Transition Rate Model Research Articles

Cotranscriptional folding of RNA pseudoknots with different rates

We investigate and compare the refolding and cotranscriptional folding process of RNA pseudoknot including PK5 pseudoknot, human telomerase RNA (hTR) pseudoknot and its mutants by using helix-based transition rate model and master equation. It is found that in the refolding process, the final states for PKWT and two mutants PK179AG/110CU and PK△U177 are all pseudoknots. However, the final state of mutant PKDC is a stable long helix. Furthermore, the cotranscriptional folding intermediates are quite different from refolding ones. The intermediate found in refolding process for PKWT is also shown during cotranscription. For PK179AG/110CU, the two intermediates in refolding are not found in cotranscriptional folding. For PK△U177, only one of the intermediates found in refolding is not observed in cotranscription. For PKDC, the unfolding sequence in the refolding process directly transits to native helix. Two intermediates are found during cotranscription. The populations of intermediates and native structure also depend on the cotranscriptional folding rate. All these findings can offer useful insights into cotranscription folding of hTR pseudoknot with different rates.

Role of the reorganization energy for charge transport in disordered organic semiconductors

While it is commonly accepted that the activation energy of the thermally activated polaron hopping transport in disordered organic semiconductors can be decoupled into a disorder and a polaron contribution, their relative weight is still controversial. This feature is quantified in terms of the so-called $C$ factor in the expression for the effective polaron mobility: ${\ensuremath{\mu}}_{e}\ensuremath{\propto}\mathrm{exp}[\ensuremath{-}{E}_{a}/{k}_{B}T\ensuremath{-}C{(\ensuremath{\sigma}/{k}_{B}T)}^{2}]$, where ${E}_{a}$ and $\ensuremath{\sigma}$ are the polaron activation energy and the energy width of a Gaussian density of states (DOS), respectively. A key issue is whether the universal scaling relation (implying a constant $C$ factor) regarding the polaron formation energy is really obeyed, as recently claimed in the literature [Seki and Wojcik, J. Chem. Phys. 145, 034106 (2016)]. In the present work, we reinvestigate this issue on the basis of the Marcus transition rate model using extensive kinetic Monte Carlo simulations as a benchmark tool. We compare the polaron-transport simulation data with results of analytical calculations by the effective medium approximation and multiple trapping and release approaches. The key result of this study is that the $C$ factor for Marcus polaron hopping depends on first the degree of carrier localization, i.e., the coupling between the sites, further whether quasiequilibrium has indeed been reached, and finally the $\ensuremath{\sigma}/{E}_{a}$ ratio. This implies that there is no universal scaling with respect to the relative contribution of polaron and disorder effect. Finally, we demonstrate that virtually the same values of the disorder parameter $\ensuremath{\sigma}$ are determined from available experimental data using the $C$ factors obtained here irrespective of whether the data are interpreted in terms of Marcus or Miller-Abrahams rates. This implies that molecular reorganization contributes only weakly to charge transport, and it justifies the use of the zero-order Miller-Abrahams rate model for evaluating the DOS width from temperature-dependent charge transport measurements regardless of whether or not polaron effects are accounted for.

Predicting Cotranscriptional Folding Kinetics For Riboswitch.

On the basis of a helix-based transition rate model, we developed a new method for sampling cotranscriptional RNA conformational ensemble and the prediction of cotranscriptional folding kinetics. Applications to E. coli. SRP RNA and pbuE riboswitch indicate that the model may provide reliable predictions for the cotranscriptional folding pathways and population kinetics. For E. coli. SRP RNA, the predicted population kinetics and the folding pathway are consistent with the SHAPE profiles in the recent cotranscriptional SHAPE-seq experiments. For the pbuE riboswitch, the model predicts the transcriptional termination efficiency as a function of the force. The theoretical results show (a) a force-induced transition from the aptamer (antiterminator) to the terminator structure and (b) the different folding pathways for the riboswitch with and without the ligand (adenine). More specifically, without adenine, the aptamer structure emerges as a short-lived kinetic transient state instead of a thermodynamically stable intermediate state. Furthermore, from the predicted extension-time curves, the model identifies a series of conformational switches in the pulling process, where the predicted relative residence times for the different structures are in accordance with the experimental data. The model may provide a new tool for quantitative predictions of cotranscriptional folding kinetics, and results can offer useful insights into cotranscriptional folding-related RNA functions such as regulation of gene expression with riboswitches.

