On the Green’s function for a one-dimensional random walk

The Green’s function of a random walk on a lattice is defined as the inverse of the operatorK-z1, whereK is the matrix of transition rates and z is an arbitrary complex parameter. The Green’s function for a symmetrical random walk in one dimension is here explicitly given in closed form for reflecting, periodic, and absorbing boundaries, and also for an infinite lattice.     

Analysis of a one-dimensional random walk with irreversible losses at each step: applications for protein movement on DNA

We analysed a one-dimensional random walk between two points when the migrating particle could be irreversibly lost (dissociated) from the system at each step of the process. We show that in the case of losses at each step the average number of steps made by the particle that reaches the final point does not obey quadratic dependence on the distance between the starting and the final points: for long distances this dependence is linear. This is because losses "select" for shorter pathways between the starting and the final points. We applied this analysis to protein translocations within long DNA molecules.     

Chemosensory responses of microorganisms: Asymmetric diffusion as the limit of a biased random walk

A macroscopic asymmetric diffusion equation to model the responses of microbial populations to chemical attractants and repellents is derived from a biased random walk model for the motion of individual cells. The equation is different from the well-known Keller-Segel equation which contains a Fickian diffusion term. The implications of this difference for selected problems of biological interest are considered. In particular the aggregation of a population of microorganisms in a region of high concentration of attractant is discussed. Some similarities and limitations of both models are noted.     

A systematic study of the vibrational free energies of polypeptides in folded and random states

Molecular vibrations, especially low frequency motions, may be used as an indication of the rigidity or the flatness of the protein folding energy landscape. We have studied the vibrational properties of native folded as well as random coil structures of more than 60 polypeptides. The picture we obtain allows us to perceive how and why the energy landscape progressively rigidifies while still allowing potential flexibility. Compared with random coil structures, both alpha-helices and beta-hairpins are vibrationally more flexible. The vibrational properties of loop structures are similar to those of the corresponding random coil structures. Inclusion of an alpha-helix tends to rigidify peptides and so-called building blocks of the structure, whereas the addition of a beta-structure has less effect. When small building blocks coalesce to form larger domains, the protein rigidifies. However, some folded native conformations are still found to be vibrationally more flexible than random coil structures, for example, beta(2)-microglobulin and the SH3 domain. Vibrational free energy contributes significantly to the thermodynamics of protein folding and affects the distribution of the conformational substates. We found a weak correlation between the vibrational folding energy and the protein size, consistent with both previous experimental estimates and theoretical partition of the heat capacity change in protein folding.     

Xenopus MAP kinase activator: identification and function as a key intermediate in the phosphorylation cascade.

MAP kinase is thought to play a pivotal role not only in the growth factor-stimulated signalling pathway but also in the M phase phosphorylation cascade downstream of MPF. MAP kinase is fully active only when both tyrosine and threonine/serine residues are phosphorylated. We have now identified and purified a Xenopus MAP kinase activator from mature oocytes that is able to induce activation and phosphorylation on tyrosine and threonine/serine residues of an inactive form of Xenopus MAP kinase. The Xenopus MAP kinase activator itself is a 45 kDa phosphoprotein and is inactivated by protein phosphatase 2A treatment in vitro. Microinjection of the purified activator into immature oocytes results in immediate activation of MAP kinase. Further experiments using microinjection as well as cell free extracts have shown that Xenopus MAP kinase activator is an intermediate between MPF and MAP kinase. Thus, MAP kinase activator plays a key role in the phosphorylation cascade.     

A random time interval approach for analysing the impact of a possible intermediate event on a terminal event

We consider the impact of a possible intermediate event on a terminal event in an illness-death model with states 'initial', 'intermediate' and 'terminal'. One aim is to unambiguously describe the occurrence of the intermediate event in terms of the observable data, the problem being that the intermediate event may not occur. We propose to consider a random time interval, whose length is the time spent in the intermediate state. We derive an estimator of the joint distribution of the left and right limit of the random time interval from the Aalen-Johansen estimator of the matrix of transition probabilities and study its asymptotic properties. We apply our approach to hospital infection data. Estimating the distribution of the random time interval will usually be only a first step of an analysis. We illustrate this by analysing change in length of hospital stay following an infection and derive the large sample properties of the respective estimator.     

Changes in DNA distributions and ploidy of cho cells as a function of time in culture

Summary Chinese hamster ovary (CHO) cells maintained in continuous culture for 3 to 5 months may undergo subtle changes in drug sensitivity response, growth kinetics, plating efficiencies, et cetera. Our studies done independently in two different laboratories, using flow cytometry, indicate that the DNA histogram patterns change at about 11 wk, from populations with an approximate diploid DNA content to populations also composed of triploid and tetraploid cells. Chromosome counts also change from distributions of 21 to 22 to populations of cells having 21 to 22, 34, to 35 and 44 to 46 chromosomes. These alterations occur earlier (at 8 to 9 wk) in cell populations previously treated with anticancer drugs. The research was supported by NIH Grant DHEW 5 RO1 CA 15397 and funds from Upjohn Co. Kalamazoo, MI.     

