The mathematical theory of group selection. I. Full solution of a nonlinear Levins E = E(x) model

The first complete overtime solution is obtained for a group selection model of Levins E = E(x) type with recolonization but no other gene flow between islands. Assuming a subdivided population at carrying capacity, the model describes selection at a biallelic locus (A, a) where a is opposed by Mendelian selection but is favored by a lower rate of extinction of demes having high a frequency. By contrast to the linear diffusion equations encountered in classical mathematical genetics, the PDE governing the dynamics is now nonlinear in the metapopulation gene frequency distribution φ(x, t); furthermore, the initial conditions now heavily influence the equilibrium distribution φ_∞(x). A fully explicit formula (20) expressing this dependence is derived. The results indicate that a fixation is never reached, but (A, a) polymorphism in the metapopulation will result if , where s 1 parametrizes the strength of Mendelian selection, E(x) is the Levins extinction operator, h (typically in the open interval (0, 1)) is the dominance of a, and B is a parameter measuring the flatness of the initial distribution f(x) in the x → 1 limit.     

Molecular dynamics simulations of helix denaturation.

An understanding of the structural transitions that an alpha-helix undergoes will help to elucidate such motions in proteins and their role in protein folding. We present the results of molecular dynamics simulations to investigate these transitions in a short polyalanine peptide (13 residues) both in vacuo and in the presence of solvent. The denaturation of this peptide was monitored as a function of temperature (ranging from 5 to 200 degrees C). In vacuo, the helical state predominated at all temperatures, whereas in solution the helix melted with increasing temperature. The peptide was predominantly helical at low temperature in solution, while at intermediate temperatures the peptide spent the bulk of the time fluctuating between different conformations with intermediate amounts of helix, e.g. not completely helical nor entirely non-helical. Many of these conformations consisted of short helical segments with intervening non-helical residues. At high temperature the peptide unfolded and adopted various collapsed unstructured states. The intrahelical hydrogen bonds that break at high temperature were not fully compensated by hydrogen bonds with water molecules in the partially unfolded forms of the peptide. Increases in temperature disrupted both the helical structure and the peptide-water interactions. Water played a major but indirect role in facilitating unfolding, as opposed to specifically competing for the intrapeptide hydrogen bonds. The implications of our results to protein folding are discussed.     

Kinesin undergoes a 9 S to 6 S conformational transition.

Addition of NaCl or KCl in the presence of 50 nM ATP induces a shift in the sedimentation coefficient (apparent S20,w) of kinesin from 9.4 S at low ionic strength to 6.5 S at high ionic strength. The midpoint for the transition occurs at ionic strength values of 0.39, 0.25, and 0.18 for pH values of 6.3, 6.9, and 8.3, respectively. Gel filtration experiments indicate that the transition to the 6.5 S species is accompanied by a decrease in the diffusion coefficient. Under all conditions which were tested, the 64-kDa beta subunits comigrate with the 120-kDa alpha subunits without any evidence for dissociation of the alpha 2 beta 2 complex. These results are consistent with the change in sedimentation coefficient being due to a conformational transition between a folded form at low ionic strength and an extended form at high ionic strength. This conformational transition is not significantly affected by the nature of the nucleotide bound at the active site since similar results are obtained both in the presence of excess EDTA, which removes the bound ADP, and after replacement of the bound ADP with adenosine 5'-(beta,gamma-imino)triphosphate. The alpha 2 form of kinesin, which lacks the beta subunits, undergoes a similar transition between a 6.7 S form at low ionic strength and a 5.1 S form at high ionic strength with a midpoint for the transition at an ionic strength of 0.5 at pH 6.9. Electron microscopic observation also indicates a transition between a folded conformation at low ionic strength and an extended conformation at high ionic strength for both the alpha 2 beta 2 and alpha 2 species.     

Combination v. sequential therapy with melphalan, 5-fluorouracil and methotrexate for advanced ovarian cancer.

The results of a national clinical trial to compare combination and sequential chemotherapy for stage III or IV ovarian cancer are reported. Of the 253 patients from 16 centres across Canada who were admitted to the trial 13 were excluded from the analysis. All the patients were observed for 2 to 5 years from entry into the trial. There were no differences in response to therapy or in survival between the patients treated with melphalan followed by 5-fluorouracil and then by methotrexate in high dosage and the patients treated with the same agents in combination. Patients with minimal residual disease after resection of stage III ovarian cancer had a good prognosis. Other favourable prognostic factors were age (less than 55 years), performance status (90% or 100% on the Karnofsky scale) and histologic grade of the tumour.     

Electrostatic calculations for an ion channel. II. Kinetic behavior of the gramicidin A channel.

A theoretical model of the gramicidin A channel is presented and the kinetic behavior of the model is derived and compared with previous experimental results. The major assumption of the model is that the only interaction between ions in a multiply-occupied channel is electrostatic. The electrostatic calculations indicate in a multiply-occupied channel is electrostatic. The electrostatic calculations indicate that there will be potential wells at each end of the channel and, at high concentrations, that both wells can be occupied. The kinetics are based on two reaction steps: movement of the ion from the bulk solution to the well and movement between the two wells. The kinetics for this reaction rate approach are identical to those based on the Nernst-Planck equation in the limit where the movement between the two wells is rate limiting. The experimental results for sodium and potassium are consistent with a maximum of two ions per channel. To explain the thallium results it is necessary to allow three ions per channel. It is shown that this case is compatible with the electrostatic calculations if the presence of an anion is included. The theoretical kinetics are in reasonable quantitative agreement with the following experimental measurements: single channel conductance of sodium, potassium, and thallium; bi-ionic potential and permeability ratio between sodium-potassium and potassium-thallium; the limiting conductance of potassium and thallium at high applied voltages; current-voltage curves for sodium and potassium at low (but not high) concentrations; and the inhibition of sodium conductance by thallium. The results suggest that the potential well is located close to the channel mouth and that the conductance is partially limited by the rate going from the bulk solution to the well. For thallium, this entrance rate is probably diffusion limited.     

General continuum analysis of transport through pores. I. Proof of Onsager's reciprocity postulate for uniform pore.

The nonelectrolyte (Js) and volume (Jv) flux across a membrane is usually described in terms of two equations derived from the theory of irreversible thermodynamics: (see article) where delta c and delta P are the concentration and pressure difference; omega and Lp are the diffuse and hydraulic permeability; and sigma s and sigma v are the reflection coefficients. If Onsager's reciprocity postulate is assumed, it can be shown that signa s and sigma v are equal. This is an important assumption because it allows one to apply the continuum theory relationship between sigma s and the pore radius to experimental measurements of sigma v. In this paper, general continuum expressions for both the Jv (a new result) and Js equation will be derived and the equality of sigma s and sigma v proved. The proof uses only general hydrodynamic results and does not require explicit solutions for the drag coefficients or, for example, the assumption that the solute is in the center of the pore. The proof applys to arbitrarily shaped solutes and any pore whose shape is independent of axial position (uniform). In addition, new expressions for the functional dependence of omega and sigma on the pore radius are derived (including the effect of the particle lying off the pore axis). These expressions differ slightly from earlier results and are probably more accurate.     

Reversion mutation of cDNA CA8-204 minigene construct produces a truncated functional peptide that regulates calcium release in vitro and produces profound analgesia in vivo

Mammalian Genome - Intracellular calcium is critical in orchestrating neuronal excitability and analgesia. Carbonic anhydrase-8 (CA8) regulates intracellular calcium signaling through allosteric...