Noise-induced coherent switch

Taking the famous genetic toggle switch as an example, we numerically investigated the effect of noise on bistability. We found that extrinsic noise resulting from stochastic fluctuations in synthesis and degradation rates and from the environmental fluctuation in gene regulatory processes can induce coherent switch, and that there is an optimal noise intensity such that the noise not only can induce this switch, but also can amplify a weak input signal. In addition, we found that the intrinsic noise introduced through the Poisson τ-leap algorithm cannot induce such a switch.     

Noise-induced coherent switch

Taking the famous genetic toggle switch as an example,we numerically investigated the effect of noise on bistability.We found that extrinsic noise resulting from stochastic fluctuations in synthesis and degradation rates and from the environmental fluctuation in gene regulatory processes can induce coherent switch,and that there is an optimal noise intensity such that the noise not only can induce this switch,but also can amplify a weak input signal.In addition,we found that the intrinsic noise introduced through the Poisson τ-leap algorithm cannot induce such a switch.     

Toward deciphering the code to aminergic G protein-coupled receptor drug design

The trace amine-associated receptor 1 (TAAR(1)) is a biogenic amine G protein-coupled receptor (GPCR) that is potently activated by 3-iodothyronamine (1, T(1)AM) in vitro. Compound 1 is an endogenous derivative of the thyroid hormone thyroxine which rapidly induces hypothermia, anergia, and bradycardia when administered to mice. To explore the role of TAAR(1) in mediating the effects of 1, we rationally designed and synthesized rat TAAR(1) superagonists and lead antagonists using the rotamer toggle switch model of aminergic GPCR activation. The functional activity of a ligand is proposed to be correlated to its probable interactions with the rotamer switch residues; agonists allow the rotamer switch residues to toggle to their active conformation, whereas antagonists interfere with this conformational transition. These agonist and antagonist design principles provide a conceptual model for understanding the relationship between the molecular structure of a drug and its pharmacological properties.     

Comparison of approaches for parameter estimation on stochastic models: Generic least squares versus specialized approaches

Parameter estimation for models with intrinsic stochasticity poses specific challenges that do not exist for deterministic models. Therefore, specialized numerical methods for parameter estimation in stochastic models have been developed. Here, we study whether dedicated algorithms for stochastic models are indeed superior to the naive approach of applying the readily available least squares algorithm designed for deterministic models.We compare the performance of the recently developed multiple shooting for stochastic systems (MSS) method designed for parameter estimation in stochastic models, a stochastic differential equations based Bayesian approach and a chemical master equation based techniques with the least squares approach for parameter estimation in models of ordinary differential equations (ODE). As test data, 1000 realizations of the stochastic models are simulated. For each realization an estimation is performed with each method, resulting in 1000 estimates for each approach. These are compared with respect to their deviation to the true parameter and, for the genetic toggle switch, also their ability to reproduce the symmetry of the switching behavior. Results are shown for different set of parameter values of a genetic toggle switch leading to symmetric and asymmetric switching behavior as well as an immigration-death and a susceptible-infected-recovered model. This comparison shows that it is important to choose a parameter estimation technique that can treat intrinsic stochasticity and that the specific choice of this algorithm shows only minor performance differences.     

W2466.48 Opens a Gate for a Continuous Intrinsic Water Pathway during Activation of the Adenosine A2A Receptor

The question how G‐protein‐coupled receptors transduce an extracellular signal by a sequence of transmembrane conformational transitions into an intracellular response remains to be solved at molecular detail. Herein, we use molecular dynamics simulations to reveal distinct conformational transitions of the adenosine A_2A receptor, and we found that the conserved W246^6.48 residue in transmembrane helix TM6 performs a key rotamer toggle switch. Agonist binding induces the sidechain of W246^6.48 to fluctuate between two distinct conformations enabling the diffusion of water molecules from the bulk into the center of the receptor. After passing the W246^6.48 gate, the internal water molecules induce another conserved residue, Y288^7.53, to switch to a distinct rotamer conformation establishing a continuous transmembrane water pathway. Further, structural changes of TM6 and TM7 induce local structural changes of the adjacent lipid bilayer.     

