Residual motion of hemoglobin-bound spin labels and protein dynamics: viscosity dependence of the rotational correlation times

The residual motion of spin labels bound to cysteine 93 and to lysines of methemoglobin has been studied by electron paramagnetic resonance spectroscopy. To separate the influences of the solvent and the protein environment of the label fluctuations, the correlation times, , were analyzed as a function of temperature for fixed solvent viscosities, . Results show that over a wide range of viscosity the dependence of on may be empirically described by a power law ^k . The exponent k depends strongly on the location of the label on the protein surface. If one regards the spin labels as artificial amino acid side chains, characteristic values of correlation times and amplitudes of the rotational motion at the surface can be given. For =1 cP and T=297 K the correlation time of the labels bound to lysines is found to be =9 · 10^–10 s and the rotational diffusion is nearly isotropic. The spin label bound to cysteine 93 occupies a protein pocket, its rotational motion is therefore restricted. The correlation time of the label motion within a limited motion cone of semi angle =30° ± 3° is found to be =1.3 · 10^–9 s for =1 cP and T=297 K.     

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.     

Growth and reproduction of the Nile perch,Lates niloticus,an introduced predator,in the Nyanza Gulf,Lake Victoria,East Africa

Synopsis Length-frequency data suggest Nile perch, Lates niloticus, from the Nyanza Gulf grew to a total length of 9 cm by age 118 days and 23 cm by age 287 days. A modified von Bertalanffy growth curve _t = 1.35·L(1-e^–K(t-t _o)) with the parameters L = 93.1, K = 0.272 and t_o = 0.046, is suggested to describe growth up to 5 years of age and the relationship _t = 1.35·(31.96 + 7.681t) for fish aged 6 years and above. Length-weight relationships were = 0.0234·-gt^2.74 for fish between 7 and 15.9 cm total length, = 0.0151·^2.94 for fish between 16 and 45.9 cm total length, and = 0.0023·^3.44 for fish between 46 and 120 cm total length. Male Nile perch first matured between 50 and 55 cm total length when they were probably 2 years old; female Nile perch first matured between 80 and 85 cm total length when they were probably 4 years old. Small males were common, large males were rare, with the reverse holding for females. Sex change, from male to female, is a possible explanation for this size dimorphism.     

Maxi K+ channels from the apical membranes of rabbit oviduct epithelial cells

Large conductance (approximately 210 pS), K⁺-selective channels were identified in excised, insideout patches obtained from the apical membranes of both ciliated and nonciliated epithelial cells grown as monolayers from the primary culture of rabbit oviduct. The open probability of channels showing stable gating was increased at positive membrane potentials and was sensitive to the concentration of free calcium ions at the cytosolic surface of the patch ([Ca²⁺] _i ). In these respects, the channel resembled maxi K⁺ channels found in a number of other cell types. The distributions of dwell-times in the open state were most consistently described by two exponential components. Four exponential components were fitted to the distributions of dwelltimes in the closed state. Depolarizations and [Ca²⁺] _i increases had similar effects on the distribution of open dwell-times, causing increases in the two open time constants ( _o1 and _o2) and the fraction of events accounted for by the longer component of the distribution. In contrast, calcium ions and voltage had distinct effects on the distribution of closed dwelltimes. While the three shorter closed time constants ( _c1, _c2 and _c3) were reduced by depolarizing membrane potentials, increases in [Ca²⁺] _i caused decreases in the longer time constants ( _c3 and _c4). It is concluded that oviduct large conductance Ca²⁺-activated K⁺ channels can enter at least two major open states and four closed states.A.F.J. was supported by a research fellowship from the Japan Society for the Promotion of Science and received a grant for laboratory expenses from the Ministry of Education, Science and Culture, Japan. The authors wish to thank Dr. Shigetoshi Oiki for valuable discussion of the analysis of gating kinetics and Dr. Jeman Kim (Kyoto Pharmaceutical University) for making the transmission electron micrographs.     

Existence and uniqueness of a sharp travelling wave in degenerate non-linear diffusion Fisher-KPP equations

In this paper we use a dynamical systems approach to prove the existence of a unique critical value c ^* of the speed c for which the degenerate density-dependent diffusion equation u _ct = [D(u)u _x ] _x + g(u) has: 1. no travelling wave solutions for 0 < c < c ^*, 2. a travelling wave solution u(x, t) = (x - c ^* t) of sharp type satisfying (– ) = 1, () = 0 ^*; '(^*–) = – c ^*/D'(0), '(^*+) = 0 and 3. a continuum of travelling wave solutions of monotone decreasing front type for each c > c ^*. These fronts satisfy the boundary conditions (– ) = 1, '(– ) = (+ ) = '(+ ) = 0. We illustrate our analytical results with some numerical solutions.     

