Microbial expansion–collision dynamics promote cooperation and coexistence on surfaces

Microbes colonizing a surface often experience colony growth dynamics characterized by an initial phase of spatial clonal expansion followed by collision between neighboring colonies to form potentially genetically heterogeneous boundaries. For species with life cycles consisting of repeated surface colonization and dispersal, these spatially explicit “expansion‐collision dynamics” generate periodic transitions between two distinct selective regimes, “expansion competition” and “boundary competition,” each one favoring a different growth strategy. We hypothesized that this dynamic could promote stable coexistence of expansion‐ and boundary‐competition specialists by generating time‐varying, negative frequency‐dependent selection that insulates both types from extinction. We tested this experimentally in budding yeast by competing an exoenzyme secreting “cooperator” strain (expansion–competition specialists) against nonsecreting “defectors” (boundary–competition specialists). As predicted, we observed cooperator–defector coexistence or cooperator dominance with expansion–collision dynamics, but only defector dominance otherwise. Also as predicted, the steady‐state frequency of cooperators was determined by colonization density (the average initial cell–cell distance) and cost of cooperation. Lattice‐based spatial simulations give good qualitative agreement with experiments, supporting our hypothesis that expansion–collision dynamics with costly public goods production is sufficient to generate stable cooperator–defector coexistence. This mechanism may be important for maintaining public–goods cooperation and conflict in microbial pioneer species living on surfaces.     

Correlation of Electrical and Permeability Properties of Ion-Selective Membranes

The linear phenomenological equations giving particle and practical fluxes of a single electrolyte across an ion-selective membrane are stated and interrelated. It is shown that the experimental measurements commonly made in biological and synthetic membrane studies may be used, with minor modification, to obtain the phenomenological transport coefficients and their concentration dependences. It is demonstrated that the electrical properties of a homogeneous membrane may be obtained as functions of the bathing solution concentration by combining fluxes measured under open and short circuit. Attention is paid to the use of radiotracers when measuring ionic fluxes. To obtain all the phenomenological coefficients at least one measurement must be made under a pressure gradient. The experimental difficulties in such measurements are discussed and the merits and demerits of various experiments considered. The problems of measuring potentials and concentrations at the low pressure face of a supported membrane make several mathematically simple approaches experimentally unattractive. The best methods appear to be either the measurement of a succession of “apparent osmotic pressures” under concentration differences sufficiently small that the membrane does not require support or the study of “reverse osmosis”. Sets of equations are given which enable the phenomenological coefficients to be evaluated from convenient experiments. With a stable homogeneous membrane nine coefficients may be obtained thus enabling either the applicability of the reciprocal relations or the applicability of linear theory under the conditions of the experiments to be tested. For a discontinuous system the six independent coefficients may be obtained from experiments in a single membrane cell.     

Data handling for interactive metabolomics: tools for studying the dynamics of metabolome-macromolecule interactions

All published metabolomics studies investigate changes in either absolute or relative quantities of metabolites. However, blood plasma, one of the most commonly studied biofluids for metabolomics applications, is a complex, heterogeneous mixture of lipoproteins, proteins, small organic molecules and ions which together undergo a variety of possible molecular interactions including metal complexation, chemical exchange processes, micellular compartmentation of metabolites, enzyme-mediated biotransformations and small-molecule-macromolecule binding. In particular, many low molecular weight (MW) compounds (including drugs) can exist both ‘free’ in solution and bound to proteins or within organised aggregates of macromolecules. To study the effects of e.g. disease on these interactions we suggest that new approaches are needed. We have developed a technique termed ‘interactive metabolomics’ or i-metabolomics. i-metabolomics can be defined as: “The study of interactions between low MW biochemicals and macromolecules in heterogeneous biosamples such as blood plasma, without pre-selection of the components of interest”. Standard 1D NMR experiments commonly used in metabolomics allow metabolite concentration differences between samples to be investigated because the intensity of each peak depends on the concentration of the compound in question. On the other hand, the instrument can be set-up to measure molecular interactions by monitoring the diffusion coefficients of molecules. According to the Stokes–Einstein equation, the diffusion coefficient of a molecule is inversely proportional to its effective size, as represented by the hydrodynamic radius. Therefore, when low MW compounds are non-covalently bound to proteins, the observed diffusion coefficient for the compound will be intermediate between those of its free and bound forms. By measuring diffusion by NMR, the degree of protein binding can be estimated for either low MW endogenous biochemicals or xenobiotics. This type of experiment is referred to as either Diffusion-Ordered Spectroscopy (DOSY) or Diffusion-Edited Spectroscopy, depending on the type of post-acquisition data processing applied to the spectra. Results presented in this paper demonstrate approaches for the non-selective modelling of metabolite-macromolecule interactions (i-metabolomics), whilst additionally highlighting some of the all too frequently ignored issues associated with interpretation of data derived from profiling of blood plasma.     

