The Evolution of One- and Two-Locus Systems

Assuming age-independent fertilities and mortalities and random mating, continuous-time models for a monoecious population are investigated for weak selection. A single locus with multiple alleles and two alleles at each of two loci are considered. A slow-selection analysis of diallelic and multiallelic two-locus models with discrete nonoverlapping generations is also presented. The selective differences may be functions of genotypic frequencies, but their rate of change due to their explicit dependence on time (if any) must be at most of the second order in s, (i.e., O( s²)), where s is the intensity of natural selection. Then, after several generations have elapsed, in the continuous time models the time-derivative of the deviations from Hardy-Weinberg proportions is of O(s²), and in the two-locus models the rate of change of the linkage disequilibrium is of O(s²). It follows that, if the rate of change of the genotypic fitnesses is smaller than second order in s (i.e., o(s²)), then to O(s²) the rate of change of the mean fitness of the population is equal to the genic variance. For a fixed value of s, however, no matter how small, the genic variance may occasionally be smaller in absolute value than the (possibly negative) lower order terms in the change in fitness, and hence the mean fitness may decrease. This happens if the allelic frequencies are changing extremely slowly, and hence occurs often very close to equilibrium. Some new expressions are derived for the change in mean fitness. It is shown that, with an error of O( s), the genotypic frequencies evolve as if the population were in Hardy-Weinberg proportions and linkage equilibrium. Thus, at least for the deterministic behavior of one and two loci, deviations from random combination appear to have very little evolutionary significance.     

Esterase-6 polymorphism inDrosophila melanogaster:Effects of temperature and methyl malonate on genotypic trajectories in polymorphic populations set up with highly inbred lines

It is generally difficult to identify possible effects of selection at a specific locus because of the heterogeneity of the genetic background. Geographical patterns ofEst-6 gene frequencies suggest that there is selection at this locus but selection on loci closely linked to it cannot be excluded. Differences in catalytic properties between allozymes have been shownin vitro; further, several laboratory studies have shown apparent fitness differences between allozymes. Our study used inbred lines highly homogeneous in the genetic background. Four populations were set up fromEst-6s andEst-6F homozygous females inseminated by males of the same genotype at each combination of three factors: temperature (18 and 25°C); methyl malonate (presence or absence); input gene frequencies [p(S) = 0.2 and 0.8]. The populations were sampled periodically for about 28 generations. Methyl malonate was chosen to exert pressure in the enzymatic function of esterase-6. Statistical analyses show that: there are no sex differences; gene frequencies change from input values to those of the first sampling, when only individuals of the first generation are present at 18^oC or individuals of the second generation just begin to appear at 25°C; gene frequencies do not change thereafter and Hardy-Weinberg equilibrium is established. The changes in gene frequencies observed in the first generations suggest thatEst-6 can under certain conditions be a target of selection. Such conditions may not, however, occur in natural populations.     

Adaptive Topography in Fertility-Viability Selection Models: The Haplodiploid Case

A linear combination of partial changes of mean fitnesses from one generation to the next one is shown to be approximately equal to the additive genetic variance in fitness after enough generations and away from equilibrium in random mating haplodiploid populations under arbitrary weak frequency-dependent selection on sex-differentiated viability of individuals and sex-differentiated fertility of matings controlled at a single multiallelic locus. The result can be applied to X-linked locus models in diploid populations. The result is used to deduce approximate adaptive topographies far frequency-independent selection models in the cases of nonsex-differentiated fertilities and multiplicative sex-differentiated fertilities and for kin selection models in family-structured populations under the assumptions of single insemination and multiple insemination of females. Multiple insemination creates frequency-dependent selection regimes.     

