Dependency as a measure to estimate the order and the values of Markov processes

To evaluate the order and the values of Markov properties of the time series of events, we have proposed a statistical measure dependency:D _m = (H ₀ –H _m )/H ₀ , whereH ₀ andH _m are Shannon's entropy and them-th order conditional entropy, respectively. It is indicated that is a better point estimator ofD _m, giving a total value of them-th order Markov process. Here and are the estimate ofD _m and the arithmetic mean of when them-th order shuffling is made many times for a given observed series, respectively. The value represents Markov value of the orderm. Under the assumption that the series has continuous variables and the normal distribution, simplified dependency is defined by, where |S _m | is the determinant of serial correlation coefficients. It is shown that is practically useful for the estimation of the order and the values of Markov processes with small sample size. It is also indicated that analysis is basically equivalent to the least mean-square analysis of autoregressive models.     

Time-resolved fluorescence of conifers exposed to environmental pollutants

Summary With regard to an early diagnosis of defects within the photosynthetic system of conifers by air pollutants, we measured the chlorophyll fluorescence from microscopic parts of individual pine and spruce needles. In particular, different spruces had been exposed before to well-defined doses and concentrations of ozone and SO₂. In addition to spectral distributions and time courses of fluorescence intensity, fluorescence lifetimes were detected after picosecond laser pulse excitation. Time constants of ₁ = (0.10 ± 0.02) ns and ₂ = (0.50 ± 0.10) ns were measured for intact photosynthesis; an increase of ₂ and a further time constant ₃ = (2.5 ± 0.5) ns were found, if defects within the photosynthetic system occurred. Most significant defects were so far measured after exposition to high ozone doses during longer time periods.Paper presented at the Conference on Chlorophyll Fluorescence in Ecology, February 20–21, 1986, Hannover, FRG     

Passive cable properties of locust ocellar L-neurons

Summary The passive electrical cable properties of ocellar L-neurons were determined by applying current steps and recording the voltage transients using a two-electrode intracellular current clamp system. Morphological data were obtained following intracellular staining with Lucifer yellow.Two groups of neurons were distinguished physiologically. In the first group both the membrane time constant _m and the first equalizing time constant ₁ could be determined. In the second group only _m was measurable. The ratio of the physiological groups was equal to the ratio of the morphological types ML:(M1 plus M2) in the median ocellar nerve. Thus the first group probably consists of ML-type L-neurons. The passive cable properties of this group were calculated by combining the physiological and morphological data. The following values were obtained: electrotonic lengthL=1.35; membrane time constant _m =7.6 ms; length constant =0.22 cm; membrane resistivityR _m=2.0 · 10³ · cm²; membrane capacitanceC _m=3.8 F · cm^–2; intracellular resistivityR _i=24 · cm. Evidence is presented that the membrane parameters of the other types of L-neurons have the same values. The results are discussed with special reference to transmission in the ocellar system.     

Application of the Criterion of Biological Time (τ n /τ0) to the Studies of Embryogenesis in Birds

It was shown on the example of chick embryo that the number ₀ ( _n /₀) can be recommended as a measure of biological time and, for this purpose, the duration of the minimal mitotic cycle during synchronous cleavage divisions should be determined (in minutes) in various avian species. Based on the preliminary data, one can propose the comparability and similarity of the temporal programs of gastrulation and somitogenesis in the chick embryo and embryos of some fish and amphibians.     

Malate degradation by Schizosaccharomyces yeasts included in alginate beads

Schizosaccharomyces yeasts can be used for deacidification of grape musts. To this aim, we studied malic acid degradation by yeasts included in double layer alginate beads in a bubble column reactor. Use of immobilized micro-organisms allowed a continuous process with high dilution rates giving a deacidification capacity of 0.032 g of malate/hour/dm³/g of beads. The pneumatic agitation was very convenient in this case.List of Symbols D h^–1 Dilution rate for continuous culture - h Residence time for continuous culture - dM/dt kg/(m³ · h) Rate of degradation of malic acid - dS/dt kg/(m³ · h) Rate of consumption of glucose - _max h^–1 Maximal specific rate of growth     

