Configuration-dependent properties of randomly coiling polynucleotide chains. II. The role of the phosphodiester linkage

The dependence of the unperturbed dimensions of randomly coiling polynucleotides on the rotations about the phosphodiester linkages of the chain has been examined in order to understand the conformational discrepancies, set forth in paper I, regarding these angles (ω′ and ω). Large values of the characteristic ratio 〈r²〉₀/nl² , which agree with the experimental behavior of the chain, are obtained only if a sizeable proportion of the polymer residues have trans ω′ values. The asymmetric torsional potential that is believed to arise from gauche effects associated with the P-O bonds has been approximated using a hard core model. The calculated characteristic ratio exhibits a strong dependence upon the magnitude of this torsional barrier (separating trans and gauche conformations) and shows agreement with experimental values for polyribonucleotides only if this energy difference is 1 kcal/mol or less.     

Estimating cell lineage from distributions of randomly introduced markers

Cell lineage of a multicellular organism has been analysed by introducing a genetic or chemical marker that is inherited from a cell to its daughter cells and is detectable even after several cell divisions. To construct a complete cell lineage, all the cells at different developmental stages need to be identified, and then the intracellular marker must be introduced to each cell. In this paper, I study a new method of estimating cell lineage based on distributions of intercellular markers observed at a single stage, which are introduced randomly at earlier stages. Assumptions are: (1) cell lineage is invariant between embryos; (2) a small number of cells are marked in each experiment; and (3) the total number of replicate experiments is sufficiently large. Then we identify the most likely cell lineage pattern (or tree topology) as the one that requires the least marker insertions to be compatible with the observed distributions of cell markers. This method is essentially the same as the principle of persimony widely used for ancestral phylogeny reconstruction in evolutionary biology. When the total number of cells is small, we can generate all the possible cell lineages and calculate the minimum number of marker insertions for each candidate, and then choose the cell lineage that requires the least marker insertions. If the number of cells is large, we can use clustering method in which a pair of cells with the highest correlation in marker labelling are merged sequentially. The efficiency of the clustering method in estimating the correct cell lineage is confirmed by computer simulations. Finally, the clustering method is applied to reconstruct the cell lineage of ascidian from experimental data.     

Nonhomogeneous spatial distributions of populations

Summary Spatial inhomogeneities such as nonconstant population densities usually will be attributed to random effects or to an inhomogeneous substrate. Such an explanation may be incorrect since from certain chemical reactions it is known that the interaction of species together with diffusion may generate nonhomogeneous spatial structures. However, the effect of boundary conditions has been so far neglected. In this paper nonlinear and linear interaction-diffusion models are investigated under various side-conditions by analytic methods and by computer simulations. A remarkable fact, as compared with earlier results in the field, is the example of an interaction-diffusion process which in the whole space has only the constant as a stable limit distribution, whereas the introduction of a side condition, e.g. a population reservoir or a barrier, leads to standing spatial population waves.     

The measurement of spatial precursor distributions in cell culture

Summary The distribution of incorporated radioactive precursors, for both DNA and protein synthesis, has been measured with a resolution of about 1 mm in cell cultures, using a scanning technique. Either γ radiation and X-rays or β radiation (electrons) were detected by scintillation detectors. Spectrophotometer measurements with a resolution of 1 mm gave good estimates of cell density changes. Glioma cell colonies were used to compared this technique with autoradiography. Variables such as the density of labelled cells and percentage of labelled cells could be estimated rather accurately. For example, an increased cell density was correlated to a local decrease in DNA synthesis. The work has been supported financially by the Swedish Cancer Society and the Swedish Natural Science Research Council.     

