On the appropriateness of use of a continuous formulation for the modelling of discrete multireactant systems following Michaëlis–Menten kinetics

The possibility of solving the mass balances to a multiplicity of substrates within a CSTR in the presence of a chemical reaction following Michaelis-Menten kinetics using the assumption that the discrete distribution of said substrates is well approximated by an equivalent continuous distribution on the molecular weight is explored. The applicability of such reasoning is tested with a convenient numerical example. In addition to providing the limiting behavior of the discrete formulation as the number of homologous substrates increases, the continuous formulation yields in general simpler functional forms for the final distribution of substrates than the discrete counterpart due to the recursive nature of the solution in the latter case.List of Symbols C{N. M} mol/m³ concentration of substrate containing N monomer residues each with molecular weight M - {N, M} normalized value of C{N. M} - C {M} mol/m³ da concentration of substrate of molecular weight M - _in normalized value of C {M} at the i-th iteration of a finite difference method - {M} normalized value of C {M} - C ₀{N.M} mol/m³ inlet concentration of substrate containing N monomer residues each with molecular weight M - {N ·M} normalized value of C₀{N. M} - _{0 i} normalized value of C ₀ {M} at the i-th iteration of a finite difference method - C ₀ {M} mol/m³ da initial concentration of substrate of molecular weight M - C _tot mol/m³ (constant) overall concentration of substrates (discrete model) - C _tot mol/m³ (constant) overall concentration of substrates (continuous model) - D deviation of the continuous approach relative to the discrete approach - i dummy integer variable - I arbitrary integration constant - j dummy integer variable - k dummy integer variable - K _m mol/m³ Michaëlis-Menten constant for the substrates - l dummy integer variable - M da molecular weight of substrate - M normalized value of M - M da maximum molecular weight of a reacting substrate - N number of monomer residues of a reacting substrate - N maximum number of monomer residues of a reacting substrate - N total number of increments for the finite difference method - Q m³/s volumetric flow rate of liquid through the reactor - S inert product molecule - S _i substrate containing i monomer residues - V m³ volume of the reactor - v _max mol/m³ s reaction rate under saturating conditions of the enzyme active site with substrate - v _max{N. M} mol/m³ s reaction rate under saturating conditions of the enzyme active site with substrate containing N monomer residues with molecular weight M - _max{N · M} dimensionless value of v_max{N. M} (discrete model) - _max{M} dimensionless value of v _max {M} (continuous model) - mol/m³ s molecular weight-averaged value of v_max (discrete model) - mol.da/m³s molecular weight-averaged value of v_max (continuous model) - v _max {M} mol.da/m³s reaction rate under saturating conditions of the enzyme active site with substrate with molecular weight M - _max {M} dimensionless value of v_max{M} - _{max, (i)} dimensionless value of v_max{M} at the i-th iteration of a finite difference method - v _max mol/m³ s reference constant value of v _max Greek Symbols dimensionless operating parameter (discrete distribution) - dimensionless operating parameter (continuous distribution) - M da (average) molecular weight of a monomeric subunit - M selected increment for the finite difference method - auxiliary corrective factor (discrete model)     

Altitudinal and seasonal effects on aerobic metabolism of deer mice

Summary I compared the maximal aerobic metabolic rates ( ), field metabolic rates (FMR), aerobic reserves ( -FMR), and basal metabolic rates (BMR) of wild and recently captured deer mice from low (440 m) and high (3800 m) altitudes. To separate the effects of the thermal environment from other altitudinal effects, I examined mice from different altitudes, but similar thermal environments (i.e., summer mice from high altitude and winter mice from low altitude). When the thermal environment was similar, , FMR, and aerobic reserve of low and high altitude mice did not differ, but BMR was significantly higher at high altitude. Thus, in the absence of thermal differences, altitude had only minor effects on the aerobic metabolism of wild or recently captured deer mice.At low altitude, there was significant seasonal variation in , FMR, and aerobic reserve, but not BMR. BMR was correlated with , but not with FMR. The significant positive correlation of BMR with indicates a cost of high , because higher BMR increases food requirements and energy use during periods of thermoneutral conditions.Abbreviations BMR basal metabolic rate - FMR field metabolic rate - partial pressure of oxygen - T _a ambient temperature - T _b body temperature - T _e operative temperature - maximal aerobic metabolic rate     