Involvement of apamin-sensitive SK channels in spike frequency adaptation of neurons in nucleus tractus solitarii of the rat

We delineated the role of Ca²⁺-activated K⁺ channels in the phenomenon of spike frequency adaptation (SFA) exhibited by neurons in the caudal region of nucleus tractus solitarius (cNTS) using intracellular recording coupled with the current-clamp technique in rat brain slices. Intracellular injection of a constant depolarizing current evoked a train of action potentials whose discharge frequency declined rapidly to a lower steady-state level of irregular discharges. This manifested phenomenon of SFA was found to be related to extracellular Ca²⁺. Low Ca²⁺ (0.25 mM) or Cd²⁺ (0.5 mM) in the perfusing medium resulted in a significant increase in the adaptation time constant (_adap) and an appreciable reduction in the percentage adaptation of spike frequency (F_adap). In addition, the evoked discharges were converted from an irregular to a regular pattern, accompanied by a profound increase in mean firing rate. Intriguingly, similar alterations in _adap, F_adap, discharge pattern and discharge rate were elicited by apamin (1 µM), a selective blocker for small-conductance Ca²⁺-activated K⁺ (SK) channels. On the other hand, charybdotoxin (0.1 µM), a selective blocker for large-conductance Ca²⁺-activated K⁺ channels, was ineffective. Our results suggest that SK channels of cNTS neurons may subserve the generation of both SFA and irregular discharge patterns displayed by action potentials evoked with a prolonged depolarizing current.     

Interaction among anion,cation and glucose transport proteins in the human red cell

Summary The time course of binding of the fluorescent stilbene anion exchange inhibitor, DBDS (4,4-dibenzamido-2,2-stilbene disulfonate), to band 3 can be measured by the stopped-flow method. We have previously used the reaction time constant, _DBDS, to obtain the kinetic constants for binding and, thus, to report on the conformational state of the band 3 binding site. To validate the method, we have now shown that the ID₅₀ (0.3±0.1 m) for H₂-DIDS (4,4-diisothiocyano-2,2-dihydrostilbene disulfonate) inhibition of _DBDS is virtually the same as the ID₅₀ (0.47±0.04 m) for H₂-DIDS inhibition of red cell Cl^– flux, thus relating _DBDS directly to band 3 anion exchange. The specific glucose transport inhibitor, cytochalasin B, causes significant changes in _DBDS, which can be reversed with intracellular, but not extracellular,d-glucose. ID₅₀ for cytochalasin B modulation of _DBDS is 0.1±0.2 m in good agreement withK _D =0.06±0.005 m for cytochalasin B binding to the glucose transport protein. These experiments suggest that the glucose transport protein is either adjacent to band 3, or linked to it through a mechanism, which can transmit conformational information. Ouabain (0.1 m), the specific inhibitor of red cell Na⁺,K⁺-ATPase, increases red cell Cl^– exchange flux in red cells by a factor of about two. This interaction indicates that the Na⁺,K⁺-ATPase, like the glucose transport protein, is either in contact with, or closely linked to, band 3. These results would be consistent with a transport proteincomplex, centered on band 3, and responsible for the entire transport process, not only the provision of metabolic energy, but also the actual carriage of the cations and anions themselves.     

