Dwell time symmetry in random walks and molecular motors

The statistics of steps and dwell times in reversible molecular motors differ from those of cycle completion in enzyme kinetics. The reason is that a step is only one of several transitions in the mechanochemical cycle. As a result, theoretical results for cycle completion in enzyme kinetics do not apply to stepping data. To allow correct parameter estimation, and to guide data analysis and experiment design, a theoretical treatment is needed that takes this observation into account. In this article, we model the distribution of dwell times and number of forward and backward steps using first passage processes, based on the assumption that forward and backward steps correspond to different directions of the same transition. We extend recent results for systems with a single cycle and consider the full dwell time distributions as well as models with multiple pathways, detectable substeps, and detachments. Our main results are a symmetry relation for the dwell time distributions in reversible motors, and a relation between certain relative step frequencies and the free energy per cycle. We demonstrate our results by analyzing recent stepping data for a bacterial flagellar motor, and discuss the implications for the efficiency and reversibility of the force-generating subunits.     

Synchronous cell growth occurs upon synchronizing the two regulatory steps of the Saccharomyces cerevisiae cell cycle

There are two known asynchronous steps in the budding yeast Saccharomyces cerevisiae cell cycle, where an asynchronous step is one which is completed in different lengths of time by different cells in an isogenic population. It is shown here that elimination of the asynchrony due to cell size by preincubation of cells with the mating pheromone alpha-factor, and decreasing the asynchrony in the cdc28 'start' step by lowering the pH, yields highly synchronous cell growth measured as the time period between the emergence of buds. In one experiment, cell budding for 92% of cells occurred within a 12-min period for at least two generations. Under identical conditions, cell number increase is not as synchronous as bud emergence indicating that there is a third asynchronous step, which is concluded to be at cell separation. These results are consistent with there being two--and only two--asynchronous steps in the cell cycle, measured from bud emergence to bud emergence. Surprisingly, these two steps are also the two major regulatory steps of the cell cycle. It is concluded that asynchrony may be a general feature of cell cycle regulatory steps. The asynchrony in the completion of the cdc28 'start' step which occurs in the first cell cycle after alpha-factor washout is shown here to be almost or entirely eliminated for the second passage through this step after alpha-factor washout. The 'true' time between the onset of budding and the point where 50% of cells have budded (called t50BE) is 17 and less than or equal to 2 min for the first and second budding, respectively, after alpha-factor washout. The cell cycle models requiring a transition probability, or asynchrony, at 'start' for every cell cycle are therefore incorrect.     

Kinesin steps do not alternate in size

Kinesin is a two-headed motor protein that transports cargo inside cells by moving stepwise on microtubules. Its exact trajectory along the microtubule is unknown: alternative pathway models predict either uniform 8-nm steps or alternating 7- and 9-nm steps. By analyzing single-molecule stepping traces from “limping” kinesin molecules, we were able to distinguish alternate fast- and slow-phase steps and thereby to calculate the step sizes associated with the motions of each of the two heads. We also compiled step distances from nonlimping kinesin molecules and compared these distributions against models predicting uniform or alternating step sizes. In both cases, we find that kinesin takes uniform 8-nm steps, a result that strongly constrains the allowed models.     

Spectrophotometric monitoring in continuous-flow Boc-based solid-phase peptide synthesis.

It has been demonstrated that SPPS with Boc amino group protection can be monitored spectrophotometrically if it is performed in a continuous-flow reactor of variable volume. It is shown that this approach provides useful and adequate evidence on the beginning/end-point of most steps of the SPPS cycle. At the deprotection step the spectrophotometric monitoring enables real-time recording of the initial and final moments of the process. When synthesizing a 'difficult' polyalanine sequence, we were able to monitor variation in the deprotection dynamics associated with the aggregation phenomena. The time actually necessary for the Boc protecting group removal appeared to be significantly smaller than that usually preset in the available Boc-SPPS protocols.     

