion below 0.08% measured across the full audio bandwidth at 15 W. The class D amplifier begins assisting at 2 W, and below this value, the distortion was below 0.03%. Complete circuitry is given, showing the simplicity of the additional class D amplifier and its corresponding control circuitry.

Hysteretic multilevel NPC converter control for a Switch Mode Assisted Linear Amplifier

A Switch-Mode Assisted Linear Amplifier (SMALA) combines the high quality of a linear amplifier required for audio applications with the high efficiency of a switch-mode amplifier. The careful choice of current sense point and switch placement allows a simple non-isolated hysteresis current controller for the switch-mode section. This paper explains the extension of the hysteresis current controller for the control of a three level Neutral Point Clamped (NPC) converter, with simulations as proof of concept. The NPC topology allows the use of lower voltage switches and lower switching frequencies to implement high power audio amplifiers using the SMALA topology.