The photosynthetic F1-α3β3 and α1β1 catalytic core complexes

Minimal photosynthetic catalytic F₁() core complexes, containing equimolar ratios of the and subunits, were isolated from membrane-bound spinach chloroplast CF₁ and Rhodospirillum rubrum chromatophore RrF₁. A CF₁-₃₃ hexamer and RrF₁-₁₁ dimer, which were purified from the respective F₁() complexes, exhibit lower rates and different properties from their parent F₁-ATPases. Most interesting is their complete resistance to inhibition by the general F₁ inhibitor azide and the specific CF₁ inhibitor tentoxin. These inhibitors were earlier reported to inhibit multisite, but not unisite, catalysis in all sensitive F₁-ATPases and were therefore suggested to block catalytic site cooperativity. The absence of this typical property of all F₁-ATPases in the ₁₁ dimer is consistant with the view that the dimer contains only a single catalytic site. The ₃₃ hexamer contains however all F₁ catalytic sites. Therefore the observation that CF₁-₃₃ can bind tentoxin and is stimulated by it suggests that the F₁ subunit, which is required for obtaining inhibition by tentoxin as well as azide, plays an important role in the cooperative interactions between the F₁-catalytic sites.Abbreviations CF₀F₁ chloroplast F₀F₁ - CF₁ chloroplast F₁ - CF₁ chloroplast F₁ subunit - CF₁ chloroplast F₁ subunit - CF₁() a complex containing equal amounts of the CF₁ and subunits - MF₁ mitochondrial F₁ - RrF₀F₁ Rhodospirillum rubrum F₀F₁ - RrF₁ R. rubrum F₁ - RrF₁ R. rubrum F₁ subunit - RrF₁ R. rubrum F₁ subunit - RrF₁() a complex containing equal amounts of the RrF₁ and subunits - Rubisco Ribulose-1,5-bisphosphate carboxylase - TF₁ thermophilic bacterium PS3 F₁     

Thermoregulation,gas exchange,and ventilation in Adelie penguins (Pygoscelis adeliae)

Summary Adelie penguins (Pygoscelis adeliae) experience a wide range of ambient temperatures (T _a) in their natural habitat. We examined body temperature (T _b), oxygen consumption ( ), carbon dioxide production ( ), evaporative water loss ( ), and ventilation atT _a from –20 to 30 °C. Body temperature did not change significantly between –20 and 20°C (meanT _b=39.3°C).T _b increased slightly to 40.1 °C atT _a=30°C. Both and were constant and minimal atT _a between –10 and 20°C, with only minor increases at –20 and 30°C. The minimal of adult penguins (mean mass 4.007 kg) was 0.0112 ml/[g·min], equivalent to a metabolic heat production (MHP) of 14.9 Watt. The respiratory exchange ratio was approximately 0.7 at allT _a. Values of were low at lowT _a, but increased to 0.21 g/min at 30°C, equivalent to 0.3% of body mass/h. Dry conductance increased 3.5-fold between –20 and 30°C. Evaporative heat loss (EHL) comprised about 5% of MHP at lowT _a, rising to 47% of MHP atT _a=30°C. The means of ventilation parameters (tidal volume [VT], respiration frequency [f], minute volume [I], and oxygen extraction [ ]) were fairly stable between –20 and 10°C (VT did not change significantly over the entireT _a range). However, there was considerable inter- and intra-individual variation in ventilation patterns. AtT _a=20–30°C,f increased 7-fold over the minimal value of 7.6 breaths/min, and I showed a similar change. fell from 28–35% at lowT _a to 6% atT _a=30°C.Abbreviations C thermal conductance - EHL evaporative heat loss - oxygen extraction - f respiratory frequency - MHP metabolic heat production - evaporative water loss - LCT lower critical temperature - RE respiratory exchange ratio - T _a ambient temperature - T _b body temperature - rate of oxygen consumption - rate of carbon dioxide production - I inspiratory minute volume - VT tidal volume     

Substitutions of the Conserved Thr42 Increased the Roles of the ε-Subunit of Maize CF1 as CF1 Inhibitor and Proton Gate

The conserved residue Thr42 of -subunit of the chloroplast ATP synthase of maize (Zea mays L.) was substituted with Cys, Arg, and Ile, respectively, through site-directed mutagenesis. The over-expressed and refolded -proteins were purified by chromatography on DEAE-cellulose and FPLC on mono-Q column, which were as biologically active (inhibiting Ca²⁺-ATPase activity and blocking proton gate) as the native subunit isolated from chloroplasts. The T42C and T42R showed higher inhibitory activities on the soluble CF₁(–) Ca²⁺-ATPase than the WT. The T42I inhibited the Ca²⁺-ATPase activity of soluble CF₁ and restored photophosphorylation activity of membrane-bound CF₁ deficient in the most efficiently. Far-ultraviolet CD spectra showed that the portions of -helix and -sheet structures of the three mutants were somewhat different from WT. Thus the conserved residue Thr42 may be important for maintaining the structure and function of the -subunit and the basic functions of the -subunit as far as an inhibitor of Ca²⁺-ATPase and the proton gate are related.     