Extracting dwell time sequences from processive molecular motor data

Processive molecular motors, such as kinesin, myosin, or dynein, convert chemical energy into mechanical energy by hydrolyzing ATP. The mechanical energy is used for moving in discrete steps along the cytoskeleton and carrying a molecular load. Single-molecule recordings of motor position along a substrate polymer appear as a stochastic staircase. Recordings of other single molecules, such as F1-ATPase, RNA polymerase, or topoisomerase, have the same appearance. We present a maximum likelihood algorithm that extracts the dwell time sequence from noisy data, and estimates state transition probabilities and the distribution of the motor step size. The algorithm can handle models with uniform or alternating step sizes, and reversible or irreversible kinetics. A periodic Markov model describes the repetitive chemistry of the motor, and a Kalman filter allows one to include models with variable step size and to correct for baseline drift. The data are optimized recursively and globally over single or multiple data sets, making the results objective over the full scale of the data. Local binary algorithms, such as the t-test, do not represent the behavior of the whole data set. Our method is model-based, and allows rapid testing of different models by comparing the likelihood scores. From data obtained with current technology, steps as small as 8 nm can be resolved and analyzed with our method. The kinetic consequences of the extracted dwell sequence can be further analyzed in detail. We show results from analyzing simulated and experimental kinesin and myosin motor data. The algorithm is implemented in the free QuB software.     

Stochastic properties of actomyosin motor

The epoch-making techniques for manipulating a single myosin molecule have recently been developed, and the unitary mechanical reactions of a single actomyosin, muscle motor molecule, are directly measured. The data show that the unitary mechanical step during sliding along an actin filament of approximately 5.5 nm, but groups of two to five rapid steps in succession produce displacements of approximately 11-30 nm. The instances of multiple stepping are produced by single myosin heads during one biochemical cycle of ATP hydrolysis. Thus, the coupling between ATP hydrolysis cycle and mechanical step is variable, i.e. loose-coupling. Such a unique operation of actomyosin molecules is different from that of man-made machines, and most likely explains the flexible and effective mechanisms of molecular machines in the biosystems.     

Removal of ECG interference from surface respiratory electromyography

The signal to noise ratio (SNR) of surface respiratory electromyography signal is very low. Indeed EMG signal is contaminated by different types of noise especially the cardiac artefact ECG. This article explores the problem of removing ECG artefact from respiratory EMG signal. The new method uses an adaptive structure with an electrocardyographic ECG reference signal carried out by wavelet decomposition. The proposed algorithm requires only one channel to both estimating the adaptive filter input reference noise and the respiratory EMG signal. This new technique demonstrates how two steps will be combined: the first step decomposes the signal with forward discrete wavelet transform into sub-bands to get the wavelet coefficients. Then, an improved soft thresholding function was applied. And the ECG input reference signal is reconstructed with the transformed coefficients whereas, the second uses an adaptive filter especially the LMS one to remove the ECG signal. After trying statistical as well as mathematical analysis, the complete investigation ensures that all details and steps make proof that our rigorous method is appropriate. Compared to the results obtained using previous techniques, the results achieved using the new algorithm show a significant improvement in the efficiency of the ECG rejection.     

Model-based optimization of a sequencing batch reactor for biological nitrogen removal

An optimal operating mode for a sequencing batch reactor was determined via a model-based optimization. Synthetic wastewater containing mainly organic matter (as glucose) and nitrogen (as ammonium chloride) was treated without any addition of an external carbon source to accomplish denitrification step. A simplified model was used to describe process dynamics, comprised of six ordinary differential equations and an empirical correlation for oxygen consumption rate. Batch cycle time was the chosen objective function to be minimized for a fixed volume of waste to be treated. Furthermore, as SBR operation is divided in two major phases - aerobic and anoxic, to achieve total pollutants removal within minimum time, these phases can be repeatedly alternated. To ensure availability of organic matter necessary for denitrification, these two phases were combined with feed steps. Different feed strategies were tested using one, two or three feed steps. A successive quadratic programming algorithm was used, and maximum values for final COD, nitrate and ammonium concentrations, as well as maximum feed pump flow rate were some the process constraints. One step feed strategy was indicated by the optimization leading to a batch cycle time of 5h.     

Power line interference rejection from surface electromyography signal using an adaptive algorithm

This work focuses on the power line interference (PLI) rejection from surface EMG signal. It contains three parts: the algorithm, the experimental setting and the results. This study begins with describing the new technique, which consists in filtering respiratory surface electromyogram signals (EMG + PLI), then, becoming familiar with it. The proposed algorithm requires only one channel to both estimating the adaptive filter input reference noise and the EMG signal. The algorithm of PLI rejection has been organized into two steps. The first step insists to apply adaptive filter, especially the LMS one, in which the reference input is mathematically constructed using two different cosine functions; 50 Hz (the fundamental) function and 150 Hz (the first harmonic) function. Whereas, the second step applies the matching pursuit algorithm that uses the cosine packet dictionary to improve the result of PLI obtained at the first step. After trying statistical, as well as mathematical analysis, the complete investigation ensures that all details and steps make proof that our rigorous method is appropriate, we have also compared our method with the previous known techniques.     