Gas exchange strategy in the Nile crocodile: a morphometric study

Summary The respiratory surface area (S_AR) per kilogram body mass (M_B), the harmonic mean thickness of the air-blood barrier (_htR) in the gas exchange tissue, and the anatomical diffusion factor (ADF=S_AR/_htR per M_B) were calculated for four juvenile Nile crocodiles. The ADF of three small specimens (mean M_B=3.59 kg) was 625 cm²·m^–1·kg^–1. The values varied considerably among individuals and were similar to that of a 5.68-kg specimen (593 cm²·m^–1·kg^–1). Only 9% of the ADF is located in the anterior third of the lung, which because of its conical shape makes up only 14 percent of the total lung volume. Particularly in the middle third of the lung, the proximal region near the intrapulmonary bronchus displays a greater ratio of respiratory/non-respiratory surface areas than do more distally located sampling sites. The _htR is also significantly smaller proximally than distally. The cumulative ADF per unit M_B is greater than that previously reported for this species on the basis of overall estimates of S_AR and _htR, but is still less than that of lizards and testudinids. The disposition of ADF between distal air storage region and the intrapulmonary bronchus is consistent with a bidirectional cross-current gas exchange model.Abbreviations ADF anatomical diffusion factor - %AR percent of S_A included in the effective respiratory zone - M _B body mass - NVP non-ventilatory period - %P percent of total lung volume containing parenchyma - S _A total surface area of intrapulmonary septa - S _ANR that portion ofS _A lying out the effective respiratory zone - S _V surface-to-volume ratio in the parenchyma - _htR harmonic mean thickness of the air-blood tissue barrier within the respiratory zone - V _P parenchymal volume - VP ventilatory period     

A simple apparatus for generating stretched polyacrylamide gels, yielding uniform alignment of proteins and detergent micelles*

Compressed and stretched polyacrylamide hydrogels previously have been shown to offer a robust method for aligning proteins. A simple, funnel-like apparatus is described for generating uniformly stretched hydrogels. For prolate-shaped proteins, gels stretched in the direction of the magnetic field yield two-fold larger alignment than gels compressed to the same aspect ratio in this direction. Empirically, protein alignment is found to be proportional to (c–2.3)² [(d_o/d_N)³-1], where d_o and d_N are the diameters of the cylindrical gels before and after stretching, respectively, and c is the polyacrylamide weight fraction in percent. Low gel densities, in the 4–7% range, are found to have minimal effects on macromolecular rotational correlation times, _c, and no effect of the compression ratio on _c could be discerned over the range studied (d_o/d_N le1.4). Application is demonstrated for a sample containing the first Ig-binding domain of protein G, and for a detergent-solubilized peptide.     

Sodium channel opening as a precursor to inactivation

The time constant of the process producing the delay in Na inactivation development as determined by the two pulse method (_delay) was extracted and compared to that of the slowest Na activation process ₃ for the I _Na during the conditioning pulse of that same determination. _delay and two pulse inactivation _c values were computer generated using a nonlinear least squares algorithm. _h and single pulse inactivation _h values were independently generated for each determination also with the aid of the computer using the same non-linear least squares algorithm. In one determination at 2 mV, _c was 4.68 and _delay 0.494 ms while _h was 4.70 and ₃ 0.491 ms for a _c/_h of 0.996 and a _delay/₃ of 1.006. Mean _delay/₃ from five determinations in four axons, both Cs and K perfused, and spanning a potential range of-27 to 2mV was 1.068. The precursor process to inactivation is channel opening. Some fraction of channels presumably inactivate via another route where prior channel opening is not required.     

An empirical relationship between rotational correlation time and solvent accessible surface area

Structure–dynamics interrelationships are important in understanding protein function. We have explored the empirical relationship between rotational correlation times (_c and the solvent accessible surface areas (SASA) of 75 proteins with known structures. The theoretical correlation between SASA and _c through the equation SASA = K_rc ^(2/3) is also considered. SASA was determined from the structure, _c ^calc was determined from diffusion tensor calculations, and _c ^expt was determined from NMR backbone¹³ C or ¹⁵N relaxation rate measurements. The theoretical and experimental values of _c correlate with SASA with regression analyses values of K_r as 1696 and 1896 m²s^-(2/3), respectively, and with corresponding correlation coefficients of 0.92 and 0.70.     

