Reaction coordinates for the flipping of genetic switches

We present a detailed analysis, based on the Forward Flux Sampling (FFS) simulation method, of the switching dynamics and stability of two models of genetic toggle switches, consisting of two mutually-repressing genes encoding transcription factors (TFs); in one model (the exclusive switch), they mutually exclude each other's binding, while in the other model (general switch) the two transcription factors can bind simultaneously to the shared operator region. We assess the role of two pairs of reactions that influence the stability of these switches: TF-TF homodimerisation and TF-DNA association/dissociation. We factorise the flipping rate k into the product of the probability rho(q*) of finding the system at the dividing surface (separatrix) between the two stable states, and a kinetic prefactor R. In the case of the exclusive switch, the rate of TF-operator binding affects both rho(q*) and R, while the rate of TF dimerisation affects only R. In the case of the general switch both TF-operator binding and TF dimerisation affect k, R and rho(q*). To elucidate this, we analyse the transition state ensemble (TSE). For the exclusive switch, varying the rate of TF-operator binding can drastically change the pathway of switching, while changing the rate of dimerisation changes the switching rate without altering the mechanism. The switching pathways of the general switch are highly robust to changes in the rate constants of both TF-operator and TF-TF binding, even though these rate constants do affect the flipping rate; this feature is unique for non-equilibrium systems.Comment: 24 pages, 7 figure

Forward Flux Sampling-type schemes for simulating rare events: Efficiency analysis

We analyse the efficiency of several simulation methods which we have recently proposed for calculating rate constants for rare events in stochastic dynamical systems, in or out of equilibrium. We derive analytical expressions for the computational cost of using these methods, and for the statistical error in the final estimate of the rate constant, for a given computational cost. These expressions can be used to determine which method to use for a given problem, to optimize the choice of parameters, and to evaluate the significance of the results obtained. We apply the expressions to the two-dimensional non-equilibrium rare event problem proposed by Maier and Stein. For this problem, our analysis gives accurate quantitative predictions for the computational efficiency of the three methods.Comment: 19 pages, 13 figure

Radial Squeezed States and Rydberg Wave Packets

We outline an analytical framework for the treatment of radial Rydberg wave packets produced by short laser pulses in the absence of external electric and magnetic fields. Wave packets of this type are localized in the radial coordinates and have p-state angular distributions. We argue that they can be described by a particular analytical class of squeezed states, called radial squeezed states. For hydrogenic Rydberg atoms, we discuss the time evolution of the corresponding hydrogenic radial squeezed states. They are found to undergo decoherence and collapse, followed by fractional and full revivals. We also present their uncertainty product and uncertainty ratio as functions of time. Our results show that hydrogenic radial squeezed states provide a suitable analytical description of hydrogenic Rydberg atoms excited by short-pulsed laser fields.Comment: published in Physical Review

Hydrophobic interactions: an overview

We present an overview of the recent progress that has been made in understanding the origin of hydrophobic interactions. We discuss the different character of the solvation behavior of apolar solutes at small and large length scales. We emphasize that the crossover in the solvation behavior arises from a collective effect, which means that implicit solvent models should be used with care. We then discuss a recently developed explicit solvent model, in which the solvent is not described at the atomic level, but rather at the level of a density field. The model is based upon a lattice-gas model, which describes density fluctuations in the solvent at large length scales, and a Gaussian model, which describes density fluctuations at smaller length scales. By integrating out the small length scale field, a Hamiltonian is obtained, which is a function of the binary, large-length scale field only. This makes it possible to simulate much larger systems than hitherto possible as demonstrated by the application of the model to the collapse of an ideal hydrophobic polymer. The results show that the collapse is dominated by the dynamics of the solvent, in particular the formation of a vapor bubble of critical size. Implications of these findings to the understanding of pressure denaturation of proteins are discussed.Comment: 10 pages, 4 figure

Spatio-temporal correlations can drastically change the response of a MAPK pathway

Multisite covalent modification of proteins is omnipresent in eukaryotic cells. A well-known example is the mitogen-activated protein kinase (MAPK) cascade, where in each layer of the cascade a protein is phosphorylated at two sites. It has long been known that the response of a MAPK pathway strongly depends on whether the enzymes that modify the protein act processively or distributively: distributive mechanism, in which the enzyme molecules have to release the substrate molecules in between the modification of the two sites, can generate an ultrasensitive response and lead to hysteresis and bistability. We study by Green's Function Reaction Dynamics, a stochastic scheme that makes it possible to simulate biochemical networks at the particle level and in time and space, a dual phosphorylation cycle in which the enzymes act according to a distributive mechanism. We find that the response of this network can differ dramatically from that predicted by a mean-field analysis based on the chemical rate equations. In particular, rapid rebindings of the enzyme molecules to the substrate molecules after modification of the first site can markedly speed up the response, and lead to loss of ultrasensitivity and bistability. In essence, rapid enzyme-substrate rebindings can turn a distributive mechanism into a processive mechanism. We argue that slow ADP release by the enzymes can protect the system against these rapid rebindings, thus enabling ultrasensitivity and bistability