On the stall force for growing microtubules

The assembly of microtubules generates forces that play a role in cellular motility processes such as the motion of chromosomes during mitosis. Recently, Mogilner and Oster proposed a model for the growth of microtubules that agrees quantitatively with the force-velocity relation measured for individual microtubules. In addition, the authors predicted that the stall force for any polymer consisting of N independently growing protofilaments should increase as the square root of N. We simulated this model and found that the stall force increases linearly with N, and is in fact consistent with the maximum force predicted by thermodynamic arguments. We show that this discrepancy can be explained by a more careful treatment of the “off-term” in the Mogilner-Oster model. Received: 27 September 1999 / Revised version: 12 December 1999 / Accepted: 20 December 1999     

Stereotyped sequence of mating behavior in the Far Eastern catfish, Silurus asotus, from Lake Biwa

 Mating behavior of the Far Eastern catfish, Silurus asotus (Siluriformes: Siluridae), was observed in a ricefield system facing the shore of Lake Biwa in mid-May to early June in 1990–1997. A set behavioral sequence similar to those of two other silurid fishes, S. biwaensis and S. lithophilus, both endemic to the Lake Biwa system, was observed: “chasing,”“clinging,”“enfolding” while “squeezing” by the male, and “circling” by the spawning pair. This form of mating behavior is quite different from that of S. asotus reported from the Ooi River system in Kyoto Prefecture, which mainly spawns in running water in ditches. Received: April 10, 2001 / Revised: November 5, 2001 / Accetped: November 20, 2001     

Biochemical Mechanisms for Regulating Protrusion by Nematode Major Sperm Protein

Crawling motion is ubiquitous in eukaryotic cells and contributes to important processes such as immune response and tumor growth. To crawl, a cell must adhere to the substrate, while protruding at the front and retracting at the rear. In most crawling cells protrusion is driven by highly regulated polymerization of the actin cytoskeleton, and much of the biochemical network for this process is known. Nematode sperm utilize a cytoskeleton composed of Major Sperm Protein (MSP), which is considered to form a simpler, yet similar, crawling motility apparatus. Key components involved in the polymerization of MSP have been identified; however, little is known about the chemical kinetics for this system. Here we develop a model for MSP polymerization that takes into account the effects of several of the experimentally identified cytosolic and membrane-bound proteins. To account for some of the data, the model requires force-dependent polymerization, as is predicted by Brownian ratchet mechanisms. Using the tethered polymerization ratchet model with our biochemical kinetic model for MSP polymerization, we find good agreement with experimental data on MSP-driven protrusion. In addition, our model predicts the force-velocity relation that is expected for in vitro protrusion assays.     

New insights into microtubule structure and function from the atomic model of tubulin

The structure of tubulin has recently been solved by electron crystallography of zinc-induced tubulin sheets. Because tubulin was studied in a polymerized state, the model contains information on the interactions between monomers that give rise to the αβ dimer as well as contacts between adjacent dimers that result in the structure of the protofilament. The model includes the binding site of taxol, an anti-cancer agent that acts by stabilizing microtubules. The present tubulin model gives the first structural framework for understanding microtubule polymerization and its regulation by nucleotides and anti-mitotic drugs at the molecular level. Received: 15 December 1997 / Revised version: 25 January 1998 / Accepted: 2 February 1998     

Simple models for excitable and oscillatory neural networks

 Chains of coupled oscillators of simple “rotator” type have been used to model the central pattern generator (CPG) for locomotion in lamprey, among numerous applications in biology and elsewhere. In this paper, motivated by experiments on lamprey CPG with brainstem attached, we investigate a simple oscillator model with internal structure which captures both excitable and bursting dynamics. This model, and that for the coupling functions, is inspired by the Hodgkin–Huxley equations and two-variable simplifications thereof. We analyse pairs of coupled oscillators with both excitatory and inhibitory coupling. We also study traveling wave patterns arising from chains of oscillators, including simulations of “body shapes” generated by a double chain of oscillators providing input to a kinematic musculature model of lamprey.. Received: 25 November 1996 / Revised version: 9 December 1997     

The nicotinic acetylcholine receptor: from molecular model to single-channel conductance

