In vitro investigation of the geometric contraction behavior of chemo-mechanical P-protein aggregates (forisomes)

We investigated the contracting behavior of forisomes from Vicia faba by carrying out precise measurements of their changing geometric parameters in vitro in the absence and in the presence of dissolved oxygen. Furthermore, we investigated the fine structure of forisomes by scanning electron microscopy. For the first time, single forisomes were titrated with Ca(2+), protons, and hydroxide ions recording the complete progression of their contractions. An apparent Ca(2+)-binding constant of (22+/-3) muM was calculated from two complete titration curves. The forisomes also contracted in the presence of Ba(2+) and Sr(2+) ions, but the amplitudes of contraction were smaller under the same measuring conditions. The time taken to change from the longitudinally expanded into the longitudinally contracted state was up to 2 s shorter in 10 mM Ca(2+) in comparison to 0.2mM Ca(2+). However, the contraction time was prolonged by decreasing the Ca(2+) concentration. In the absence of dissolved oxygen, the transition between the two final states of the forisomes was almost reversible and the amplitude of contraction remained almost constant during the first 25 contraction cycles. In the presence of dissolved oxygen the forisomes denaturated after a few cycles and lost their ability to contract, just after only a few cycles with 10 min in the contracted state. Denaturation of the forisomes occurred appreciably in the contracted state. We propose a cycle process to explain the thermodynamic basis of the Ca(2+)-induced contraction and its reversal by EDTA. Reducing the pH-value from 7.3 to 4.0 caused the forisomes to shorten by approximately 15%, while increasing the pH to 11.0 caused them to shorten by 28 to 30%. In both cases, the increases of the forisomes volume were greater than during the Ca(2+) induced contraction. The pH values of 4.7+/-0.3, and 10.2+/-0.2 marked the inflection points of the acid base titration of different forisomes.     

Strategies to fit pattern-mixture models

Whereas most models for incomplete longitudinal data are formulated within the selection model framework, pattern-mixture models have gained considerable interest in recent years (Little, 1993, 1994). In this paper, we outline several strategies to fit pattern-mixture models, including the so-called identifying restrictions strategy. Multiple imputation is used to apply this strategy to realistic settings, such as quality-of-life data from a longitudinal study on metastatic breast cancer patients.     

A simple method to fit geometric series and broken stick models in community ecology and island biogeography

Species abundance distributions are widely used in explaining natural communities, their natural evolution and the impacts of environmental disturbance. A commonly used approach is that of rank-abundance distributions. Favored, biologically founded models are the geometric series (GS) and the broken stick (BS) model. Comparing observed abundance distributions with those predicted by models is an extremely time-consuming task. Also, using goodness-of-fit tests for frequency distributions (like Chi-square or Kolmogorov–Smirnov tests) to compare observed with expected frequencies is problematic because the best way to calculate expected frequencies may be controversial. More important, the Chi-square test may prove if an observed distribution statistically differs from a model, but does not allow the investigator to choose among competing models from which the observed distribution does not differ. Both models can be easily tested by regression analysis. In GS, if a log scale is used for abundance, the species exactly fall along a straight line. The BS distribution shows up as nearly linear when a log scale is used for the rank axis. Regression analysis is proposed here as a simpler and more efficient method to fit the GS and BS models. Also, regression analysis (1) does not suffer from assumptions related to Chi-square tests; (2) obviates the need to establish expected frequencies, and (3) offers the possibility to choose the best fit among competing models. A possible extension of abundance-rank analysis to species richness on islands is also proposed as a method to discriminate between relict and equilibrial models. Examples of application to field data are also presented.     

Inherited neuropathies: new genes don't fit old models

Mutations in GARS cause dominantly inherited neuropathies in humans. GARS encodes glycyl-tRNA synthetase, the enzyme that couples glycine to its tRNA. In this issue of Neuron, Seburn et al. have identified and characterized a mutant mouse with a dominantly inherited axonal neuropathy caused by a Gars mutation that is inferred to have a gain of function.     