General methods for analysis of sequential "n-step" kinetic mechanisms: application to single turnover kinetics of helicase-catalyzed DNA unwinding

Helicase-catalyzed DNA unwinding is often studied using "all or none" assays that detect only the final product of fully unwound DNA. Even using these assays, quantitative analysis of DNA unwinding time courses for DNA duplexes of different lengths, L, using "n-step" sequential mechanisms, can reveal information about the number of intermediates in the unwinding reaction and the "kinetic step size", m, defined as the average number of basepairs unwound between two successive rate limiting steps in the unwinding cycle. Simultaneous nonlinear least-squares analysis using "n-step" sequential mechanisms has previously been limited by an inability to float the number of "unwinding steps", n, and m, in the fitting algorithm. Here we discuss the behavior of single turnover DNA unwinding time courses and describe novel methods for nonlinear least-squares analysis that overcome these problems. Analytic expressions for the time courses, f(ss)(t), when obtainable, can be written using gamma and incomplete gamma functions. When analytic expressions are not obtainable, the numerical solution of the inverse Laplace transform can be used to obtain f(ss)(t). Both methods allow n and m to be continuous fitting parameters. These approaches are generally applicable to enzymes that translocate along a lattice or require repetition of a series of steps before product formation.     

The Properties of Adaptive Walks in Evolving Populations of Fungus

The rarity of beneficial mutations has frustrated efforts to develop a quantitative theory of adaptation. Recent models of adaptive walks, the sequential substitution of beneficial mutations by selection, make two compelling predictions: adaptive walks should be short, and fitness increases should become exponentially smaller as successive mutations fix. We estimated the number and fitness effects of beneficial mutations in each of 118 replicate lineages of Aspergillus nidulans evolving for approximately 800 generations at two population sizes using a novel maximum likelihood framework, the results of which were confirmed experimentally using sexual crosses. We find that adaptive walks do indeed tend to be short, and fitness increases become smaller as successive mutations fix. Moreover, we show that these patterns are associated with a decreasing supply of beneficial mutations as the population adapts. We also provide empirical distributions of fitness effects among mutations fixed at each step. Our results provide a first glimpse into the properties of multiple steps in an adaptive walk in asexual populations and lend empirical support to models of adaptation involving selection towards a single optimum phenotype. In practical terms, our results suggest that the bulk of adaptation is likely to be accomplished within the first few steps.     

Estimation of temporal gait parameters using Bayesian models on acceleration signals

The purpose of this study is to develop a system capable of performing calculation of temporal gait parameters using two low-cost wireless accelerometers and artificial intelligence-based techniques as part of a larger research project for conducting human gait analysis. Ten healthy subjects of different ages participated in this study and performed controlled walking tests. Two wireless accelerometers were placed on their ankles. Raw acceleration signals were processed in order to obtain gait patterns from characteristic peaks related to steps. A Bayesian model was implemented to classify the characteristic peaks into steps or nonsteps. The acceleration signals were segmented based on gait events, such as heel strike and toe-off, of actual steps. Temporal gait parameters, such as cadence, ambulation time, step time, gait cycle time, stance and swing phase time, simple and double support time, were estimated from segmented acceleration signals. Gait data-sets were divided into two groups of ages to test Bayesian models in order to classify the characteristic peaks. The mean error obtained from calculating the temporal gait parameters was 4.6%. Bayesian models are useful techniques that can be applied to classification of gait data of subjects at different ages with promising results     

Rapid vasoregulatory mechanisms in exercising human skeletal muscle: dynamic response to repeated changes in contraction intensity

