Calcium cyclotron resonance and diatom mobility

The hypothesis that movement of biological ions may be predicted by cyclotron resonance theory applied to cell membranes is tested in these experiments. Diatoms (Amphora coffeaeformis) were chosen as the biosystem since they move or don't move, depending on how much calcium is transported across the membrane. The experiments demonstrate that a particular ion (calcium) is apparently moved across the cell membrane in response to the DC and AC values of magnetic flux densities (B) and the frequency derived from the cyclotron resonance theory. A clear resonance is shown and a rather sharp frequency response curve is demonstrated. The experiments also show a dose response as the AC value of the flux density is varied, and that odd harmonics of the basic cyclotron frequency are also effective.     

A theory of cell swelling in high concentrations of KCl and other chloride salts

A theory of the cell volume is presented with emphasis on the swelling effect of high concentrations of KCl and other chloride salts. In this theory a particular cell volume represents a state of balance between the tendency of the cell water to build deeper layers of polarized water and the restraining forces exerted by the salt linkages and H-bonds. Taking into account also the different structure-breaking effects of different salts, theoretical curves can be constructed which describe the complex multiple peak-plateau of swelling curve observed in frog muscle in response to increasing concentrations of different chloride salts. Presented at the Society for Mathematical Biology Meeting, University of Pennsylvania, Philadelphia, August 19–21, 1976.     

The geometric theory of adaptive evolution: trade-off and invasion plots

The purpose of this paper is to take an entirely geometrical path to determine the evolutionary properties of ecological systems subject to trade-offs. In particular we classify evolutionary singularities in a geometrical fashion. To achieve this, we study trade-off and invasion plots (TIPs) which show graphically the outcome of evolution from the relationship between three curves. The first invasion boundary (curve) has one strain as resident and the other strain as putative invader and the second has the roles of the strains reversed. The parameter values for one strain are used as the origin with those of the second strain varying. The third curve represents the trade-off. All three curves pass through the origin or tip of the TIP. We show that at this point the invasion boundaries are tangential. At a singular TIP, in which the origin is an evolutionary singularity, the invasion boundaries and trade-off curve are all tangential. The curvature of the trade-off curve determines the region in which it enters the singular TIP. Each of these regions has particular evolutionary properties (EUS, CS, SPR and MI). Thus we determine by direct geometric argument conditions for each of these properties in terms of the relative curvatures of the trade-off curve and invasion boundaries. We show that these conditions are equivalent to the standard partial derivative conditions of adaptive dynamics. The significance of our results is that we can determine whether the singular strategy is an attractor, branching point, repellor, etc. simply by observing in which region the trade-off curve enters the singular TIP. In particular we find that, if and only if the TIP has a region of mutual invadability, is it possible for the singular strategy to be a branching point. We illustrate the theory with an example and point the way forward.     

Solvent effects on the cooperative order-disorder transition of aqueous solutions of schizophyllan, a triple-helical polysaccharide

A triple helical polysaccharide schizophyllan in aqueous solution exhibited a highly cooperative transition between ordered and disordered states associated with the conformation of its side chains and nearby water molecules. The transition was followed by optical rotation and calorimetry using water containing additives such as NaOH and DMSO as solvents. The ordered state was stabilized or destabilized depending on the kind and amount of the additive employed; in particular, the addition of DMSO had a remarkable stabilizing effect. This effect was analyzed by means of a statistical mechanical theory of linear cooperative transitions, where DMSO was assumed to interact favorably with the ordered side chains. A small amount of NaOH in a solvent mixture stabilized the ordered state and made the transition curve very gradual. No molecular mechanism was elucidated to account for the role of NaOH.     

A dynamical model of communities and a new species-abundance distribution

It is known to many field biologists that biosurveys of natural communities tend to produce a J-shaped curve when the numbers of species are plotted against abundance. In other words, when the number of species of abundance k is plotted against k (running from 1 to some large number), the resulting distribution peaks at the lowest abundance, then forms a concave ramp as it approaches zero at the far end of the abundance axis. Does this distribution represent a single formula operating behind the scenes, or does it represent several formulas, appropriate for different types of community? Or does it represent no particular formula at all? The research reported here has three components: (1) The analysis of a new dynamical system that simulates multispecies communities (producing J-curves in the process) and the derivation of the "logistic-J" distribution, as the underlying community equilibrium curve; (2) the summary of a general theory of sampling as a bridge between natural communities and samples of them; (3) the evaluation of extant proposals for species-abundance distributions by application of a general theory of sampling or by cross-comparison via 100 biosurveys randomly selected from the literature.     

Identification of protein domains on topological basis

A theoretical method is proposed to identify structural domains in proteins of known structures. It is based on the distribution of the local axes of the polypeptide chain. In particular, a statistical analysis is applied to the contributions of the local axes to the absolute writhing number, a topological property of a space curve resulting from the number of self-crossings in the curve projections onto a unit sphere. This finding supports the hypothesis that topological requirements should be satisfied in the process of protein folding and in the final organization of the tertiary structures.     