The nicotinic acetylcholine receptor (nAChR) is the archetypal ligand-gated ion channel. A model of the α7 homopentameric nAChR is described in which the pore-lining M2 helix bundle is treated atomistically and the remainder of the molecule is treated as a “low resolution” cylinder. The surface charge on the cylinder is derived from the distribution of charged amino acids in the amino acid sequence (excluding the M2 segments). This model is explored in terms of its predicted single-channel properties. Based on electrostatic potential profiles derived from the model, the one-dimensional Poisson-Nernst-Planck equation is used to calculate single-channel current/voltage curves. The predicted single-channel conductance is three times higher (ca. 150 pS) than that measured experimentally, and the predicted ion selectivity agrees with the observed cation selectivity of nAChR. Molecular dynamics (MD) simulations are used to estimate the self-diffusion coefficients (D) of water molecules within the channel. In the narrowest region of the pore, D is reduced ca. threefold relative to that of bulk water. Assuming that the diffusion of ions scales with that of water, this yields a revised prediction of the single-channel conductance (ca. 50 pS) in good agreement with the experimental value. We conclude that combining atomistic (MD) and continuum electrostatics calculations is a promising approach to bridging the gap between structure and physiology of ion channels. Received: 2 August 1999 / Revised version: 5 November 1999 / Accepted: 9 November 1999     

Analytical solution to isometric mechanogram of hill’s model of striated muscle

The two-element muscle model considered consists of a contractile element defined by a hyperbolic force-velocity relation connected in series with an “exponential spring”. Differential equations for the isometrically developed force during a tetanic contraction and the corresponding contractile element shortening velocity are derived and their stability is investigated. Analytical solutions to both equations are obtained. Two numerical examples are given, the second chosen to illustrate pressure-induced hypertrophy of a cardiac muscle.     

High-frequency in vitro flowering of Murraya paniculata (L.) Jack

Shoots of orange jessamine (Murraya paniculata) a member of the Rutaceae family flowered in vitro on half-strength MT basal medium containing 5% sucrose. The highest percentage (95%) of flowering was obtained on medium supplemented with 0.1 mg l^–1 N⁶-benzyladenine and pH 5.7. A “floral gradient” was detected among the stem internodes and root segments derived from seedlings, with shoot and flower formation significantly influenced by position on the shoot internodes and root segments. Flower buds originating from shoots derived from seeds but not other tissues developed into normal flowers and produced zygotic embryos. Received: 10 December 1997 / Revision received: 5 November 1998 / Accepted: 2 December 1998     

Integrated analysis of metallic resource flows

In January 1997, the German Research Association (DFG) established a special research programme for an integrated analysis of metallic resource flows. The programme is a joint interdisciplinary effort of the Technical University of Aachen and of the Research Centre Jiilich. Apart from many other activities, a series of conferences is organised within this programme. In October 1997, a first conference was held on “The Economics of Resource Flows: The Case of Aluminium”. In December 1997, a second conference took place on “Life Cycle Assessment of Aluminium: Methods and Applications”. In April 1998 the third workshop was held entitled “Methodological Aspects of a Resource-oriented Analysis of Material Flows”. The next conference is planned for December 1998 on “Environmental related Aspects of Aluminium Production”. Finally, a conference on “Methods for an Integrated Evaluation of Material Flows” is under consideration for 1999.     

Detection of QTLs for crossability in wheat using a doubled-haploid population

 An intervarietal molecular-marker map was used for the detection of genomic regions influencing crossability between wheat (Triticum aestivum L. em Thell) and rye (Secale cereale L.). Analysis of deviance and logistic marker-regression methods were conducted on data from doubled haploid lines from a cross between “Courtot” and “Chinese Spring”. A major quantitative trait locus (QTL) involved in crossability, associated with the marker Xfba367-5B, was detected on the short arm of chromosome 5B. An additional locus, Xwg583-5B, was indicated on the long arm of chromosome 5B. This minor QTL might correspond to Kr1 which was presumed to be the major gene controlling crossability. Another locus of the genome, Xtam51-7A on chromosome 7A, was significantly associated with this trait. Alleles of “non-crossability” were contributed by the non-crossable cultivar “Courtot”. The three-marker model explains 65% of the difference in crossability between the two parents. The present results are discussed in relation to those previously carried out to locate the Kr genes by using the telocentric mapping technique. Received: 27 February 1998 / Accepted: 15 May 1998     