We tested the hypothesis that vasoregulatory mechanisms exist in humans that can rapidly adjust muscle blood flow to repeated increases and decreases in exercise intensity. Six men and seven women (age, 24.4+/-1.3 yr) performed continuous dynamic forearm handgrip contractions (1- to 2-s contraction-to-relaxation duty cycle) during repeated step increases and decreases in contraction intensity. Three step change oscillation protocols were examined: Slow (7 contractions per contraction intensityx10 steps); Fast (2 contractions per contraction intensityx15 steps); and Very Fast (1 contraction per contraction intensityx15 steps). Forearm blood flow (FBF; Doppler and echo ultrasonography), heart rate (ECG), and mean arterial pressure (arterial tonometry) were examined for the equivalent of a cardiac cycle during each relaxation phase (FBFrelax). Mean arterial pressure and heart rate did not change during repeated step changes (P=0.352 and P=0.190). For both Slow and Fast conditions, relaxation phase FBFrelax adjusted immediately and repeatedly to both increases and decreases in contraction intensity, and the magnitude and time course of FBFrelax changes were virtually identical. For the Very Fast condition, FBFrelax increased with the first contraction and thereafter slowly increased over the course of repeated contraction intensity oscillations. We conclude that vasoregulatory mechanisms exist in human skeletal muscle that are capable of rapidly and repeatedly adjusting muscle blood flow with ongoing step changes in contraction intensity. Importantly, they demonstrate symmetry in response magnitude and time course with increasing versus decreasing contraction intensity but cannot adjust to very fast exercise intensity oscillations.     

A dependent pathway of gene functions leading to chromosome segregation in Saccharomyces cerevisiae

Methyl-benzimidazole-2-ylcarbamate (MBC) inhibits the mitotic cell cycle of Saccharomyces cerevisiae at a stage subsequent to DNA synthesis and before the completion of nuclear division (Quinlan, R. A., C. I. Pogson, and K, Gull, 1980, J Cell Sci., 46: 341-352). The step in the cell cycle that is sensitive to MBC inhibition was ordered to reciprocal shift experiments with respect to the step catalyzed by cdc gene products. Execution of the CDC7 step is required for the initiation of DNA synthesis and for completion of the MBC-sensitive step. Results obtained with mutants (cdc2, 6, 8, 9, and 21) defective in DNA replication and with an inhibitor of DNA replication (hydroxyurea) suggest that some DNA replication required for execution of the MBC-sensitive step but that the completion of replication is not. Of particular interest were mutants (cdc5, 13, 14, 15, 16, 17, and 23) that arrest cell division after DNA replication but before nuclear division since previous experiments had not been able to resolve the pathway of events in this part of the cell cycle. Execution of the CDC17 step was found to be a prerequisite for execution of the MBC- sensitive step; the CDC13, 16 and 23 steps are executed independently of the MBC-sensitive step; execution of the MBC-sensitive step is prerequisite for execution of the MBC-sensitive step; execution of the MBC-sensitive step is prerequisite for execution of the CDC14 and 23 steps. These results considerably extend the dependent pathway of events that constitute the cell cycle of S. cerevisiae.     

Library-based numerical reduction of the Hodgkin–Huxley neuron for network simulation

We present an efficient library-based numerical method for simulating the Hodgkin–Huxley (HH) neuronal networks. The key components in our numerical method involve (i) a pre-computed high resolution data library which contains typical neuronal trajectories (i.e., the time-courses of membrane potential and gating variables) during the interval of an action potential (spike), thus allowing us to avoid resolving the spikes in detail and to use large numerical time steps for evolving the HH neuron equations; (ii) an algorithm of spike-spike corrections within the groups of strongly coupled neurons to account for spike-spike interactions in a single large time step. By using the library method, we can evolve the HH networks using time steps one order of magnitude larger than the typical time steps used for resolving the trajectories without the library, while achieving comparable resolution in statistical quantifications of the network activity, such as average firing rate, interspike interval distribution, power spectra of voltage traces. Moreover, our large time steps using the library method can break the stability requirement of standard methods (such as Runge–Kutta (RK) methods) for the original dynamics. We compare our library-based method with RK methods, and find that our method can capture very well phase-locked, synchronous, and chaotic dynamics of HH neuronal networks. It is important to point out that, in essence, our library-based HH neuron solver can be viewed as a numerical reduction of the HH neuron to an integrate-and-fire (I&F) neuronal representation that does not sacrifice the gating dynamics (as normally done in the analytical reduction to an I&F neuron).     

Anisotropic adaptive finite element method for modelling blood flow

In this study, we present an adaptive anisotropic finite element method (FEM) and demonstrate how computational efficiency can be increased when applying the method to the simulation of blood flow in the cardiovascular system. We use the SUPG formulation for the transient 3D incompressible Navier–Stokes equations which are discretised by linear finite elements for both the pressure and the velocity field.