Data handling for interactive metabolomics: tools for studying the dynamics of metabolome-macromolecule interactions

All published metabolomics studies investigate changes in either absolute or relative quantities of metabolites. However, blood plasma, one of the most commonly studied biofluids for metabolomics applications, is a complex, heterogeneous mixture of lipoproteins, proteins, small organic molecules and ions which together undergo a variety of possible molecular interactions including metal complexation, chemical exchange processes, micellular compartmentation of metabolites, enzyme-mediated biotransformations and small-molecule-macromolecule binding. In particular, many low molecular weight (MW) compounds (including drugs) can exist both ‘free’ in solution and bound to proteins or within organised aggregates of macromolecules. To study the effects of e.g. disease on these interactions we suggest that new approaches are needed. We have developed a technique termed ‘interactive metabolomics’ or i-metabolomics. i-metabolomics can be defined as: “The study of interactions between low MW biochemicals and macromolecules in heterogeneous biosamples such as blood plasma, without pre-selection of the components of interest”. Standard 1D NMR experiments commonly used in metabolomics allow metabolite concentration differences between samples to be investigated because the intensity of each peak depends on the concentration of the compound in question. On the other hand, the instrument can be set-up to measure molecular interactions by monitoring the diffusion coefficients of molecules. According to the Stokes–Einstein equation, the diffusion coefficient of a molecule is inversely proportional to its effective size, as represented by the hydrodynamic radius. Therefore, when low MW compounds are non-covalently bound to proteins, the observed diffusion coefficient for the compound will be intermediate between those of its free and bound forms. By measuring diffusion by NMR, the degree of protein binding can be estimated for either low MW endogenous biochemicals or xenobiotics. This type of experiment is referred to as either Diffusion-Ordered Spectroscopy (DOSY) or Diffusion-Edited Spectroscopy, depending on the type of post-acquisition data processing applied to the spectra. Results presented in this paper demonstrate approaches for the non-selective modelling of metabolite-macromolecule interactions (i-metabolomics), whilst additionally highlighting some of the all too frequently ignored issues associated with interpretation of data derived from profiling of blood plasma.

     

A mathematical model for the batch reactor kinetics of algae growth

A mathematical model based on the Einstein law of photochemical equivalence is proposed to describe the batch growth of unicellular algae. The model was applied in an integrated form to cell concentration versus growth time data taken over an extended range of cell concentrations which include both the regions of “exponential” and “linear” growth. It is shown that a certain function of cell concentration contained in the integrated form of the model is linearly dependent on the growth time over both the “exponential” and “linear” growth regions.     

Two-enzyme active transport in vitro with ph induced asymmetrical functional structures.: III. Discussions based on numerical treatments of the time-dependent evolutions

Three complementary models have been considered in which pH gradients (step function. linear pH or linear H^?) impose asymmetry on a two-enzyme mixture. If the “combined pH dependences” of enzymes is pro-asymmetrical, the pH gradient induces an asymmetrical distribution of potential activities (“latent” asymmetry of functional structure). When substrate is added, “developed” asymmetry of effective activities appears which results in “substrate space wave” and pumping when the catalysed reaction couple is “inversible”. It is shown that only one steady state exists for a given boundary condition and is attained when the “combined effective activity” of enzymes is nil: the stationary flux with symmetrical boundaries or the stationary load with moving boundaries is proportional to “effective global activities” of enzymes. “Equivalent square models” could be proposed that would be able to describe “functional” or “permanent” structure pumps as well. These models belong to the thermodynamic branch and the asymmetrical “space wave” substrate concentration profiles obtained must be distinguished from dissipative structures. It appears that such primary active transport pumps are chemical equivalents of heat pumps.     