Theoretical stability diagram of solvent-containing black lipid films

Recently, we have developed an analytical, semi-microscopic theory for the macroscopic behavior of a solvent-containing black lipid film subjected to an electric cross film voltage, . Here we employ the theoretical expressions derived for the disjoining pressure, _D, the film elasticity, _F, and the film tension, _F, to construct the stability diagram of the film, in the _D-. Depending on its state (_D, ), the film is stable or is prone to squeezing or bending deformations. For a monooleate film we show how the destruction of the plane film due to a periodic thickness fluctuation (squeezing) is facilitated by two mechanisms: i) lowering of _D at fixed ; ii) lowering of at fixed _D, provided that the film is in a stable state characterized by _D<–7.03×10³ dyne/cm² and >0 mV. Bending of a low tension film (single interface tension _s 0.025 dyne/cm¹) can be achieved only for >170 mV and _D > –8.7 × 10⁴ dyne/cm². Finally, we demonstrate the existence of a marginal state ( _D ⁰ , ⁰) where the film is predicted to exhibit strong fluctuations both in the squeezing and in the bending mode.     

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     

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.     

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.     

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]     

Effects of divalent cations on toad end-plate channels

Summary Miniature end-plate currents (MEPCs) and acetylcholine-induced current fluctuations were recorded in voltageclamped, glycerol-treated toad sartorius muscle fibers in control solution and in solutions with added divalent cations. In isosmotic solutions containing 20mm Ca or Mg, MEPCs had time constants of decay ( _D ) which were about 30% slower than normal. In isotonic Ca solutions (Na-free), greater increases in both _D and channel lifetime were seen; the null potential was –34 mV, and single-channel conductance decreased to approximately 5 pS. Zn or Ni, at concentrations of 0.1–5mm, were much more effective in increasing _D than Ca or Mg, although they did not greatly affect channel conductance. The normal temperature and voltage sensitivity of was not significantly altered by any of the added divalent cations. Surface potential shifts arising from screening of membrane fixed charge by divalent cations cannot entirely explain the observed increases in , especially when taken together with changes in channel conductance.     

Interrelation between HeLa-S3 cell transfection and hemolysis in red blood cell suspension using pulsed ultrasound of various duty cycles

We have studied the in vitro transfection of a plasmid DNA with the lacZ gene to HeLa-S3 cells and hemolysis in a red blood cell (RBC) suspension under pulsed ultrasound with duty cycles of 10, 20 and 30% using a digital sonifier at a frequency of 20 kHz and an intensity of 6.2 W/cm² on the surface of a horn tip. Cultured HeLa-S3 cells in suspension were exposed to pulsed ultrasound for an apparent exposure time t from 0 to 60 s. HeLa-S3 viability decreased as a single exponential function of the total exposure time t=t with a common time constant =3.8 s for three duty cycles. Transfection was evaluated by counting the number of -galactosidase(-Gal)-positive cells relative to the total number of cells. Pulsed ultrasound provided an enhanced transfer of the -Gal plasmid to HeLa-S3 cells, 3.4-fold as compared with that in the case of the control. The optimal transfection efficiencies were 0.75, 0.80 and 0.74% near t= with =10, 20 and 30%, respectively. The number ratio of -Gal-positive cells to the surviving cells after exposure increased with t according to a modified logistic equation. The degree of hemolysis also increased exponentially with t at a time constant =₀/ for the RBC suspension in physiological saline at a hematocrit concentration of 0.5% with ₀=0.9 s. Thus the total exposure time for the optimal transfection efficiency was , that is, nearly four times of ₀. Hemolysis in the RBC suspension may be a useful model for determining optimal transfection by pulsed ultrasound of various duty cycles.     

Effects of zwitterionic detergents on the electronic structure of the primary donor and the charge recombination kinetics of P+Q A − in native and mutant reaction centers from Rhodobacter sphaeroides