On the phytochrome phototransformation kinetics in mustard seedlings

Summary The in vivo phototransformation kinetics of mustard hook and cotyledon phytochrome exhibit a deviation from a single first order curve, quite similar to that for pumpkin hooks as reported in a previous paper (Boisard, Marmé and Schäfer, 1971). The P _frP_rkinetics can be characterized by the ratios _fr, ^I · P _fr ^I / _fr, ^II · P _fr, ^II and where P _fr ^I and P _fr ^II are two populations of phytochrome molecules which convert to P _rwith a first order half-life of and . These ratios depend on the length of time of etiolation. The ratio _fr, ^I · P _fr ^I / _fr, ^II · P _fr, ^II is independent of the amount of total P _frpresent at the beginning of the P _frP_rphototransformation after a non-saturating dose of red light. The half-lives of the two populations, however, depend on the concentration of total P _frinitially present. P _frP_rphototransformation kinetics with different light intensities show that reciprocity holds.     

Temperature induced peripheral blood flow changes in lizards

Summary The influence of local temperature changes within the posterior portion of the body on dorsal aorta blood flow ( ), femoral arterial pressure (P _a ), peripheral resistance (R), skin blood flow ( ) and skeletal muscle blood flow ( ) was examined in unanesthetized lizards (Iguana iguana andTubinambis nigropunctatus). In response to local heating of the hind legs and tail and increased,P _a was generally unchanged,R decreased and decreased or was unchanged (Fig. 2). It is suggested that the acquisition of heat may be favored by diverting the increase in away from the muscle to the warmer skin. In response to cooling and decreased,P _a was generally unchanged, R increased and increased or was unchanged. Hence, during cooling the retention of heat may be favored by diverting blood away from the skin to the deeper muscle. The muscle-skin shunt is under sympathetic control since following blockade with phenoxybenzamine HCL (Dibenzyline) muscle blood flow changes in response to temperature were qualitatively similar to those of skin (Fig. 4). These changes in peripheral circulatory patterns are independent of changes in heart rate or deep body temperature.Baker and Weathers were predoctoral and postdoctoral trainees, respectively, under USPHS Grant HE-05696. This study was also supported by NSF Grant GB-8523 and Los Angeles County Heart Association Grant 437IG.     

Energy conservation in whole cells of the methylotrophic bacterium Methylophilus methylotrophus

Respiratory chain phosphorylation has been investigated in the methylotrophic bacterium Methylophilus methylotrophus following the addition of oxidisable substrates to aerobic, whole cell suspensions. Initial-rate experiments showed that ATP synthesis occurred at the overall expense of AMP and inorganic phosphate via the sequential action of the ATP phosphohydrolase and adenylate kinase; some of the nascent ATP was rapidly used to synthesis nonadenine nucleoside triphosphates. After being corrected for ATP turnover, Pi/O quotients of 0.46 to 0.54, 0.77 and 1.37 nmol/ng-atom O were obtained for the oxidation of methanol dehydrogenase-linked substrates (methanol, ethanol and acetaldehyde), duroquinol and formate (NAD⁺-linked) respectively. These values were proportional to the H⁺/O and/or K⁺/O quotients exhibited by these substrates, and yielded an average H⁺/ATP (H⁺/Pi) quotient of 4.2 ng-ion H⁺/nmol. Steady-state experiments showed that the extent of cellular energisation varied with the respiration rate but was always in the order methanol > duroquinol > acetaldehyde, thus indicating that under these longer-term conditions methanol was completely oxidised to yield PQQH₂ and 2NAD(P)H. These results are discussed in terms of the various reactions which lead to the generation or utilisation of the protonmotive force in this organism.Abbreviations FCCP carbonylcyanide p-trifluoromethyxyphenyl-hydrazone - bulk phase, transmembrane electrochemical potential difference of protons ( ) - pH bulk phase, transmembrane pH difference (pH_in–pH_out) - bulk phase, transmembrane electrical potential difference (_in - _out) - [P] concentration of anhydride phosphate bonds in adenine nucleotides (2[ATP]+[ADP]) - FPLC fast protein liquid chromatography - PQQ pyrroloquinoline quinone - Gp phosphorylation potential     