Computational Modeling of Channelrhodopsin-2 Photocurrent Characteristics in Relation to Neural Signaling

Channelrhodopsins-2 (ChR2) are a class of light sensitive proteins that offer the ability to use light stimulation to regulate neural activity with millisecond precision. In order to address the limitations in the efficacy of the wild-type ChR2 (ChRwt) to achieve this objective, new variants of ChR2 that exhibit fast mon-exponential photocurrent decay characteristics have been recently developed and validated. In this paper, we investigate whether the framework of transition rate model with 4 states, primarily developed to mimic the biexponential photocurrent decay kinetics of ChRwt, as opposed to the low complexity 3 state model, is warranted to mimic the mono-exponential photocurrent decay kinetics of the newly developed fast ChR2 variants: ChETA (Gunaydin et al., Nature Neurosci. 13:387-392, 2010) and ChRET/TC (Berndt et al., Proc. Natl. Acad. Sci. 108:7595-7600, 2011). We begin by estimating the parameters of the 3-state and 4-state models from experimental data on the photocurrent kinetics of ChRwt, ChETA, and ChRET/TC. We then incorporate these models into a fast-spiking interneuron model (Wang and Buzsaki, J.Neurosci. 16:6402-6413, 1996) and a hippocampal pyramidal cell model (Golomb et al., J.Neurophysiol. 96:1912-1926, 2006) and investigate the extent to which the experimentally observed neural response to various optostimulation protocols can be captured by these models. We demonstrate that for all ChR2 variants investigated, the 4 state model implementation is better able to capture neural response consistent with experiments across wide range of optostimulation protocol. We conclude by analytically investigating the conditions under which the characteristic specific to the 3-state model, namely the monoexponential photocurrent decay of the newly developed variants of ChR2, can occur in the framework of the 4-state model.

Excitation, relaxation, and quantum diffusion of CO on copper

We investigate the effect of intermode coupling and anharmonicity on the excitation and relaxation dynamics of CO on Cu(100). The nonadiabatic coupling of the adsorbate to the surface is treated perturbatively using a position-dependent state-resolved transition rate model. Using the potential energy surface of Marquardt et al. [J. Chem. Phys. 132, 074108 (2010)], which provides an accurate description of intermode interactions, we propose a four-dimensional model that represents simultaneously the diffusion and the desorption of the adsorbate. The system is driven by both rational and optimized infrared laser pulses to favor either selective mode and state excitations or lateral displacement along the diffusion coordinate. The dissipative dynamics is simulated using the reduced density matrix in its Lindblad form. We show that coupling between the degrees of freedom, mediated by the creation and annihilation of electron-hole pairs in the metal substrate, significantly affects the system excitation and relaxation dynamics. In particular, the angular degrees of freedom appear to play an important role in the energy redistribution among the molecule-surface vibrations. We also show that coherent excitation using simple IR pulses can achieve population transfer to a specific target to some extent but does not allow enforcement of the directionality to the diffusion motion.

