Generalized monotonicity, integral conditions and partial survival

 An interesting paper of Vance and Coddington concerning the scalar equation x˙=xf (t, x) is improved by a drastic weakening of the assumptions. Surprising as it may seem, this weakening simplifies the analysis and leads to stronger conclusions. An extension to scalar inequalities of similar structure is applied to a large class of vector equations describing the evolution of n interacting species. Thus we obtain new criteria for extinction and for partial survival, in the sense that each of the separate species may come arbitrarily close to extinction but the population as a whole does not. Received: 5 March 1999 / Revised version: 24 August 1999     

Determination of equilibrium constants and maximum binding capacities in complexIn vitro systems: I. The mammillary system

It is shown that in a system containingn types of mutually noninteracting binding sites, the association constants are then roots of annth order polynomial while the maximum binding capacities can be evaluated by solving a set ofn simultaneous linear equations. Thenth order polynomial and the system ofn linear equations are defined in terms of 2n intermediate coefficients, the coefficients being themselves evaluated by substituting 2n sets of appropriate experimental data into an auxiliary system of 2n linear equations. The existence and uniqueness of the solutions are established.     

On the Application of Widom's Test Particle Method to Homogeneous and Inhomogeneous Fluids

Abstract

Chemical potentials of a homogeneous and an inhomogeneous Lennard-Jones fluid have been determined by molecular dynamics simulations on the vector computer CYBER 205 by applying essentially the fictitious test particle method of Widom. For the homogeneous fluid we find, contrary to the previous result of Guillot and Guissani, that the simulated chemical potential is independent of the particle number. The crucial point, however, is a sufficiently large cut-off radius in the evaluation of the Boltzmann factor. Comparing with our WCA-type perturbation theory, we get agreement in the chemical potentials within 0.1 kT up to the density n[sgrave]³ = 0.80 and a difference of 0.2 kT at n[sgrave]³ = 0.85. For the inhomogeneous case we consider a fluid in a cylindrical pore and integrate Widom's equation over a certain probe volume as suggested earlier by us. Chemical potentials are then calculated independently in five different probe volumes, which are cylindrical shells. The results agree well from the second to the fourth shell. Inaccuracies in the innermost cylinder can be easily explained by bad statistics. In the shell close to the wall the extremely high local density is responsible for the inaccuracies. Extending the probe volume over all cylindrical shells besides the one closest to the wall is thought to yield rather reliable results for the chemical potential. As a by-product of the simulations we also obtained diffusion coefficients, which are given in an appendix.     

Curvature in models of the photosynthesis‐irradiance response

An equation for the rate of photosynthesis as a function of irradiance introduced by T. T. Bannister included an empirical parameter b to account for observed variations in curvature between the initial slope and the maximum rate of photosynthesis. Yet researchers have generally favored equations with fixed curvature, possibly because b was viewed as having no physiological meaning. We developed an analytic photosynthesis‐irradiance equation relating variations in curvature to changes in the degree of connectivity between photosystems, and also considered a recently published alternative, based on changes in the size of the plastoquinone pool. When fitted to a set of 185 observed photosynthesis‐irradiance curves, it was found that the Bannister equation provided the best fit more frequently compared to either of the analytic equations. While Bannister's curvature parameter engendered negligible improvement in the statistical fit to the study data, we argued that the parameter is nevertheless quite useful because it allows for consistent estimates of initial slope and saturation irradiance for observations exhibiting a range of curvatures, which would otherwise have to be fitted to different fixed‐curvature equations. Using theoretical models, we also found that intra‐ and intercellular self‐shading can result in biased estimates of both curvature and the saturation irradiance parameter. We concluded that Bannister's is the best currently available equation accounting for variations in curvature precisely because it does not assign inappropriate physiological meaning to its curvature parameter, and we proposed that b should be thought of as the expression of the integration of all factors impacting curvature.     

Local Connectivity of Neutral Networks

This paper studies local connectivity of neutral networks of RNA secondary and pseudoknot structures. A neutral network denotes the set of RNA sequences that fold into a particular structure. It is called locally connected, if in the limit of long sequences, the distance of any two of its sequences scales with their distance in the n-cube. One main result of this paper is that is the threshold probability for local connectivity for neutral networks, considered as random subgraphs of n-cubes. Furthermore, we analyze local connectivity for finite sequence length and different alphabets. We show that it is closely related to the existence of specific paths within the neutral network. We put our theoretical results into context with folding algorithms into minimum-free energy RNA secondary and pseudoknot structures. Finally, we relate our structural findings with dynamics by discussing the role of local connectivity in the context of neutral evolution.     

