Quasielastic light scattering from migrating chemotactic bands of Escherichia coli. II. Analysis of anisotropic bacterial motions.

Chemotactic effects of dissolved oxygen on motions of Escherichia coli in a motility buffer solution have been studied by measurements of quasielastic light scattering. Under conditions where the bacteria form a sharp band in an oxygen concentrations gradient created by their metabolism, components of motions along the direction of the gradient and perpendicular to it were studied separately at each point within the band profile. A theoretical model for bacterial self correlation function based on two-state motions has been developed to extract the mean square speed of run motion and the relative probability of twiddle vs. run at each point of the band profile. A combined novel experimental set-up and new data analysis method allowed us to extract also the mean square displacements at short times along and perpendicular to the direction of the gradient. Parameters extracted from the measured correlation functions have been discussed in the framework of the established picture of bacterial motions under chemotaxis.     

A non-local model for a swarm

 This paper describes continuum models for swarming behavior based on non-local interactions. The interactions are assumed to influence the velocity of the organisms. The model consists of integro-differential advection-diffusion equations, with convolution terms that describe long range attraction and repulsion. We find that if density dependence in the repulsion term is of a higher order than in the attraction term, then the swarm profile is realistic: i.e. the swarm has a constant interior density, with sharp edges, as observed in biological examples. This is our main result. Linear stability analysis, singular perturbation theory, and numerical experiments reveal that weak, density-independent diffusion leads to disintegration of the swarm, but only on an exponentially large time scale. When density dependence is put into the diffusion term, we find that true, locally stable traveling band solutions occur. We further explore the effects of local and non-local density dependent drift and unequal ranges of attraction and repulsion. We compare our results with results of some local models, and find that such models cannot account for cohesive, finite swarms with realistic density profiles. Received: 17 September 1997 / Revised version: 17 March 1998     

Quasi-elastic light scattering from migrating chemotactic bands of Escherichia coli. III. Studies of band formation propagation and motility in oxygen and serine substrates.

A series of light scattering experiments have been performed to study both macroscopic aspects of band formation and propagation and microscopic motility parameters of Escherichia coli in the combined substrate gradients of oxygen and serine. From the band formation experiment the conclusion is drawn that a minimum threshold gradient of the substrate is required for bacteria to form a band. From the band propagation experiment in the serine substrate the motility coefficient mu and chemotactic coefficient delta are determined. A separate quasi-elastic scattering experiment has been made with a propagating band to obtain three microscopic motility parameters: mean twiddle time tau 1, mean run time tau 2, and mean run speed V2. Finally, a scaling argument is made to connect the macroscopic parameters mu and delta with the microscopic parameters tau 1, tau 2, and V2, thus achieving a unified understanding of macroscopic and microscopic aspect of chemotaxis.     

Measurement of leukocyte motility and chemotaxis parameters with a linear under-agarose migration assay

The interpretation of quantitative assays for leukocyte chemotactic migration is usually made in terms of measurements such as leading front distance, total migrating cells, and leukotactic index. These quantities allow comparison of cellular migration behavior under specified conditions. They are not useful; however, for comparisons between systems or for correlation with in vivo performance, because they depend upon specific physical aspects of the assay system, such as the geometry, chemoattractant concentration and diffusivity, and observation time. It would be more helpful to measure intrinsic properties of cell movement that could be used for comparison between systems, for correlation with in vivo studies, and to increase our understanding of the cell physiology. In this paper we demonstrate a means of quantitating leukocyte random motility, chemokinesis, and chemotaxis in terms of parameters that do characterize intrinsic cell properties. These parameters are the random motility coefficient and the chemotaxis coefficient, which appear in theoretical models of cell migration. We examine how well such a model describes the leukocyte density profile data observed in a modified under-agarose assay having a linear geometry. Furthermore, we obtain values for the random motility coefficient (and its dependence upon the concentration of the attractant peptide FNLLP) and for the chemotaxis coefficient for leukocytes responding to FNLLP.     