Precision of neural timing: effects of convergence and time-windowing

We study the improvement in timing accuracy in a neural system having n identical input neurons projecting to one target neuron. The n input neurons receive the same stimulus but fire at stochastic times selected from one of four specified probability densities, f, each with standard deviation 1.0 msec. The target cell fires if and when it receives m inputs within a time window of msec. Let _n,m, denote the standard deviation of the time of firing of the target neuron (i.e. the standard deviation of the target neuron's latency relative to the arrival time of the stimulus). Mathematical analysis shows that _n,m, is a very complicated function of n, m, and . Typically, _n,m, is a non-monotone function of m and and the improvement of timing accuracy is highly dependent of the shape of the probability density for the time of firing of the input neurons. For appropriate choices of m, , and f, the standard deviation _n,m, may be as low as . Thus, depending on these variables, remarkable improvements in timing accuracy of such a stochastic system may occur.     

Thermodynamics of Mn2+-binding to goat α-lactalbumin

By means of reaction calorimetry we measured the apparent enthalpy change, H^app, of the binding of Mn²⁺-ions to goat -lactalbumin as a function of temperature. The observed H^app can be written as the sum of contributions resulting from a conformational and a binding process. In combination with the thermal unfolding curve of goat -lactalbumin, we succeeded in separating the complete set of thermodynamic parameters (H, G, S, C_p) into the binding and conformational contributions. By circular dichroism we showed that NH ₄ ⁺ -ions, upon binding to bovine a-lactalbumin, induce the same conformational change as do Na⁺ and K⁺: the binding constant equals 98 ± 9 M^–1.Abbreviations BLA bovine -lactalbumin - GLA goat -lactalbumin - HLA human -lactalbumin - CD circular dichroism Offprint requests to: H. Van DaelDeceased     

The Tryptophan Fluorescence of Tetracarbidium conophorum Agglutinin II and a Solution-Based Assay for the Binding of a Biantennary Glycopeptide

The plant lectin Tetracarbidium conophorum agglutinin II binds to glycoproteins and glycopeptides in a structurally specific manner [Animashaun et al., (1994) Glycoconjugate J. 11, 299–303]. We have characterized the steady-state and time-resolved fluorescence of the tryptophan residues of this lectin. The fluorescence (_ex = 295 nm, _em = 350 nm) decay is complex and can be described by four decay times with the following values: ₁ = 7.4nsec, ₁ = 0.22; ₂ = 2.9 nsec, ₂ = 0.25; ₃ = l.0 nsec, ₃ = 0.34; ₄ = 0.2 nsec, ₄ = 0.18. The addition of a biantennary glycopeptide to the lectin results in a quench and an 8 nm blue shift of the emission spectrum. The effect is saturable, and is described by an association constant of 1.8×10⁵ M^–1. The tryptophan fluorescence of Tetracarbidium conophorum agglutinin II may therefore be utilized to characterize thermodynamically the binding interactions between this lectin and complex glycoprotein.     

A simple method to quantitatively measure polypeptide JHNHα coupling constants from TOCSY or NOESY spectra

A simple linear relationship between the J coupling constant and the linewidth (_1/2) of in-phase NMR peaks has been identified. This relationship permits the rapid and accurate determination of polypeptide J coupling constants from a simple inspection of amide cross peaks in homonuclear ¹H TOCSY or ¹H NOESY spectra. By using the appropriate set of processing parameters we show that J = 0.5(_1/2) – MW/5000 + 1.8 for TOCSY spectra and J = 0.6(_1/2) – MW/5000 – 0.9 for NOESY spectra, where _1/2 is the half-height linewidth in Hz and MW is the molecular weight of the protein in Da. The simplicity of this relationship, combined with the ease with which _1/2 measurements can be made, means that J coupling constants can now be rapidly determined (up to 100 measurements in less than 30 min) without the need for any complex curve-fitting algorithms. Tests on 11 different polypeptides involving more than 650 separate J measurements have shown that this method yields coupling constants with an rmsd error (relative to X-ray data) of less than 0.9 Hz. Furthermore, the correlation coefficient between the predicted NMR coupling constants and those derived from high-resolution X-ray crystal structures is typically better than 0.89. These simple linear relationships have been found to be valid for peptides as small as 1 kDa to proteins as large as 20 kDa. Despite the method's simplicity, these results are comparable to the accuracy and precision of the best techniques published to date.     