Comparison of 15N- and 13C-determined parameters of mobility in melittin

Backbone and tryptophan side-chain mobilities in the 26-residue, cytolytic peptide melittin (MLT) were investigated by ¹⁵N and ¹³C NMR. Specifically, inverse-detected ¹⁵N T₁ and steady-state NOE measurements were made at 30 and 51 MHz on MLT at 22 °C enriched with ¹⁵N at six amide positions and in the Trp¹⁹ side chain. Both the disordered MLT monomer (1.2 mM peptide at pH 3.6 in neat water) and -helical MLT tetramer (4.0 mM peptide at pH 5.2 in 150 mM phosphate buffer) were examined. The relaxation data were analyzed in terms of the Lipari and Szabo model-free formalism with three parameters: _m, the correlation time for the overall rotation; S², a site-specific order parameter which is a measure of the amplitude of the internal motion; and _e, a local, effective correlation time of the internal motion. A comparison was made of motional parameters from the ¹⁵N measurements and from ¹³C measurements on MLT, the latter having been made here and previously [Kemple et al. (1997) Biochemistry, 36, 1678–1688]. _m and _e values were consistent from data on the two nuclei. In the MLT monomer, S² values for the backbone N-H and C-H vectors in the same residue were similar in value but in the tetramer the N-H order parameters were about 0.2 units larger than the C-H order parameters. The Trp side-chain N-H and C-H order parameters, and _e values were generally similar in both the monomer and tetramer. Implications of these results regarding the dynamics of MLT are examined.     

Kinetics of transient pump currents generated by the (H,K)-ATPase after an ATP concentration jump

Summary (H,K)-ATPase containing membranes from hog stomach were attached to black lipid membranes. Currents induced by an ATP concentration jump were recorded and analyzed. A sum of three exponentials ( ₁ ^-1 400 sec^–1, ₂ ^-1 100 sec^–1, ₃ ^-1 10 sec^–1; T = 300 K, pH 6, MgCl₂ 3 mm, no K⁺) was fitted to the transient signal. The dependence of the resulting time constants and the peak current on electrolyte composition, ATP conversion rate, temperature, and membrane conductivity was recorded. The results are consistent with a reaction scheme similar to that proposed by Albers and Post for the NaK-ATPase. Based on this model the following assignments were made: ₂ corresponds to ATP binding and exchange with caged ATP. ₁ describes the phosphorylation reaction E₁ · ATP E₁P. The third, slowest time constant ₃ is tentatively assigned to the E₁P E₂P transition. This is the first electrogenic step and is accelerated at high pH and by ATP via a low affinity binding site. The second electrogenic step is the transition from E₂K to E₁H. The E₂K E₁H equilibrium is influenced by potassium with an apparent K _0.5 of 3 mm and by the pH. Low pH and low potassium concentration stabilize the E₁ conformation.The authors wish to thank Dr. E. Grell and Mr. G. Schimmack. MPI Frankfurt, for synthesizing caged ATP, Mrs. S. Meister, Hoechst AG Frankfurt, for valuable help to prepare the (H,K)-ATPase, and Dr. W. Haase, MPI Frankfurt, for electron microscope pictures. (H,K)-ATPase for preliminary experiments was provided by Dr. W. Beil, Medizinische Hochschule Hannover, Dr. H. Swarts, University of Nijmegen, and Dr. G. Metzger, Hoechst AG Frankfurt. The work was supported by the Deutsche Forschungsgemeinschaft (SFB 169).     

Apparent yield stress of xanthan solutions and broths

Apparent yield stress is a very useful rheological property which is important in determining the extent of mixing in xanthan fermentations as well as the suspending ability of the gum solutions. Using a previously developed stress relaxation technique, three commercial products, one home-made product and one dehydrated-reconstituted fermentation broth (DRFB) were characterized in terms of the apparent yield stress _y of solutions containing different polymer concentrations and when mono and divalent salts or sucrose were added and also when exposing the samples to heat treatment in the case of DRFB. Sodium, potassium, calcium, magnesium, acetate, pyruvate, the mean molecular weight (MMW) and the molecular weight distribution (MWD) were determined. Although the four products showed differences in their chemical characteristics, the pyruvic acid content and the mean molecular weight played the main role in determining the yield stress patterns. With no salt added, the slope of the _y vs gum concentration plot was a strong and inverse function of the pyruvate content. With NaCl 0.5%, the mentioned slope correlated linearly with the MMW. The three commercial xanthans showed very similar MWD. Xanthan broths showed an exponential, rather than a linear (as it was the case for end-products) function of _y in terms of xanthan concentration. No significative differences were found in _y depending on the type of salt. Sucrose decreased _y and this effect was more pronounced in DRFB than in a solution of a commercial xanthan.This work was supported in part by CONACyT (grant 1020-N9111). We are grateful to S. Rodríguez for the atomic absorption determinations. We thank G. Araiza for some _y measurements and N. Zambrano for helping us with the pyruvate and acetate determinations. We especially thank L. Güereca for his valuable assistance and advise in developing the GPC technique and Prof. A. W. Nienow (University of Birmingham, U.K.) for kindly allowing us to use the Contraves 30 rheometer for the MMW estimation.     