A Time-Series DDP for Functional Proteomics Profiles

Summary Using a new type of array technology, the reverse phase protein array (RPPA), we measure time-course protein expression for a set of selected markers that are known to coregulate biological functions in a pathway structure. To accommodate the complex dependent nature of the data, including temporal correlation and pathway dependence for the protein markers, we propose a mixed effects model with temporal and protein-specific components. We develop a sequence of random probability measures (RPM) to account for the dependence in time of the protein expression measurements. Marginally, for each RPM we assume a Dirichlet process model. The dependence is introduced by defining multivariate beta distributions for the unnormalized weights of the stick-breaking representation. We also acknowledge the pathway dependence among proteins via a conditionally autoregressive model. Applying our model to the RPPA data, we reveal a pathway-dependent functional profile for the set of proteins as well as marginal expression profiles over time for individual markers.     

Direct negative density‐dependence in a pond‐breeding frog population

Understanding population dynamics is critical for the management of animal populations. Comparatively little is known about the relative importance of endogenous (i.e. density‐dependent) and exogenous (i.e. density‐independent) factors on the population dynamics of amphibians with complex life cycles. We examined the potential effects of density‐dependent and ‐independent (i.e. climatic) factors on population dynamics by analyzing a 15‐yr time series data of the agile frog Rana dalmatina population from Târnava Mare Valley, Romania. We used two statistical models: 1) the partial rate correlation function to identify the feedback structure and the potential time lags in the time series data and 2) a Gompertz state‐space model to simultaneously investigate direct and delayed density dependence as well as climatic effects on population growth rate. We found evidence for direct negative density dependence, whereas delayed density dependence and climate did not show a strong influence on population growth rate. Here we demonstrated that direct density dependence rather than delayed density dependence or climate determined the dynamics of our study population. Our results confirm the findings of many experimental studies and suggest that density dependence may buffer amphibian populations against environmental stress. Consequently, it may not be easy to scale up from individual‐level effects to population‐level effects.     

Evidence of protein collective motions on the picosecond timescale

We investigate the presence of structural collective motions on a picosecond timescale for the heme protein, cytochrome c, as a function of oxidation and hydration, using terahertz (THz) time domain spectroscopy and molecular dynamics simulations. The THz response dramatically increases with oxidation, with the largest increase for lowest hydrations, and highest frequencies. For both oxidation states the THz response rapidly increases with hydration saturating above ∼25% (g H₂O/g protein). Quasiharmonic vibrational modes and dipole-dipole correlation functions were calculated from molecular dynamics trajectories. The collective mode density of states alone reproduces the measured hydration dependence, providing strong evidence of the existence of these motions. The large oxidation dependence is reproduced only by the dipole-dipole correlation function, indicating the contrast arises from diffusive motions consistent with structural changes occurring in the vicinity of buried internal water molecules. This source for the observed oxidation dependence is consistent with the lack of an oxidation dependence in nuclear resonant vibrational spectroscopy measurements.     

Longitudinal Data Analysis with Event Time as a Covariate

We consider the estimation of a nonparametric smooth function of some event time in a semiparametric mixed effects model from repeatedly measured data when the event time is subject to right censoring. The within-subject correlation is captured by both cross-sectional and time-dependent random effects, where the latter is modeled by a nonhomogeneous Ornstein–Uhlenbeck stochastic process. When the censoring probability depends on other variables in the model, which often happens in practice, the event time data are not missing completely at random. Hence, the complete case analysis by eliminating all the censored observations may yield biased estimates of the regression parameters including the smooth function of the event time, and is less efficient. To remedy, we derive the likelihood function for the observed data by modeling the event time distribution given other covariates. We propose a two-stage pseudo-likelihood approach for the estimation of model parameters by first plugging an estimator of the conditional event time distribution into the likelihood and then maximizing the resulting pseudo-likelihood function. Empirical evaluation shows that the proposed method yields negligible biases while significantly reduces the estimation variability. This research is motivated by the project of hormone profile estimation around age at the final menstrual period for the cohort of women in the Michigan Bone Health and Metabolism Study.     