Analysis of complex leaf and flower characters in Rhododendron using a molecular linkage map

 A molecular linkage map of Rhododendron has been constructed by using a segregating population from an interspecific cross. Parent-specific maps based on 239 RAPD, 38 RFLP, and two microsatellite markers were aligned using markers heterozygous in both parents. The map of the male parent ‘Cunningham’s White’ comprised 182 DNA markers in 13 linkage groups corresponding to the basic chromosome number. In the female parent ‘Rh 16’ 168 markers were located on 18 linkage groups. An assignment of putative homologous linkage groups was possible for 11 groups of each parent. QTL analyses based on the non-parametric Kruskal-Wallis rank-sum test were performed for the characters “leaf chlorosis” and “flower colour” scored as quantitative traits. For leaf chlorosis, two genomic regions bearing QTLs with significant effects on the trait were identified on two linkage groups of the chlorosis-tolerant parent. RAPD marker analysis of additional lime-stressed genotypes tested under altered environmental conditions verified the relationship between marker allele frequencies and the expression of chlorosis. Highly significant QTL effects for flower colour were found on two chromosomes indicating major genes located in these genome areas. The prospects for utilization of a linkage map in Rhododendron are discussed. Received: 28 September 1998 / Accepted: 5 November 1998     

Force generation by actin polymerization II: the elastic ratchet and tethered filaments

The motion of many intracellular pathogens is driven by the polymerization of actin filaments. The propulsive force developed by the polymerization process is thought to arise from the thermal motions of the polymerizing filament tips. Recent experiments suggest that the nucleation of actin filaments involves a phase when the filaments are attached to the pathogen surface by a protein complex. Here we extend the "elastic ratchet model" of Mogilner and Oster to incorporate these new findings. We apply this "tethered ratchet" model to derive the force-velocity relation for Listeria and discuss relations of our theoretical predictions to experimental measurements. We also discuss "symmetry breaking" dynamics observed in ActA-coated bead experiments, and the implications of the model for lamellipodial protrusion in migrating cells.     

Diffusion inside microtubules

Recent high-resolution analysis of tubulin's structure has led to the prediction that the taxol binding site and a tubulin acetylation site are on the interior of microtubules, suggesting that diffusion inside microtubules is potentially a biologically and clinically important process. To assess the rates of transport inside microtubules, predictions of diffusion time scales and concentration profiles were made using a model for diffusion with parameters estimated from experiments reported in the literature. Three specific cases were considered: 1) diffusion of αβ-tubulin dimer, 2) diffusion/binding of taxol, and 3) diffusion/binding of an antibody specific for an epitope on the microtubule's interior surface. In the first case tubulin is predicted to require only ∼1 min to reach half the equilibrium concentration in the center of a 40 μm microtubule open at both ends. This relatively rapid transport occurs because of a lack of appreciable affinity between tubulin and the microtubule inner surface and occurs in spite of a three-fold reduction in diffusivity due to hindrance. By contrast the transport of taxol is much slower, requiring days (at nm concentrations) to reach half the equilibrium concentration in the center of a 40 μm microtubule having both ends open. This slow transport is the result of fast, reversible taxol binding to the microtubule's interior surface and the large capacity for taxol (∼12 mm based on interior volume of the microtubule). An antibody directed toward an epitope in the microtubule's interior is predicted to require years to approach equilibrium. These results are difficult to reconcile with previous experimental results where substantial taxol and antibody binding is achieved in minutes, suggesting that these binding sites are on the microtubule exterior. The slow transport rates also suggest that microtubules might be able to serve as vehicles for controlled-release of drugs. Received: 2 March 1998 / Revised version: 3 May 1998 / Accepted: 3 May 1998     

Dive form and function in belugas Delphinapterus leucas of the eastern Canadian High Arctic