Contributions to the mathematical biophysics of the central nervous system with special reference to learning

A learning theory based on the lowering of thresholds of neurons under certain conditions is applied to two “random net” models. The first, a so-called “ganglion-brain” is characterized by completely random connections of all afferent tracts except certain ones which form the pathways for unconditioned responses. Certain expressions are derived which measure the learning potentiality of the ganglion— in particular, with respect to the number of responses which can be learned (conditioning potential) and the amount of interference between the learned responses (redundance potential). The second model concerns the progressive refinement of a response. The efficiency of learning in this case is reflected in the eventual specificity of the response which, in turn, depends on the modification of the distribution of thresholds associated with the neurons governing the responses. Expressions are derived relating the initial distribution of thresholds, the relative effectiveness of the various responses, and certain other parameters to the final distribution of thresholds. For a particular choice of the effectiveness distribution of responses the progressive sharpening of the threshold curve (i.e., progressive specificity of response) is demonstrated. Some implications of the model with respect to the evolution of nervous systems are discussed.     

A selective model of plasma protein catabolism

Recent data suggest that the catabolism of certain plasma protein could be a stepwise process, the actual breakdown selectively acting only on the molecules which have undergone a characteristic change. Based on this assumption a kinetic model of plasma protein catabolism is built up, giving the analytic expression for a catabolic curve. Assuming a relatively small fraction of the modified form, this expression fits the existing experimental data with the same accuracy range as the classical random breakdown curve. A testing criterion able to discriminate between the two possibilities is suggested and some particular cases are briefly discussed.     

Hermitian splines for modeling biological soft tissue systems that exhibit nonlinear force-elongation curves

Numerical simulation of soft tissue mechanical properties is a critical step in developing valuable biomechanical models of live organisms. A cubic Hermitian spline optimization routine is proposed in this paper to model nonlinear experimental force-elongation curves of soft tissues, in particular when modeled as lumped elements. Boundary conditions are introduced to account for the positive definiteness and the particular curvature of the experimental curve to be fitted. The constrained least-square routine minimizes user intervention and optimizes fitting of the experimental data across the whole fitting range. The routine provides coefficients of a Hermitian spline or corresponding knots that are compatible with a number of constraints that are suitable for modeling soft tissue tensile curves. These coefficients or knots may become inputs to user-defined component properties of various modeling software. Splines are particularly advantageous over the well-known exponential model to account for the traction curve flatness at low elongations and to allow for more flexibility in the fitting process. This is desirable as soft tissue models begin to include more complex physical phenomena.     

Statistical theory of combinatorial libraries of folding proteins: energetic discrimination of a target structure

A self-consistent theory is presented that can be used to estimate the number and composition of sequences satisfying a predetermined set of constraints. The theory is formulated so as to examine the features of sequences having a particular value of Delta=E(f)-(u), where E(f) is the energy of sequences when in a target structure and (u) is an average energy of non-target structures. The theory yields the probabilities w(i)(alpha) that each position i in the sequence is occupied by a particular monomer type alpha. The theory is applied to a simple lattice model of proteins. Excellent agreement is observed between the theory and the results of exact enumerations. The theory provides a quantitative framework for the design and interpretation of combinatorial experiments involving proteins, where a library of amino acid sequences is searched for sequences that fold to a desired structure.     

Relationship between helix-coil transition and gene organization of ColE1 plasmid DNA. Differential scanning calorimetric and theoretical studies

Differential scanning calorimetry (DSC) was carried out to analyze the transition of helix to coil state of DNA, using ColE1 DNA molecules digested with EcoRI. The DSC curves showed multimodal transition, consisting of nine to 11 peaks over a temperature range, depending on the ionic strength of the DNA solution. These DSC curves were essentially in good agreement with the optical melting curves of ColE1 DNA. The theoretical melting profiles of ColE1 DNA were predicted from calculations based on the helix-coil transition theory and the nucleotide sequence of the DNA. These profiles resembled the DSC curves and made it possible to assign the peaks seen in the DSC curves to the helix-coil transition of particular regions of the nucleotide sequence of ColE1. The helix-coil transition of each of the small genes gave rise to a single peak in the DSC curve, while the helix-coil transition of large genes contributed to two or more peaks in the DSC curve. This multimodal transition within a single coding region might correspond to the melting of individual segments encoding the different domains of the proteins. The helix-coil transition at the specific sites including ori, the origin of replication of ColE1, was also found to occur in a particular temperature range. DSC, a simple method, is thus useful for analyzing the multimodal helix-coil transition of DNA, and for providing information on the genetic organization of DNA.     

A Mechanistic Model of PCR for Accurate Quantification of Quantitative PCR Data

Background

Quantitative PCR (qPCR) is a workhorse laboratory technique for measuring the concentration of a target DNA sequence with high accuracy over a wide dynamic range. The gold standard method for estimating DNA concentrations via qPCR is quantification cycle () standard curve quantification, which requires the time- and labor-intensive construction of a standard curve. In theory, the shape of a qPCR data curve can be used to directly quantify DNA concentration by fitting a model to data; however, current empirical model-based quantification methods are not as reliable as standard curve quantification.