Effects of ambient and local cutaneous temperatures on hand blood flow

The hand blood flow ( ) was investigated in response to a wide range of general and local cutaneous thermal stimuli (0–36°C and 4–42°C respectively), the local stimulus consisting of a thermostatically controlled water bath for the right hand (T_w), and the general stimulus, the ambient room temperature (T_a). was measured at the right wrist by strain gauge plethysmography; it was seen to respond more significantly to variations in T_w than to those in T_a at cold to comfortable ambient temperatures (T_a<22°C). A paradoxical vasodilatation was observed at T_w=4°C (Lewis' hunting phenomenon). The graphs of versus T at average to high local cutaneous temperatures (T_w > 33°C) are remarkably similar, except for an upward shift at successively higher values of T_w. The slope (or vasomotor reactivity) is interpreted as being controlled by variations in T_a. The curves exhibited maximum values at T_a = 31°C. Their subsequent decrease could represent a thermoregulatory adaptation to environment-organism heat transfer, the relative vasoconstriction tending to reduce the transfer. Although the qualitative response was the same for both sexes, the absolute value of was generally greater in male than in female subjects.     

Flight of the honey bee VI: energetics of wind tunnel exhaustion flights at defined fuel content,speed adaptation and aerodynamics

To gain information on extended flight energetics, quasi-natural flight conditions imitating steady horizontal flight were set by combining the tetheredflight wind-tunnel method with the exhaustion-flight method. The bees were suspended from a two-component aerodynamic balance at different, near optimum body angle of attack and were allowed to choose their own speed: their body mass and body weight was determined before and after a flight; their speed, lift, wingbeat frequency and total flight time were measured throughout a flight. These values were used to determine thrust, resultant aerodynamic force (magnitude and tilting angle), Reynolds number, total flight distance and total flight impulse. Flights in which lift was body weight were mostly obtained. Bees, flown to complete exhausion, were refed with 5, 10, 15 or 20 l of a 1.28-mol·l^-1 glucose solution (energy content w=18.5, 37.0, 55.5 or 74.0 J) and again flown to complete exhaustion at an ambient temperature of 25±1.5°C by a flight of known duration such that the calculation of absolute and relative metabolic power was possible. Mean body mass after exhaustion was 76.49±3.52 mg. During long term flights of 7.47–31.30 min similar changes in flight velocity, lift, thrust, aerodynamic force, wingbeat frequency and tilting angle took place, independent of the volume of feeding solution. After increasing rapidly within 15 s a more or less steady phase of 60–80% of total flight time, showing only a slight decrease, was followed by a steeper, more irregular decrease, finally reaching 0 within 20–30 s. In steady phases lift was nearly equal to resultant aerodynamic force; tilting angle was 79.8±4.0°, thrust to lift radio did not vary, thrust was 18.0±7.4% of lift, lift was somewhat higher/equal/lower than body mass in 61.3%, 16.1%, 22.6% of all totally analysable flights (n=31). The following parameters were varied as functions of volume of feeding solution (5–20 l in steps of 5 l) and energy content. (18.5–74.0 J in steps of 18.5 J): total flight time, velocity, total flight distance, mean lift, thrust, mean resultant aerodynamic force, tilting angle, total flight impulse, wingbeat frequency, metabolic power and metabolic power related to body mass, the latter related to empty, full and mean (=100 mg) body mass. The following positive correlations were found: L=1.069·10^-9 f ^2.538; R=1.629·10^-9 f ^2.464; P _m=7.079·10^-8 f ^2.456; P _m=0.008v+0.008; P _m=18.996L+0.022; P _m=19.782R+0.021; P _m=82.143T+0.028; P _m=1.245·bm _f ^1.424 ; P _{mrel e}=6.471·bm _f ^1.040 ; =83.248+0.385. The following negative correlations were found: V=3.939–0.032; T=1.324·10^-4–0.038·10^-4. Statistically significant correlations were not found in T(f), L(), R(), f(), P _m(bm _e), P _{m rel e}(bm _e), P _{m rel f}(bm _e), P _{m rel f}(bm _f).Abbreviations A(m²) frontal area - bl(m) body length - bm(mg) body mass - c(mol·1^-1) glucose concentration of feeding solution - c _D (dimensionless) drag coefficient, related to A - D(N) drag - F _w(N) body weight - F _wp weight of paper fragment lost at flight start - f wingbeat frequency (s^-1) - g(=9.81 m·s^-2) gravitational acceleration - I(Ns)=R(t) dt total impulse of a flight - L(N) lift vertical sustaining force component - P _m(J·s^-1=W) metabolic power - P_{m ret} (W·g^-1) metabolic power, related to body mass - R(N) resultant aerodynamic force - Re v·bl·v ^-1 (dimensionless) Reynolds number, related to body length - s(m) v(t) dt virtual flight distance of a flight - s(km) total virtual flight distance - T (N) thrust horizontal force component of horizontal flight - T _a (°C) ambient temperature - t(s) time - t _tot (s or min) total flight time - v(m·s^-1) flight velocity - v(l) volume of feeding solution - W (J) energy and energy content of V - ( °) body angle of attack between body longitudinal axis and flow direction - ( °) tilting angle ( 90°) between R and the horizont in horizontal flight v(=1.53·10^-5m²·s^-1 for air at 25°) kinematic viscosity - (=1.2 kg·m^-3 at 25°C) air density     

