Variation in per capita interaction strength: Thresholds due to nonlinear dynamics and nonequilibrium conditions

I measured the strength of interaction between a marine herbivore and its growing resource over a realistic range of absolute and relative abundances. The herbivores (hermit crabs: Pagurus spp.) have slow and/or weak functional and numerical responses to epiphytic diatoms (Isthmia nervosa), which show logistic growth in the absence of consumers. By isolating this interaction in containers in the field, I mimicked many of the physical and biological variables characteristic of the intertidal while controlling the densities of focal species. The per capita effects of consumers on the population dynamics of their resource (i.e., interaction strength) were defined by using the relationship between hermit crab density and proportional change in the resource. When this relationship is fit by a Weibull function, a single parameter distinguishes constant interaction strength from one that varies as a function of density. Constant interaction strength causes the proportion of diatoms to fall linearly or proportionally as hermit crab density increases whereas per capita effects that increase with density cause an accelerating decline. Although many mathematical models of species interactions assume linear dynamics and invariant parameters, at least near equilibrium, the per capita effects of hermit crabs on diatoms varied substantially, apparently crossing a threshold from weak to strong when consumption exceeded resource production. This threshold separates a domain of coexistence from one of local extinction of the resource. Such thresholds may help explain trophic cascades, resource compensation, and context-dependent interaction strengths, while indicating a way to predict trophic effects, despite nonlinearities, as a function of vital rates.

Electrostatic interaction between helical macromolecules in dense aggregates: An impetus for DNA poly- and meso-morphism

DNA exhibits a surprising multiplicity of structures when it is packed into dense aggregates. It undergoes various polymorphous transitions (e.g., from the B to A form) and mesomorphous transformations (from hexagonal to orthorhombic or monoclinic packing, changes in the mutual alignment of nearest neighbors, etc). In this report we show that such phenomena may have their origin in the specific helical symmetry of the charge distribution on DNA surface. Electrostatic interaction between neighboring DNA molecules exhibits strong dependence on the patterns of molecular surface groups and adsorbed counter-ions. As a result, it is affected by such structural parameters as the helical pitch, groove width, the number of base pairs per helical turn, etc. We derive expressions which relate the energy of electrostatic interaction with these parameters and with the packing variables characterizing the axial and azimuthal alignment between neighboring macromolecules. We show, in particular, that the structural changes upon the B-to-A transition reduce the electrostatic energy by ≈kcal/mol per base pair, at a random adsorption of counter ions. Ion binding into the narrow groove weakens or inverts this effect, stabilizing B-DNA, as it is presumably the case in Li+-DNA assemblies. The packing symmetry and molecular alignment in DNA aggregates are shown to be affected by the patterns of ion binding.

Polymer Models of Meiotic and Mitotic Chromosomes

Polymers tied together by constraints exhibit an internal pressure; this idea is used to analyze physical properties of the bottle-brush–like chromosomes of meiotic prophase that consist of polymer-like flexible chromatin loops, attached to a central axis. Using a minimal number of experimental parameters, semiquantitative predictions are made for the bending rigidity, radius, and axial tension of such brushes, and the repulsion acting between brushes whose bristles are forced to overlap. The retraction of lampbrush loops when the nascent transcripts are stripped away, the oval shape of diplotene bivalents between chiasmata, and the rigidity of pachytene chromosomes are all manifestations of chromatin pressure. This two-phase (chromatin plus buffer) picture that suffices for meiotic chromosomes has to be supplemented by a third constituent, a chromatin glue to understand mitotic chromosomes, and explain how condensation can drive the resolution of entanglements. This process resembles a thermal annealing in that a parameter (the affinity of the glue for chromatin and/or the affinity of the chromatin for buffer) has to be tuned to achieve optimal results. Mechanical measurements to characterize this protein–chromatin matrix are proposed. Finally, the propensity for even slightly chemically dissimilar polymers to phase separate (cluster like with like) can explain the apparent segregation of the chromatin into A+T- and G+C-rich regions revealed by chromosome banding.

Brownian flocculation of polymer colloids in the presence of a secondary minimum

Most analyses of Brownian flocculation apply to conditions where London–van der Waals attractive forces cause particles to be strongly bound in a deep interparticle potential well. In this paper, results are reported that show the interaction between primary- and secondary-minimum flocculation when the interparticle potential curve reflects both attractive and electrostatic repulsive forces. The process is highly time-dependent because of transfer of particles from secondary- to primary-minimum flocculation. Essential features of the analysis are corroborated by experiments with 0.80-μm polystyrene spheres suspended in aqueous solutions of NaCl over a range of ionic strengths. In all cases, experiments were restricted to the initial stage of coagulation, where singlets and doublets predominate.

Temperature effects in hydrophobic interaction chromatography.

The effect of temperature from 5 degrees C to 50 degrees C on the retention of dansyl derivatives of amino acids in hydrophobic interaction chromatography (HIC) was investigated by HPLC on three stationary phases. Plots of the logarithmic retention factor against the reciprocal temperature in a wide range were nonlinear, indicative of a large negative heat capacity change associated with retention. By using Kirchoff's relations, the enthalpy, entropy, and heat capacity changes were evaluated from the logarithmic retention factor at various temperatures by fitting the data to a logarithmic equation and a quadratic equation that are based on the invariance and on an inverse square dependence of the heat capacity on temperature, respectively. In the experimental temperature interval, the heat capacity change was found to increase with temperature and could be approximated by the arithmetic average. For HIC retention of a set of dansylamino acids, both enthalpy and entropy changes were positive at low temperatures but negative at high temperatures as described in the literature for other processes based on the hydrophobic effect. The approach presented here shows that chromatographic measurements can be not only a useful adjunct to calorimetry but also an alternative means for the evaluation of thermodynamic parameters.

Analysis of the interaction of ZAP-70 and syk protein-tyrosine kinases with the T-cell antigen receptor by plasmon resonance.

Tyrosine phosphorylation of a 17-amino acid immunoreceptor tyrosine-based activation motif (ITAM), conserved in each of the signaling subunits of the T-cell antigen receptor (TCR), mediates the recruitment of ZAP-70 and syk protein-tyrosine kinases (PTKs) to the activated receptor. The interaction between the two tandemly arranged Src-homology 2 (SH2) domains of this family of PTKs and each of the phosphotyrosine-containing ITAMs was examined by real-time measurements of kinetic parameters. The association rate and equilibrium binding constants for the ZAP-70 and syk SH2 domains were determined for the CD3 epsilon ITAM. Both PTKs bound with ka and Kd values of 5 x 10(6) M-1.sec-1 and approximately 25 nM, respectively. Bindings to the other TCR ITAMs (zeta 1, zeta 2, gamma, and delta ITAMs) were comparable, although the zeta 3 ITAM bound approximately 2.5-fold less well. Studies of the affinity of a single functional SH2 domain of ZAP-70 provided evidence for the cooperative nature of binding of the dual SH2 domains. Mutation of either single SH2 domain decreased the Kd by > 100-fold. Finally, the critical features of the ITAM for syk binding were found to be similar to those required for ZAP-70 binding. These data provide insight into the mechanism by which the multisubunit TCR interacts with downstream effector molecules.