Evolution under Fertility and Viability Selection

Evolution at a single multiallelic locus under arbitrary weak selection on both fertility and viability is investigated. Discrete, nonoverlapping generations are posited for autosomal and X-linked loci in dioecious populations, but monoecious populations are studied in both discrete and continuous time. Mating is random. The results hold after several generations have elapsed. With an error of order s [i.e., O(s)], where s represents the selection intensity, the population evolves in Hardy-Weinberg proportions. Provided the change per generation of the fertilities and viabilities due to their explicit time dependence (if any) is O(s2), the rate of change of the deviation from Hardy-Weinberg proportions is O(s2). If the change per generation of the viabilities and genotypic fertilities is smaller than second order [i.e., o(s2)], then to O(s2) the rate of change of the mean fitness is equal to the genic variance. The mean fitness is the product of the mean fertility and the mean viability; in dioecious populations, the latter is the unweighted geometric mean of the mean viabilities of the two sexes. Hence, as long as there is significant gene frequency change, the mean fitness increases. If it is the fertilities of matings that change slowly [at rate o(s2)], the above conclusions apply to a modified mean fitness, defined as the product of the mean viability and the square root of the mean fertility.     

Distribution of Gene Frequency as a Test of the Theory of the Selective Neutrality of Polymorphisms

The variation in gene frequency among populations or between generations within a population is a result of breeding structure and selection. But breeding structure should affect all loci and alleles in the same way. If there is significant heterogeneity between loci in their apparent inbreeding coefficients F=s_p²/p(1-p), this heterogeneity may be taken as evidence for selection. We have given the statistical properties of F and shown how tests of heterogeneity can be made. Using data from human populations we have shown highly significant heterogeneity in F values for human polymorphic genes over the world, thus demonstrating that a significant fraction of human polymorphisms owe their current gene frequencies to the action of natural selection. We have also applied the method to temporal variation within a population for data on Dacus oleae and have found no significant evidence of selection.     

Simulation of internal transport barriers by means of the canonical profile transport model

Models with critical gradients are widely used to describe energy balance in L-mode discharges. The so-called first critical gradient can be found from the canonical temperature profile. Here, it is suggested that discharge regimes with transport barriers can be described based on the idea of the second critical gradient. If, in a certain plasma region, the pressure gradient exceeds the second critical gradient, then the plasma bifurcates into a new state and a transport barrier forms in this region. This idea was implemented in a modified canonical profile transport model that makes it possible to describe the energy and particle balance in tokamak plasmas with arbitrary cross sections and aspect ratios. The magnitude of the second critical gradient was chosen by comparing the results calculated for several tokamak discharges with the experimental data. It is found that the second critical gradient is related to the magnetic shear s. The criterion of the transport barrier formation has the form (a ²/r)d/drln(p/p _c ) > z ₀ (r), where r is the radial coordinate, a is the plasma minor radius, p is the plasma pressure, p _c is the canonical pressure profile, and the dimensionless function z _O(r) = C _O + C ₁ s (with C _0i ～1, C _0e ～3, and C _1i,e ～2) describes the difference between the first and second critical gradients. Simulations show that this criterion is close to that obtained experimentally in JET. The model constructed here is used to simulate internal transport barriers in the JET, TFTR, DIII-D, and MAST tokamaks. The possible dependence of the second critical gradient on the plasma parameters is discussed.     

Natural selection under population regulation

The dynamical behavior of multi-allele, one-locus systems is analyzed under population regulation. Weak selection is assumed. It is shown that for sufficiently large times, t, the nth time derivative of the population number N(t) is of order n}+1 in the selection coefficients. These order relations imply there is an asymptotic “quasi-equilibrium” in which population size and mean fitness change slowly relative to changes in gene frequencies. Consistent with the results of other authors, in quasi-equilibrium the mean fitness is second-order in the selection coefficients. In an effort to understand dynamic behavior beyond the immediate neighborhood of equilibrium, the topology of mean fitness surfaces is explored. In general, population regulation leads to regions of decreasing mean fitness in which there are important changes in gene frequencies. To illustrate this and other related phenomena, I analyze models in which there is logarithmic population control, and in which genotypic fitnesses W_i(x) are linear in the allele frequencies x. Exact solutions for mean fitness W(x) are obtained for two- and three-allele systems with symmetric fertilities and mortalities.     

