It has been proposed' that gene-regulatory circuits with virtually any desired property can be constructed from networks of simple regulatory elements. These properties, which include multistability and oscillations, have been found in specialized gene circuits such as the bacteriophage lambda switch and the Cyanobacteria circadian oscillator. However, these behaviours have not been demonstrated in networks of non-specialized regulatory components. Here we present the construction of a genetic toggle switch-a synthetic, bistable gene-regulatory network-in Escherichia coli and provide a simple theory that predicts the conditions necessary for bistability. The toggle is constructed from any two repressible promoters arranged in a mutually inhibitory network. It is flipped between stable states using transient chemical or thermal induction and exhibits a nearly ideal switching threshold. As a practical device, the toggle switch forms a synthetic, addressable cellular memory unit and has implications for biotechnology, biocomputing and gene therapy.

Construction of a genetic toggle switch in Escherichia coli

The mammalian ionotropic glutamate receptor family encodes 18 gene products that coassemble to form ligand-gated ion channels containing an agonist recognition site, a transmembrane ion permeation pathway, and gating elements that couple agonist-induced conformational changes to the opening or closing of the permeation pore. Glutamate receptors mediate fast excitatory synaptic transmission in the central nervous system and are localized on neuronal and non-neuronal cells. These receptors regulate a broad spectrum of processes in the brain, spinal cord, retina, and peripheral nervous system. Glutamate receptors are postulated to play important roles in numerous neurological diseases and have attracted intense scrutiny. The description of glutamate receptor structure, including its transmembrane elements, reveals a complex assembly of multiple semiautonomous extracellular domains linked to a pore-forming element with striking resemblance to an inverted potassium channel. In this review we discuss International Union of Basic and Clinical Pharmacology glutamate receptor nomenclature, structure, assembly, accessory subunits, interacting proteins, gene expression and translation, post-translational modifications, agonist and antagonist pharmacology, allosteric modulation, mechanisms of gating and permeation, roles in normal physiological function, as well as the potential therapeutic use of pharmacological agents acting at glutamate receptors.

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Glutamate Receptor Ion Channels: Structure, Regulation, and Function

The spatiotemporal expression of genes in an organism is determined by regulatory systems that involve a large number of genes connected through a complex network of interactions. As an intuitive understanding of the behavior of these systems is hard to obtain, computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This report reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, ordinary and partial differential equations, stochastic equations, Boolean networks and their generalizations, qualitative differential equations, and rule-based formalisms. In addition, the report discusses how these formalisms have been used in the modeling and simulation of regulatory systems.

/pdf/modeling-and-simulation-of-genetic-regulatory-systems-a-2pgggkutcb.pdf

Modeling and simulation of genetic regulatory systems: a literature review.

In cellular regulatory networks, genetic activity is controlled by molecular signals that determine when and how often a given gene is transcribed. In genetically controlled pathways, the protein product encoded by one gene often regulates expression of other genes. The time delay, after activation of the first promoter, to reach an effective level to control the next promoter depends on the rate of protein accumulation. We have analyzed the chemical reactions controlling transcript initiation and translation termination in a single such “genetically coupled” link as a precursor to modeling networks constructed from many such links. Simulation of the processes of gene expression shows that proteins are produced from an activated promoter in short bursts of variable numbers of proteins that occur at random time intervals. As a result, there can be large differences in the time between successive events in regulatory cascades across a cell population. In addition, the random pattern of expression of competitive effectors can produce probabilistic outcomes in switching mechanisms that select between alternative regulatory paths. The result can be a partitioning of the cell population into different phenotypes as the cells follow different paths. There are numerous unexplained examples of phenotypic variations in isogenic populations of both prokaryotic and eukaryotic cells that may be the result of these stochastic gene expression mechanisms.

https://www.pnas.org/content/pnas/94/3/814.full.pdf

Stochastic mechanisms in gene expression

There are two fundamental ways to view coupled systems of chemical equations:  as continuous, represented by differential equations whose variables are concentrations, or as discrete, represented by stochastic processes whose variables are numbers of molecules. Although the former is by far more common, systems with very small numbers of molecules are important in some applications (e.g., in small biological cells or in surface processes). In both views, most complicated systems with multiple reaction channels and multiple chemical species cannot be solved analytically. There are exact numerical simulation methods to simulate trajectories of discrete, stochastic systems, (methods that are rigorously equivalent to the Master Equation approach) but these do not scale well to systems with many reaction pathways. This paper presents the Next Reaction Method, an exact algorithm to simulate coupled chemical reactions that is also efficient:  it (a) uses only a single random number per simulation event, and (b) ...

Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels

Calcium-dependent conformational states of calmodulin (CaM) were probed by thrombin to determine quantitative differences in the susceptibility of two bonds: Arg37-Ser38 (R37-S38, near site I in the N-terminal domain) and Arg106-His107 (R106-H107, near site III in the C-terminal domain). Quantitative thrombin footprinting of a discontinuous equilibrium calcium titration of wild-type calmodulin showed that the R37-S38 bond of the apoprotein was cleaved at a barely detectable level while the R106-H107 bond was maximally susceptible. Calcium binding to sites III and IV monotonically protected R106-H107 from proteolysis; concomitantly, the susceptibility of R37-S38 increased. However, calcium binding to sites I and II protected R37-S38 from cleavage, yielding a peaked biphasic profile composed of equal and opposite transitions. Both bonds were fully protected when calmodulin was saturated with calcium. Susceptibility profiles resolved from the fractional abundance of primary cleavage products (peptides 1-37, 38-148, 1-106, 107-148) were interpreted as directly reflecting calcium-induced conformational changes in whole calmodulin; free energies of calcium binding and cooperativity were estimated. Secondary cleavage was never observed; both R37 and R106 were sites of thrombinolysis in whole calmodulin only. In studies of E140Q-CaM (having a mutation in site IV), the susceptibility of R37-S38 decreased monotonically. Thus, the biphasic character of cleavage of R37 in helix B was not intrinsic to that domain but depended on propagation of effects of calcium-induced changes in the C-terminal domain. The observed patterns of susceptibility indicated that partially saturated wild-type calmodulin adopts at least one intermediate conformation whose structure is determined by calcium-mediated interactions between the domains.

Calcium-Induced Interactions of Calmodulin Domains Revealed by Quantitative Thrombin Footprinting of Arg37 and Arg106†

Apo-calmodulin binds with its c-terminal domain to the N-methyl-D-aspartate receptor NR1 C0 region

Calmodulin (CaM) is an intracellular calcium-binding protein essential for many pathways in eukaryotic signal transduction. Although a structure of Ca(2+)-saturated Paramecium CaM at 1.0 A resolution (1EXR.pdb) provides the highest level of detail about side-chain orientations in CaM, information about an end state alone cannot explain driving forces for the transitions that occur during Ca(2+)-induced conformational switching and why the two domains of CaM are saturated sequentially rather than simultaneously. Recent studies focus attention on the contributions of interdomain linker residues. Electron paramagnetic resonance showed that Ca(2+)-induced structural stabilization of residues 76-81 modulates domain coupling [Qin and Squier (2001) Biophys. J. 81, 2908-2918]. Studies of N-domain fragments of Paramecium CaM showed that residues 76-80 increased thermostability of the N-domain but lowered the Ca(2+) affinity of sites I and II [Sorensen et al. (2002) Biochemistry 41, 15-20]. To probe domain coupling during Ca(2+) binding, we have used (1)H-(15)N HSQC NMR to monitor more than 40 residues in Paramecium CaM. The titrations demonstrated that residues Glu78 to Glu84 (in the linker and cap of helix E) underwent sequential phases of conformational change. Initially, they changed in volume (slow exchange) as sites III and IV titrated, and subsequently, they changed in frequency (fast exchange) as sites I and II titrated. These studies provide evidence for Ca(2+)-dependent communication between the domains, demonstrating that spatially distant residues respond to Ca(2+) binding at sites I and II in the N-domain of CaM.

Calcium-induced conformational switching of Paramecium calmodulin provides evidence for domain coupling.

Calmodulin (CaM) is a ubiquitous, essential calcium-binding protein that regulates diverse protein targets in response to physiological calcium fluctuations. Most high-resolution structures of CaM-target complexes indicate that the two homologous domains of CaM are equivalent partners in target recognition. However, mutations between calcium-binding sites I and II in the N-domain of Paramecium calmodulin (PCaM) selectively affect calcium-dependent sodium currents. To understand these domain-specific effects, N-domain fragments (PCaM1–75) of six of these mutants were examined to determine whether energetics of calcium binding to sites I and II or conformational properties had been perturbed. These PCaM(1–75) sequences naturally contain 5 Phe residues but no Tyr or Trp; calcium binding was monitored by observing the reduction in intrinsic phenylalanine fluorescence at 280 nm. To assess mutation-induced conformational changes, thermal denaturation of the apo PCaM(1–75) sequences, and calcium-dependent changes in Stokes radii were determined. The free energy of calcium binding to each mutant was within 1 kcal/mole of the value for wild type and calcium reduced the Rs of all of them. A striking trend was observed whereby mutants showing an increase in calcium affinity and Rs had a concomitant decrease in thermal stability (by as much as 18°C). Thus, mutations between the binding sites that increased disorder and reduced tertiary constraints in the apo state promoted calcium coordination. This finding underscores the complexity of the linkage between calcium binding and conformational change and the difficulty in predicting mutational effects.

Phenylalanine fluorescence studies of calcium binding to N-domain fragments of Paramecium calmodulin mutants show increased calcium affinity correlates with increased disorder

Madeline A. Shea

Papers

Calcium-Induced Interactions of Calmodulin Domains Revealed by Quantitative Thrombin Footprinting of Arg37 and Arg106†

Apo-calmodulin binds with its c-terminal domain to the N-methyl-D-aspartate receptor NR1 C0 region

Calcium-induced conformational switching of Paramecium calmodulin provides evidence for domain coupling.

Phenylalanine fluorescence studies of calcium binding to N-domain fragments of Paramecium calmodulin mutants show increased calcium affinity correlates with increased disorder

Thermodynamic Linkage Between Calmodulin Domains Binding Calcium and Contiguous Sites in the C-Terminal Tail of CaV1.2