Role of the Actin Ala-108–Pro-112 Loop in Actin Polymerization and ATPase Activities

Actin plays fundamental roles in a variety of cell functions in eukaryotic cells. The polymerization-depolymerization cycle, between monomeric G-actin and fibrous F-actin, drives essential cell processes. Recently, we proposed the atomic model for the F-actin structure and found that actin was in the twisted form in the monomer and in the untwisted form in the filament. To understand how the polymerization process is regulated (Caspar, D. L. (1991) Curr. Biol. 1, 30–32), we need to know further details about the transition from the twisted to the untwisted form. For this purpose, we focused our attention on the Ala-108–Pro-112 loop, which must play crucial roles in the transition, and analyzed the consequences of the amino acid replacements on the polymerization process. As compared with the wild type, the polymerization of P109A was accelerated in both the nucleation and the elongation steps, and this was attributed to an increase in the frequency factor of the Arrhenius equation. The multiple conformations allowed by the substitution presumably resulted in the effective formation of the collision complex, thus accelerating polymerization. On the other hand, the A108G mutation reduced the rates of both nucleation and elongation due to an increase in the activation energy. In the cases of polymerization acceleration and deceleration, each functional aberration is attributed to a distinct elementary process. The rigidity of the loop, which mediates neither too strong nor too weak interactions between subdomains 1 and 3, might play crucial roles in actin polymerization.     

Distance between AER and ZPA Is Defined by Feed-Forward Loop and Is Stabilized by their Feedback Loop in Vertebrate Limb Bud

In the development of organs, multiple morphogen sources are often involved, and interact with each other. For example, the apical ectodermal ridge (AER) and the zone of polarizing activity (ZPA) are major morphogen sources in the limb bud formation of vertebrates. Fgf expression in the AER and Shh expression in the ZPA are maintained by their positive feedback regulation mediated by diffusible molecules, FGF and SHH. A recent experimental observation suggests that the FGF-signal regulates the Shh expression in a feed-forward manner with activation and repression regulatory pathways. We study the coupled dynamics of Shh expression in the ZPA and Fgf expression in the AER, and the relationship of the relative position between AER and ZPA. We first show that with the feed-forward regulation only, the peak of ZPA activity can be formed distant from the AER as observed experimentally. Then, we clarify that the robustness of the ZPA spatial pattern to changes in system parameters is enhanced by adding the feedback regulation between the AER and the ZPA. Furthermore, sensitivity analysis shows that there exists the optimal feedback strength where the robustness is the most improved.     

Establishment Probability in Fluctuating Environments: A Branching Process Model

We study the establishment probability of invaders in stochastically fluctuating environments and the related issue of extinction probability of small populations in such environments, by means of an inhomogeneous branching process model. In the model it is assumed that individuals reproduce asexually during discrete reproduction periods. Within each period, individuals have (independent) Poisson distributed numbers of offspring. The expected numbers of offspring per individual are independently identically distributed over the periods. It is shown that the establishment probability of an invader varies over the reproduction periods according to a stable distribution. We give a method for simulating the establishment probabilities and approximations for the expected establishment probability. Furthermore, we show that, due to the stochasticity of the establishment success over different periods, the expected success of sequential invasions is larger then that of simultaneous invasions and we study the effects of environmental fluctuations on the extinction probability of small populations and metapopulations. The results can easily be generalized to other offspring distributions than the Poisson.     