Sperm competition games: Sperm size (mass) and number under raffle and displacement, and the evolution of P2

We examine models for evolution of sperm size (i.e. mass m) and number (s) under three mechanisms of sperm competition at low ‘risk’ levels: (i) raffle with no constraint on space available for competing sperm, (ii) direct displacement mainly by seminal fluid, and (iii) direct displacement mainly by sperm mass. Increasing sperm mass increases a sperm's ‘competitive weight’ against rival sperm through a diminishing returns function, r(m). ESS total ejaculate expenditure (the product m^?s^?) increases in all three models with sperm competition risk, q. If r(m), or ratio r′(m)/r(m), is independent of ESS sperm numbers, ESS sperm mass remains constant, and the sperm mass/number ratio (m^?/s^?) therefore decreases with risk. Dependency of sperm mass on risk can arise if r(m) depends on competing sperm density (sperm number / space available for sperm competition). Such dependencies generate complex relationships between sperm mass and number with risk, depending both on the mechanism and how sperm density affects r(m). While numbers always increase with risk, mass can either increase or decrease, but m^?/s^? typically decreases with risk unless sperm density strongly influences r(m). Where there is no extrinsic loading due to mating order, ESS paternity of the second (i.e. last) male to mate (P₂) under displacement always exceeds 0.5, and increases with risk (in the raffle P₂=0.5). Caution is needed when seeking evidence for a sperm size-number trade off. Although size and number trade-off independently against effort spent on acquiring matings, their product, m^?s^?, is invariant or fixed at a given risk level, effectively generating a size-number trade off. However, unless controlled for the effects of risk, the relation between m^? and s^? can be either positive or negative (a positive relation is usually taken as evidence against a size-number trade off).     

Reaction of cythchrome c with one-electron redox reagents. I. Reduction of ferricytochrome c by the hydrated electron produced by pulse radiolysis

Pulse radiolysis-kinetic spectrometry has been used to investigate the reaction of hydrated electrons with ferricytochrome c in dilute aqueous solution at pH 6.5–7.0. Time resolutions from 2·10^?7 to 1 s were employed. Transient spectra from 320 to 580 nm were characterized with a wavelength resolution of ±0.5 nm. 1 In neutral salt-free solution, k(ferricytochrome c+e^?_aq)=(6.0±0.9)·10¹⁰ M^?1·s^?1 and k(ferricytochrome c+H)=(1.2±0.2)·10¹⁰ M^?1·s^?1. The reaction of ferricytochrome c with hydrated electrons is sensitive to ionic strength; in 0.1 M NaClO₄, k(ferricytochrome c+e^?_aq)=(2.4±0.4)·10¹⁰ M^?1·s^?1. In contrast, k(ferricytochrome c+H) is insensitive to ionic strength. Time resolution of three spectral stages has been accomplished. The primary spectrum is the first observable spectrum detectable after irradiation and is formed in a second-order process. Its rate of formation is indisting-uishable from the rate of disappearance of the electron spectrum. The secondary spectrum is generated in a true first order intramolecular process, k(p→s)=(1.2±0.1)·10⁵ s^?1. The tertiary spectrum is also generated in a true first-order process, k(s→t)=(1.3±0.2)·10² s^?1. The specific rates of both transformations are independent of the wavelength of measurement. The tertiary spectrum, observable 50 ms after initial reaction and remaining unchanged thereafter for at least 1 s, shows that relaxed ferrocytochrome c is the only detectable product. This product is not autoxidizable, as expected for native reduced enzyme. It is more probable that the intramolecular changes responsible for the p→s and s→t spectral transformations involve the influence of conformational relaxation of ferrocytochrome c upon electronic energy states then that they are intramolecular transmission of reducing equivalents from primary sites of electron attachment.     