Photocurrent kinetics of purple-membrane sheets bound to planar bilayer membranes

Summary The kinetics of light-driven proton transport by bacteriorhodopsin has been studied in a model system consisting of a planar lipid bilayer membrane to which purple membrane fragments have been attached. After excitation with a 10-nsec laser flash a fast negative current-transient occurs, followed by a positive transient which decays to zero. The time course of the photocurrent may be represented by a sum of four exponentials with time constants ₁= 1.2sec, ₂= 17sec, ₄= 57sec, ₁= 950sec (at 25°C). In a D₂O medium ₂ and ₃ are increased by a factor of 2.6 and 2.9, respectively, whereas ₁ remains unaffected. The observed components of the photocurrent can be correlated to photochemical reaction steps inferred from flash-photometric experiments on the basis of the observed time constants, the activation energies, and the effects of pH and D₂O. From the photocurrent signals information may be obtained on the magnitude of the charge displacement associated with the elementary transitions of the bacteriorhodopsin molecule.     

Mercuric(II) chloride modulates single-channel properties of carbachol-activated Cl− channels in cultured neurons ofAplysia californica

Summary 1. The effect of mercuric(II) chloride on kinetic parameters of carbacholactivated single chloride channels were studied in cultured neurons of the marinemollusk, Aplysia californica.2. Single neurons ofAplysia were cultured in L-15 medium containing 1 mM -d-xyloside, which improved the success rate for gigaseal formation by 46%. Carbachol-activated single chloride channels were recorded in the cell-attached patch clamp configuration. Recordings with control solution (1 µM carbachol) and with test solution (1 µM carbachol +1 µM HgCl₂) were performed successively on the same neuron.3. In both the control and the test solution the open and closed time distributions were fitted with a double-exponential function. However, kinetic analysis revealed that Hg²⁺ caused a significant reduction of the mean closed time (10.37±1.08 vs. 3.32±0.02 msec) and of the second time constant ₂ of the closed time distribution (2.09±0.05 vs. 0.66±0.5 msec). The reduction of ₂, i.e., fewer events in the longer closed state under the action of Hg²⁺, may be the physical cause for the reduction of the mean closed time and thus underlies the increased open probabilityp ₀ (0.13±0.01 vs. 0.29±0.01 msec) of carbachol-activated chloride channels.4. Inorganic Hg²⁺ affects the acetylcholine receptor at lower concentrations than previously reported.     

Dependency representing Markov properties of nonstationary spike trains recorded from the cat's optic tract fibers

The order and the values of Markov properties of nonstationary stochastic processes are inferred by the use of them-th order Markov value and simplified dependency, respectively: and HereK=0.5log₂ e, and is the correlation coefficient determinant obtained from the ensemble averages of sample records. When an observed value is greater than or equal to the critical value,, the null hypothesis of the (m-1)th order,, is rejected at the level of significance . Here ₁ ² () is the chi-square value with one degree of freedom at andN is sample size. With these statistics it was shown that the order and the values of Markov properties of spike trains of optic tractX- andY-fibers became higher and larger, respectively, after the light spot presentation; and that the values due to negative correlation came to increase and returned to the maintained level earlier inY-fibers than inX-fibers, while the maximum values forX-fibers continued to the light off. It is discussed that Markov properties of spike trains of optic tract fibers in the visual pathway seem to constitute a significant component of the neural information code.     