Configuration-dependent properties of randomly coiling polynucleotide chains. I. A comparison of theoretical energy estimates

Various theoretical estimates of the conformational energy associated with polynucleotides in solution have been compared with each other and also with the experimentally observed conformations found in X-ray crystallographic investigations of low-molecular-weight nucleic acid analogs. In view of the disparities between these data, certain configuration-dependent properties (i.e., the mean-square unperturbed end-to-end distance 〈r²〉₀ and the average vicinal nmr coupling constant 〈J〉) appropriate to randomly coiling polynucleotides described by either the energy estimates or by the crystallographically preferred conformations have also been calculated and compared with the known solution behavior of polynucleotide chains. Both the theoretical energy surfaces and the X-ray data show good agreement with the nmr coupling constant indications of the preferred rotations about the O-C and C-C bonds of the chain backbone. The principal discrepancies between the theoretical methods and X-ray data arise in their ability to predict successfully the preferred rotations about the two phosphodiester bonds of the chain backbone and the unperturbed dimensions of randomly coiling polynucleotide chains.     

Colonization rules and spatial distributions in ecology

Because they are intuitive and mathematically straight-forward, colonization rules are often used to model spatial patterns in ecology. Colonization rules assign individuals to categories according to the locations of previous colonists. In this note, a compact introduction to colonization rules in ecology is presented with implications for autocorrelation and spatial distributions. I use the colonization rule approach to unify a diverse set of spatial and species diversity analyses, exploring future extensions to incorporate greater realism.     

Landscape configuration drives persistent spatial patterns of occupant distributions

Variation in the density of organisms among habitat patches is often attributed to variation in inherent patch properties. For example, higher quality patches might have higher densities because they attract more colonists or confer better post-colonization survival. However, variation in occupant density can also be driven by landscape configuration if neighboring patches draw potential colonists away from the focal habitat (a phenomenon we call propagule redirection). Here, we develop and analyze a stochastic model to quantify the role of landscape configuration and propagule redirection on occupant density patterns. We model a system with a dispersive larval stage and a sedentary adult stage. The model includes sensing and decision-making in the colonization stage and density-dependent mortality (a proxy for patch quality) in the post-colonization stage. We demonstrate that spatial variation in colonization is retained when the supply of colonists is not too high, post-colonization density-dependent survival is not too strong, and colonization events are not too frequent. Using a reef fish system, we show that the spatial variation produced by propagule redirection is comparable to spatial variation expected when patch quality varies. Thus, variation in density arising from the spatial patterning of otherwise identical habitat can play an important role in shaping long-term spatial patterns of organisms occupying patchy habitats. Propagule redirection is a potentially powerful mechanism by which landscape configuration can drive variation in occupant densities, and may therefore offer new insights into how populations may shift as landscapes change in response to natural and anthropogenic forces.     

Modeling of spatial metabolite distributions in the cardiac sarcomere

Although a high ATP diffusion rate implies homogeneous distribution of the principal energetic currency in the cytosol, local diffusion barriers represented by macromolecular structures can render ATP concentrations to be inhomogeneous. A method is presented here that provides apparent diffusion coefficient values in local intracellular regions and allows the estimation of spatial metabolite distribution. The apparent local diffusion coefficient for ATP in cardiac myofibrils was determined from the analysis of diffusion-dependent rightward shift of the substrate dependence for actomyosin ATPase activity using the reaction-diffusion model, which accounted for the properties of phosphotransfer reactions. This functional analysis, which took into account the local diffusional ATP delivery to the active sites, provided an apparent value that was three orders of magnitude lower than that defined by direct methods for the cytosol. The low value of the diffusion coefficient was shown to define unusual properties of the intracellular space in working heart, where small reductions in ATP levels in the surrounding cytosol result in a large drop in [ATP] inside myofibrils. This drop is critical for vital cellular functions, and the analysis presented here defines its physical basis. The diffusion barriers thus defined explain the coexistence of pathological energy deficit with almost normal average ATP levels.     

Uncertainty analysis for temperature prediction of biological bodies subject to randomly spatial heating

An analytical solution to the Pennes bioheat transfer equation in three-dimensional geometry with practical hyperthermia boundary conditions and random heating was obtained in this paper. Uncertainties for the predicted temperatures of tissues due to approximate parameters were studied based on analyzing one-dimensional heat transfer in the biological bodies subject to a spatially decay heating. Contributions from each of the thermal parameters such as heat conductivity, blood perfusion rate, and metabolic rate of the tissues, the scattering coefficient and the surface power flux of the heating apparatus were compared and the uncertainty limit for temperature distribution in this case was estimated. The results are useful in a variety of clinical hyperthermia and biological thermal parameter measurement.     