The McClure and Weiss models of Fe–O2 bonding for oxyhemes, and the HbO2 + NO reaction

For the Fe–O₂(S = 0) linkages of oxyhemes, valence bond (VB) structures are re-presented for the McClure [Fe^II(S = 1) + O₂(S = 1)], Pauling–Coryell [Fe^II(S = 0) + O₂*(S = 0)], and Weiss [Fe^III(S = ½) + O₂ ^?(S = ½)] models of bonding. The VB structures for the McClure and Weiss models are of the increased-valence type, with more electrons participating in bonding than occur in their component Lewis structures. The Fe–O bond number and O–O bond order for the McClure structure are correlated with measured Fe–O and O–O bond lengths for oxymyoglobin. Back-bonding from O ₂ ^? to Fe^III of the Weiss structure gives a restricted form of the McClure structure. The McClure and Weiss increased-valence structures are used to provide VB formulations of mechanisms for the oxyhemoglobin + NO reaction. The products of these two formulations are Hb⁺ and NO₃ ^? (where Hb is hemoglobin) and Hb⁺ and OONO^?, respectively. Because Hb⁺ and NO₃ ^? are the observed products, they provide an experimental procedure for distinguishing the McClure and Weiss models. It is also shown that the same type of agreement between McClure-type theory and experiment occurs for oxycoboglobin + NO, cytochrome P450 monooxygenases, and related hydrogen atom transfer reactions. In the appendices, the results of density functional theory and multireference molecular orbital calculations for oxyhemes are related to one formulation of the increased-valence wavefunction for the McClure model, and theory is presented for the calculation of approximate weights for the Lewis structures that are components of the McClure increased-valence structure.     

Subunit-subunit interactions in TF1 as revealed by ligand binding to isolated and integrated α and β subunits

The binding of 3′-O-(1-naphthoyl)adenosinetriphosphate (1-naphthoyl-ATP), ATP and ADP to TF₁ and to the isolated α and β subunits was investigated by measuring changes of intrinsic protein fluorescence and of fluorescence anisotropy of 1-naphthoyl-ATP upon binding. The following results were obtained. (1) The isolated α and β subunits bind 1 mol 1-naphthoyl-ATP with a dissociation constant (K_D(1-naphthoyl-ATP)) of 4.6 μM and 1.9 μM, respectively. (2) The K_D(ATP) for α and β subunits is 8 μM and 11 μM, respectively. (3) The K_D(ADP) for α and β subunits is 38 μM μM and 7 μM, respectively. (4) TF₁ binds 2 mol 1-naphthoyl-ATP per mol enzyme with K_D = 170 nM. (5) The rate constant for 1-naphthoyl-ATP binding to α and β subunit is more than 5 · 10⁴ M⁻¹s⁻¹. (6) The rate constant for 1-naphthoyl-ATP binding to TF₁ is 6.6 · 10³ M⁻¹ · s⁻¹ (monophasic reaction); the rate constant for its dissociation in the presence of ATP is biphasic with a fast first phase (k^A₋₁ = 3 · 10⁻³s⁻¹) and a slower second phase (k^A₋₂ < 0.2 · 10⁻³s⁻¹). From the appearance of a second peak in the fluorescence emission spectrum of 1-naphthoyl-ATP upon binding it is concluded that the binding sites in TF₁ are located in an environment more hydrophobic than the binding sites on isolated α and β subunits. The differences in kinetic and thermodynamic parameters for ligand binding to isolated versus integrated α and β subunits, respectively, are explained by interactions between these subunits in the enzyme complex.     

Assay of both activities of the bifunctional tRNA-modifying enzyme MnmC reveals a kinetic basis for selective full modification of cmnm5s2U to mnm5s2U

Transfer RNA (tRNA) contains a number of complex ‘hypermodified’ nucleosides that are essential for a number of genetic processes. Intermediate forms of these nucleosides are rarely found in tRNA despite the fact that modification is not generally a complete process. We propose that the modification machinery is tuned into an efficient ‘assembly line’ that performs the modification steps at similar, or sequentially increasing, rates to avoid build-up of possibly deleterious intermediates. To investigate this concept, we measured steady-state kinetics for the final two steps of the biosynthesis of the mnm⁵s²U nucleoside in Escherichia coli tRNA^Glu, which are both catalysed by the bifunctional MnmC enzyme. High-performance liquid chromatography-based assays using selectively under-modified tRNA substrates gave a K_m value of 600 nM and k_cat 0.34 s⁻¹ for the first step, and K_m 70 nM and k_cat 0.31 s⁻¹ for the second step. These values show that the second reaction occurs faster than the first reaction, or at a similar rate at very high substrate concentrations. This result indicates that the enzyme is kinetically tuned to produce fully modified mnm⁵(s²)U while avoiding build-up of the nm⁵(s²)U intermediate. The assay method developed here represents a general approach for the comparative analysis of tRNA-modifying enzymes.     

