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.

A model of ocular dominance column development by competition for trophic factor

Recent experimental evidence has shown that application of certain neurotrophic factors (NTs) to the developing primary visual cortex prevents the development of ocular dominance (OD) columns. One interpretation of this result is that afferents from the lateral geniculate nucleus compete for postsynaptic trophic factor in an activity-dependent manner. Application of excess trophic factor eliminates this competition, thereby preventing OD column formation. We present a model of OD column development, incorporating Hebbian synaptic modification and activity-driven competition for NT, which accounts for both normal OD column development as well as the prevention of that development when competition is removed. In the “control” situation, when available NT is below a critical amount, OD columns form normally. These columns form without weight normalization procedures and in the presence of positive inter-eye correlations. In the “experimental” case, OD column development is prevented in a local neighborhood in which excess NT has been added. Our model proposes a biologically plausible mechanism for competition between neural populations that is motivated by several pieces of experimental data, thereby accounting for both normal and experimentally perturbed conditions.

The contrasting roles of ICE family proteases and interleukin-1beta in apoptosis induced by trophic factor withdrawal and by copper/zinc superoxide dismutase down-regulation.

We compare here the mechanisms of apoptotic death of PC12 cells induced by down-regulation of Cu2+,Zn2+ superoxide dismutase (SOD1) and withdrawal of trophic support (serum/nerve growth factor). Our previous results indicated that the initiating causes of death are different in each paradigm. However, bcl-2 rescues cells in either paradigm, suggesting common downstream elements to the cell death pathway. To determine whether the ICE [interleukin 1beta converting enzyme] family of proteases, which is required for apoptosis on trophic factor withdrawal, is also required for apoptosis induced by oxidative stress, we have developed a novel peptide inhibitor that mimics the common catalytic site of these enzymes and thereby blocks their access to substrates. This differs from the more usual pseudosubstrate approach to enzyme inhibition. Blockade of ICE family proteases by either this inhibitor or by a permeant competitive ICE family antagonist rescues PC12 cells from apoptotic death following apoptosis induced by down-regulation of SOD1, as well as from trophic factor/nerve growth factor deprivation. SOD1 down-regulation results in an increase in interleukin 1beta (IL- 1beta) production by the cells, and cell death under these conditions can be prevented by either blocking antibodies against IL-1beta or the IL-1 receptor antagonist (IL-1Ralpha). In contrast, trophic factor withdrawal does not increase IL-1beta secretion, and the blocking antibody failed to protect PC12 cells from trophic factor withdrawal, whereas the receptor antagonist was only partially protective at very high concentrations. There were substantial differences in the concentrations of pseudosubstrate inhibitors which rescued cells from SOD1 down-regulation and trophic factor deprivation. These results suggest the involvement of different members of the ICE family, different substrates, or both in the two different initiating causes of cell death.