Seasonal changes in hydraulic conductance, xylem embolism and leaf area in Eucalyptus tetrodonta and Eucalyptus miniata saplings in a north Australian savanna

Eucalypt saplings in north Australian savannas commonly die back, sometimes to ground level, during the 5 months of the long dry season. Water potentials are lower in saplings than large trees during the dry season, and we hypothesized that low water potentials may lead to high levels of xylem embolism and consequent death of branches and whole shoots. As the dry season progressed, hydraulic conductance of terminal branches decreased by 50% in Eucalyptus tetrodonta but not in Eucalyptus miniata saplings. Hydraulic conductance per leaf area decreased seasonally by 34% in E. tetrodonta branches. These decreases may be associated with the loss of leaves recorded from E. tetrodonta but not E. miniata branches. We modelled the effect of sequential loss of parallel resistors, representing petioles on a branch. This showed there is a non-linear decrease in flow as basal resistors are lost, which can lead to a decrease in mean flow per resistor due to increased mean path-length. Thus the observed loss of basal leaves, together with xylem embolism, probably contributed to the seasonal loss of hydraulic conductance in E. tetrodonta saplings. Loss of hydraulic conductance due to xylem embolism was generally low ( < 15%) in both species, and the seasonal increase in embolism could not fully account for the decline in hydraulic conductance of E. tetrodonta branches. There was little evidence that branch and shoot death was caused by these levels of embolism. Developing an embolism vulnerability curve for species with long vessels is problematic and this issue is discussed.     

Ultrastructure of the Oral Apparatus of Mesodinium rubrum from Korea

Mesodinium rubrum Lohmann is a photosynthetic marine ciliate that has functional chloroplasts of cryptophyte origin. Little is known about the oral ultrastructure of M. rubrum compared with several reports on the sequestration of nuclei and plastids from prey organisms, such as Geminigera cryophila and Teleaulax species. Here, we describe the fine structure of the oral apparatus of a M. rubrum strain from Gomso Bay, Korea. The cytopharynx was cone‐shaped and supported by 20–22 ribbons of triplet microtubules. At the anterior end of the cytopharynx, an annulus anchored small cylinders composed of 11 microtubules. The small cylinders were spaced at regular intervals, each reinforced by one set of the triplet microtubules. At the opening of the cytostome, larger 14‐membered microtubular cylinders were set adjacent to the small, 11‐membered microtubular cylinders, each pair surrounded by separate membranes, however, only the large cylinders extended into the oral tentacles. There were 20–22 oral tentacles each having one to five extrusomes at its tip. At the anterior end of the oral apparatus, microtubular bands supporting the cytostome curved posteriad, extending beneath the cell cortex to the kinetosomes of the somatic cirri. The microtubular bands were connected by striated fibers and originated from kinetosomes anchored by fibers. Each cirrus consisted of eight cilia associated with 16 kinetosomes. The ultrastructure of M. rubrum from Korea provides information useful for taxonomic characterization of the genus Mesodinium and relevant to developing a better understanding of the acquisition of foreign organelles through phagocytosis by M. rubrum.     

A spatial genetics approach to inform vector control of tsetse flies (Glossina fuscipes fuscipes) in Northern Uganda

Tsetse flies (genus Glossina) are the only vector for the parasitic trypanosomes responsible for sleeping sickness and nagana across sub‐Saharan Africa. In Uganda, the tsetse fly Glossina fuscipes fuscipes is responsible for transmission of the parasite in 90% of sleeping sickness cases, and co‐occurrence of both forms of human‐infective trypanosomes makes vector control a priority. We use population genetic data from 38 samples from northern Uganda in a novel methodological pipeline that integrates genetic data, remotely sensed environmental data, and hundreds of field‐survey observations. This methodological pipeline identifies isolated habitat by first identifying environmental parameters correlated with genetic differentiation, second, predicting spatial connectivity using field‐survey observations and the most predictive environmental parameter(s), and third, overlaying the connectivity surface onto a habitat suitability map. Results from this pipeline indicated that net photosynthesis was the strongest predictor of genetic differentiation in G. f. fuscipes in northern Uganda. The resulting connectivity surface identified a large area of well‐connected habitat in northwestern Uganda, and twenty‐four isolated patches on the northeastern margin of the G. f. fuscipes distribution. We tested this novel methodological pipeline by completing an ad hoc sample and genetic screen of G. f. fuscipes samples from a model‐predicted isolated patch, and evaluated whether the ad hoc sample was in fact as genetically isolated as predicted. Results indicated that genetic isolation of the ad hoc sample was as genetically isolated as predicted, with differentiation well above estimates made in samples from within well‐connected habitat separated by similar geographic distances. This work has important practical implications for the control of tsetse and other disease vectors, because it provides a way to identify isolated populations where it will be safer and easier to implement vector control and that should be prioritized as study sites during the development and improvement of vector control methods.     