The effects of detergents on the electronic structure of the oxidized primary donor P⁺ and the time constant _AP of the P⁺Q _A ^– charge recombination at ambient temperatures have been investigated in native and mutant reaction centers (RCs) from Rhodobacter sphaeroides. It is shown that N-lauryl-N,N-dimethyl-3-ammonio-1-propane sulfonate (SB12) induces a transition to a second distinct conformation of the RC. In the case of the wild type and the mutant FY(M197), in which a hydrogen bond is introduced to the 2-acetyl group of the dimer half of P that is associated with the M-subunit of the RC, the conformational change causes a more asymmetric spin density distribution between the two bacteriochlorophyll moieties of P⁺ in favor of the L-half. For both types of RCs the time constant _AP depends on the SB12/RC ratio as does the position of the long-wavelength band of P, _max. The increase of _AP by 30 ms and the shift of _max from 866 nm to 851 nm are indicative for the conformational change. In addition, a smaller linear increase of _AP with increasing SB12/RC ratio is superimposed on the variation of _AP due to the conformational change. Similar effects of SB12 on the optical spectra as well as on _AP are also observed for the two heterodimer mutants HL(L173) and HL(M202), in which one of the bacteriochlorophylls of P is replaced by a bacteriopheophytin. There are no clear indications for a correlation of _AP with the localization of the positive charge in P⁺. Furthermore, it is concluded from the dependence of _AP on the SB12/RC ratio that the single-site mutations do not affect the standard free energy difference of the two conformations to a measurable extent.     

Interactions between anion exchange and other membrane proteins in rabbit kidney medullary collecting duct cells

Summary In separated outer medullary collecting duct (MCD) cells, the time course of binding of the fluorescent stilbene anion exchange inhibitor, DBDS (4,4-dibenzamido-2,2-stilbene disulfonate), to the MCD cell analog of band 3, the red blood cell (rbc) anion exchange protein, can be measured by the stopped-flow method and the reaction time constant, _DBDS, can be used to report on the conformational state of the band 3 analog. In order to validate the method we have now shown that the ID_50,DBDS,MCD (0.5±0.1 m) for the H₂-DIDS (4,4-diisothiocyano-2,2-dihydrostilbene disulfonate) inhibition of _DBDS is in agreement with the ID_50,Cl ^–,_MCD (0.94±0.07 m) for H₂-DIDS inhibition of MCD cell Cl^– flux, thus relating _DBDS directly to anion exchange. The specific cardiac glycoside cation transport inhibitor, ouabain, not only modulates DBDS binding kinetics, but also increases the time constant for Cl^– exchange by a factor of two, from _Cl=0.30±0.02 sec to 0.56±0.06 sec (30mm NaHCO₃). The ID_50,DBDS,MCD for the ouabain effect on DBDS binding kinetics is 0.003±0.001 m, so that binding is about an order of magnitude tighter than that for inhibition of rbc K⁺ flux (K _I,K ⁺,_rbc=0.017 m). These experiments indicate that the Na⁺,K^–-ATPase, required to maintain cation gradients across the MCD cell membrane, is close enough to the band 3 analog that conformational information can be exchanged. Cytochalasin E (CE), which binds to the spectrin/actin complex in rbc and other cells, modulates DBDS binding kinetics with a physiological ID_50,DBDS,MCD (0.076±0.005 m); 2 m CE also more than doubles the Cl^– exchange time constant from 0.20±0.04 sec to 0.50±0.08 sec (30mm NaHCO₃). These experiments indicate that conformational information can also be exchanged between the MCD cell band 3 analog and the MCD cell cytoskeleton.     

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.     

Carotenogenesis and asparagine inLeptosphaeria michotii (West) Sacc.

Summary InLeptosphaeria michotii U¹⁴C-asparagine was incorporated into the coloured carotenoids, the synthesis of which carried on till day 8. The pigment turnover, obvious from day 6, was not modified by the light conditions used.Nicotine (0.25 to 4.5 mM) has been used to study carotenogenesis and sporulation rhythm regulation inL. michotii fed with asparagine 2.6 mM. Control cultures contained in darkness -carotene only and in continuous light -carotene 98% and lycopene 2%. The mold receiving nicotine 0.25 mM in darkness contained -carotene 98% and lycopene 2%. For nicotine 0.5 mM and upwards -carotene decreased, lycopene increased and -carotene appeared, the balance between these pigments also depending on the light conditions. Whereas period length () of the sporulation rhythm increased from one cycle to the next in control cultures in darkness, it was stabilized either by continuous light ( 27 h) or by nicotine 0.25 mM ( 30 h). For nicotine 0.5 mM sporulation was uniform in darkness or in light.     