Principal Findings

We have developed a two-parameter mass action kinetic model of PCR (MAK2) that can be fitted to qPCR data in order to quantify target concentration from a single qPCR assay. To compare the accuracy of MAK2-fitting to other qPCR quantification methods, we have applied quantification methods to qPCR dilution series data generated in three independent laboratories using different target sequences. Quantification accuracy was assessed by analyzing the reliability of concentration predictions for targets at known concentrations. Our results indicate that quantification by MAK2-fitting is as reliable as standard curve quantification for a variety of DNA targets and a wide range of concentrations.

Significance

We anticipate that MAK2 quantification will have a profound effect on the way qPCR experiments are designed and analyzed. In particular, MAK2 enables accurate quantification of portable qPCR assays with limited sample throughput, where construction of a standard curve is impractical.     

Theory for growth of plants derived from the nitrogen productivity concept

A theory is developed on the assumption that growth of plants is determined by the current amount of nitrogen in the plants. The nitrogen-growth relation is formalized in the nitrogen productivity concept (amount of biomass produced per amount of nitrogen in the biomass and per unit of time), which is essentially a constant for a given species under fixed environmental conditions. A number of results follow for increases in whole plant biomass: (A) The relative growth rate is a linear function of the internal nitrogen concentration. (B) The maximal relative growth rate uniquely determines the scaling of the time axis. (C) Exponential growth is consistent only with stable internal nitrogen concentration. Dose-response curves expressed in reduced variables (the ratio between a variable and the same variable for a plant growing under optimal conditions) are universal, so that all species and all environmental conditions yield the same curve. This is confirmed by experimental data. The shape (linear, exponential, etc.) of the nitrogen uptake curve is the only parameter differentiating these universal curves. The Mitscherlich curve or variations of it can be fitted very closely to the derived dose-response curves, except under exponential growth. A conclusion drawn from the analysis is that the results of nutrition experiments cannot be properly interpreted unless the variation with time of the amount of nitrogen in the plant is known. The theory can be extended to more complex situations, for example, time-varying environmental conditions.     

Mapping quantitative trait loci for longitudinal traits in line crosses

Quantitative traits whose phenotypic values change over time are called longitudinal traits. Genetic analyses of longitudinal traits can be conducted using any of the following approaches: (1) treating the phenotypic values at different time points as repeated measurements of the same trait and analyzing the trait under the repeated measurements framework, (2) treating the phenotypes measured from different time points as different traits and analyzing the traits jointly on the basis of the theory of multivariate analysis, and (3) fitting a growth curve to the phenotypic values across time points and analyzing the fitted parameters of the growth trajectory under the theory of multivariate analysis. The third approach has been used in QTL mapping for longitudinal traits by fitting the data to a logistic growth trajectory. This approach applies only to the particular S-shaped growth process. In practice, a longitudinal trait may show a trajectory of any shape. We demonstrate that one can describe a longitudinal trait with orthogonal polynomials, which are sufficiently general for fitting any shaped curve. We develop a mixed-model methodology for QTL mapping of longitudinal traits and a maximum-likelihood method for parameter estimation and statistical tests. The expectation-maximization (EM) algorithm is applied to search for the maximum-likelihood estimates of parameters. The method is verified with simulated data and demonstrated with experimental data from a pseudobackcross family of Populus (poplar) trees.     

Preferences for familiarity and novelty: a model for the simultaneous development of both

Many developing animals show an increasing preference for familiar companions and objects. They may also come to prefer things which are slightly different from the familiar. A model which shows how both processes can occur simultaneously is developed with particular reference to imprinting in birds. It shows how a biphasic curve would be obtained if preferences were measured in choice tests during the course of familiarization. The model predicts that shape of the preference curve will depend on the difference between the familiar and unfamiliar objects. It also predicts that the shape will be altered if inexperienced animals show a preference for one object over the other.     

Mathematical modeling of measuring the hydraulic conductivity of roots by the relaxation method

The continuum model of radial mass transfer in plant roots developed previously has been used for processing the nonstationary experiments on determining the root hydraulic conductivity. In contrast to compartmental models, our model allows describing the shape of the relaxation curve, in particular, separating segments with different relaxation times. It is shown that to correctly determine the hydraulic conductivity, the method of data processing should be modified. A method for estimating the extracellular to intracellular conductivity ratio is proposed.     

Performance comparison of a neural network with human observers on a visual target detection task

An experiment is described which compares the performance of a neural network to human performance on a visual task which consists of detecting a target in a background image of correlated noise. A three-layer, feed-forward, multi-layer perceptron is trained to indicate the presence or absence of a target in images also presented to human observers. The basis for the comparison between the network and the human observers is the receiver operating characteristic (ROC) curve. Network performance is comparable to human performance for this particular task.