Temperature dependence of single channel currents and the peptide libration mechanism for ion transport through the gramicidin A transmembrane channel

Summary A study of the temperature dependence of gramicidin A conductance of K⁺ in diphytanoyllecithin/n-decane membranes shows the plot of In (single channel conductance) as a function of reciprocal temperature to be nonlinear for the most probable set of conductance, states. These results are considered in terms of a series of barriers, of the dynamics of channel conformation,vis-a-vis the peptide libration mechanism, and of the effect of lipid viscosity on side chain motions again as affecting the energetics of peptide libration.     

Design of a secondary alcohol degradation pathway from <Emphasis Type="Italic">Pseudomonas fluorescens</Emphasis> DSM 50106 in an engineered <Emphasis Type="Italic">Escherichia coli</Emphasis>

The genes encoding an alcohol dehydrogenase, Baeyer–Villiger monooxygenase and an esterase from P. fluorescens DSM 50106, which seemed to be metabolically connected based on the sequence of the corresponding open reading frames, were cloned into one vector (pABE) and functionally expressed in Escherichia coli. Overall expression levels were quite low, however, using whole cells of E. coli JM109 pABE expressing the three recombinant enzymes, conversion of secondary alcohols (C_n) to the corresponding primary alcohols (C_n−2) and acetic acid via ketone and ester was possible. In this way, 2-decanol was almost completely converted within 20 h at 30°C. Thus, it could be shown that the three enzymes are metabolically connected and that they are most probably involved in alkane degradation via sub-terminal oxidation of the acyclic aliphatic hydrocarbons.     

Spatial genetic analysis of two polyploid macrophytes reveals high connectivity in a modified wetland

相似文献   

Leaf Conductance as Related to Xylem Water Potential and Carbon Dioxide Concentration in Sitka Spruce

Current year shoots of Sitka spruce [Picea sitchensis Bong. (Carr.)] from the forest canopy were equilibrated in a leaf chamber. The shoots were excised in air, and removed at differing times in order to establish a relationship between stomatal conductance and xylem water potential. The experiment was repeated at five ambient CO₂ concentrations. A second set of excised forest shoots, and shoots excised from 2-year- old nursery seedlings were allowed to evaporate freely in a controlled environment wind tunnel until a constant rate of transpiration was measured, to establish a relationship between cuticular conductance and xylem water potential. Cuticular conductance was estimated to be 0.012 cm s^-1 at high water potential and declined linearly to 0.007 cm s^-1 at ?3.5 MPa. The implication of this decline in the subsequent calculation of stomatal and mesophyll conductance is considered. Stomatal conductance remained constant at water potentials above ?1.4 MPa and was not affected by ambient carbon dioxide concentrations between 20 and 600 cm^-3. At lower water potentials, stomatal conductance declined and approached zero at ?2.5 to ?2.6 MPa. The results suggest that stomatal aperture is not controlled by either ambient or intercellular space carbon dioxide concentration, and that stomatal closure at low water potential is unlikely to be mediated by carbon dioxide.     