Kinetics of CO substitution in Co4(CO)12 and Rh4(CO)12

The kinetics of rapid CO substitution by PPh₃ in Co₄(CO)₁₂ and Rh₄(CO)₁₂ have been examined by stopped-flow and low temperature FT-IR methods. In Co₄(CO)₁₂ rapid (k_obs ∼ 1.8 s⁻¹) substitution of CO occurs after a 1–15 s induction period at 28 °C in C₆H₅Cl solvent by a catalytic process. Addition of PPh₃ to Rh₄(CO)₁₂ yields Rh₄(CO)₁₁(PPh₃) according to a predominantly second order rate law k₁[Rh₄- (CO)₁₂] + k₂[Rh₄(CO)₁₂][PPh₃] with k₁ = 25 ± 11 s⁻¹ and k₂ = 2.97 ± 0.27 X 10⁴ M⁻¹ s⁻¹ at 28 °C. Substitution of a second CO ligand also occurs rapidly with k₁ = 0.15 ± 0.09 s⁻¹ and k₂ = 6.54 ± 0.07 X 10² M⁻¹ s⁻¹ at 28 °C. The reactivity of Rh₄(CO)₁₂ toward associative substitution is 10⁴– 10¹¹ faster than for the Co and Ir analogues, In Rh₄(CO)₁₁(PPh₃) the increase in CO substitution rates over Co and Rh analogues is 10²–10⁷. The ordering of associative substitution rates Co << Rh >>> Ir in these clusters exaggerates the trend seen in mononuclear metal complexes.     

Comparison of linear and nonlinear models for human population dynamics

In standard demographic practice, population projections are commonly based on one-sex linear models of the Lotka-Leslie type. We demonstrate here that such projections based solely on time-invariant, age-specific male fertilities and mortalities are incompatible with those based solely on female fertilities and mortalities. This incompatibility obtains even in the singular case where effective male and female fertility functions are equal, and generate equal ultimate rates of growth. In standard demographic practice, the incompatibility is initially masked, since one-sex fertility functions are generally calculated from the same initial-time data and thereby tautologically forced to initially concur; however, with the passage of any finite time, the incompatibility reasserts itself—the only exception being the uninteresting case where the system is already in the stationary age and sex distribution of balanced exponential growth.An example is adduced of a nonlinear (age-free) system whose true rate of ultimate growth is correctly bracketed by the male and female one-sex rates of ultimate growth. Analysis of more general two-sex models shows that the two one-sex growth rates, calculated for arbitrary male and female initial age distributions, need not bracket the true rate. We show, however, that models exist such that with appropriate choices of initial conditions, this bracketing will occur.     

Use of cadmium hydroxide gel for isolation of extracellular catalases from Penicillium piceum and characterization of purified enzymes

We optimized the conditions for isolation of extracellular catalases from Penicillium piceum F-648 and P. piceum A3 by means of volume chromatography with cadmium hydroxide gel. Our study showed that 55–57 mg wet gel are sufficient for the maximum sorption of catalase from 1 ml of culture fluid. This gel was formed in 1 ml 70 mM Cd(NO₃)₂ after addition of NaOH (Cd(NO₃)₂/NaOH molar ratio 1: 2.2). The eluting solution contained 50 mM NaH₂PO₄(pH 7.0), 5.0 mM dithiothreitol, and 0.3% sodium cholate and was potent in desorbing catalase from the gel. Subsequent ultrafiltration of the eluate on the membrane with a retention limit of 50 kDa allowed us to concentrate and purify the sample from low-molecular-weight protein impurities. NH₄Cl (1.0 M) containing 0.3% sodium cholate was used to wash the sample from low-molecular-weight aromatic metabolites. Purified catalases included 33–34% antiparallel β-structures and 9%-spirals. Under optimal conditions in the medium of 10 mM phosphate buffered saline (pH 7.0) at 30°C, catalases from P. piceum F-648 were characterized by the following parameters: K _M, 158.8 mM; catalytic constant, 2.83 × 10⁶ s^?1; enzyme inactivation rate constant in H₂O₂ decomposition, 3.5 × 10^?2 s^?1; and constant of the interaction between catalase complex I and second molecule of H₂O₂, 1.8 × 10⁷M^?1 s^?1.     