Permeance of Cs+ and Rb+ through the inwardly rectifying K+ channel in guinea pig ventricular myocytes

Summary Inward currents carried by external Cs, Rb, NH₄ and K through theI _K1 channel were studied using a whole-cell voltage clamp technique. Cs, NH₄, and Rb currents could be recorded negative to –40 mV following depolarizing prepulses (0 mV and 200–1000 msec in duration). The current activation displayed an instantaneous component followed by a monoexponential increase () to a peak amplitude. Subsequent inactivation was fit by a single exponential, _i. With hyperpolarization, and _i decreasede-fold per 36 and 25 mV, respectively. In Ca-free external solutions (pipette [Mg]0.3mm), inactivation was absent, consistent with the hypothesis that inactivation represents time- and voltage-dependent block of Cs, NH₄, and Rb currents by external Ca. The inactivation and degree of steady-state block was greatest when Cs was the charge carrier, followed by NH₄, and then Rb. K currents, however, did not inactivate in the presence of Ca. Na and Li did not carry any significant current within the resolution of our recordings. Comparison ofpeak inward current ratios (I _x/I_K) as an index of permeability revealed a higher permeance of Cs (0.15), NH₄ (0.30), and Rb (0.51) relative to K (1.0) than that obtained by comparing thesteady-state current ratios (CsNH₄RbK0.010.060.211.0). At any given potential, was smaller the more permeant the cation. In the absence of depolarizing prepulses, the amplitude of was reduced. Divalent-free solutions did not significantly affect activatio in the presence of 0.3mm pipette [Mg]. When pipette [Mg] was buffered to 50 m, however, removal of external Ca and Mg lead to a four- to fivefold increase in Cs currents and loss of both time-dependent activation and inactivation (reversible upon repletion of external Ca).These results suggest that (i) permeability ratios forI _K1 should account for differences in the degree to which monovalent currents are blocked by extracellular Ca and (ii) extracellular or intracellular divalent cations contribute to the slow phase of activation which may represent either (a) the actual rate of Mg or Ca extrusion from the channel into the cell, a process which may be enhanced by repulsive interaction with the incoming permeant monovalent cation or (b) an intrinsic gating process that is strongly modulated by the permeant monovalent ion and divalent cations.     

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.     

Changes of fluorescence lifetime and rotational correlation time of bovine serum albumin labeled with 1-dimethylaminonaphthalene-5-sulfonyl chloride in guanidine and thermal denaturations

The nanosecond fluorescence depolarization method was applied to measure the fluorescence lifetime () and the rotational correlation time () of bovine serum albumin (BSA) labeled with 1-dimethylaminonaphthalene-5-sulfonyl chloride (dansyl-Cl). Changes of and of dansyl BSA in the guanidine denaturation and in the thermal denaturation were examined. In parallel, the secondary structural change of dansyl BSA was followed by circular dichroism measurements. The magnitude of was almost unchanged between 1 and 2 M guanidine, where the secondary structure of the protein was predominantly disrupted; whereas that of began to increase before the disruption of secondary structure in the guanidine denaturation. In the thermal denaturation, in contrast, changes of both and occurred in a temperature range where the secondary structure was predominantly disrupted. The volume of equivalent sphere (V _e ) and the axial ratio () for the BSA were 3.6–3.8×10^–19 cm³ and 3.6 at 2M guanidine as against 2.1×10^–19 cm³ and 2.2 in the absence of guanidine (25°C), respectively. The magnitudes ofV _e and were 4.9×10^–19 cm³ and 4.5 at 65°C, respectively. Although the secondary structural change of dansyl BSA was irreversible in the thermal denaturation,V _e and were reversible.     

The quantitative analysis of chromosome pairing and chiasma formation based on the relative frequencies of M I configurations

Whilst reliable estimates of chiasma frequencies can usually not be obtained, the probability (b) of a chromosome arm to be bound by at least one chiasma can often be determined. In the absence of interference this probability equals (1–e ^–2), where 2 is the average chiasma frequency of the chromosome arm and the average crossover frequency or map length. In the presence of interference is shown to retain its genetic meaning as an additive metric that may describe the chromosome arm or other distinctive chromosome segment in terms of genetic recombination. It is a form of potential map length, comparable to, but numerically different from the regular map length. It is termed provisionally crossing-over potential.A chromosome with armsm andn with crossing-over potentials and will form ring bivalents with a frequency (1–e ^–2).(1–e ^–2); open bivalents with a frequency (1–e ^–2).e ^–2+(1–e ^–2).e ^–2; univalent pairs with a frequencye ^–2.e ^–2. Estimates of these frequencies yield equations from which and may be solved. In rye (Secale cereale) their ratio (q) is approximately two and differs from the mitotic arm length ratio of 1.4, indicating localization of chiasmata in the long arms.Graphs are given to show how, with constantq, the relation between the probabilitiesb _m andb _n of the two arms being bound changes with changing averageb.Data are presented on chiasma frequencies in M I, and compared with the frequencies expected in the absence of interference to give an impression of the degree of interference. Apparent fusion of chiasmata simulates interference.