INFERRING THE RATES OF BRANCHING AND EXTINCTION FROM MOLECULAR PHYLOGENIES

Molecular techniques provide ancestral phylogenies of extant taxa with estimated branching times. Here we studied the pattern of ancestral phylogeny of extant taxa produced by branching (or cladogenesis) and extinction of taxa, assuming branching processes with time-dependent rates. (1) If the branching rate b and extinction rate c are constant, the semilog plot of the number of ancestral lineages over time is not a straight line but is curvilinear, with increasing slope toward the end, implying that ancestral phylogeny shows apparent increase in the branching rate near the present. The estimate of b and c based on nonlinear fitting is examined by computer simulation. The estimate of branching rate can be usable for a large phylogeny if b is greater than c, but the estimate of extinction rate c is unreliable because of large bias and variance. (2) Gradual decrease in the slope of the semilog plot of the number of ancestral lineages over time, as was observed in a phylogeny of bird families based on DNA hybridization data, can be explained equally well by either the decreasing branching rate or the increasing extinction rate. Infinitely many pairs of branching and extinction rates as functions of time can produce the same ancestral phylogeny. (3) An explosive branching event in the past would appear as a quick increase in the number of ancestral lineages. In contrast, mass extinction occurring in a brief period, if not accompanied by an increase in branching rate, does not produce any rapid change in the number of ancestral lineages at the time. (4) The condition in which the number of ancestral lineages of extant species changes in parallel with the actual number of species in the past is derived.     

Palmelloid Formation of Chlamydomonas II. Mechanism of Palmelloid Formation by Organic Acids

To clarify the mechanism of palmelloid formation by organic acids, the dissociation of the suspension of palmelloids in different media was studied. It was found that the palmelloids can be dissociated by the calcium ion at the low concentration of 6.8 × 10^-5M, but not by the magnesium ion. The dissociation is suppressed by the phosphate ion. Furthermore, Chlamydomonas cells grown in media containing EDTA or GEDTA or in media deficient in calcium, are induced to form palmelloids. These results indicate that the effect of organic acids on the formation of palmelloids are due to their ability to chelate with calcium.     

Light-induced protein conformational changes in the photolysis of octopus rhodopsin.

Light-induced protein conformational changes in the photolysis of octopus rhodopsin were measured with a highly sensitive time-resolved transient UV absorption spectrophotometer with nanosecond time resolution. A negative band around 280 nm in the lumirhodopsin minus rhodopsin spectra suggests that alteration of the environment of some of the tryptophan residues has taken place before the formation of lumirhodopsin. A small recovery of the absorbance at 280 nm was observed in the transformation of lumirhodopsin to mesorhodopsin. Kinetic parameters suggest that major conformational changes have taken place in the transformation of mesorhodopsin to acid metarhodopsin. In this transformation, drastic changes of amplitude and a shift of a difference absorption band around 280 nm take place, which suggest that some of the tryptophan residues of rhodopsin become exposed to a hydrophilic environment.     

Force generation in the outer hair cell of the cochlea.

The outer hair cell of the mammalian cochlea has a unique motility directly dependent on the membrane potential. Examination of the force generated by the cell is an important step in clarifying the detailed mechanism as well as the biological importance of this motility. We performed a series of experiments to measure force in which an elastic probe was attached to the cell near the cuticular plate and the cell was driven with voltage pulses delivered from a patch pipette under whole-cell voltage clamp. The axial stiffness was also determined with the same cell by stretching it with the patch pipette. The isometric force generated by the cell is around 0.1 nN/mV, somewhat smaller than 0.15 nN/mV, predicted by an area motor model based on mechanical isotropy, but larger than in earlier reports in which the membrane potential was not controlled. The axial stiffness obtained, however, was, on average, 510 nN per unit strain, about half of the value expected from the mechanical isotropy of the membrane. We extended the area motor theory incorporating mechanical orthotropy to accommodate the axial stiffness determined. The force expected from the orthotropic model was within experimental uncertainties.     

Optimal age-dependent sustainable harvesting of natural resource populations: Sustainability value

We studied the optimal age-dependent harvesting of a natural resource population that achieves a maximum income under the constraint of sustainability, i.e. the reproductive adults numbers must exceed a given minimum. The resource species is assumed to be semelparous (a single reproduction over a life). The economic value and natural mortality coefficient can vary with age. The optimal age-dependent harvesting under the sustainability constraint is obtained using Pontryagin’s maximum principle. The constraint of resource sustainability can be treated as an additional term measured in the same units as economic income. Specifically, three terms: (1) current harvesting value, (2) future harvesting value, and (3) sustainability value, are calculated for each age, and the resources should be harvested at the maximum rate when their current harvesting value is greater than the sum of future harvesting value and sustainability value, and should not be harvested otherwise. Numerical analyses of several cases demonstrated that the optimal harvesting schedule depends critically on the natural mortality coefficient and the functional form of the economic value of the resource.