Non-stationary forward flux sampling

We present a method, Non-Stationary Forward Flux Sampling, that allows efficient simulation of rare events in both stationary and non-stationary stochastic systems. The method uses stochastic branching and pruning to achieve uniform sampling of trajectories in phase space and time, leading to accurate estimates for time-dependent switching propensities and time-dependent phase space probability densities. It is suitable for equilibrium or non-equilibrium systems, in or out of stationary state, including non-Markovian or externally driven systems. We demonstrate the validity of the technique by applying it to a one-dimensional barrier crossing problem that can be solved exactly, and show its usefulness by applying it to the time-dependent switching of a genetic toggle switch.     

Relaxation processes in mixtures of liquid crystals and polymers near phase boundaries and during phase separation

We present experimental studies of the relaxation of concentration fluctuations in a semidilute solution of polystyrene (PS) (30% by weight) in 4-cyano-4'-n-octyl-biphenyl (8CB) (70% by weight) using the photon correlation spectroscopy (PCS). In the homogeneous phase there are two modes of relaxation. The slow one (typical time scale is taus = 0.001 s) is due to the diffusion of polymer chains (of molecular mass 65,000) in the LC matrix (of molecular mass 290), while the fast one has the time scale of the order of tauf approximately 0.00001 s. The amplitude of the fast mode is much weaker than the one for the slow mode. Moreover it does not depend on the scattering wave vector, q. The value of the diffusion coefficient, Dc = 1/(tausq2) for the slow mode decreases with temperature according to the Arhenius law until we reach the coexistence curve. Its value close to the coexistence is Dc = 4 x 10(5) nm2/s and the activation energy in the homogeneous mixture is Ec=127 kJ/mol. If we gradually undercool the mixture below the coexistence into the metastable two-phase region without inducing the phase separation we find unexpectedly that Dc does not change with temperature even 4 degrees below the coexistence curve. The characteristic time of the fast mode does not depend on the scattering wave vector indicating that it is related to the transient gel structure. We have shown that it is possible to measure the short time relaxation of concentration fluctuations during the phase separation in the mixture. At low temperature close to the isotropic-nematic phase transition we have observed that the relaxation is well separated in time from the typical time of the domain growth. This relaxation mode is characterized by the large diffusion coefficient D = 2 x 10(8) nm2/s. The mode probably comes from the coupling between the orientational dynamics of liquid crystals and the transient gel structure of polymers.     

Confinement of polar solvents within beta-cyclodextrins

Using molecular dynamics techniques, we examined equilibrium and dynamical characteristics pertaining to the solvation of a single beta-cyclodextrin (CD) in water and in dimethylsulfoxide (DMSO). Compared to its global minimum structure, the overall shape of the solute in solution is reasonably well preserved. While in aqueous solutions, the average number of solvent molecules retained within the central cavity of the oligosaccharide is close to 5, for DMSO, that number reduces to approximately 1. No evidence of significant orientational correlations of the trapped molecules were found in either solvent. The main contributions to the hydrogen-bond (HB) connectivity between the solute and the bulk phases are due to the more distal HO6-O6 hydroxyl groups, acting as HB donors and acceptors. The average residence time for retained DMSO was found to be in the nanosecond range, and it is, at least, 1 order of magnitude longer that the one observed for water. We also analyzed the characteristics of the solvation of the beta-CD in an equimolar water-DMSO mixture. In this environment, we found a preferential localization of a single DMSO molecule in the interior of the CD and a very minor retention of water. In the mixture, the characteristic time of residence of the trapped DMSO molecule increases by a factor of approximately 2. The observed difference was rationalized in terms of the fluctuations of the local concentrations of the two species in the vicinity of the CD top and bottom rims.     

Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation

We present computer-assisted methods for analyzing stochastic models of gene regulatory networks. The main idea that underlies this equation-free analysis is the design and execution of appropriately initialized short bursts of stochastic simulations; the results of these are processed to estimate coarse-grained quantities of interest, such as mesoscopic transport coefficients. In particular, using a simple model of a genetic toggle switch, we illustrate the computation of an effective free energy Phi and of a state-dependent effective diffusion coefficient D that characterize an unavailable effective Fokker-Planck equation. Additionally we illustrate the linking of equation-free techniques with continuation methods for performing a form of stochastic "bifurcation analysis"; estimation of mean switching times in the case of a bistable switch is also implemented in this equation-free context. The accuracy of our methods is tested by direct comparison with long-time stochastic simulations. This type of equation-free analysis appears to be a promising approach to computing features of the long-time, coarse-grained behavior of certain classes of complex stochastic models of gene regulatory networks, circumventing the need for long Monte Carlo simulations.     

Kinetic paths, time scale, and underlying landscapes: a path integral framework to study global natures of nonequilibrium systems and networks

We developed a general framework to quantify three key ingredients for dynamics of nonequilibrium systems through path integrals in length space. First, we identify dominant kinetic paths as the ones with optimal weights, leading to effective reduction of dimensionality or degrees of freedom from exponential to polynomial so large systems can be treated. Second, we uncover the underlying nonequilibrium potential landscapes from the explorations of the state space through kinetic paths. We apply our framework to a specific example of nonequilibrium network system: lambda phage genetic switch. Two distinct basins of attractions emerge. The dominant kinetic paths from one basin to another are irreversible and do not follow the usual steepest descent or gradient path along the landscape. It reflects the fact that the dynamics of nonequilibrium systems is not just determined by potential gradient but also the residual curl flux force, suggesting experiments to test theoretical predictions. Third, we have calculated dynamic transition time scales from one basin to another critical for stability of the system through instantons. Theoretical predictions are in good agreements with wild type and mutant experiments. We further uncover the correlations between the kinetic transition time scales and the underlying landscape topography: the barrier heights along the dominant paths. We found that both the dominant paths and the landscape are relatively robust against the influences of external environmental perturbations and the system tends to dissipate less with less fluctuations. Our general framework can be applied to other nonequilibrium systems.     

Transient ordering in a quasi-two-dimensional liquid near freezing

We report the results of a theoretical study of locally ordered fluctuations in a quasi-two-dimensional colloid fluid. The fluctuations in the equilibrium state are monitored by the aperture cross-correlation function of radiation scattered by the fluid, as calculated from molecular dynamics simulations of near hard spheres with diameter sigma confined between smooth hard walls. These locally ordered fluctuations are transient; their decay can be monitored as a function of the time between the cross-correlated scattered radiation signals, but only the single-time cross-correlated signals are discussed in this paper. Systems with thicknesses less than two hard sphere diameters were studied. For wall separation H in the range 1 sigma/=1.57 sigma, hexagonal fluctuations persist in the dense liquid up to H=1.75 sigma, and fluctuations with square ordered symmetry, that of the solid to which the liquid freezes, only emerge at densities approximately 2% below freezing. For H=1.8 sigma and 1.85 sigma, hexagonal ordered flucuations are no longer found, and the square ordered fluctuations dominate the dense liquid region as the system freezes into a two layer square solid. For H=1.9 sigma and 1.95 sigma, where the liquid freezes into a two layer hexagonal solid, both square and hexagonal ordered fluctuations are observed. At lower densities, the ordered fluctuations only exhibit square symmetry. Hexagonal ordered fluctuations appear at densities approximately 7% below freezing and become more dominant as the density is increased, but the square ordered fluctuations persist until the system is converted into the solid.     

Fluidic low pass filter for hydrodynamic flow stabilization in microfluidic environments

