Multiple steps of phosphorylation of activated rhodopsin can account for the reproducibility of vertebrate rod single-photon responses

Single-photon responses (SPRs) in vertebrate rods are considerably less variable than expected if isomerized rhodopsin (R*) inactivated in a single, memoryless step, and no other variability-reducing mechanisms were available. We present a new stochastic model, the core of which is the successive ratcheting down of R* activity, and a concomitant increase in the probability of quenching of R* by arrestin (Arr), with each phosphorylation of R* (Gibson, S.K., J.H. Parkes, and P.A. Liebman. 2000. Biochemistry. 39:5738-5749.). We evaluated the model by means of Monte-Carlo simulations of dim-flash responses, and compared the response statistics derived from them with those obtained from empirical dim-flash data (Whitlock, G.G., and T.D. Lamb. 1999. Neuron. 23:337-351.). The model accounts for four quantitative measures of SPR reproducibility. It also reproduces qualitative features of rod responses obtained with altered nucleotide levels, and thus contradicts the conclusion that such responses imply that phosphorylation cannot dominate R* inactivation (Rieke, F., and D.A. Baylor. 1998a. Biophys. J. 75:1836-1857; Field, G.D., and F. Rieke. 2002. Neuron. 35:733-747.). Moreover, the model is able to reproduce the salient qualitative features of SPRs obtained from mouse rods that had been genetically modified with specific pathways of R* inactivation or Ca2+ feedback disabled. We present a theoretical analysis showing that the variability of the area under the SPR estimates the variability of integrated R* activity, and can provide a valid gauge of the number of R* inactivation steps. We show that there is a heretofore unappreciated tradeoff between variability of SPR amplitude and SPR duration that depends critically on the kinetics of inactivation of R* relative to the net kinetics of the downstream reactions in the cascade. Because of this dependence, neither the variability of SPR amplitude nor duration provides a reliable estimate of the underlying variability of integrated R* activity, and cannot be used to estimate the minimum number of R* inactivation steps. We conclude that multiple phosphorylation-dependent decrements in R* activity (with Arr-quench) can confer the observed reproducibility of rod SPRs; there is no compelling need to invoke a long series of non-phosphorylation dependent state changes in R* (as in Rieke, F., and D.A. Baylor. 1998a. Biophys. J. 75:1836-1857; Field, G.D., and F. Rieke. 2002. Neuron. 35:733-747.). Our analyses, plus data and modeling of others (Rieke, F., and D.A. Baylor. 1998a. Biophys. J. 75:1836-1857; Field, G.D., and F. Rieke. 2002. Neuron. 35:733-747.), also argue strongly against either feedback (including Ca2+-feedback) or depletion of any molecular species downstream to R* as the dominant cause of SPR reproducibility.     

Mathematical modeling of combinatorial regulation suggests that apparent positive regulation of targets by miRNA could be an artifact resulting from competition for mRNA

MicroRNAs bind to and regulate the abundance and activity of target messenger RNA through sequestration, enhanced degradation, and suppression of translation. Although miRNA have a predominantly negative effect on the target protein concentration, several reports have demonstrated a positive effect of miRNA, i.e., increase in target protein concentration on miRNA overexpression and decrease in target concentration on miRNA repression. miRNA–target pair-specific effects such as protection of mRNA degradation owing to miRNA binding can explain some of these effects. However, considering such pairs in isolation might be an oversimplification of the RNA biology, as it is known that one miRNA interacts with several targets, and conversely target mRNA are subject to regulation by several miRNAs. We formulate a mathematical model of this combinatorial regulation of targets by multiple miRNA. Through mathematical analysis and numerical simulations of this model, we show that miRNA that individually have a negative effect on their targets may exhibit an apparently positive net effect when the concentration of one miRNA is experimentally perturbed by repression/overexpression in such a multi-miRNA multitarget situation. We show that this apparent unexpected effect is due to competition and will not be observed when miRNA interact noncompetitively with the target mRNA. This result suggests that some of the observed unusual positive effects of miRNA may be due to the combinatorial complexity of the system rather than due to any inherently unusual positive effect of the miRNA on its target.     