A critique of the “ultra‐high risk” and “transition” paradigm

The transdiagnostic expression of psychotic experiences in common mental disorder (anxiety/depression/substance use disorder) is associated with a poorer prognosis, and a small minority of people may indeed develop a clinical picture that meets criteria for schizophrenia. However, it appears neither useful nor valid to observe early states of multidimensional psychopathology in young people through the “schizo”‐prism, and apply misleadingly simple, unnecessary and inefficient binary concepts of “risk” and “transition”. A review of the “ultra‐high risk” (UHR) or “clinical high risk” (CHR) literature indicates that UHR/CHR samples are highly heterogeneous and represent individuals diagnosed with common mental disorder (anxiety/depression/substance use disorder) and a degree of psychotic experiences. Epidemiological research has shown that psychotic experiences are a (possibly non‐causal) marker of the severity of multidimensional psychopathology, driving poor outcome, yet notions of “risk” and “transition” in UHR/CHR research are restrictively defined on the basis of positive psychotic phenomena alone, ignoring how baseline differences in multidimensional psychopathology may differentially impact course and outcome. The concepts of “risk” and “transition” in UHR/CHR research are measured on the same dimensional scale, yet are used to produce artificial diagnostic shifts. In fact, “transition” in UHR/CHR research occurs mainly as a function of variable sample enrichment strategies rather than the UHR/CHR “criteria” themselves. Furthermore, transition rates in UHR/CHR research are inflated as they do not exclude false positives associated with the natural fluctuation of dimensional expression of psychosis. Biological associations with “transition” thus likely represent false positive findings, as was the initial claim of strong effects of omega‐3 polyunsatured fatty acids in UHR samples. A large body of UHR/CHR intervention research has focused on the questionable outcome of “transition”, which shows lack of correlation with functional outcome. It may be more productive to consider the full range of person‐specific psychopathology in all young individuals who seek help for mental health problems, instead of “policing” youngsters for the transdiagnostic dimension of psychosis. Instead of the relatively inefficient medical high‐risk approach, a public health perspective, focusing on improved access to a low‐stigma, high‐hope, small scale and youth‐specific environment with acceptable language and interventions may represent a more useful and efficient strategy.     

On the mutability of the yeast mitochondrial genome.

A mechanism is proposed to explain how a mutation in a single molecule of mitochondrial DNA (mitDNA) can come to affect all the other mitDNA molecules of a yeast cell. It is suggested that an initial mutation may be “amplified” by a process which is, in fact, intended to ensure the identity of the cell's complement of mitDNA molecules. It is postulated that this process involves a small number of “reference” copies of mitDNA to which all other (“derived”) copies are compared and corrected once per cell cycle. Asymmetric gene conversion is proposed as the correction mechanism and the means of “amplifying” mutations. The model is shown to be compatible with current data on spontaneous and induced mitochondrial mutation in Saccharomyces cerevisiae.     

Homology in Trivaline Complex Formation with dsDNA and ssRNA

Abstract

It has been shown by the equilibrium dialysis that at a polyU concentration above the “critical” one, the complete polymer saturation with trivaline reaches approximately 0.7 trivaline molecules per one phosphate group. i.e. at these conditions peptide dimer occupies on polyU a site of three bases (phosphates) in length. The trivaline complex with polyU at a concentration lower than the “critical” one does not reveal any noticeable fluorescence, but has rather significant positive linear dichroism at 265 and 330 nm. The trivaline-nucleic acids complex has a significant fluorescence at any dsDNA concentration while with polyU it is only so at a concentration above the “critical” one. Electron microscopy has shown that at a rather high concentration of dsDNA molecules in solution a “biduplex” structure undergoes an additional stage of compaction, during which the extended particles more than 30 nm in diameter are formed.

Schematic models for the trivaline complexes and compact structures with dsDNA and ssRNA are propose     

The Routine Fitting of Kinetic Data to Models: A Mathematical Formalism for Digital Computers

A mathematical formalism is presented for use with digital computers to permit the routine fitting of data to physical and mathematical models. Given a set of data, the mathematical equations describing a model, initial conditions for an experiment, and initial estimates for the values of model parameters, the computer program automatically proceeds to obtain a least squares fit of the data by an iterative adjustment of the values of the parameters. When the experimental measures are linear combinations of functions, the linear coefficients for a least squares fit may also be calculated. The values of both the parameters of the model and the coefficients for the sum of functions may be unknown independent variables, unknown dependent variables, or known constants. In the case of dependence, only linear dependencies are provided for in routine use. The computer program includes a number of subroutines, each one of which performs a special task. This permits flexibility in choosing various types of solutions and procedures. One subroutine, for example, handles linear differential equations, another, special non-linear functions, etc. The use of analytic or numerical solutions of equations is possible.     