Signs of stabilisation and stable coexistence

Many empirical studies motivated by an interest in stable coexistence have quantified negative density dependence, negative frequency dependence, or negative plant–soil feedback, but the links between these empirical results and ecological theory are not straightforward. Here, we relate these analyses to theoretical conditions for stabilisation and stable coexistence in classical competition models. By stabilisation, we mean an excess of intraspecific competition relative to interspecific competition that inherently slows or even prevents competitive exclusion. We show that most, though not all, tests demonstrating negative density dependence, negative frequency dependence, and negative plant–soil feedback constitute sufficient conditions for stabilisation of two‐species interactions if applied to data for per capita population growth rates of pairs of species, but none are necessary or sufficient conditions for stable coexistence of two species. Potential inferences are even more limited when communities involve more than two species, and when performance is measured at a single life stage or vital rate. We then discuss two approaches that enable stronger tests for stable coexistence‐invasibility experiments and model parameterisation. The model parameterisation approach can be applied to typical density‐dependence, frequency‐dependence, and plant–soil feedback data sets, and generally enables better links with mechanisms and greater insights, as demonstrated by recent studies.     

The peculiarities of the microwave in the frequency range of 51-52 GHz spectrum effects on E. coli cells

The effects of microwaves on conformation of nucleoids in E. coli cells were studied by the method of anomalous viscosity time dependence (AVTD) at various frequencies in the range of 51-52 GHz and the power flux density of 100 microW/cm(2) . Linearly polarized microwaves resulted in significant effects within specific frequency windows of resonance type. The distances between frequency windows were in the range of 55-180 MHz. Only one of two possible circular polarizations, left-handed or right-handed, was shown to be effective at each frequency window. The sign of effective circular polarization alternated between frequency windows. We show that the effects of microwaves on E. coli cells as measured by the AVTD technique are not caused by adhesion of cells. The half-width of the 51.575 GHz resonance was measured to be 120+/-20 MHz. This value is very close to the half-width of the 51.755 GHz resonance as it has previously been determined at the same power flux density. The obtained data suggest similar targets for effects of microwaves at these two resonance frequencies and provide evidence for non-thermal nature of observed microwave effects.     

First principles study of the electronic structure and optical properties of chrysene under pressure

Structural parameters, electronic and optical properties of chrysene have been investigated using the plane-wave ultrasoft pseudopotential technique based on the first principles density functional theory. The pressure dependence of the electronic band structure, density of states and partial density of states of chrysene were presented. Meanwhile, the complex dielectric function, refractive index, absorption coefficient, reflectivity, and the extinction coefficient are calculated and analysed. According to our work, we found that the optical properties of chrysene undergo a red shift with increasing pressure.     

A model of excitation and adaptation in bacterial chemotaxis.

We present a model of the chemotactic mechanism of Escherichia coli that exhibits both initial excitation and eventual complete adaptation to any and all levels of stimulus ("exact" adaptation). In setting up the reaction network, we use only known interactions and experimentally determined cytosolic concentrations. Whenever possible, rate coefficients are first assigned experimentally measured values; second, we permit some variation in these rate coefficients by using a multiple-well optimization technique and incremental adjustment to obtain values that are sufficient to engender initial response to stimuli (excitation) and an eventual return of behavior to baseline (adaptation). The predictions of the model are similar to the observed behavior of wild-type bacteria in regard to the time scale of excitation in the presence of both attractant and repellent. The model predicts a weaker response to attractant than that observed experimentally, and the time scale of adaptation does not depend as strongly upon stimulant concentration as does that for wild-type bacteria. The mechanism responsible for long-term adaptation is local rather than global: on addition of a repellent or attractant, the receptor types not sensitive to that attractant or repellent do not change their average methylation level in the long term, although transient changes do occur. By carrying out a phenomenological simulation of bacterial chemotaxis, we find that the model is insufficiently sensitive to effect taxis in a gradient of attractant. However, by arbitrarily increasing the sensitivity of the motor to the tumble effector (phosphorylated CheY), we can obtain chemotactic behavior.     

Identifying the density-dependent structure underlying ecological time series

A central problem in ecology is explaining the causes of population fluctuations, and an important step in the solution is determining the structure of the negative feedback (density dependent) process regulating population dynamics. The conventional way to determine the dimension or order of density dependence in a time series is to calculate the partial autorcorrelation function (PACF). We maintain, however, that PACF is not designed with biological populations in mind and has the wrong null model for detecting the structure of density dependence. We suggest an alternative diagnostic, the partial rate correlation function (PRCF), which is specifically designed for biological populations and has an appropriate null model for detecting their density dependent structures. Tests with simulated data show PRCF to be superior to PACF in detecting the underlying density dependent structure of two simple mathematical models.     

Dynamic light scattering from solutions of microtubules.