Holling's “hungry mantid” model for the invertebrate functional response considered as a Markov process. Part I: The full model and some of its limits

In this paper we give an analytical reformulation of Holling's (1966) simulation model for invertebrate predatory behaviour. To this end we represent a population of predators as a frequency distribution over a space of (physiological) states. The functional response of a predator is calculated from the (stable) equilibrium distribution of its state as a function of prey density.Starting from the general model various other models are obtained by limit processes, some of them new and some of them old. The more interesting of which will be studied in further papers in this series.List of Notation a rate constant of digestion - b maximum of rate constant of prey encounter in the mantid - b maximum pursuit duration in the mantid (_p(0)) - c satiation threshold for search - c satiation threshold for pursuit in the mantid: c=c(b-D_s/v)/b - D _m maximum sighting distance - D _p pursuit distance - D _s strike distance - expectation operator - f, f ₀ rate of change of satiation during search - f ₁ rate of change of satiation during prey handling - F functional response: number of prey eaten per unit of time by one predator - g rate constant of effective prey encounter in the gobbler and sucker - g₀ rate constant of prey encounter - g₁ probability of no prey loss from pursuit - g₂ probability of no prey escaping during pursuit - H Holling secretary correction factor in the sucker: fraction of the time spent searching - k _R density of R - k_T probability density of maximum prey handling time - K probability that maximum prey handling time is _e, i.e. pursuit duration is zero - K _R distribution function of R - N number of prey caught - p (marginal) density of S - p₀ density of S in search - p₁ simultaneous density of S and T - P probability - p ₁ marginal density of S in handling prey - q probability of strike success - R ratio of realized to maximum sighting distance - s, S satiation - satiation axis - t time - handling time axis - u eating speed - U homogeneous(0,1) random variable - v pursuit speed - V exponential(1) random variable - w prey weight - W exponential(_m) random variable - x prey density - ratio of maximum successful pursuit duration to meal duration (_pm/_e) - _pm - relative duration of successful pursuit (_p/_pm) - ratio of shortest to largest sighting distance - x_e - time already spent handling a prey item - rate of prey loss during prey handling - prey escape rate during pursuit - prey biomass density (xw) - , T maximum time still to be spent handling a prey item - _e meal duration - _m maximum handling time ( _e+ _p) - _p duration of successful pursuit - _pm maximum duration of successful pursuit (_p(0)) - hazard rate - _m maximum of hazard rate - scaled functional response (wF) - minimal i-state space     

Conformational dynamics of the anticodon loop in yeast tRNAPhe as sensed by the fluorescence of wybutine

Conformational and dynamic properties of the anticodon loop of yeast tRNA^Phe were investigated by analyzing the time resolved fluorescence of wybutine serving as a local structural probe adjacent to the anticodon GmAA on its 3 side. The influence of Mg²⁺, important for stabilizing the tertiary structure of tRNA, and of the complementary anticodon s²UUC of E. coli tRNA ₂ ^Glu were investigated.Fluorescence lifetimes and anisotropies were measured with ps time resolution using time correlated single photon counting and a mode locked synchronously pumped and frequency doubled dye laser as excitation source. From the analysis of lifetimes () and rotational relaxation times ( _R ) we conclude that wybutine occurs in various structural states: (i) one stacked conformation where the base has no free mobility and the only rotational motion reflects the mobility of the whole tRNA molecule (=6 ns, _R =19 ns), (ii) an unstacked conformation where the base can freely rotate (=100 ps, _R = 370 ps) and (iii) an intermediary state (=2 ns, _R = 1.6 ns).Under biological conditions, i. e. in the presence of Mg²⁺ and neutral salts, wybutine is found in a stacked and immobile state which is consistent with the crystallographic picture. In the presence of the complementary codon however, as exemplified by the E. coli-tRNA ₂ ^Glu anticodon, our analysis indicates that the codon-anticodon complex exists in an equilibrium of structural states with different rotational mobility of wybutine. The conformation with wybutine freely mobile is the predominant one and suggests that this conformation of the codon-anticodon structure differs from the canonical 3–5 stack.     

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]