Dependence of the internal relaxation time for DNA on salt type as inferred by quasielastic light scattering

Quasielastic light scattering methods were used to study calf thymus DNA in solutions of LiCl, NaCl, NH₄Ac, and NH₄Cl. Plots of the reciprocal relaxation time (1/τ) vs sin²(θ/2), where θ is the scattering angle, exhibit two linear regions, in accordance with theories for semiflexible polymers based on the t → 0 approximation. In these theories the slope of the linear region at low angles is associated with the translational diffusion coefficient (D_t), whereas the slope of the linear region at high angles is associated with the segmental diffusion coefficient (D_s = kT/?_s). The midpoint of the “transition” between these two linear regions is associated with the mean displacement between segments (b). Data presented here indicate that the Rouse-Zimm parameters b and ?_s are significantly different for DNA in 0.4M NH₄Cl relative to the other salts at comparable ionic strengths. It is suggested that this difference reflects local solvent structure and that both b and D_s are sensitive to the local water structure.     

Autocorrelation function and power spectrum of two-state random processes used in neurite guidance.

During development neurons extend and retract cytoskeletal structures, chiefly microtubules and filopodia, to process informational cues from the extracellular environment and thereby guide growth cone migration toward an appropriate synaptic partner. This cytoskeleton-based exploration is achieved by stochastic switching, with microtubules and filopodia alternating between growing and shortening phases apparently at random. If stabilizing signals are not detected during the growth phase, then the structures switch to a shortening state, from which they can again return to a growth phase, and so forth. A useful means of characterizing these stochastic processes in a model-independent way is by autocorrelation and spectral analysis. Previously, we compared experiment to theory by performing Monte Carlo simulations and computing the autocorrelation function and power spectrum from the simulated dynamics, an approach that is computationally intensive and requires recalculation whenever model parameters are changed. Here we present analytical expressions for the autocorrelation function and power spectrum, which compactly characterize microtubule and filopodial dynamics based on the stochastic, two-state model. The model assumes that the phase times are of variable duration and gamma-distributed, consistent with experimental evidence for microtubules assembled in vitro from purified tubulin. The analytical expressions permit the precise quantitative characterization of changes in microtubule and filopodial searching behavior corresponding to changes in the shape of the gamma distribution.     

Direct evidence for ADP-Pi-F-actin as the major intermediate in ATP-actin polymerization. Rate of dissociation of Pi from actin filaments

The sequence of reactions involved in the polymerization of ATP-actin and accompanying hydrolysis of ATP has been investigated by using a new glass-fiber filter assay. The assay allows the rapid separation of filaments from monomeric actin, and therefore the straightforward identification of the nucleotide bound to F-actin in the time course of polymerization, using double-labeled [gamma-32P,3H]ATP. The data bring a direct confirmation of the existence of the previously proposed ATP-F-actin intermediate in the time course of polymerization. Moreover, comparison of the hydrolyzed ATP (i.e., acid-labile [32P]Pi) and of 32P bound to F-actin provides direct evidence for the second intermediate ADP-Pi-F-actin in the polymerization process. This latter species is the major transient in the polymerization of ATP-actin, its lifetime being of the order of minutes.     

First capture success in two dimensions: The search for prey by a random walk predator in a comprehensive space of random walks

Random walk models are an important tool used for understanding how complex organisms redistribute themselves through space and time in search of targets such as food, shelter, or mates. These walks are easily studied with agent-based models, which can be used to ask which search strategy is best according to some efficiency metric. Current studies however, generally do not consider the full range of potential random walks, success metrics, and constraints on the walker, and implementation details vary widely. It is therefore difficult to compare results across studies. In this paper, we investigate predator search behaviour in a comprehensive space of key movement variables that allows the predator to select from a continuum of random walks ranging from Brownian walks (BWs) to correlated random walks (CorRWs) which include directional persistence, to composite random walks (ComRWs) which feature intensive and extensive search modes (ISMs and ESMs), and finally to more complex correlated composite random walks (CCRWs). We specifically focus on the search behaviour of a predator between the initiation of a search for a prey item and the first successful acquisition of a prey target: we call this interval the “search-to-capture” event. We measure the predator's success against three metrics of energetic cost: (1) the time elapsed, (2) the distance travelled, and (3) an equally weighted combination of time and distance. In addition, we explore the effect of three different constraints on the predator: (1) hunting success in the extensive search mode, (2) detection radius when in the extensive search mode, and (3) prey density. Our work confirms the broadly held notion that CCRW movement patterns should always outperform BWs, but find instructive cases where other walks are superior. We also show that, within the CCRW category, there is a wide range of possible walks and rank these according to measures of energetic cost. Our work also offers insights into the evolutionary pressures surrounding the “search-to-capture” event, and suggests that CCRW predators with low hunting success in one movement mode experience higher evolutionary pressures and are thus more likely to adopt a nearly optimal random walk. Our work highlights the need for comprehensive studies that examine several aspects of random walks simultaneously.     