Estimating the Recombination frequency for the PTC-Kell linkage

Summary Two data sets are analyzed for linkage between the PTC and Kell blood group loci. The original report of close linkage for these loci was that of Conneally et al. (1976), where the maximum likelihood estimate of was 0.05. These two new data sets give a combined maximum likelihood estimate of _m=f =0.28. Estimating the recombination frequency for the sexes separately gave _m =0.29, _f =0.23. The combined maximum likelihood estimate over all published data sets including this report is _m=f =0.14, _max=8.94. There is statistically significant evidence of heterogeneity among the published studies.     

Optimum inactivation dose and indices of radiation response based on the linear quadratic survival equation

For typical tumor-cell dose-response curves, the efficiency ratio, i.e., the ratio between the fraction of cells killed and the radiation dose administered, is a continuously decreasing function of dose. However, if the survival curve is sufficiently shouldered, this ratio has a maximum value at a dose greater than zero. In radiotherapy, one possible criterion for the ideal dose per session is a high value of the efficiency ratio for the targeted cells, but a low value for surrounding healthy cells. Efficiency ratios can be derived from dose-response relationships. Any linear quadratic dose-survival curve of the formS = exp (– D + D ²) can be completely described by two parameters,s and, where and . The former parameter is an index of radiosensitivitiy, and the latter is an index of curve shape. Using these indices, the ratio of fraction of inactivated cells to dose can be calculated and its maximum, as dose varies, determined. For values of greater than 0.55, this ratio has a maximum when the dose is approximately 1/s. However, for values of less than 0.4, this ratio is greatest when the dose is zero. Since varies widely among different cell lines, it may be possible to optimize radiotherapeutic dose-fractionation regimes using these indices. The parameterization of dose-survivial relationships in terms ofs and also simplifies conceptualization of the survival-curve characteristics. Both the mean inactivation dose and the dose required to reduce survival to 1/e are approximately equal to 1/s. The fraction surviving a dose of 1/s falls between exp(–1) and exp(–3/4). This dose is approximately equal to the mean inactivation dose; for human tumor cells, its mean is approximately 2 Gy. The dose corresponding to a fraction surviving equal to 1/e, or ln(S)= –1, falls between 1/s and 5/4s for all non-negative values of and.     

Consequences of skin color and fur properties for solar heat gain and ultraviolet irradiance in two mammals