The nature of stacking equilibria in polynucleotides

Temperature melting profiles of adenylyladenosine and cytidylylcytidine were examined by ultraviolet absorption, circular dichroism, and optical rotatory dispersion. They showed the following characteristics: profiles for different absorption wavelengths are identical as defined by least-squares computed optical and thermodynamic parameters; melting curves obtained by the three spectroscopic methods are likewise in all cases identical by a series of criteria; in terms of the operational equilibrium constant for base-stacking all van't Hoff plots are linear; absorption spectra and circular dichroism curves at a series of temperatures for both dinucleoside phosphates give excellent isosbestic points; a matrix-rank analysis of the family of complete spectra at different temperatures gives a value of two for the numbers of components in both cases. Four criteria are thus fulfilled of a two-state system for the stacking equilibrium. The results are not compatible with a multi-state scheme in which the substates are optically distinguishable. There is no measurable effect of ionic strength up to 1.0. In a presence of high concentrations of lithium chloride the criteria for two-state behavior are no longer fulfilled, and examination of infrared spectra gives evidence of complex formation by this salt, though not by sodium chloride. A destacking profile, similar to that observed on heating, is obtained by progressive addition of ethylene glycol to the solution. It is suggested that in dimers, though not in higher oligomers or polymers, the stacking equilibrium can be operationally regarded as a two-state system, and that the meaningful thermodynamic parameters can be extracted by analytical treatment, of the type here developed, of the melting profiles.     

The importance of predation,substrate and spatial refugia in determining lotic insect distributions

An experiment was conducted to evaluate the interaction between predation, substrate, and spatial refugia in the organization of a stream insect community (Reeds Creek, Pendleton Co., West Virginia). Patterns of insect colonization were compared between fish exclusion cages and open controls that allowed access to vertebrate predators. Each cage contained 4 different substrates that varied in the relative amount of spatial refugia. Fish had little influence on the diversity or abundance of any insect taxa, even when spatial refugia were limited. The only significant effect due to predation, was an increased diversity of large (>8 mm) invertebrates in the absence of predators. However, because these taxa were relatively rare, the overall role of fish predation on insect community structure was minimal.In contrast, substrate had a marked effect on insect colonization. Insects were always more abundant (number/basket) on loose substrates containing large numbers of interstitial spaces, compared to cement-embedded substrates with few refuges available. In addition, invertebrates were more abundant on loose gravel compared to loose cobbles. Howver, when substrate preferencesrd were examined according to insect density (number/m²), loose cobbles were generally the preferred substrate. The present experiment rejects the hypothesis that patterns of substrate colonization can be explained as differential insect mortality by predators, due to varying amounts of refugia. Alternative mechanisms such as differing amounts of trapped detritus and substrate surface area may account for substrate preference.     

Cluster size distributions: signatures of self-organization in spatial ecologies

Three different lattice-based models for antagonistic ecological interactions, both nonlinear and stochastic, exhibit similar power-law scalings in the geometry of clusters. Specifically, cluster size distributions and perimeter-area curves follow power-law scalings. In the coexistence regime, these patterns are robust: their exponents, and therefore the associated Korcak exponent characterizing patchiness, depend only weakly on the parameters of the systems. These distributions, in particular the values of their exponents, are close to those reported in the literature for systems associated with self-organized criticality (SOC) such as forest-fire models; however, the typical assumptions of SOC need not apply. Our results demonstrate that power-law scalings in cluster size distributions are not restricted to systems for antagonistic interactions in which a clear separation of time-scales holds. The patterns are characteristic of processes of growth and inhibition in space, such as those in predator-prey and disturbance-recovery dynamics. Inversions of these patterns, that is, scalings with a positive slope as described for plankton distributions, would therefore require spatial forcing by environmental variability.