Computational modeling of light activated ion channels

Channelrhodpsin-2 (ChR2) is a light sensitive ion channel protein currently investigated for millisecond time scale optogenetic control of neural activity [1]. Two competing mathematical models, a 3-state and a 4-state rate transition model are currently available to mimic the ChR2 photocurrent kinetics [2]. While both models are able to capture the key temporal features of ChR2 photocurrent in response to light stimulation pulses of different intensities and durations, little is known about their efficacy to model the neural response to light stimulation protocols of various frequencies and pulse width characteristics. Moreover, it is unclear to what degree the two models can capture the photocurrent kinetics of the recently engineered ChR2 mutants, designed to allow for more precise optical control of neural activity [3]. To address these issues, we investigate a 3-state and a 4-state transition rate model to mimic the photocurrent kinetic of wild type ChR2 (ChR2wt) and a newly validated ChR2 mutant with fast photocurrent kinetics (ChRETA) consistent with the experimental measurements in Gunaydin et al. [3]. We incorporate these models into a fast spiking hippocampal interneuron model [4] in order to examine to what degree the neural response to different experimental stimulation protocols can be successfully simulated. We find that the 3-state model can qualitatively reproduce the neural activity induced by periodic short time interval (2 ms) light pulse stimulation only for low frequencies (<20Hz). The model however fails to capture the experimentally observed features of neural response to higher frequencies (80 and 200 Hz) for both variants of ChR2 investigated. The 4-state model is able to reliably mimic the neural response to light pulse stimulation of all frequencies in both ChR2 variants. Furthermore, for ChR2wt, the 4-state model but not the 3-state model is able to reproduce both the burst-like neural firing activity induced by single, brief (2ms width) light pulses and the plateau potentials observed in neurons for high frequency (200 Hz) light stimulation. Both models were able to mimic the occurrence of missed spikes in ChR2wt when prolonged (60 light pulses) light stimulation is delivered, with better fidelity provided by the 4-state model. Finally, the 4-state model better captures the neural response to Poisson and Gaussian distributed light stimulation pulses. Motivated by the overall better performance of the 4-state model, we investigate the conditions under which a characteristic specific to the 3-state model, namely the mono-exponential decay of the ChR2 photocurrent kinetics (often reported in experimental literature) can occur in the 4-state model. Using analytical methods, we show that for each variant, the photocurrent component associated with the unreported decay constant is vanishingly small, which may explain the experimental difficulty in its empirical evaluation. In summary, we have systematically analyzed the 3-state and 4-state transition rate models for ChR2 photocurrent kinetics and demonstrated that independent of the variant, the 4-state model is able to better capture both qualitative and quantitative features of photocurrent kinetics and the neural response to several different light stimulation protocols. The results suggest that the 4-state transition rate model is a suitable candidate for a universal mathematical framework to model the photocurrent kinetic of ChR2 proteins.

Collective Dynamics of Multiple Microtubule Motors: Connecting In Vitro Observations to In Vivo Functions

Despite the efficiencies of many microtubule motors, sub-cellular cargos are often transported by motor teams composed of multiple processive molecular motors. Furthermore, mutant motors associated with diseases can be coupled to cargos that are also outfitted with copies of wild-type motors. Together, these observations raise important questions regarding the role of motor cooperation in intracellular transport. Although abilities to characterize the transport behaviors of multiple motor systems have improved substantially, many aspects of multiple-motor dynamics remain poorly understood. Here, I will describe our efforts to create structurally-defined complexes composed of multiple kinesin motors and examine their dynamics at the ‘single-motor’ level. I will also describe a transition rate model that predicts the load-dependent transport behaviors of these complexes from detailed measurements of a single motor's elastic and mechanochemical properties. The model reproduces key signatures found in optical trapping studies two-kinesin complexes including observations of non-monotonic dependencies of cargo velocities and motor-microtubule unbinding rates on the applied load, and predicts that multiple kinesins have generic difficulties cooperating productively. While such behavior is influenced significantly by extrinsic factors including the spatio-temporal dependence of the applied load, the net-negative cooperative behaviors exhibited by multiple kinesins appear to be directly linked to the efficiency of kinesin's stepping mechanism, and other types of less efficient and ‘weaker’ processive motors are predicted to cooperate more productively. Thus, mechanochemical efficiencies of different motor types may distinguish how effectively they function as a team, and hence, how motor copy number contributes to the regulation of cargo motion. Finally, the extension of our experimental and computational approaches to studies of multiple motor dynamics inside of living cells will be discussed.

Nearly frictionless states of ultra-high temperature amorphous matter

The almost frictionless transport of very high-temperature amorphous matter that resembles colored glass condensate (possibly having much of its origin in the RHIC heavy ion collisions) in a confined annular tube with transverse corrugations is investigated using the verified transition-rate model and boundary perturbation method. We found that for certain activation volume and energy there exist possible frictionless states that might be associated with perfect fluid formation during the early expansion stage in RHIC Au+Au collisions. We also address the possible similar scenario in LHC Pb+Pb collisions considering possible perfect fluid formation in ultra-high temperature transport of amorphous matter.