Fluctuations in flow rate invariably occur in microfluidic devices. This fluidic instability results in a deteriorating performance and the suspension of their unique functions occasionally. In this study, a fluidic-LPF (low pass filter), which is composed of an ACU (air compliance unit) and a FCSP (fluidic channel with high fluidic resistance for sufficient preload), has been proposed for providing the stabilization of hydrodynamic flow in microfluidic devices. To investigate the characteristics of various fluidic networks including our fluidic-LPF, we used a parametric identification method to estimate the time constants via a transient response that was based on a discrete parameter model. In addition, we propose the use of a pulsation index (PI) to quantify the fluctuations in flow rate. We verified the formula for PI derived herein by varying individually both the periods and the air compliance volumes in the ACU, both theoretically and experimentally. We found that the PI depended strongly on either the time constants or the periods of the flow rates at the inlet. Additionally, the normalized differences between the experimental results and the theoretical estimations were less than 6%, which shows that the proposed formula for PI can provide an accurate quantification of the fluctuations in flow, and estimate the parametric effects. Finally, we have successfully demonstrated that our fluidic-LPF can regulate fluctuations in the flow at extremely low flow rates (~ 10 μL h(-1)) and can also control severe fluidic fluctuations (PI = 0.67) with excessively long periods (100 s) via a microfluidic viscometer. We therefore believe that the stabilization of hydrodynamic flow using a fluidic-LPF could be used easily and extensively with a range of microfluidic platforms that require constant flow rates.     

Analysis of uncertainties in polymer viscoelastic properties obtained from equilibrium computer simulations

We critically evaluate the uncertainties in the stress autocorrelation function obtained from equilibrium molecular dynamics simulation of model polymer melts. This quantity is central to evaluating transport properties, e.g., the complex modulus and the viscosity. In contrast to the intuitive expectation that simulations have to be run five to six orders of magnitude longer than the chain relaxation time to reduce uncertainties to acceptable levels, our analysis shows that the majority of the uncertainty is associated with rapidly oscillating bonded interactions. These fluctuations occur on time scales which are approximately 10(4) times shorter than the relaxation time of a chain of length 80. Consequently, the effects of these oscillations on the stress autocorrelation function can be dramatically reduced by (i) conducting long simulations (typically 10(6) times longer than the bond relaxation times or only 10(2) chain relaxation times) and (ii) by performing running averages with time windows whose time scales are much longer than these oscillations. Conducting such long simulations also allows for the accurate determination of the melt viscosity and the low-frequency complex modulus, but performing running averages do not impact these quantities since they are time integrals of the stress autocorrelation function.     

Ultrafast vibrational dynamics of SCN(-) and N3(-) in polar solvents studied by nonlinear infrared spectroscopy

In this paper, we report on our investigation into the vibrational dynamics of the antisymmetric stretching modes of SCN(-) and N(3)(-) in several polar solvents. We used an infrared (IR) pump-probe method to study orientational relaxation processes. In two aprotic solvents (N,N-dimethylformamide (DMF) and dimethyl sulfoxide (DMSO)), the anisotropy decay shows a bimodal feature, whereas in other solvents the anisotropy decay can be fitted well by a single exponential function. We consider that the relative contribution of fast-decaying components is smaller in the other solvents than in DMF and DMSO. We discuss the possible origins of the different anisotropy decay behavior in different solvents. From the three-pulse IR photon echo measurements for SCN(-) and N(3)(-), we found that the time-correlation functions (TCFs) of vibrational frequency fluctuations decay on two different time scales, one of which is less than 100 fs and the other is approximately 3-6 ps. In aprotic solvents, the fast-decaying components of the TCFs on a <100 fs time scale play an important role in the vibrational frequency fluctuation, although the contribution of collective solvent reorganization in aprotic solvents was clearly observed to have small amplitudes. On the other hand, we found that the amplitude of components that decay in a few picoseconds and/or the constant offset of the TCF in protic solvents is relatively large compared with that in aprotic solvents. With the formation and dissociation of hydrogen bonds between ion solute and solvent molecules, the spectra of different solvated species are exchanged with each other and merged into one band. We considered that this exchange may be an origin of slow-decaying components of the TCFs and that the decay of the TCFs corresponds to the time scales of the exchange for protic solvents such as formamide. The mechanism of vibrational frequency fluctuations for the antisymmetric stretching modes of SCN(-) and N(3)(-) is discussed in terms of the difference between protic and aprotic solvents.     