Thresholds and Plateaus in the Hodgkin-Huxley Nerve Equations

Phase space methods and an analog computer are used to analyze the Hodgkin-Huxley non-linear differential equations for the squid giant axon membrane. V is the membrane potential, m the Na⁺ activation, h the Na⁺ inactivation, and n the K⁺ activation. V and m change rapidly, relative to h and n. The (V, m) phase plane of a reduced system of equations, with h and n held constant at their resting values, has three singular points: a stable resting point, a threshold saddle point, and a stable excited point. When h and n are allowed to vary, recovery and refractoriness result from the movement with subsequent disappearance of the threshold and excited points. Multiplying the time constant of n by 100 or more, and that of h by one-third, reproduces the experimental plateau action potentials obtained with tetraethylammonium by Tasaki and Hagiwara, including the phenomena of abolition and of refractoriness of the plateau duration. The equations have, transiently, two stable states, as found in the real axon by these authors. Since the theoretical membrane conductance curves differ significantly from the experimental ones, further experimental analysis of ionic currents with tetraethylammonium is needed to decide whether the Hodgkin-Huxley model can be generalized to explain these experiments completely.     

Generalizations of the Roginsky-Zeldovich (or Elovich) equation for charge transport across biological surfaces

The Roginsky-Zeldovich (or Elovich) equation, which is −dx/dt=m exp (nx) (x=substrate concentration,t=time,m andn=constants), describes the kinetics of various biological electron and ion transport processes, and has been derived from the concept of charge transport across an activation energy barrier at an interface between dissimilar phases, driven by a difference in redox or ion potentials, with the simplifying assumptions that charge carrier concentration is constant, backward current across the interface is zero, and diffusion of substrate is fast. If charge carrier concentration is proportional to substrate concentration, then the kinetic equation is −dx/dt=mx exp (nx). If backward current is not zero, then −dx/dt=m ₁ exp (n ₁x) −m ₂ exp (n ₂ x), wherem ₁,m ₂,n ₁ andn ₂ are constants. Kinetic equations for interfacial charge transport in the presence of a significant substrate diffusion potential are also derived.     

The probability of obtaining complex kinetic curves for enzyme mechanisms with cubic terms in the pseudo-steady state rate equations

A number of details required for the classification of 3 : 3 double reciprocal plots are provided. It is shown that the ν(S) plot for a 3 : 3 function can have at most four inflexions and at most two inflexions adjacent to a turning point. Using this information, a classification of 3 : 3 ν(S) plots into ten main varieties with several subclasses is reported. The problem of defining the probability with which a given mechanism can give rise to specific curve shape features is considered. Applying this technique, the probability with which four simple enzyme mechanisms can give rise to 3 : 3 curve shapes is computed. It is shown that a 3 : 3 saturation function can have no turning points, at most two inflexions and at most one inflexion in double reciprocal space. The probability with which the available 3 : 3 shapes can arise is also computed. It is concluded that, with realistic values for rate constants, chemically reasonable enzyme mechanisms leading to rate equations of degree n : n can generate most of the kinetic profiles available to a rational function of degree n : n with positive coefficients. The probability of obtaining specific curve shapes is not so characteristic of the particular mechanism for 3:3 rate equations as it is for 2:2 rate equations. The probability of obtaining highly complex curves with several turning points or inflexions is rather lower for the enzyme mechanisms than with general 3 : 3 rational functions. There is a high probability that 3 : 3 mechanisms will generate kinetic curves that are geometrically similar to those possible for degree 2 : 2 but this is not so for binding isotherms. Hence differentiating 3 : 3 from 2 : 2 rate equations from experimental kinetic data is more likely to be successful by non-linear regression to the whole data set than by demonstrating a specific 3 : 3 feature. Binding curves, on the other hand, for three or more sites should give Scatchard plots with inflexions, features not possible with second degree equations which are conic sections in this space.     

On shunting inhibition

The interaction between excitation and inhibition is analyzed for nerve cylinders when reversal potentials for synaptic action are included. Both impulsive and sustained conductance changes are employed to model synaptic action.Exact results, in terms of Green's functions are obtained for the solutions of the cable equation with reversal potentials when there are impulsive conductance changes. The amplification factor for an inhibitory input due to a prior excitatory input is found exactly. In the case of an infinite cylinder, the dependence of this factor on the spatial separation of the excitatory and inhibitory synapses is one plus a Gaussian density function. Similar results aply when excitation follows inhibition. There is shunting inhibition even for impulsive conductance changes in the cable, but it is very different from that for sustained conductance changes. The interaction of excitation and inhibition is also studied in the full cable equation with reversal potentials and sustained conductance changes. An exact result is obtained for the potential in response to simultaneous excitation and inhibition at the same space point in an infinite cable. The effects of timing and spatial separation of inputs is analyzed in a finite nerve cylinder by numerically integrating the cable equation by the Crank-Nicolson method. Shunting inhibition is found to be most effective, for the chosen parameter values, when inhibition quickly foolows excitation. The EPSP amplitude at the soma is found to be roughly proportional to the distance from the soma to the site of inhibition when the excitation is at the center of the nerve cylinder.Dedicated to Jane Pauley     