Given the pulsatile nature of the flow in blood vessels we have pursued adaptivity based on the average flow over a cardiac cycle. Error indicators are derived to define an anisotropic mesh metric field. Mesh modification algorithms are used to anisotropically adapt the mesh according to the desired size field. We demonstrate the efficiency of the method by first applying it to pulsatile flow in a straight cylindrical vessel and then to a porcine aorta with a stenosis bypassed by a graft. We demonstrate that the use of an anisotropic adaptive FEM can result in an order of magnitude reduction in computing time with no loss of accuracy compared to analyses obtained with uniform meshes.     

The valuation step within LCA

International human rights conventions and international environmental laws and conventions have been used to deduce criteria for a valuation procedure for life cycle assessment. The valuation procedure relates to the impact oriented assessment of the Centrum voor Milieukunde in Leiden (CML). The panel method is suitable for comparison LCAs of two systems, or optimization LCAs. The method consists of four steps. Step one is the normalization of the results of the impact assessment. In step two, a panel of experts values the results by three qualitative criteria (time, space, hazard). In step three, a ranking diagram technique is used for a formalized priority setting and a preliminary identification of the product causing the most environmental burdens. Step four includes a sensitivity analysis and a plausibility check based on an energy and waste analysis. Discrepancies between the plausibility check and step three may cause a reevaluation of parts of the valuation, impact assessment, inventory table or goal definition of the LCA.     

Insects Use Two Distinct Classes of Steps during Unrestrained Locomotion

Background

Adaptive, context-dependent control of locomotion requires modulation of centrally generated rhythmic motor patterns through peripheral control loops and postural reflexes. Thus assuming that the modulation of rhythmic motor patterns accounts for much of the behavioural variability observed in legged locomotion, investigating behavioural variability is a key to the understanding of context-dependent control mechanisms in locomotion. To date, the variability of unrestrained locomotion is poorly understood, and virtually nothing is known about the features that characterise the natural statistics of legged locomotion. In this study, we quantify the natural variability of hexapedal walking and climbing in insects, drawing from a database of several thousand steps recorded over two hours of walking time.

Results

We show that the range of step length used by unrestrained climbing stick insects is large, showing that step length can be changed substantially for adaptive locomotion. Step length distributions were always bimodal, irrespective of leg type and walking condition, suggesting the presence of two distinct classes of steps: short and long steps. Probability density of step length was well-described by a gamma distribution for short steps, and a logistic distribution for long steps. Major coefficients of these distributions remained largely unaffected by walking conditions. Short and long steps differed concerning their spatial occurrence on the walking substrate, their timing within the step sequence, and their prevalent swing direction. Finally, ablation of structures that serve to improve foothold increased the ratio of short to long steps, indicating a corrective function of short steps.

Conclusions

Statistical and functional differences suggest that short and long steps are physiologically distinct classes of leg movements that likely reflect distinct control mechanisms at work.     

Backstepping Mechanism of Kinesin-1

Kinesin-1 is an ATP-driven molecular motor that transports cellular cargo along microtubules. At low loads, kinesin-1 almost always steps forward, toward microtubule plus ends, but at higher loads, it can also step backward. Backsteps are usually 8 nm but can be larger. These larger backward events of 16 nm, 24 nm, or more are thought to be slips rather than steps because they are too fast to consist of multiple, tightly coupled 8-nm steps. Here, we propose that not only these larger backsteps, but all kinesin-1 backsteps, are slips. We show first that kinesin waits before forward steps for less time than before backsteps and detachments; second, we show that kinesin waits for the same amount of time before backsteps and detachments; and third, we show that by varying the microtubule type, we can change the ratio of backsteps to detachments without affecting forward stepping. Our findings indicate that backsteps and detachments originate from the same state and that this state arises later in the mechanochemical cycle than the state that gives rise to forward steps. To explain our data, we propose that, in each cycle of ATP turnover, forward kinesin steps can only occur before Pi release, whereas backslips and detachments can only occur after Pi release. In the scheme we propose, Pi release gates access to a weak binding K⋅ADP-K⋅ADP state that can slip back along the microtubule, re-engage, release ADP, and try again to take an ATP-driven forward step. We predict that this rescued detachment pathway is key to maintaining kinesin processivity under load.