Time dependency of molecular rate estimates and systematic overestimation of recent divergence times

Studies of molecular evolutionary rates have yielded a wide range of rate estimates for various genes and taxa. Recent studies based on population-level and pedigree data have produced remarkably high estimates of mutation rate, which strongly contrast with substitution rates inferred in phylogenetic (species-level) studies. Using Bayesian analysis with a relaxed-clock model, we estimated rates for three groups of mitochondrial data: avian protein-coding genes, primate protein-coding genes, and primate d-loop sequences. In all three cases, we found a measurable transition between the high, short-term (<1–2 Myr) mutation rate and the low, long-term substitution rate. The relationship between the age of the calibration and the rate of change can be described by a vertically translated exponential decay curve, which may be used for correcting molecular date estimates. The phylogenetic substitution rates in mitochondria are approximately 0.5% per million years for avian protein-coding sequences and 1.5% per million years for primate protein-coding and d-loop sequences. Further analyses showed that purifying selection offers the most convincing explanation for the observed relationship between the estimated rate and the depth of the calibration. We rule out the possibility that it is a spurious result arising from sequence errors, and find it unlikely that the apparent decline in rates over time is caused by mutational saturation. Using a rate curve estimated from the d-loop data, several dates for last common ancestors were calculated: modern humans and Neandertals (354 ka; 222–705 ka), Neandertals (108 ka; 70–156 ka), and modern humans (76 ka; 47–110 ka). If the rate curve for a particular taxonomic group can be accurately estimated, it can be a useful tool for correcting divergence date estimates by taking the rate decay into account. Our results show that it is invalid to extrapolate molecular rates of change across different evolutionary timescales, which has important consequences for studies of populations, domestication, conservation genetics, and human evolution.

Use of Bayesian MUNE to show differing rate of loss of motor units in subgroups of ALS

Objectives To evaluate differences among patients with different clinical features of ALS, we used our Bayesian method of motor unit number estimation (MUNE). Methods We performed serial MUNE studies on 42 subjects who fulfilled the diagnostic criteria for ALS during the course of their illness. Subjects were classified into three subgroups according to whether they had typical ALS (with upper and lower motor neurone signs) or had predominantly upper motor neurone weakness with only minor LMN signs, or predominantly lower motor neurone weakness with only minor UMN signs. In all subjects we calculated the half life of MUs, defined as the expected time for the number of MUs to halve, in one or more of the abductor digiti minimi (ADM), abductor pollicis brevis (APB) and extensor digitorum brevis (EDB) muscles. Results The mean half life of MUs was less in subjects who had typical ALS with both upper and lower motor neurone signs than in those with predominantly upper motor neurone weakness or predominantly lower motor neurone weakness. In 18 subjects we analysed the estimated size of the MUs and demonstrated the appearance of large MUs in subjects with upper or lower motor neurone predominant weakness. We found that the appearance of large MUs was correlated with the half life of MUs. Conclusions Patients with different clinical features of ALS have different rates of loss and different sizes of MUs. Significance: These findings could indicate differences in disease pathogenesis.

A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation

The fractional Fokker-Planck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the non-local property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations. In this paper, a space-time spectral method is presented for the numerical solution of the time fractional Fokker-Planck initial-boundary value problem. The proposed method employs the Jacobi polynomials for the temporal discretization and Fourier-like basis functions for the spatial discretization. Due to the diagonalizable trait of the Fourier-like basis functions, this leads to a reduced representation of the inner product in the Galerkin analysis. We prove that the time fractional Fokker-Planck equation attains the same approximation order as the time fractional diffusion equation developed in [23] by using the present method. That indicates an exponential decay may be achieved if the exact solution is sufficiently smooth. Finally, some numerical results are given to demonstrate the high order accuracy and efficiency of the new numerical scheme. The results show that the errors of the numerical solutions obtained by the space-time spectral method decay exponentially.

How does contrasting dependence of impurity-atom diffusivity on the density of host disordered medium arise?

We report results of molecular dynamics investigations into neutral impurity diffusing within an amorphous solid as a function of the size of the diffusant and density of the host amorphous matrix. We find that self diffusivity exhibits an anomalous maximum as a function of the size of the impurity species. An analysis of properties of the impurity atom with maximum diffusivity shows that it is associated with lower mean square force, reduced backscattering of velocity autocorrelation function, near-exponential decay of the intermediate scattering function (as compared to stretched-exponential decay for other sizes of the impurity species) and lower activation energy. These results demonstrate the existence of size-dependent diffusivity maximum in disordered solids. Further, we show that the diffusivity maximum is observed at lower impurity diameters with increase in density. This is explained in terms of the Levitation parameter and the void structure of the amorphous solid. We demonstrate that these results imply contrasting dependence of self diffusivity (D) on the density of the amorphous matrix, p. D increases with p for small sizes of the impurity but shows an increase followed by a decrease for intermediate sizes of the impurity atom. For large sizes of the impurity atom, D decreases with increase in p. These contrasting dependence arises naturally from the existence of Levitation Effect.