Model parameter estimation for Channelrhodopsin-2 light gated ion channels

Recently, Gunyadin et al. [1] designed and validated an engineered mutant of channelrhodopsin-2 (ChR2) labeled E123T to accelerate channel kinetics of ChR2 light gated ion channels. They reported a mono-exponential decay for E123T photocurrent after the light is turned off. This is in contrast to the photocurrent characteristics of the wild type ChR2, which not only exhibits slower channel kinetics, but the decay after the light is turned off is bi-exponential. In earlier work, Nikolic et al. [2] had captured the bi-exponential decay of wild type ChR2 in a four state transition rate model. Our goal in this work is to determine the conditions under which the four state model proposed by Nikolic et al. [2] can exhibit fast mono-exponential decay seen for the E123T mutant of ChR2. We start from the four state transition rate model proposed by Nikolic et al. [2]. This model consists of two closed dark adapted states C1 and C2 and two open light adapted conducting states O1 and O2. The unknown parameters of the model to be estimated from experimental data are: transition rate parameters: {Gd1,Gd2,Gr, e12, e21}, parameters e1 and e2 that capture the efficiency of light induced transition of the closed states, and the parameter γ, which captures the relative permeability of the two open states to ion flow. We first identify constraints on the four state model parameters based on the experimental data by Nikolic et al. [2] on wild type ChR2 photo-current generated in hippocampal cells for light stimulation with intensities I={0.9, 11} mW/mm2. We show that the problem of estimating the unknown parameters defined above from the model derived constraints represents an under-determined system. We convert the parameter estimation problem into a two-step procedure and separate the estimation of light independent and dependent parameters. The parameters are estimated using simulated annealing, a global optimization algorithm. In Table 1, we compare our estimated parameters (MPChR2) for the four state-model with those obtained by Nikolic et al. [2]. Our model parameters provide a much better fit to the experimental data on the slow and fast component of the decay current. In particular, Nikolic et al. [2] assumed Gr=0 to derive the constraints on the bi-exponential decay of the ChR2 photocurrent after the light is turned off. We relaxed this assumption and were able to obtain a better fit to the ChR2 decay current kinetics. Specifically, with Nikolic et al. [2] parameters, the ratio Islow/Ifast=0.37 for the amplitudes of the slow and fast component of the bi-exponential decay current while Islow/Ifast=0.194, using our parameters. The experimental value reported for this ratio is 0.2. We have further conducted sensitivity analysis on the estimated parameters to understand the degree of variability in the parameters given uncertainty in the experimental data. Using this framework, we then estimate the four state model parameters for E123T mutant of ChR2. We notice that the mono-exponential decay rate of E123T is similar to the fast component of the bi-exponential decay current of wild-type ChR2. This indicates that for the mutant, the amplitude of the slow component of the decay current is zero, which provides one additional constraint on the model parameters. We again use simulated annealing to determine the four state model parameters for the E123T mutant of ChR2. The results of this analysis are presented in row 4 of Table 1. Our analysis of the resulting model reveals that it fits the experimental data from Nikolic et al. [2] quite well, with our fit error matching that of Nikolic et al. [2] parameters fit error (10E-4).

Productive Cooperation among Processive Motors Depends Inversely on Their Mechanochemical Efficiency

Subcellular cargos are often transported by teams of processive molecular motors, which raises questions regarding the role of motor cooperation in intracellular transport. Although our ability to characterize the transport behaviors of multiple-motor systems has improved substantially, many aspects of multiple-motor dynamics are poorly understood. This work describes a transition rate model that predicts the load-dependent transport behaviors of multiple-motor complexes from detailed measurements of a single motor's elastic and mechanochemical properties. Transition rates are parameterized via analyses of single-motor stepping behaviors, load-rate-dependent motor-filament detachment kinetics, and strain-induced stiffening of motor-cargo linkages. The model reproduces key signatures found in optical trapping studies of structurally defined complexes composed of two kinesin motors, and predicts that multiple kinesins generally have difficulties in cooperating together. Although such behavior is influenced by the spatiotemporal dependence of the applied load, it appears to be directly linked to the efficiency of kinesin's stepping mechanism, and other types of less efficient and weaker processive motors are predicted to cooperate more productively. Thus, the mechanochemical efficiencies of different motor types may determine how effectively they cooperate together, and hence how motor copy number contributes to the regulation of cargo motion.