Summary In animals with fur or feather coats, heat gain from solar radiation is a function of coat optical, structural, and insulative characteristics, as well as skin color and the optical properties of individual hairs or feathers. In this analysis, I explore the roles of these factors in determining solar heat gain in two desert rodents (the Harris antelope squirrel,Ammospermophilus harrisi, and the round-tailed ground squirrel,Spermophilus tereticaudus). Both species are characterized by black dorsal skin, though they contrast markedly in their general coat thickness and structure. Results demonstrate that changes in coat structure and hair optics can produce differences of up to 40% in solar heat gain between animals of similar color. This analysis also confirms that the model of Walsberg et al. (1978) accurately predicts radiative heat loads within about 5% in most cases. Simulations using this model indicate that dark skin coloration increases solar heat gain by 5%. However, dark skin significantly reduces ultraviolet transmission to levels about one-sixth of those of the lighter ventral skin.Symbols and abbreviations: (unless noted, all radiation relations refer to total solar radiation) absorptivity of individual hairs - _C absorptivity of the coat - backward scattering coefficient [reflectivity] of individual hairs - _C reflectivity of coat - _S reflectivity of skin - forward scattering coefficient [transmissivity] of individual hairs - _C transmissivity of coat - _S transmissivity of the skin - transmissivity of the coat and skin - transmissivity of the coat to ultraviolet radiation - _S transmissivity of the skin to ultraviolet radiation - [(1 – )² – ²] - h _C coat thermal conductance [W/m²-°C] - h _E coat surface-to-environment thermal conductance [W/m²-°C] - I probability per unit coat depth that a ray will be intercepted by a hair [m^–1] - K volumetric specific heat of air at 20°C [1200 J/m³-°C] - l _C coat thickness [m] - l _H hair length [m] - d hair diameter [m] - n hair density per unit skin area (m^–2] - Q _ABS heat load on animal's skin from solar radiation [W/m²] - Q _I solar irradiance at coat surface [W/m²] - r _E external resistance to convective and radiative heat transfer [s/m] - r _C coat thermal resistance [s/m]     

Toward a gibbsian approach to the problems of growth and cancer

Summary Certain sections ofJosiah Willard Gibbs's thermodynamics papers might be applicable to biological equilibrium and growth, normal or abnormal.Gibbs added terms _i dm _i to the differential of the internal energy d=td–pd, (t=temperature,p=pressure,=entropy,=volume) where is the potential of substancem _i , to provide for chemical as well as thermal and mechanical equilibrium. In this article a further generalization is suggested, to include biological equilibrium by adding to de terms of the form GdN, the variableN being the number of cells, where is a growth potential that measures exactly the resistance toward spontaneous growth. The functionG, like _i is intensive in nature (i.e. depends on intensive variables only) except for a conversion factor ,M=m _i , affording possible insight into why incipient abnormal growth is often independent of the number of cells. Useful applications might follow from identities between , or and or respectively. The following new function is studied, , a natural generalization of theGibbs free energy function , the possibility of measuring it electrically, and comparison of its role with that of for the possible experimental determination ofG. Gibbs's necessary and sufficient conditions for heterogeneous equilibrium ofn components inm phases are generalized and also modified to include broader restraining conditions like ,j=1,f,n, the > being characteristic of only living cellular phases. Careful appraisal of the term biological stability is followed by new criteria for stability, instability, and limits of stability, (neutral equilibrium) in terms of derivatives ofG, with possible medical applications. Three different sections of Gibbs's works tend to indicate that, for a biological phase, lower pressure usually increases its stability. The equation , where =surface tension,p, p = pressures,r, r=radii of curvature, is applied to possible control of tissue growth at interfaces. Methods of altering the equilibrum between three phasesA, B, C by varying the interfacial tensions _AB , _BC , _AC , using relations like _AB < _AC + _BC for stability of theA, B interface, suggest different means for shifting biological equilibrium between normal and abnormal cells through the introduction of new third phases at the interface. Various devices are mentioned for possible control of growth through proper channeling of surface or other equivalent forms of energy.     

Effects of supplied cinnamic acids and biosynthetic intermediates on the anthocyanins accumulated by wild carrot suspension cultures