Effect of phosphine dose on sorption in wheat

BACKGROUND: In spite of the extensive use of phosphine fumigation around the world to control insects in stored grain, and the knowledge that grain sorbs phosphine, the effect of concentration on sorption has not been quantified. A laboratory study was undertaken, therefore, to investigate the effect of phosphine dose on sorption in wheat. Wheat was added to glass flasks to achieve filling ratios of 0.25-0.95, and the flasks were sealed and injected with phosphine at 0.1-1.5 mg L-1 based on flask volume. Phosphine concentration was monitored for 8 days at 25°C and 55% RH. RESULTS: When sorption occurred, phosphine concentration declined with time and was approximately first order, i.e. the data fitted an exponential decay equation. Percentage sorption per day was directly proportional to filling ratio, and was negatively correlated with dose for any given filling ratio. Based on the results, a tenfold increase in dose would result in a halving of the sorption constant and the percentage daily loss. Wheat was less sorptive if it was fumigated for a second time. CONCLUSIONS: The results have implications for the use of phosphine for control of insects in stored wheat. This study shows that dose is a factor that must be considered when trying to understand the impact of sorption on phosphine concentration, and that there appears to be a limit to the capacity of wheat to sorb phosphine.

Lantana (Lantana camara) Seed Bank Dynamics: Seedling Emergence and Seed Survival.

Seed persistence is poorly quantified for invasive plants of subtropical and tropical environments and Lantana camara, one of the world's worst weeds, is no exception. We investigated germination, seedling emergence, and seed survival of two lantana biotypes (Pink and pink-edged red [PER]) in southeastern Queensland, Australia. Controlled experiments were undertaken in 2002 and repeated in 2004, with treatments comprising two differing environmental regimes (irrigated and natural rainfall) and sowing depths (0 and 2 cm). Seed survival and seedling emergence were significantly affected by all factors (time, biotype, environment, sowing depth, and cohort) (P < 0.001). Seed dormancy varied with treatment (environment, sowing depth, biotype, and cohort) (P < 0.001), but declined rapidly after 6 mo. Significant differential responses by the two biotypes to sowing depth and environment were detected for both seed survival and seedling emergence (P < 0.001). Seed mass was consistently lower in the PER biotype at the population level (P < 0.001), but this variation did not adequately explain the differential responses. Moreover, under natural rainfall the magnitude of the biotype effect was unlikely to result in ecologically significant differences. Seed survival after 36 mo under natural rainfall ranged from 6.8 to 21.3%. Best fit regression analysis of the decline in seed survival over time yielded a five-parameter exponential decay model with a lower asymptote approaching −0.38 (% seed survival = [( 55 − (−0.38)) • e (k • t)] + −0.38; R2 = 88.5%; 9 df). Environmental conditions and burial affected the slope parameter or k value significantly (P < 0.01). Seed survival projections from the model were greatest for buried seeds under natural rainfall (11 yr) and least under irrigation (3 yr). Experimental data and model projections suggest that lantana has a persistent seed bank and this should be considered in management programs, particularly those aimed at eradication.

Changes in phosphine sorption in wheat after storage at two temperatures.

BACKGROUND: Wheat can be stored for many months before being fumigated with phosphine to kill insects, so a study was undertaken to investigate whether the sorptive capacity of wheat changes as it ages. Wheat was stored at 15 or 25C and 55% RH for up to 5.5 months, and samples were fumigated at intervals to determine sorption. Sealed glass flasks (95% full) were injected with 1.5 mg L-1 of phosphine based on flask volume. Concentrations were monitored for 11 days beginning 2 h after injection. Some wheat samples were refumigated after a period of ventilation. Several fumigations of wheat were conducted to determine the pattern of sorption during the first 24 h. RESULTS: Phosphine concentration declined exponentially with time from 2 h after injection. Rate of sorption decreased with time spent in storage at either 15 or 25C and 55% RH. Rate of sorption tended to be lower when wheat was refumigated, but this could be explained by time in storage rather than by refumigation per se. The data from the 24 h fumigations did not fit a simple exponential decay equation. Instead, there was a rapid decline in the first hour, with phosphine concentration falling much more slowly thereafter. CONCLUSIONS: The results have implications for phosphine fumigation of insects in stored wheat. Both the time wheat has spent in storage and the temperature at which it has been stored are factors that must be considered when trying to understand the impact of sorption on phosphine concentrations in commercial fumigations.