The underwater behaviour of 11 belugas or white whales was examined during summer using time-at-depth records relayed by satellite-linked data-loggers. Simultaneous tracking information was obtained for each whale. Eight distinct dive profiles were identified in submergences made to depths of >40 m. Four of these, together comprising 84% of these “deep” dives, were of a square profile. They were characterised by a continuous descent to a particular depth (usually the sea bed), a “bottom phase” at or near that depth, and a direct ascent to the surface. These dives are presumed to be made for benthic foraging. Other, much less common, dive shapes were “V”-shaped, parabolic and trapezoidal. “Shallow” dives (15–40 m depth) were of a variety of shapes, short duration and high average horizontal speeds. Many probably occurred during periods of directed travel. This population of belugas treats most of the water column as dead space separating resources of oxygen and nutrition. Received: 8 January 1998 / Accepted: 27 April 1998     

Two dynamic processes for the induction of long-term potentiation in hippocampal CA1 neurons

This work sets out to investigate fast and slow dynamic processes and how they effect the induction of long-term potentiation (LTP). Functionally, the fast process will work as a time window to take a spatial coincidence among various inputs projected to the hippocampus, and the slow process will work as a temporal integrator of a sequence of dynamic events. Firstly, the two factors were studied using a “burst” stimulus and a “long-interval patterns” stimulus. Secondly, we propose that, for the induction of LTP, there are two dynamic processes, fast and slow, which are productively activated by bursts and long-interval patterns. The model parameters, a time constant of short dynamics and one of long dynamics, were determined by fitting the values obtained from model simulation to the experimental data. A molecular factor or cellular factors with these two time constants are likely to be induced in LTP induction. Received: 3 November 1997 / Accepted in revised form: 18 August 1999     

The Jackprot Simulation Couples Mutation Rate with Natural Selection to Illustrate How Protein Evolution Is Not Random

Protein evolution is not a random process. Views which attribute randomness to molecular change, deleterious nature to single-gene mutations, insufficient geological time, or population size for molecular improvements to occur, or invoke “design creationism” to account for complexity in molecular structures and biological processes, are unfounded. Scientific evidence suggests that natural selection tinkers with molecular improvements by retaining adaptive peptide sequence. We used slot-machine probabilities and ion channels to show biological directionality on molecular change. Because ion channels reside in the lipid bilayer of cell membranes, their residue location must be in balance with the membrane’s hydrophobic/philic nature; a selective “pore” for ion passage is located within the hydrophobic region. We contrasted the random generation of DNA sequence for KcsA, a bacterial two-transmembrane-domain (2TM) potassium channel, from Streptomyces lividans, with an under-selection scenario, the “jackprot,” which predicted much faster evolution than by chance. We wrote a computer program in JAVA APPLET version 1.0 and designed an online interface, The Jackprot Simulation , to model a numerical interaction between mutation rate and natural selection during a scenario of polypeptide evolution. Winning the “jackprot,” or highest-fitness complete-peptide sequence, required cumulative smaller “wins” (rewarded by selection) at the first, second, and third positions in each of the 161 KcsA codons (“jackdons” that led to “jackacids” that led to the “jackprot”). The “jackprot” is a didactic tool to demonstrate how mutation rate coupled with natural selection suffices to explain the evolution of specialized proteins, such as the complex six-transmembrane (6TM) domain potassium, sodium, or calcium channels. Ancestral DNA sequences coding for 2TM-like proteins underwent nucleotide “edition” and gene duplications to generate the 6TMs. Ion channels are essential to the physiology of neurons, ganglia, and brains, and were crucial to the evolutionary advent of consciousness. The Jackprot Simulation illustrates in a computer model that evolution is not and cannot be a random process as conceived by design creationists.     

Functional trait assembly through ecological and evolutionary time

A classic community assembly hypothesis is that all guilds must be represented before additional species from any given guild enter the community. We conceptually extend this hypothesis to continuous functional traits, refine the hypothesis with an eco-evolutionary model of interaction network community assembly, and compare the resultant continuous trait assembly rule to empirical data. Our extension of the “guild assembly rule” to continuous functional traits was rejected, in part, because the eco-evolutionary model predicted trait assembly to be characterized by the expansion of trait space and trait/species sorting within trait space. Hence, the guild rule may not be broadly applicable. A “revised” assembly rule did, however, emerge from the eco-evolutionary model: as communities assemble, the range in trait values will increase to a maximum and then remain relatively constant irrespective of further changes in species richness. This rule makes the corollary prediction that the trait range will, on average, be a saturating function of species richness. To determine if the assembly rule is at work in natural communities, we compared this corollary prediction to empirical data. Consistent with our assembly rule, trait “space” (broadly defined) commonly saturates with species richness. Our assembly rule may thus represent a general constraint placed on community assembly. In addition, taxonomic scale similarly influences the predicted and empirically observed relationship between trait “space” and richness. Empirical support for the model’s predictions suggests that studying continuous functional traits in the context of eco-evolutionary models is a powerful approach for elucidating general processes of community assembly.     