Comparison of heavy metal accumulation and cadmium phytoextraction rates among ten leading tobacco (Nicotiana tabacum L.) cultivars in China

Abstract

Cadmium (Cd) contamination is one of the most serious global environmental problems, and phytoremediation, which uses Cd-accumulator plants, is potentially one of the sustainable solutions. Pot experiments with natural and Cd-amended soils were conducted to investigate the accumulation of heavy metals in 10 leading cultivars of tobacco in China. The extraction ability and profiles of Cd accumulation among plant organs were also analyzed. The tobacco roots accumulated cobalt, nickel, and Cd, while the leaf highly bioaccumulated Cd and lowly accumulated zinc, selenium and mercury. The transport from the tobacco stem to the leaf plays a critical role in the accumulation of these elements. The ratios of Cd concentration in the leaves at lower, middle and upper positions were comparatively stable. The high Cd-extracting cultivars were “Hongda”, “NC89” and “Zhongyan 100” when grown in normal soils, “CuiBi 1” and “Hongda” in moderately contaminated soils, and “YuYan 87”, “LongJiang 851” and “K326” in severely contaminated soils. Tobacco leaves could accumulate about 80% of the total Cd extracted from the soil by the plant. Considering the Cd-extraction limitations exhibited by leading tobacco cultivars, screening of germplasm resources for high or low levels of Cd-accumulation is still an important target for the future.     

Biochemical studies on sub-fractions of rat liver mitochondria

Highly purified mitochondria from rat liver were separated into six sub-fractions by differential centrifugation. The sub-fractions represent a spectrum from “heavy” to “very light” mitochondria. Enzymes representative of mitochondrial compartments were assayed to see whether functional differences occurred among the various mitochondrial sub-fractions. Respiratory control and NADH oxidase activity, both of which are indicators of mitochondrial structural integrity, were also measured. An enzyme marker for endoplasmic reticulum (glucose-6-phosphatase, G-6-Pase) was also assayed. Specific activities for monoamine oxidase (outer membrane marker), cytochrome oxidase (inner membrane marker) and malate-cytochrome c reductase did not vary within experimental error in all sub-fractions; similarly, for respiratory control and NADH oxidase activity. Malate dehydrogenase, a component of malate-cytochrome c reductase is located within the matrix surrounded by the inner membrane. Specific activity of adenylate kinase (located between the outer and inner membrane) decreased markedly from the “heavy” mitochondria to the “very light” fractions. Specific activity for G-6-Pase, very low in the “heavy” fractions, increased markedly in the “light” to “very light” fractions. Isopycnic density centrifugation on a linear sucrose density gradient of each of the fractions indicated that the correlation coefficient for the sucrose concentrations at which cytochrome oxidase and G-6-Pase activities peaked was 0.995. Thus the “light” to “very light” mitochondria may represent mitochondria whose outer membrane is still contiguous with the endoplasmic reticulum. Microsomes containing the endoplasmic reticulum peaked on the gradient at a significantly lower sucrose concentration than any of the mitochondrial sub-fractions. A buoyant effect of endoplasmic reticulum still attached to any of the mitochondrial sub-fractions would be expected to lower the density of attached mitochondria and thus give rise to “light” and “very light” mitochondria.     

A model of gradient interpretation based on morphogen binding

We propose a model in which pattern formation is controlled by several concentration gradients of “morphogens” and by allosteric proteins which bind them. In this model, each protein can bind up to two molecules of each morphogen and has an “active state” when one molecule of each morphogen is bound. The concentration of the active state of such a “morphogen binding protein” varies with position in a way that depends on the values given the binding constants. In a contour map of the active state concentration, the contours can have a variety of simple shapes.Simply-shaped regions of cell differentiation can be defined directly by concentration contours of a morphogen binding protein using a threshold-sensing mechanism. More complex shapes may be generated using several proteins and a “winner-take-all” rule according to which each protein specifies some particular sort of cell differentiation and the differentiation of cells in any position is governed by the protein with the highest active state concentration.We present an application of our model to the vertebrate limb skeleton; we use the “winner-take-all” mechanism and thirteen morphogen binding proteins, eleven of which specify cartilage formation. In this model we use one morphogen binding protein to specify the shaft of a typical long bone and one for each epiphysis. Our model is reasonably successful in imitating the in vivo positions and orientations of developing bones and in generating simple, plausible-looking articular surfaces.In addition to the morphogen-binding model we propose a mechanism which could transform morphogen-binding patterns into high-amplitude patterns capable of controlling the activity of structural genes. This “amplifying mechanism” can account for two previously unexplained features of limb skeletal development: the early formation of the diffusely-bounded “scleroblastema” in the limb bud and the center-to-edge gradations in cartilage formation rate which are later seen within individual chondrification foci.A simple modification of the morphogen-binding model provides an explanation for the general anatomical phenomenon of metamerism: The model can account for the formation of inexactly repeating patterns (such as the pattern of the vertebral column) and suggests a mechanism by which such patterns could (1) evolve from exactly repeating patterns, and (2) acquire, in further evolution, a high degree of specialization of the individual repeating units.The most promising approach for testing the morphogen-binding model would appear to involve experiments in which cytoplasm is transferred between cells at various stages of pattern development. Support for the model could also come from the discovery of certain kinds of hereditary limb defects.     