Anisotropic elastic bending models of DNA

Simplified elastic rod models of DNA were developed in which the rigidity of DNA is sequence dependent and asymmetrical, i.e. the bending is facilitated towards the major groove. By subjecting the models to bending load in various directions perpendicular to the longitudinal axis of DNA, the bending deformation and the average conformation of the models can be estimated using finite element methods. Intrinsically curved sequence motifs [(aaaattttgc)_n, (tctctaaaaaatatataaaaa)_n] are found to be curved by this modelling procedure whereas the average conformation of homopolymers and straight motifs [(a)_n, (atctaatctaacacaacaca)_n] show negligible or no curvature. This suggests that sequence dependent asymmetric rigidity of DNA can provide an explanation in itself for intrinsic DNA curvature. The average rigidity of various DNA sequences was calculated and a good correlation was found with such quantities as the free energy change upon the binding of the Cro repressor, the base stacking energy and the thermal fluctuations at room temperature.     

Native and artificial forisomes: functions and applications

Forisomes are remarkable protein bodies found exclusively in the phloem of the Fabaceae. When the phloem is wounded, forisomes are converted from a condensed to a dispersed state in an ATP-independent reaction triggered by Ca²⁺, thereby plugging the sieve tubes and preventing the loss of photoassimilates. Potentially, forisomes are ideal biomaterials for technical devices because the conformational changes can be replicated in vitro and are fully reversible over a large number of cycles. However, the development of technical devices based on forisomes has been hampered by the laborious and time-consuming process of purifying native forisomes from plants. More recently, the problem has been overcome by the production of recombinant artificial forisomes. This is a milestone in the development of forisome-based devices, not only because large quantities of homogeneous forisomes can be produced on demand, but also because their properties can be tailored for particular applications. In this review, we discuss the physical and molecular properties of native and artificial forisomes, focusing on their current applications in technical devices and potential developments in the future.     

Filopodia: Complex models for simple rods

Filopodia are prominent cell surface projections filled with bundles of linear actin filaments that drive their protrusion. These structures are considered important sensory organelles, for instance in neuronal growth cones or during the fusion of sheets of epithelial tissues. In addition, they can serve a precursor function in adhesion site or stress fibre formation. Actin filament assembly is essential for filopodia formation and turnover, yet the precise molecular mechanisms of filament nucleation and/or elongation are controversial. Indeed, conflicting reports on the molecular requirements of filopodia initiation have prompted researchers to propose different types and/or alternative or redundant mechanisms mediating this process. However, recent data shed new light on these questions, and they indicate that the balance of a limited set of biochemical activities can determine the structural outcome of a given filopodium. Here we focus on discussing our current view of the relevance of these activities, and attempt to propose a molecular mechanism of filopodia assembly based on a single core machinery.     

Effective size in simple metapopulation models

A coalescent argument is used to derive the effective size in simple models with recurrent local extinctions. Several alternative methods of derivation of this result are given and compared to earlier analyses of this problem. The different methods described in this paper all give the same result, which differs from earlier ones. For two published sets of estimates of demographic parameters, metapopulation structure appears to result in a moderate reduction of effective size relative to total adult population size.     

The theory of sliding filament models for muscle contraction. II. Biochemically-based models of the contraction cycle

A seven-state sliding filament model is proposed which differs from the model of Eisenberg & Greene. It is based on a simplified version of the in-vitro contraction cycle of Stein et al., and also has some desirable dynamical features of the empirical three-state model of Nishiyama & Murase. Appropriate x-dependences for all reaction rates are derived from the transition-state theory. The seventh-state is assumed to be a high-tension intermediate of A.M.ATP, from which direct but x-dependent dissociation can occur. If the final A.M.ATP state has a sufficiently lower tension than that of A.M.ADP.Pi, then the dominant escape path from the intermediate state is shown to be direct dissociation of the actin-myosin bond. This leads to an approximate five-state model for active and relaxed muscle in which A.M and the final A.M.ATP state are omitted.     