Mapping the intramolecular signal propagation pathways in protein using Bayesian change point analysis of atomic motions

We propose to use change points of atomic positions in the molecular dynamics trajectory as indicators of the propagating signals in protein. We designate these changes as signals because they can propagate within the molecule in the form of “perturbation wave”, transmit energy or information between different parts of protein, and serve as allosteric signals. We found that change points can distinguish between thermal fluctuations of atoms (noise) and signals in a protein despite the differences in the motility of amino acid residues. Clustering of the spatially close residues that were experiencing change points close in time, allowed us to map pathways of signal propagation in a protein at the atomic level of resolution. We propose a potential mechanism for the origin of the signal and its propagation that relies on the autonomic coherence resonance in atomic fluctuations. According to this mechanism, random synchronization of fluctuations of neighboring atoms results in a resonance, which increases amplitude of vibration of these atoms. This increase can be transmitted to the atoms colliding with the resonant atoms, leading to the propagating signal. The wavelet-based coherence analysis of the inter-atomic distances between carbon-alpha atoms and surrounding atoms for the residue pairs that belong to the same communication pathway allowed us to find time periods with temporarily locked phases, confirming the occurrence of conditions for resonance. Analysis of the mapped pathways demonstrated that they form a network that connects different regions of the protein.     

Subsecond luminescence intensity fluctuations of single CdSe quantum dots

Photoluminescence (PL) intermittency characteristics are examined for single quantum dots (QDs) in a CdSe QD sample synthesized at a slow rate at 75 degrees C. Although the PL quantum efficiency was relatively low ( approximately 0.25), we noticed that the PL intensity of single CdSe QDs fluctuated on a subsecond time scale with short-lived "on" and "off" states. The subsecond PL intensity fluctuations of CdSe QDs are different from "on" and "off" PL blinking generally observed for QDs fluctuating on a millisecond to minute time scale. We characterized single QDs by identifying polarized excitations, topographic imaging using atomic force microscopy (AFM), and transmission electron microscopy (TEM). From analysis of the PL intensity trajectories from >100 single CdSe QDs, the average intermittency time was 213 ms. From the PL quantum efficiency, slow growth of QDs, intensity trajectory analyses, and previous reports relating surface trap states and PL properties of QDs, we attribute the subsecond PL intensity fluctuations of single CdSe QDs and short-lived "on" and "off" states to a high-density distribution of homogeneous surface trap states.     

Influence of environment induced correlated fluctuations in electronic coupling on coherent excitation energy transfer dynamics in model photosynthetic systems

Two-dimensional photon-echo experiments indicate that excitation energy transfer between chromophores near the reaction center of the photosynthetic purple bacterium Rhodobacter sphaeroides occurs coherently with decoherence times of hundreds of femtoseconds, comparable to the energy transfer time scale in these systems. The original explanation of this observation suggested that correlated fluctuations in chromophore excitation energies, driven by large scale protein motions could result in long lived coherent energy transfer dynamics. However, no significant site energy correlation has been found in recent molecular dynamics simulations of several model light harvesting systems. Instead, there is evidence of correlated fluctuations in site energy-electronic coupling and electronic coupling-electronic coupling. The roles of these different types of correlations in excitation energy transfer dynamics are not yet thoroughly understood, though the effects of site energy correlations have been well studied. In this paper, we introduce several general models that can realistically describe the effects of various types of correlated fluctuations in chromophore properties and systematically study the behavior of these models using general methods for treating dissipative quantum dynamics in complex multi-chromophore systems. The effects of correlation between site energy and inter-site electronic couplings are explored in a two state model of excitation energy transfer between the accessory bacteriochlorophyll and bacteriopheophytin in a reaction center system and we find that these types of correlated fluctuations can enhance or suppress coherence and transfer rate simultaneously. In contrast, models for correlated fluctuations in chromophore excitation energies show enhanced coherent dynamics but necessarily show decrease in excitation energy transfer rate accompanying such coherence enhancement. Finally, for a three state model of the Fenna-Matthews-Olsen light harvesting complex, we explore the influence of including correlations in inter-chromophore couplings between different chromophore dimers that share a common chromophore. We find that the relative sign of the different correlations can have profound influence on decoherence time and energy transfer rate and can provide sensitive control of relaxation in these complex quantum dynamical open systems.