Modeling soil–root water transport and competition for single and mixed crops

A knowledge of above and below ground plant interactions for water is essential to understand the performance of intercropped systems. In this work, root water potential dynamics and water uptake partitioning were compared between single crops and intercrops, using a simulation model. Four root maps having 498, 364, 431 and 431 soil-root contacts were used. In the first and second cases, single crops with deep and surface roots were considered, whereas in the third and fourth cases, roots of two mixed crops were simultaneously considered with different row spacing (40 cm and 60 cm). Two soils corresponding to a clay and a silty clay loam were used in the calculations. A total maximum evapotranspiration of 6 mm d^-1 for both single or mixed crops was considered, for the mixed crops however, two transpiration distributions between the crops were analyzed (3:3 mm d^-1, or 4:2 mm d^-1 for each crop, respectively). The model was based on a previous theoretical framework applied to single or intercropped plants having spatially distributed roots in a two-dimensional domain. Although water stress occurred more rapidly in the loam than in the clay, due to the rapid decrease of the soil water reserve in the loam, the role of the root arrangement appeared to be crucial for water availability. Interactions between the distribution of transpiration among mixed crops and the architecture of the root systems which were in competition led to water movements from zones with one plant to another, or vice versa, which corresponded to specific competition or facilitation effects. Decreasing the distances between roots may increase competition for water, although it may determine greater water potential gradients in the soil that increase lateral or vertical water fluxes in the soil profile. The effects of the root competition on water uptake were quite complicated, depending on both environmental conditions, soil hydrodynamic properties, and time scales. Although some biological adaptive mechanisms were disregarded in the analysis, the physically 2-D based model may be considered as a tool to study the exploitation of environmental heterogeneity at microsite scales.     

Ligand-insensitive State of Cardiac ATP-sensitive K+ Channels : Basis for Channel Opening

The mechanism by which ATP-sensitive K⁺ (K_ATP) channels open in the presence of inhibitory concentrations of ATP remains unknown. Herein, using a four-state kinetic model, we found that the nucleotide diphosphate UDP directed cardiac K_ATP channels to operate within intraburst transitions. These transitions are not targeted by ATP, nor the structurally unrelated sulfonylurea glyburide, which inhibit channel opening by acting on interburst transitions. Therefore, the channel remained insensitive to ATP and glyburide in the presence of UDP. “Rundown” of channel activity decreased the efficacy with which UDP could direct and maintain the channel to operate within intraburst transitions. Under this condition, the channel was sensitive to inhibition by ATP and glyburide despite the presence of UDP. This behavior of the K_ATP channel could be accounted for by an allosteric model of ligand-channel interaction. Thus, the response of cardiac K_ATP channels towards inhibitory ligands is determined by the relative lifetime the channel spends in a ligand-sensitive versus -insensitive state. Interconversion between these two conformational states represents a novel basis for K_ATP channel opening in the presence of inhibitory concentrations of ATP in a cardiac cell.     

Increase in leaf mass per area benefits plant growth at elevated CO2 concentration

An increase in leaf mass per area (MLA) of plants grown at elevated [CO2] is often accompanied by accumulation of non-structural carbohydrates, and has been considered to be a response resulting from source-sink imbalance. We hypothesized that the increase in MLA benefits plants by increasing the net assimilation rate through maintaining a high leaf nitrogen content per area (NLA). To test this hypothesis, Polygonum cuspidatum was grown at ambient (370 micro mol mol-1) and elevated (700 micro mol mol-1) [CO2] with three levels of N supply. Elevated [CO2] significantly increased MLA with smaller effects on NLA and leaf mass ratio (fLM). The effect of change in MLA on plant growth was investigated by the sensitivity analysis: MLA values observed at ambient and elevated [CO2] were substituted into a steady-state growth model to calculate the relative growth rate (R). At ambient [CO2], substitution of a high MLA (observed at elevated [CO2]) did not increase R, compared with R for a low MLA (observed at ambient [CO2]), whereas at elevated [CO2] the high MLA always increased R compared with R at the low MLA. These results suggest that the increase in MLA contributes to growth enhancement under elevated [CO2]. The optimal combination of fLM and MLA to maximize R was determined for different [CO2] and N availabilities. The optimal fLM was nearly constant, while the optimal MLA increased at elevated [CO2], and decreased at higher N availabilities. The changes in fLM of actual plants may compensate for the limited plasticity of MLA.