Calf brain microtubule protein was assembled in vitro to form dilute solutions of microtubules (240 A diameter) having lengths greater than 1 micrometer. The microtubule solutions were examined by dynamic laser light scattering techniques. The angular dependence of the correlation function leads to the conclusion that the correlation function is measuring the translational diffusion constant of the particles. The length dependence of the correlation function, however, shows that the translational diffusion constant is not being measured and that the diffusion constant for the microtubules cannot be straightforwardly determined. These results suggest that a collective property of the rods is being measured by the laser light scattering. Although specific microtubule-microtubule interactions are a possible explanation for the observed results, we present arguments that suggest that the solution can be adequately modeled as a network of entangled polymers.     

Potassium channel of cardiac sarcoplasmic reticulum is a multi-ion channel

We have characterized mechanisms of ionic permeation in the K channel of canine cardiac sarcoplasmic reticulum (SR K channel). Ionic selectivity, as measured by relative permeabilities, followed Eisenman sequence l, a low field strength sequence. Slope conductance measured in symmetrical solutions across the bilayer followed Eisenman sequence V. In all cases, the selectivity characteristics of the prominent subconductance state (O1) were similar to those of the main-state (O2). Further, our studies have revealed that this channel differs in three significant ways from the highly characterized SR K channel of skeletal muscle. First, the ratio of permeabilities Cs+ to K+ was a complex function of ion concentration. Second, the concentration dependence of conductance was not well described by the Michaelis-Menten formalism. Instead, we modeled the observed relations using a more general approach based on classical rate theory. Third, mole fraction experiments (Cs+ with K+) demonstrated a prominent anomalous effect. Certain of our Cs+ data required the Eyring rate theory approach for adequate interpretation. We adopted a symmetrical energy profile incorporating ion-ion interaction and thereby accounted for much of the data. We conclude that the canine cardiac SR K channel is significantly different from that of skeletal muscle, and it may accommodate more than one ion at a time.     

Cell-density dependent effects of low-dose ionizing radiation on E. coli cells

The changes in genome conformational state (GCS) induced by low-dose ionizing radiation in E. coli cells were measured by the method of anomalous viscosity time dependence (AVTD) in cellular lysates. Effects of X-rays at doses 0.1 cGy--1 Gy depended on post-irradiation time. Significant relaxation of DNA loops followed by a decrease in AVTD. The time of maximum relaxation was between 5-80 min depending on the dose of irradiation. U-shaped dose response was observed with increase of AVTD in the range of 0.1-4 Gy and decrease in AVTD at higher doses. No such increase in AVTD was seen upon irradiation of cells at the beginning of cell lysis while the AVTD decrease was the same. Significant differences in the effects of X-rays and gamma-rays at the same doses were observed suggesting a strong dependence of low-dose effects on LET. Effects of 0.01 cGy gamma-rays were studied at different cell densities during irradiation. We show that the radiation-induced changes in GCS lasted longer at higher cell density as compared to lower cell density. Only small amount of cells were hit at this dose and the data suggest cell-to-cell communication in response to low-dose ionizing radiation. This prolonged effect was also observed when cells were irradiated at high cell density and diluted to low cell density immediately after irradiation. These data suggest that cell-to-cell communication occur during irradiation or within 3 min post-irradiation. The cell-density dependent response to low-dose ionizing radiation was compared with previously reported data on exposure of E. coli cells to electromagnetic fields of extremely low frequency and extremely high frequency (millimeter waves). The body of our data show that cells can communicate in response to electromagnetic fields and ionizing radiation, presumably by reemission of secondary photons in infrared-submillimeter frequency range.     

Predictions of Taylor's power law, density dependence and pink noise from a neutrally modeled time series

There has recently been increasing interest in neutral models of biodiversity and their ability to reproduce the patterns observed in nature, such as species abundance distributions. Here we investigate the ability of a neutral model to predict phenomena observed in single-population time series, a study complementary to most existing work that concentrates on snapshots in time of the whole community. We consider tests for density dependence, the dominant frequencies of population fluctuation (spectral density) and a relationship between the mean and variance of a fluctuating population (Taylor's power law). We simulated an archipelago model of a set of interconnected local communities with variable mortality rate, migration rate, speciation rate, size of local community and number of local communities. Our spectral analysis showed ‘pink noise’: a departure from a standard random walk dynamics in favor of the higher frequency fluctuations which is partly consistent with empirical data. We detected density dependence in local community time series but not in metacommunity time series. The slope of the Taylor's power law in the model was similar to the slopes observed in natural populations, but the fit to the power law was worse. Our observations of pink noise and density dependence can be attributed to the presence of an upper limit to community sizes and to the effect of migration which distorts temporal autocorrelation in local time series. We conclude that some of the phenomena observed in natural time series can emerge from neutral processes, as a result of random zero-sum birth, death and migration. This suggests the neutral model would be a parsimonious null model for future studies of time series data.     