Sorption and desorption of sulfuryl fluoride by wheat, flour and semolina

Sulfuryl fluoride (SF) has been developed as a fumigant for control of insect pests in stored grain. However, there is very limited information on the sorption behaviour of this fumigant, which can be critical to its bioactivity, application and potential for residues. We undertook a comprehensive laboratory study of the sorption and desorption of SF by wheat (bread and durum), flour and semolina at 15, 25 and 35 °C, moisture contents 12% and 15%, and concentration × time combinations at CT = 1500 mgh/L (4.167 mg/L × 360 h, 8.928 mg/L × 168 h and 31.25 mg/L × 48 h). At each dosage, sorption rate increased as commodity temperature and moisture content increased. The highest rates of sorption occurred at 35 °C and 15% m.c., and lowest rates at 15 °C and 12% m.c., and the rate was independent of initial concentration. Sorption followed first order reaction kinetics described by the exponential decay equation, Ct = C0·e−k*t, where k is the sorption rate constant. The most important factors determining the rate of sorption were commodity particle size (exposed surfaces) and temperature. Little sorption of fumigant occurred within the first 24 h whereas longer fumigation times resulted in significant sorption. Unbound SF was rapidly lost from the commodity upon aeration with no further desorption detected under any of the test conditions.

Dynamics of Barrierless and Activated Chemical Reactions in a Dispersive Medium within the Fractional Diffusion Equation Approach

Barrierless chemical reactions have often been modeled as a Brownian motion on a one-dimensional harmonic potential energy surface with a position-dependent reaction sink or window located near the minimum of the surface. This simple (but highly successful) description leads to a nonexponential survival probability only at small to intermediate times but exponential decay in the long-time limit. However, in several reactive events involving proteins and glasses, the reactions are found to exhibit a strongly nonexponential (power law) decay kinetics even in the long time. In order to address such reactions, here, we introduce a model of barrierless chemical reaction where the motion along the reaction coordinate sustains dispersive diffusion. A complete analytical solution of the model can be obtained only in the frequency domain, but an asymptotic solution is obtained in the limit of long time. In this case, the asymptotic long-time decay of the survival probability is a power law of the Mittag−Leffler functional form. When the barrier height is increased, the decay of the survival probability still remains nonexponential, in contrast to the ordinary Brownian motion case where the rate is given by the Smoluchowski limit of the well-known Kramers' expression. Interestingly, the reaction under dispersive diffusion is shown to exhibit strong dependence on the initial state of the system, thus predicting a strong dependence on the excitation wavelength for photoisomerization reactions in a dispersive medium. The theory also predicts a fractional viscosity dependence of the rate, which is often observed in the reactions occurring in complex environments.

Levitation effect in zeolites: Quasielastic neutron scattering and molecular dynamics study of pentane isomers in zeolite NaY

We report the quasielastic neutron scattering (QENS) and molecular dynamics (MD) investigations into diffusion of pentane isomers in zeolite NaY. The molecular cross section perpendicular to the long molecular axis varies for the three isomers while the mass and the isomer-zeolite interaction remains essentially unchanged. Both QENS and MD results show that the branched isomers neopentane and isopentane have higher self-diffusivities as compared with n-pentane at 300 K in NaY zeolite. This result provides direct experimental evidence for the existence of nonmonotonic, anomalous dependence of self-diffusivity on molecular diameter known as the levitation effect. The energetic barrier at the bottleneck derived from MD simulations exists for n-pentane which lies in the linear regime while no such barrier is seen for neopentane which is located clearly in the anomalous regime.Activation energy is in the order E-a(n-pentane)>E-a(isopentane)>E-a(neopentane) consistent with the predictions of the levitation effect. In the liquid phase, it is seen thatD(n pentane)>D(isopentane)>D(neopentane) and E-a(n-pentane)< E-a(isopentane)< E-a(neopentane). Intermediate scattering function for small wavenumbers obtained from MD follows a single exponential decay for neopentane and isopentane. For n-pentane, a single exponential fit provides a poor fit especially at short times. Cage residence time is largest for n-pentane and lowest for neopentane. For neopentane, the width of the self-part of the dynamic structure factor shows a near monotonic decrease with wavenumber. For n-pentane a minimum is seen near k=0.5 A degrees(-1) suggesting a slowing down of motion around the 12-ring window, the bottleneck for diffusion. Finally, the result that the branched isomer has a higher diffusivity as compared with the linear analog is at variation from what is normally seen.