Honeybee navigation: linear perception of short distances travelled

Recent evidence indicates that honeybees measure distance flown to a food source by integrating, over time, the apparent visual motion of the environment that they experience en route to the goal. Is the bee's perception of distance travelled a linear function of distance, or is it some other function? This question was investigated by training bees to fly into a tunnel and receive a food reward. The walls and floor of the tunnel were lined with a random texture, and the reward was placed at one of two fixed distances, “near” or “far”, from the tunnel entrance. The feeder containing the reward was placed in a box which could be accessed through one of two openings, one on the left side of the box, and the other on the right. When the box was at the “near” position, the reward could only be accessed through the left-hand opening; when the box was at the “far” position, the reward could only be accessed through the right-hand opening. When the trained bees were tested individually in an identical, fresh tunnel with the reward removed from the box, they showed a strong preference for the left-hand opening when tested at the “near” distance, and for the right-hand opening when tested at the “far” distance. At intermediate positions, the bees' preference for the two openings varies linearly with distance. These findings suggest that the honeybee's perception of distance travelled is linear, at least over the distances and range of image motions experienced in our experiments. The implications for navigation and for the encoding of distance information in the dance are discussed.     

Analytical solution to the initial-value problem for traveling bands of chemotactic bacteria

The governing parabolic partial differential equations for the diffusion and chemotactic transport of a distribution of bacteria and for the diffusion and bacterial degradation of a distribution of chemotactic agent are supplemented with boundary and initial conditions that model the recent capillary tube experiments on the formation and propagation of traveling bands of chemotactic bacteria. An iteration procedure that takes the exact solution to the “diffusionless” problem as a first approximation is applied to solve the equations of the complete theoretical model. It is shown that satisfactory agreement with experiment obtains for the analytical results of the first approximation which relate the velocity of propagation and total number of bacteria cells per unit cross-sectional area in a traveling band to the constant parameters in the governing equations and supplementary conditions. The second approximation is shown to yield approximate analytical expressions for the solution functions which are in close correspondence with previously derived traveling band solutions for values of time after the initial period of formation.     

Lineweaver-Burk,Hanes, Eadie-Hofstee and Dixon plots in non-steady-state situations

Lineweaver-Burk, Hanes, Eadie-Hofstee and Dixon plots can only be used when a true initial rate is measured. Despite the fact that this point has often been stressed, it is far too often ignored in favour of restricting the assay time to one where low amounts of substrate are used. When one or several irreversible and slow steps occur with an inactivator during the incubation of a ternary enzyme-substrate-inactivator mixture, the rate of the enzyme-catalysed reaction progressively decreases. Even under these conditions, the present computer simulations investigations show that apparently linear Lineweaver-Burk, Hanes, Eadie-Hofstee and Dixon graphs can be obtained when the amount of product formed is mistakenly assumed to represent the true initial rate. Moreover, the observed pattern can change with time, going for instance from non-competitive to competitive. “Ki's” measured under these conditions also vary with time and bear little relationship to the true constants involved in the interaction.     

Induction of lordosis in female rats: two modes of estrogen action and the effect of adrenalectomy.

In ovariectomized female rats, progesterone treatment alone does not induce lordosis, but following estrogen treatment by an appropriate interval it greatly enhances the performance of lordosis compared to that with estrogen alone. This “facilitating” effect of progesterone is thought to act synergistically with the initial “priming” effect of estrogen. In the present experiments a second estrogen treatment given to estrogen-primed ovariectomized rats in place of progesterone was found to facilitate lordosis. Latency of the facilitation of lordosis following this second estrogen treatment was similar to that of progesterone and was much shorter than that required for the usual “priming” effect, but higher doses were needed for the “facilitatory” effect. Experiments with adrenalectomized-ovariectomized female rats showed that this short latency effect of second estrogen treatment need not be mediated by the adrenals. These results raise the possibility that estrogen acts on the central nervous system in more than one way to induce lordosis.