A Micromechanical Model of Cargo Transport by Multiple Microtubule Motors

Although the motions of many sub-cellular cargos are known to be driven by teams of microtubule motor proteins, understanding the role collective motor function plays in intracellular transport has been difficult to characterize. One confounding issue is that a team of molecular motors can adopt a spectrum of microtubule-associated configurations, depending on the number of bound motors and their organization on the microtubule. Since each microstate configuration can confer different mechanical and dynamic properties to a cargo, understanding how molecular motors function collectively ultimately requires knowledge of their relative contribution to cargo motility. To address this issue, we have developed methods to examine the load-dependent transport properties of structurally-defined multiple motor systems composed of two kinesin-1 molecules. Herein, we describe a discrete microstate transition-rate model of two-kinesin mechanics that can explain several unexpected behaviors observed in our assays. While this model accounts for a comprehensive spectrum of geometric arrangements of motors between a cargo and the microtubule, transition rates between microstate configurations are almost exclusively parameterized using data from single-kinesin optical trapping measurements. Overall, our model shows strong agreement with our data and recapitulates the central experimental finding that configurations where two kinesins both assume a portion of the applied load are rare and short-lived, causing two kinesins to exhibit negative cooperativity and properties that resemble the action of a single motor molecule. The bottom-up construction of our model also allows us to explore the effects of changes in single motor properties such as compliance, force-velocity relationship, and forward/backward stepping behavior on the dynamics of the system as a whole. This now provides a foundation for analyses of transport behaviors produced by more complex systems composed of different numbers, types and geometric arrangements of motors.

Control of neural synchrony using channelrhodopsin-2: a computational study

In this paper, we present an optical stimulation based approach to induce 1:1 in-phase synchrony in a network of coupled interneurons wherein each interneuron expresses the light sensitive protein channelrhodopsin-2 (ChR2). We begin with a transition rate model for the channel kinetics of ChR2 in response to light stimulation. We then define "functional optical time response curve (fOTRC)" as a measure of the response of a periodically firing interneuron (transfected with ChR2 ion channel) to a periodic light pulse stimulation. We specifically consider the case of unidirectionally coupled (UCI) network and propose an open loop control architecture that uses light as an actuation signal to induce 1:1 in-phase synchrony in the UCI network. Using general properties of the spike time response curves (STRCs) for Type-1 neuron model (Ermentrout, Neural Comput 8:979-1001, 1996) and fOTRC, we estimate the (open loop) optimal actuation signal parameters required to induce 1:1 in-phase synchrony. We then propose a closed loop controller architecture and a controller algorithm to robustly sustain stable 1:1 in-phase synchrony in the presence of unknown deviations in the network parameters. Finally, we test the performance of this closed-loop controller in a network of mutually coupled (MCI) interneurons.

Critical transport of polymeric electrolytes in wavy-rough microtube

We obtain the steady velocities and volume flow rates (up to the second order) of polymeric electrolytes along the cross-section of an (approximated) wavy-rough microtube by using the verified Eyring’s transition rate model and boundary perturbation method. Our numerical results show that the wavy-roughness could tune the electric-field-driven transport especially for larger forcing due to the larger surface-to-volume ratio and slip-velocity effect. We also found a rather low electrical resistance for certain critical temperature after careful selection of geometric and material parameters.

Coupling between motor proteins determines dynamic behaviors of motor protein assemblies.

Transport of intracellular cargos by multiple microtubule motor proteins is believed to be a common and significant phenomenon in vivo, yet signatures of the microscopic dynamics of multiple motor systems are only now beginning to be resolved. Understanding these mechanisms largely depends on determining how grouping motors affect their association with microtubules and stepping rates, and hence, cargo run lengths and velocities. We examined this problem using a discrete state transition rate model of collective transport. This model accounts for the structural and mechanical properties in binding/unbinding and stepping transitions between distinct microtubule-bound configurations of a multiple motor system. In agreement with previous experiments that examine the dynamics of two coupled kinesin-1 motors, the energetic costs associated with deformations of mechanical linkages within a multiple motor assembly are found to reduce the system's overall microtubule affinity, producing attenuated mean cargo run lengths compared to cases where motors are assumed to function independently. With our present treatment, this attenuation largely stems from reductions in the microtubule binding rate and occurs even when mechanical coupling between motors is weak. Thus, our model suggests that, at least for a variety of kinesin-dependent transport processes, the net 'gains' obtained by grouping motors together may be smaller than previously expected.