Solvation dynamics in dipolar liquids

The time dependent response of a polar solvent to a changing charge distribution is studied in solvation dynamics. The change in the energy of the solute is measured by a time domain Stokes shift in the fluorescence spectrum of the solute. Alternatively, one can use sophisticated non-linear optical spectroscopic techniques to measure the energy fluctuation of the solute at equilibrium. In both methods, the measured dynamic response is expressed by the normalized solvation time correlation function, S(t). The latter is found to exhibit uniquefeatures reflecting both the static and dynamic characteristics of each solvent. For water, S(t) consists of a dominant sub-50 fs ultrafast component, followed by a multi-exponential decay. Acetonitrile exhibitsa sub-100 fs ultrafast component, followed by an exponential decay. Alcohols and amides show features unique to each solvent and solvent series. However, understanding and interpretation of these results have proven to be difficult, and often controversial. Theoretical studiesand computer simulations have greatly facilitated the understanding ofS(t) in simple systems. Recently solvation dynamics has been used extensively to explore dynamics of complex systems, like micelles and reverse micelles, protein and DNA hydration layers, sol-gel mixtures and polymers. In each case one observes rich dynamical features, characterized again by multi-exponential decays but the initial and final time constants are now widely separated. In this tutorial review, we discuss the difficulties in interpreting the origin of the observed behaviour in complex systems.

Origin of the Enhanced Photoluminescence from Semiconductor CdSeS Nanocrystals

Internal structures of extraordinarily luminescent semiconductor nanoparticles are probed with photoelectron spectroscopy, establishing a gradient alloy structure as an essential ingredient for the observed phenomenon. Comparative photoluminescence lifetime measurements provide direct evidence for a minimization of nonradiative decay channels because of the removal of interfacial defects due to a progressive change in the lattice parameters in such graded structures, exhibiting a nearly single exponential decay Quantum mechanical, calculations suggest a differential extent of spatial collapse of the electron and the hole wave functions in a way that helps to enhance the photoluminescence efficiency, while at the same time increasing the lifetime of the excited state, as observed in the experiments.

Ions in water: Role of attractive interactions in size dependent diffusivity maximum

A molecular dynamics study of model ions in water is reported. The van der Waals diameter of both the cations and anions is varied. We have carried out two sets of simulations-with and without dispersion interaction-between the ion and water. Self-diffusivity of the ions exhibits an anomalous maximum as a function of the van der Waals diameter for both these sets. This existence of a maximum in self-diffusivity when there is no dispersion interaction between the ion and the water is attributed to the attractive term from electrostatic interactions. Detailed analysis of this effect shows that the solvent shell is more strongly defined in the presence of dispersion interactions. A smaller ion exhibits biexponential decay while a single exponential decay is seen for the ion with maximum diffusivity in the self-part of the intermediate scattering function. The solvent structure around the ion appears to determine much of the dynamics of the ion. Interesting trends are seen in the activation energies and these can be understood in terms of the levitation effect. (C) 2010 American Institute of Physics. doi:10.1063/1.3481656]

Nonlinear hydrodynamics of a hard-sphere fluid near the glass transition

We conduct a numerical study of the dynamic behavior of a dense hard-sphere fluid by deriving and integrating a set of Langevin equations. The statics of the system is described by a free-energy functional of the Ramakrishnan-Yussouff form. We find that the system exhibits glassy behavior as evidenced through a stretched exponential decay and a two-stage relaxation of the density correlation function. The characteristic times grow with increasing density according to the Vogel-Fulcher law. The wave-number dependence of the kinetics is extensively explored. The connection of our results with experiment, mode-coupling theory, and molecular-dynamics results is discussed.

Conjectures about phase turbulence in the complex Ginzburg-Landau equation

In the complex Ginzburg-Landau equation, we consider possible ''phase turbulent'' regimes, where asymptotic correlations are controlled by phase fluctuations rather than by topological defects. Conjecturing that the decay of such correlations is governed by the Kardar-Parisi-Zhang (KPZ) model of growing interfaces, we derive the following results: (1) A scaling ansatz implies that equal-time spatial correlations in 1d, 2d, and 3d decay like e(-Ax2 zeta), where A is a nonuniversal constant, and zeta=1/2 in 1d. (2) Temporal correlations decay as exp(-t(2 beta)h(t/L(z))), with the scaling law <(beta)over bar> = <(zeta)over bar>/z, where z = 3/2, 1.58..., and 1.66..., for d = 1,2, and 3 respectively. The scaling function h(y) approaches a constant as y --> 0, and behaves like y(2(beta-<(beta)over bar>)), for large y. If in 3d the associated KPZ model turns out to be in its weak-coupling (''smooth'') phase, then, instead of the above behavior, the CGLE exhibits rotating long-range order whose connected correlations decay like 1/x in space or 1/t(1/2) in time. (3) For system sizes, L, and times t respectively less than a crossover length, L(c), and time, t(c), correlations are governed by the free-field or Edwards-Wilkinson (EW) equation, rather than the KPZ model. In 1d, we find that L(c) is large: L(c) similar to 35,000; for L < L(c) we show numerical evidence for stretched exponential decay of temporal correlations with an exponent consistent with the EW value beta(EW)= 1/4.