Patch clamping VDAC in liposomes containing whole mitochondrial membranes

Summary Whole mitochondrial membranes isolated fromNeurospora crassa were reconstituted into liposomes and patch clamped. Clear activity characteristic of the mitochondrial channel VDAC was found, namely: open state conductance of 650 pS (in 150mm KCl, 1mm CaCl₂, 20mm HEPES, pH 7.2), voltage-dependent closure at both positive and negative potentials, change in conductance upon channel closure of about 450 pS in response to negative and positive potentials, and increased voltage dependence in the presence of König's polyanion. This is the first clear demonstration of VDAC single channels using the patch-clamp technique, even though others used this method before to study whole mitochondrial membranes and liposomes containing mitochondrial proteins. We also found one other channel with a conductance change of about 120 pS.     

Characteristics of GABAA channels in rat dentate gyrus

Single channel currents were activated by GABA (0.5 to 5 m) in cell-attached and inside-out patches from cells in the dentate gyrus of rat hippocampal slices. The currents reversed at the chloride equilibrium potential and were blocked by bicuculline (100 m). Several different kinds of channel were seen: high conductance and low conductance, rectifying and nonrectifying. Channels had multiple conductance states. The open probability (P _o ) of channels was greater at depolarized than at hyperpolarized potentials and the relationship between P _o and potential could be fitted with a Boltzmann equation with equivalent valency (z) of 1. The combination of outward rectification and potentialdependent open probability gave very little chloride current at hyperpolarized potentials but steeply increasing current with depolarization, useful properties for a tonic inhibitory mechanism.     

Electrical potentials and ionic fluxes in ion exchangers: I. “n type” non-ideal systems with zero current

In this paper a derivation, based on the Nernst-Planck flux equations extended for non-ideal behavior, is given for the electrical potentials and cationic fluxes occurring across a one-phase ion exchange system separating two aqueous solutions. It is assumed that the activities of the cations in the exchanger are proportional to thenth power of their concentrations, a relationship of broad empirical validity. This paper deals only with the case of the quasi-stationary state in which no net electrical current flows. The profles of the cationic concentrations and of the diffusion potential in the exchanger are found to be, in general, exponential and linear respectively. An equation is derived for the stationary-state potential of an ion exchange phase interposed between two aqueous solutions containing mixtures of two cations. The potential selectivity constant of this equation is found to equal the product of the ion exchange equilibrium constant and thenth power of the mobility ratio.     

Statistical Mechanical Approach for Predicting the Transition to Non-B DNA Structures in Supercoiled DNA

Abstract

Supercoiling causes global twist of DNA structure and the supercoiled state has wide influence on conformational transition. A statistical mechanical approach was made for prediction of the transition probability to non-B DNA structures under torsional stress. A conditional partition function was defined as the sum over all possible states of the DNA sequence with basepair 1 and basepair n being in B-form helix and a recurrence formula was developed which expressed the partition function for basepair n with those for less number of pairs. This new definition permits a quick enumeration of every configuration of secondary structures. Energetic parameters of all conformations concerned, involving B-form, interior loop, cruciform and Z-form, were included in the equation. The probability of transition to each non-B conformation could be derived from these conditional partition functions. For treatment of effects of superhelicity, supercoiling energy was considered, and a twist of each conformation was determined to minimize the supercoiling energy. As the twist itself affects the transition probability, the whole scheme of equations was solved by renormalization technique. The present method permits a simultaneous treatment of serveral types of conformations under a common torsional stress.

A set of energetic parameters of DNA secondary structures has been chosen for calculation. Some DNA sequences were submitted to the calculation, and all the sequences that we submitted gave stable convergence. Some of them have been investigated the critical supercoil density for the transition to non-B DNA structures. Even though the reliability of the set of parameters was not enough, the prediction of secondary structure transition showed good agreement with reported observation. Hence, the present algorithm can estimate the probability of local conformational change of DNA under a given supercoil density, and also be employed to predict some specific sequences in which conformational change is sensitive to superhelicity.