Anthocyanins isolated and characterized from the wild carrot suspension cultures used here were 3-O--D-glucopyranosyl-(16)-[-D-xylopyranosyl-(12)-]-D<-galactopyranosylcyanidin (1), 3-O-[-D- xylopyranosyl-(12)--D-galactopyranosyl]cyanidin (2), 3-O-(6-O-sinapoyl)--D-glucopyranosyl-(16)-[-D- xylopyranosyl-(12)-]-D-galactopyranos ylcyanidin (3), 3-O-(6-O-feruoyl)--D-glucopyranosyl-(16)-[- D-xylopyranosyl-(12)-]-D-galactopyranosylcyanidin (4), 3-O-(6-O-coumaroyl)--D-glucopyranosyl-(16)- [-D-xylopyranosyl-(12)-]-D-galactopyrano sylcyanidin (5), 3-O-[6-O-(3,4,5-trimethoxycinnamoyl)]-- D-glucopyranosyl-(16)-[-D-xylopyranosyl-(12)-]-D-galactopyranosylcyanidin (6), 3-O-[6-O-(3,4-dime- thoxycinnamoyl)]--D-glucopyranosyl-(16)-[-D-xylopyranosyl-(12)-]-D-galactopyranosylcyanidin (7), 3-O-[(6-O-sinapoyl)--D-glucopyranosyl-(16)--D-galactopyranosyl]cyanidin (8), and 3-O-(-D-galactopyranosyl)cyanidin (9). Except when cinnamic acids were provided in the culture medium, the major anthocyanin present in the two clones examined was 2. When the naturally occurring and some non-naturally occurring cinnamic acids were provided individually in the medium, 1 and 2 were minor components and the anthocyanin acylated with the supplied cinnamic acid, namely 3, 4, 5, 6, or 7 was the major anthocyanin present in the tissue. When caffeic acid was provided the major anthocyanin in the tissue was 4, thereby suggesting that the caffeic acid was methylated before its use in anthocyanin biosynthesis. Other cinnamic acids supplied had limited effects on the anthocyanins accumulated and appeared not to result in the accumulation of new anthocyanins by the tissue. Thus the tissue can use some but not all analogues of sinapic acid to acylate anthocyanins. Additional anthocyanins were detected in extracts of the wild carrot tissue cultures using mass spectrometry (both MS/MS and HPLC/MS). The additional compounds detected have also been found in cultures of black carrot, an Afghan cultivar of Daucus carota ssp. sativa and the flowers of wild carrot giving no evidence for qualitative differences in the anthocyanins synthesized by subspecies, cell cultures from subspecies, or clones from cell cultures. There are major differences in the amounts of individual anthocyanins found in cultures from different subspecies and in different clones from cell cultures. Here anthocyanins without acyl groups were usually found in the tissues and their accumulation is discussed. On the basis of the structures of the isolated anthocyanins, a likely pathway from cyanidin to the accumulated anthocyanins is proposed and discussed.Abbreviations Sin sinapoyl - Fer feruoyl - 4-Coum. 4-coumaroyl - 3,4-MeO₂Cin 3,4-dimethoxyeinnamoyl - 3,4,5-MeO₃Cin 3,4,5-trimethoxycinnamoyl - Cya cyanidin     

Oxygen mass transfer in a bubble column bioreactor containing lysed yeast suspensions

Summary Liquid-phase volumetric oxygen transfer coefficients were evaluated in a bubble column containing yeast suspensions, using the instationary oxygen absorption method and a polarographic oxygen electrode. The electrode time lag was found to be independent of both the system studied and the operating conditions. The volumetric oxygen mass transfer coefficients k _L a could be reasonably predicted by calculating k _L from the equation derived by Bhavaraju et al. or the empirical equation of Calderbank and Moo-Young and a from the experimental gas hold-up values.Nomenclature a Exponent in Eq.6 or specific gas-liquid interfacial area based on reactor volume m - b Exponent in Eq. 6 - C Constant in Eq 6 or oxygen concentration in the liquid phase g/ml - C ^* Equilibrium oxygen concentration g/ml - C ₀ Oxygen concentration in the liquid phase at t=0 g/ml - C _E Oxygen concentration as determined by the polarographic electrode g/ml - D _B Bubble equivalent diameter mm - D _l Oxygen diffusivity in the liquid phase m²/s - g Acceleration of gravity m/s² - K Consistency index Pasⁿ - K _L Liquid-phase mass transfer coefficient m/s - n Power law exponent - Pe _sw Peclet number based on bubble swarm velocity - S _C Schmidt number - Sh Sherwood number - i Time s - U _B Bubble rise velocity in infinite medium m/s - U _g Superficial air velocity based on column cross-sectional area m/s - U _sw Bubble swarm velocity defined by Eq.15 m/s - Y _MSW Mass transfer coeficient correction factor for mobile interfaces in pseudo-plastic fluids Eq. 7 - Y _MSW Mass transfer coefficient correction factor for immobile interface in pseudo-plastic fluids Eq. 8 Greek letters _l Density of liquid g/ml - _sus Density of unaerated suspension g/ml - _{wet cell} Density of yeast wet cells g/ml - _l Viscosity of the liquid Pas - _app Apparent viscosity of power law fluid Pas - _E Electrode time lag s - _l Time lag due to resistance of the gas-liquid interface s - _g Gas hold-up, volume fraction occupied by the gas phase - _l Liquid hold-up - _c Wet cell volume fraction