A biomechanically derived minimum work model of the fish gill lamellar system exhibits its exquisite morphological arrangement and perfusate regulation for oxygen uptake from water

To evaluate the efficiency of oxygen (O₂) uptake from water through the fish gill lamellar system, a cost function (CF) representing mechanical power expenditure for water ventilation and blood circulation through the gill was formulated, by applying steady-state fluid mechanics to a homogeneous lamellar-channel model. This approach allowed us to express CF as the function of inter-lamellar water channel width (w) and to derive an analytical solution of the width (w_min) at the minimum CF. Morphometric and physiological data for rainbow trout in the literature were referred to calculate CF(w) curves and their w_min values at five intensity stages of swimming exercise. Obtained w_min values were evenly distributed around the standard measure of the width (w_s = 24 μm) in this fish. Individual levels of CF(w_min) were also fairly close to the corresponding CF(w_s) values within a 10% deviation, suggesting the reliability of approximating [CF(w_min) = CF(w_s)]. The cost-performance of O₂ uptake through the gill (η_g) was then assessed from reported data of total O₂ uptake/CF(w_s) at each intensity stage. The η_g levels at any swimming stage exceeded 95% of the theoretical maximum value, implying that O₂ uptake is nearly optimally performed in the lamellar-channel system at all swimming speeds. Further analyses of O₂ transport in this fresh water fish revealed that the water ventilation by the buccal/opercular pumping evokes a critical limit of swimming velocity, due to confined O₂ supply to the peripheral skeletal muscles, which is avoided in ram ventilators such as tuna.     

Interactions of superoxide anion with enzyme radicals: Kinetics of reaction with lysozyme tryptophan radicals and corresponding effects on tyrosine electron transfer

The kinetics of O^·-₂ reaction with semi-oxidized tryptophan radicals in lysozyme, Trp^·(Lyz) have been investigated at various pHs and conformational states by pulse radiolysis. The Trp^·(Lyz) radicals were formed by Br^·-₂ oxidation of the 3–4 exposed Trp residues in the protein. At pH lower than 6.2, the apparent bimolecular rate is about 2 × 10⁸M^-1s^-1; but drops to 8 × 10⁷M^-1s^-1 or less above pH 6.3 and in CTAC micelles. Similarly, the apparent bimolecular rate constant for the intermolecular Trp^·(Lyz) + Trp^·(Lyz) recombination reaction is about (4-7 × 10⁶M^-1s^-1) at/or below pH 6.2 then drops to 1.3-1.6 × 10⁶M^-1s^-1 at higher pH or in micelles. This behavior suggests important conformational and/or microenvironmental rearrangement with pH, leading to less accessible semioxidized Trp^· residues upon Br^·-₂ reaction. The kinetics of Trp^·(Lyz) with ascorbate, a reducing species rather larger than O^·-₂ have been measured for comparison. The well-established long range intramolecular electron transfer from Tyr residues to Trp radicals-leading to the repair of the semi-oxidized Trp^·(Lyz) and formation of the tyrosyl phenoxyl radical is inhibited by the Trp^·(Lyz)+O^·-₂ reaction, as is most of the Trp^·(Lyz)+Trp^·(Lyz) reaction. However, the kinetic behavior of Trp^·(Lyz) suggests that not all oxidized Trp residues are involved in the intermolecular recombination or reaction with O^·-₂. As the kinetics are found to be quite pH sensitive, this study demonstrates the effect of the protein conformation on O^·-₂ reactivity. To our knowledge, this is the first report on the kinetics of a protein-O^·-₂ reaction not involving the detection of change in the redox state of a prosthetic group to probe the reactivity of the superoxide anion.     