Stability in simple grazing models: effects of explicit functions

A class of simple models of a grazed pasture is based on the assumption that the dynamics of green biomass can be expressed as a balance between rates of growth and consumption, both of which are functions only of the total amount of green biomass present. Graphical analysis, using only the general shape of these functions, has shown that the pasture may be either continuously or discontinuously stable under grazing. Further results require explicit specification of these functions. Four growth functions and four consumption functions are considered here and their mathematical and biological properties discussed. The stability properties of the 16 models resulting from combinations of these functions are compared by plotting the isoclines of zero pasture growth, and by obtaining expressions in terms of the parameters for some critical points and quantities. Both methods show considerable similarity between the models in their qualitative behaviour and in the role of certain parameters in determining critical values. There are substantial differences in quantitative predictions of critical values and particularly of the boundary between continuous and discontinuous stability. In the absence of an ungrazable residual, some models are discontinuously stable in the whole parameter space, others only in a limited region of it-albeit the region in which most real systems may be.     

Some simple models of cannibalism

A sequence of mathematical models for a species which engages in cannibalism are investigated. The models treat the species as age-structured, and assume that adults consume the unhatched eggs of their own kind. The McKendrick or von Foerster partial differential equation model is first converted into a set of three coupled, nonlinear ordinary differential equations, and then adjusted to describe cannibalism. Some rather unusual dynamical effects are discovered. These include both a Hopf bifurcation and a catastrophic transition from an asymptotically stable equilibrium point to a stable limit cycle.     

Stochastic resonance in two simple compare-and-fire models

Two neural models are analysed and shown to exhibit the stochastic resonance effect. Namely, they respond to an underthreshold sinusoidal signal with an output signal whose signal-to-noise ratio (SNR) firstly increases then decreases as the intensity of noise affecting the system increases. The resonance curves are determined, analytically for the first and simplest model and by a synthetic method for the second one, and the respective resonant behaviours are illustrated and interpreted.     

Time delay in simple chemostat models.

The models of Monod and Williams, for the growth of unicellular organisms in chemostats, give strongly damped transients in the biomass and cell number when the flow rate of the chemostat is changed. A simple trick is used to incorporate time delay in these models while still allowing a conventional stability analysis. For long enough time delays the equilibrium point is unstable and limit cycles can be compared. Results obtained using Williams' model, with weakly damped transients as a result of using moderately long time delay, are compared with his data in which cell numbers show weak damping but biomass shows strong damping.     

Protein folding: simple models for a complex process

Twenty-eight years after its original publication, the diffusion-collision model has successfully been applied to describe the folding kinetics of two proteins with the same native structure but different sequences (Islam et al., this issue of Structure). The calculations show the relative importance of the primary and tertiary structure on the sequence of events and folding. For both proteins, the model suggests parallel folding pathways, a finding which has wide implications for the interpretations of experiments.     

Anisotropic AAA: Computational comparison between four and two fiber family material models

Abdominal aortic aneurysm (AAA) is a cardiovascular disease with high incidence among elderly population. Biomechanical computational analyses can provide fundamental insights into AAA pathogenesis and clinical management, but modeling should be sufficiently accurate. Several constitutive models of the AAA wall are present in the literature, and some of them seem to well describe the experimental behavior of the aneurysmatic human aorta. In this work we compare a two (2FF) and a four (4FF) fiber families constitutive models of the AAA wall. Both these models satisfactorily fit literature data from biaxial tests on the aneurysmatic tissue. To investigate the peculiar characteristics of these models, we considered the problem of AAA inflation, and solved it by implementing the constitutive equations in a finite element code. A 20% axial stretch was imposed to the aneurysm ends, to simulate the physiological condition. Although fitted on the same dataset, the two material models lead to considerably different outcomes. In particular, adopting a 4FF strain energy function (SEF), an increase of the circumferential stress values can be observed, while higher axial stresses are recorded for the 2FF model. These differences can be attributed to the intrinsic characteristics of the SEFs and to the effective stress field, with respect to the one experienced in biaxial experimental tests on which the fitting is based. In fact the two SEFs appear similar within the region of the stress-strain experimental data, but become different outside it, as in case of aneurysms, due to the effects of the data extrapolation process. It is suggested that experimental data should be obtained for conditions similar to those of the application for which they are intended.