Binding of ligands to a one-dimensional heterogeneous lattice. III. Kinetic model and relaxation study of the interaction of tilorone with DNA and polynucleotides

A temperature-jump relaxation study of the interaction of tilorone with different polynucleotides and DNA has been performed. A single relaxation time, attributed to the intercalation step, has been observed in the case of poly[d(A-T)]·poly[d(A-T)], poly[d(A-C)]·poly[d(G-T)], poly[d(G-C)]·poly[d(G-C)], and poly(dG)·poly(dC). No intercalation into poly(dA)·poly(dT) occurs, and the interaction with poly(dG)·poly(dC) is different from what is observed with the other intercalating homopolymers. Refinement of the binding model is suggested from the analysis of the kinetic data. The relaxation curves obtained with DNA are well simulated based on a binding mechanism where DNA is considered a heterogeneous lattice and each type of site behaves as if it were located in the corresponding homopolymer. Poly(dA)·poly(dT) shows a unique behavior: studies of the effects of concentration and temperature indicate that tilorone acts as a probe of a process involving the polynucleotide alone. This process appears to be related to the dynamic structure of the nucleic acid and is detectable only when the bound dye is not intercalated.     

Detection of rye DNA in wheat-rye hybrids and wheat translocations stocks using total genomic DNA as a probe

The online version of the original article can be found at     

Photoperiodic induction in quail as a function of the period of the light-dark cycle: implications for models of time measurement.

The earliest detectable event in the photoperiodic response of quail is a rise in luteinizing hormone (LH) secretion beginning at about hour 20 on the first long day. The timing of this rise was measured in castrated quail after entrainment to short daylengths which cause significant phase angle differences in the circadian system: (1) LD 2:22 and LD 10:14, and (2) LD 3:21 (T = 24 hr) and LD 3:24 (T = 27 hr). The quail were then exposed to 24 hr of light (by delaying lights-off), and the time of the first LH rise was measured; it was similar in all schedules. Quail were also entrained to LD 3:21 or LD 3:24 and then given a single 6-hr nightbreak 6-12, 7-13, or 13-19 hr after dawn. The earlier pulse was marginally more inductive in the 27-hr cycle. Thus the entrainment characteristics of the photoinducible rhythm (phi i) in quail appear very different from those of the locomotor circadian rhythm, and raise doubts as to whether phi i is a primary circadian oscillator.     

Detection of rye DNA in wheat-rye hybrids and wheat translocation stocks using total genomic DNA as a probe

Total DNA was extracted formSecale cereale L. cv. ‘Petkus’ and labeled with biotin-11-dUPT. Labeled rye DNA and non-labeled wheat DNA in a mixture of 1∶1 were used as a probe on chromosome preparations of Welsh triticale and Kavkaz wheat, a wheat translocation stock. Hybridization of denatured probe and chromosomes took place overnight at 37°C in the presence of 10% (w/v) dextran sulfate, 50% (v/v) formamide, 10 mM PIPES, 0.1 mMEDTA and 0.3 M NaC1. Biotin-labeled rye DNA was detected using streptavidin-horseradish peroxidase conjugate. Staining was made with diaminobenzidine tetrahydrochloride and hydrogen peroxide. Observations made on Giesma counter-stained slides indicated that the rye chromosomes in Welsh triticale and the two short arms of a pair of satellite chromosomes (1RS) in Kavkaz wheat were preferentially labeled. Hybridization signals were seen as dark brown to bluish black in color. The technique described above is simple. It does not require the isolation of a species-specific probe. Itallows rapid identification of hybrids and/or chromosome translocations in wide hybridizations.     

A mathematical model for the computation of carboxyhaemoglobin in human blood as a function of exposure time.

A mathematical model is developed for the carbon monoxide (CO) uptake by the blood by taking into account the molecular diffusion, convection, facilitated diffusion and the non-equilibrium kinetics of CO with haemoglobin. The overall rate for the combination of CO with haemoglobin is derived by including the dissociation of CO from carboxyhaemoglobin (COHb). The resulting coupled system of nonlinear partial differential equation with physiologically relevant initial, entrance and boundary conditions is solved numerically. A fixed point iterative technique is used to deal with nonlinearities. The concentration of COHb in the blood is computed as a function of exposure time and ambient CO concentration. The COHb levels computed from our model are in good agreement with those measured experimentally. Also, results computed from our model give better approximation to the experimental values compared with the results from other models. The time taken by the blood COHb to attain 95% of its equilibrium value is computed. The COHb concentration in the blood increases with the increase in ventilation rate, association rate coefficient of CO with haemoglobin and total haemoglobin content in the blood, and with the decrease in dissociation rate coefficient of CO with haemoglobin and mean capillary blood PO2. It is found that the COHb level in the blood is not affected significantly because of endogenous production of CO in the body under normal condition. However, the effect may be significant in the patients with haemolytic anaemia.