Bacterial denitrifying nitric oxide reductases and aerobic respiratory terminal oxidases use similar delivery pathways for their molecular substrates

The superfamily of heme?copper oxidoreductases (HCOs) include both NO and O₂ reductases. Nitric oxide reductases (NORs) are bacterial membrane enzymes that catalyze an intermediate step of denitrification by reducing nitric oxide (NO) to nitrous oxide (N₂O). They are structurally similar to heme?copper oxygen reductases (HCOs), which reduce O₂ to water. The experimentally observed apparent bimolecular rate constant of NO delivery to the deeply buried catalytic site of NORs was previously reported to approach the diffusion-controlled limit (10⁸–10⁹?M^?1?s^?1). Using the crystal structure of cytochrome-c dependent NOR (cNOR) from Pseudomonas aeruginosa, we employed several protocols of molecular dynamics (MD) simulation, which include flooding simulations of NO molecules, implicit ligand sampling and umbrella sampling simulations, to elucidate how NO in solution accesses the catalytic site of this cNOR. The results show that NO partitions into the membrane, enters the enzyme from the lipid bilayer and diffuses to the catalytic site via a hydrophobic tunnel that is resolved in the crystal structures. This is similar to what has been found for O₂ diffusion through the closely related O₂ reductases. The apparent second order rate constant approximated using the simulation data is ~5?×?10⁸?M^?1?s^?1, which is optimized by the dynamics of the amino acid side chains lining in the tunnel. It is concluded that both NO and O₂ reductases utilize well defined hydrophobic tunnels to assure that substrate diffusion to the buried catalytic sites is not rate limiting under physiological conditions.     

Population Size and Selection Intensity Effects on Long-Term Selection Response in Mice

Long-term response to within full-sib family selection for increased postweaning gain was evaluated in lines having different effective population sizes (N_e) and selection intensities (i). Line designations were I4(4), I8(2), I16(2), M4(4), M8(2) and M16(2), where I and M indicate selection of the top 50% and 25%, respectively; 4, 8 and 16 represent the number of parental pairs per replicate and number of replicates is given in parentheses. Realized within full-sib family heritabilities (h_R²) in the first phase of selection (0-14 generations) were larger in 16-pair lines than in 4- and 8-pair lines. In the second phase of selection (>14 generations), h_R² declined significantly (P<.01) in all lines, and only the I16 and M16 lines had h_R² values significantly (P<.01) greater than zero. Realized genetic correlations involving number born, 12-day litter weight, weaning weight and six-week weight tended to decline in the second phase of selection. The I16, M16 and control (C16) replicates were crossed in all combinations at generation 14. Crosses were then selected within litters for high postweaning gain. The h_R² values in the crossbred lines were all larger than those in the second selection phase for M16-1, M16-2 and I16-1, but not for I16-2. Within each N_e level, total response was significantly (P<.01) less for I lines compared with M lines. Total response increased as N_e increased, within each level of i. Relatively small differences in realized i values among N_e lines could not account for this result. The difference in total response among the N_e lines at a given selection intensity may be due to inbreeding depression and a combination of interactions involving "drift" and selection. By crossing replicates of the M lines with the C16 control, the effects of inbreeding depression were removed. Inbreeding depression and genetic drift, as defined herein, were equally important in accounting for differences among N_e lines in total response.     

Disequilibrium, Selection, and Recombination: Limits in Two-Locus, Two-Allele Models

All possible combinations of equilibria and fitnesses in two-locus, two-allele, deterministic, discrete-generation selection models are enumerated. This knowledge is used to obtain limits (which can be calculated to arbitrary precision) to the relationships among disequilibrium, selection and recombination for fixed values of allele frequencies. In all cases, the inequality|rD| < s/10 holds, where r is recombination and D is disequilibrium, and all selection coefficients lie between 1 - s and 1 + s times that of the double heterozygote. Linear programming techniques are used to calculate the minimum strength of selection needed to explain several observed nonzero values of D reported in the literature. One conclusion is that the failure to observe nonzero values of D is not surprising.