Sex differences in optimal incubation temperatures in a scincid lizard species

Most theoretical models for the evolution of temperature-dependent sex determination (TSD) rely upon differential fitness of male and female offspring incubated under different thermal regimes. However, there are few convincing data on this topic. We studied incubation effects in a lizard species (Bassiana duperreyi, Scincidae) with genotypic sex determination, so that we could separate effects due to incubation temperatures from those due to offspring gender. We incubated eggs under two different fluctuating-temperature regimes that simulated hot and cold natural nest-sites. The effects of our incubation treatments on phenotypes of the hatchling lizards (morphology and locomotor performance) differed between the sexes. Females emerging from eggs exposed to the “hot nest” treatment (diel cycling, 23–31°C) were larger, and ran faster, than did their sisters from the “cold nest” treatment (16–24°C). Males showed a smaller and less consistent phenotypic response than females. These incubation-induced responses were relatively stable during the first few weeks of life post-hatching, at least in captive lizards maintained under laboratory conditions. These kinds of sex differences in the phenotypic responses of hatchling reptiles to incubation conditions provide a plausible basis for the evolution of temperature-dependent sex determination in reptiles. Received: 07 May 1998 / Accepted: 16 November 1998     

The redistribution of soil water by tree root systems

Plant roots transfer water between soil layers of different water potential thereby significantly affecting the distribution and availability of water in the soil profile. We used a modification of the heat pulse method to measure sap flow in roots of Grevillea robusta and Eucalyptus camaldulensis and demonstrated a redistribution of soil water from deeper in the profile to dry surface horizons by the root system. This phenomenon, termed “hydraulic lift” has been reported previously. However, we also demonstrated that after the surface soils were rewetted at the break of season, water was transported by roots from the surface to deeper soil horizons – the reverse of the “hydraulic lift” behaviour described for other woody species. We suggest that “hydraulic redistribution” of water in tree roots is significant in maintaining root viability, facilitating root growth in dry soils and modifying resource availability. Received: 26 January 1998 / Accepted: 15 April 1998     

Salt tolerance in Lycopersicon spp. VII. Pleiotropic action of genes controlling earliness on fruit yield

 The change from vegetative to reproductive development (earliness) in Lycopersicon chesmannii line L2 was delayed for 20 weeks when compared to other Lycopersicon species under greenhouse conditions. The interspecific hybrid of L. chesmannii L2 and L. esculentum E9, a cherry tomato cultivar, also showed this delay in reproductive development. The distribution of this character in the F₂-derived population showed a bimodal shape, plants could be scored easily as “early” or “late” in two nutrient conditions (optimum and high salinity). A QTL with major effects on earliness was detected in salinity, which explained 35.6% of the phenotypic variation. The effect of this QTL greatly diminished under control conditions, indicating differences in the genetic control of earliness between treatments. ACC synthase or phytochrome B2 are the products of candidate genes for such a major QTL. Other QTLs with minor effects, and epistatic interactions, are also involved in earliness under both conditions. A “late” F₂ subpopulation yielded twice as much as an “early” F₂; conversely, “early” plants were taller than “late” plants, regardless of the treatment. QTL analysis, carried out in both subpopulations, showed that yield differences may be explained by chesmannii alleles showing negative additive effects at some QTLs only in the “early” subpopulation. The effect of population subdivision on QTL analysis was investigated by computer simulations to show sample-size or random effects; thus, important pleiotropic or regulatory effects of genes controlling earliness on yield that affect QTL analysis, have been reveiled. Therefore alleles controlling earliness in L. chesmannii have to be taken into account for a more efficient utilization of the genetic resources of this species. Received: 30 June 1998 / Accepted: 31 August 1998