Understanding hierarchical protein evolution from first principles.

We propose a model that explains the hierarchical organization of proteins in fold families. The model, which is based on the evolutionary selection of proteins by their native state stability, reproduces patterns of amino acids conserved across protein families. Due to its dynamic nature, the model sheds light on the evolutionary time-scales. By studying the relaxation of the correlation function between consecutive mutations at a given position in proteins, we observe separation of the evolutionary time-scales: at short time intervals families of proteins with similar sequences and structures are formed, while at long time intervals the families of structurally similar proteins that have low sequence similarity are formed. We discuss the evolutionary implications of our model. We provide a "profile" solution to our model and find agreement between predicted patterns of conserved amino acids and those actually observed in nature.     

Mechanical properties of inner-arm dynein-f (dynein I1) studied with in vitro motility assays

Inner-arm dynein-f of Chlamydomonas flagella is a heterodimeric dynein. We performed conventional in vitro motility assays showing that dynein-f translocates microtubules at the comparatively low velocity of approximately 1.2 microm/s. From the dependence of velocity upon the surface density of dynein-f, we estimate its duty ratio to be 0.6-0.7. The relation between microtubule landing rate and surface density of dynein-f are well fitted by the first-power dependence, as expected for a processive motor. At low dynein densities, progressing microtubules rotate erratically about a fixed point on the surface, at which a single dynein-f molecule is presumably located. We conclude that dynein-f has high processivity. In an axoneme, however, slow and processive dynein-f could impede microtubule sliding driven by other fast dyneins (e.g., dynein-c). To obtain insight into the in vivo roles of dynein-f, we measured the sliding velocity of microtubules driven by a mixture of dyneins -c and -f at various mixing ratios. The velocity is modulated as a function of the ratio of dynein-f in the mixture. This modulation suggests that dynein-f acts as a load in the axoneme, but force pushing dynein-f molecules forward seems to accelerate their dissociation from microtubules.     

Interspike interval correlations in neuron models with adaptation and correlated noise

The generation of neural action potentials (spikes) is random but nevertheless may result in a rich statistical structure of the spike sequence. In particular, contrary to the popular renewal assumption of theoreticians, the intervals between adjacent spikes are often correlated. Experimentally, different patterns of interspike-interval correlations have been observed and computational studies have identified spike-frequency adaptation and correlated noise as the two main mechanisms that can lead to such correlations. Analytical studies have focused on the single cases of either correlated (colored) noise or adaptation currents in combination with uncorrelated (white) noise. For low-pass filtered noise or adaptation, the serial correlation coefficient can be approximated as a single geometric sequence of the lag between the intervals, providing an explanation for some of the experimentally observed patterns. Here we address the problem of interval correlations for a widely used class of models, multidimensional integrate-and-fire neurons subject to a combination of colored and white noise sources and a spike-triggered adaptation current. Assuming weak noise, we derive a simple formula for the serial correlation coefficient, a sum of two geometric sequences, which accounts for a large class of correlation patterns. The theory is confirmed by means of numerical simulations in a number of special cases including the leaky, quadratic, and generalized integrate-and-fire models with colored noise and spike-frequency adaptation. Furthermore we study the case in which the adaptation current and the colored noise share the same time scale, corresponding to a slow stochastic population of adaptation channels; we demonstrate that our theory can account for a nonmonotonic dependence of the correlation coefficient on the channel’s time scale. Another application of the theory is a neuron driven by network-noise-like fluctuations (green noise). We also discuss the range of validity of our weak-noise theory and show that by changing the relative strength of white and colored noise sources, we can change the sign of the correlation coefficient. Finally, we apply our theory to a conductance-based model which demonstrates its broad applicability.