Force-velocity relations for multiple-molecular-motor transport

A transition rate model of cargo transport by N molecular motors is proposed. Under the assumption of steady state, the force-velocity curve of multimotor system can be derived from the force-velocity curve of a single motor. Our work shows, in the case of low load, that the velocity of multimotor system can decrease or increase with increasing motor number, which is dependent on the single motor force-velocity curve; and most commonly, the velocity decreases. This gives a possible explanation to some recent experimental observations.

Role of relaxation in the quantum measurement of a superconducting qubit using a nonlinear oscillator

We analyze the relaxation of a superconducting flux qubit during measurement. The qubit state is measured with a nonlinear oscillator driven across the threshold of bifurcation, acting as a switching dispersive detector. This readout scheme is of quantum nondemolition type. Two successive readouts are used to analyze the evolution of the qubit and the detector during the measurement. We introduce a simple transition rate model for characterizing the qubit relaxation and the detector switching process. Corrected for qubit relaxation the readout fidelity is at least 95%. Qubit relaxation strongly depends on the driving strength and the state of the oscillator.

A sickle transition-rate model with starting threshold

Billari (2001) introduced a new type of single-spell parametric transition-rate model: transition-rate models with a starting threshold. In such models, the transition-rate function is composed of two additive terms. The first term is a constant that holds for any given duration; the second is a ‘traditional’ transition-rate function with the threshold as its time origin, and it is added after a certain threshold point. The possibility of allowing for the presence of long-term survivors in the social process has not yet been dealt with, and it is of specific interest in several domains of application. In this paper, we develop the specific case of the sickle model. We discuss its features, its implementation as a starting threshold model, and the estimation of its parameters. The sickle model with starting threshold is then applied to the union formation of Italian men and women, using the Fertility and Family Survey data.

Is it a Timing or a Probability Effect? Four Simulations and an Application of Transition Rate Models to the Analysis of Unemployment Exit

Among the applications of event history analysis, in the last 10 years the lion's share has been played by proportional transition rate model. This type of models suffers from a major draw-back: it does not allow us to distinguish whether a covariate affects the event timing (the event occurs sooner/later) or the overall probability of the ultimate event occurrence (the chances of occurrence are constantly higher/lower). Thus, a positive/negative effect of a covariate found using a proportional transition rate model might reflect an acceleration/deceleration in the timing of the event and/or a high/low probability of the ultimate event occurrence (Yamaguchi, 1992). This paper shows how this problem can be reformulated in terms of the proportionality/non proportionality of the covariate effects. A twofold solution to disentangle the timing/probability problem is presented: this solution consists of a test of the proportionality of the covariate effects and a computation of the survival function at the end of the time interval studied. Two applications are discussed. The first one is based on four simulated processes. The second is based on an analysis of unemployment exit in Italy, with particular attention being paid to the effects of unemployment benefits. In the conclusion, implications for future applications of event history analysis are discussed.

A log-logistic regression model for a transition rate with a starting threshold

The paper presents a new type of parametric transition rate model that is particularly suitable for studying household and union formation. In such studies, it is often not easy to determine the moment at which individuals actually enter the population at risk - or at least when the risk begins to become socially important. Even in the presence of regulations stipulated by law, one might be interested in studying ‘social’ timetables. We assume that there is a constant rate for any duration and that after a certain threshold point a log-logistic rate is added, with this threshold as its time origin. This can be justified in a behavioural sense by assuming that random and social transitions arise from separate processes. We then apply the model to union formation in Italy and show how threshold and intensity effects generated by theoretical hypotheses can be revealed.

A transition rate model for first admissions to psychiatric institutions.

This paper describes the application of a parametric transition rate model, the generalized log-logistic model, to the duration of first admissions to psychiatric institutions. The final model included diagnosis, gender, age, living conditions and year of admission as covariates. Characteristics of the log-logistic model are described extensively. Parametric transition models offer challenging and promising possibilities to model duration of hospital stay.