Electrolytes control flows of water and sucrose through collagen membranes

Summary The physical state of a collagen membrane is determined, among other factors, by the concentration of electrolytes in the bathing solutions, going from a crystalline to an amorphous phase as the concentration increases. Thus, the permeation of uncharged solutes and water is strongly dependent upon the salts in the bathing solutions, which through the induced phase transition control not only the thickness and the solvent content of the membrane but also affect the magnitudes of the frictional coefficients of transport. These changes in physical parameters are reflected in variations of several hundred per cent in the values of the phenomenological coefficients _s ,L _p and . Experiments were performed to determine the physical state and the permeability properties of the membrane as functions of the controlling electrolyte, in this instance CaCl₂, in the bathing solutions. In particular the filtration coefficientL _p , the permeability coefficient for sucrose _s , and the reflection coefficient for sucrose were determined via flow measurements at different salt concentrations. Complementary measurements of swelling and length variations were made. Data were reduced to membrane thickness, solvent volume-fraction, and the phenomenological coefficients. These in turn were reduced to the frictionsf _sm,f _sw andf _wm ; there was a direct correlation between the behavior of these frictions and the physical state of the collagen membrane as indicated by the length and volume variations.Thesis presented at the Institute of Physics of the University of Genoa, Italy as a partial requirement for the degree in physics.     

The role of membrane in osmotic flow

Osmosis as a phenomenon caused by internal forces goes on without the necessity for the presence of any external forces. Therefore pressure gradient plays no special role in osmotic flow. Membrane as a component of solution with its molecules possessing some kind of mobility ceases to be a passive obstacle to the flow of other components, but becomes also a co-determining factor in osmotic flow. This has been shown by using the methods of irreversible thermodynamics. In the state of osmotic equilibrium osmosis does not occur. So also the mobility of water molecules which may then be found in tracer experiment does not determine the osmotic permeability coefficient. The coefficientsσ andω as defined by the parameters of the system under the condition of zero volume flow are not directly connected to L_p.     

Unifying mass-action kinetics and Newtonian mechanics by means of Nambu brackets

We demonstrate that elementary biochemical reactions defined by mass-action kinetics satisfy a particular Nambu structure. To this end, we express biochemical reaction equations in terms of Nambu brackets and certain ω-factors. The ω-factors account for the fact that mass-action kinetics exhibits in general flow fields with finite divergence. The proposed approach by means of Nambu brackets and ω-factors unifies divergence freeflow fields of Newtonian mechanics and flow fields with finite divergence of mass-action kinetics.     

A note on imitative behavior

In a preceding paper (Bull. Math. Biophysics,27, 175–185) the distribution function ofφ=ɛ ₁-ɛ ₂,—the difference of excitations in the two mutually inhibiting centers, has been derived in terms of the distribution functionsf ₁(ɛ ₁) andf ₂(ɛ ₂) of the two excitations. In the present note some properties of the distribution functionf(ϕ) in terms of the propertiesf ₁(ɛ ₁) andf ₂(ɛ ₂) are derived.     

Some generalized conjugacy theorems and the concepts of fitness and survival in logistic growth models

Current research into the dynamics of iterative ecological and biological models has lead to a number of theorems concerning the existence of various types of iterative dynamical behavior. In particular, much study has been done on the dynamical behavior of the “simplest dynamical system”f _b(x)=bx(1−x), which is just the canonical discrete form of logistic growth equations found in ecology, sociobiology, and population biology. In this paper, we make use of some of the techniques and concepts of topological dynamics to construct a number of generalized conjugacy theorems. These theorems are then used to demonstrate that the mappingf _b has a number of conjugacy classes in which the dynamics of the iterates is equivalent to within a change of variables. The concepts of fitness and survival in logistic equations are then shown to be independent, if we follow certain intuitive definitions for these concepts. This conclusion follows from a comparison of the conjugacy classes of the functionf _b and the extinction sets off _b.     

Some comments on the conductance of slow inward current in cardiac muscle

Voltage clamp experiments, which determine the kinetic parameters of calcium conductance of cardiac muscle, (d _∞,f _∞, τ _d and τ _f ) are analyzed with a generally accepted expression for slow inward currentI _s=g _sdf (E-E _R). Activation (d) and inactivation (f) reach the final valuesd _∞ andf _∞ with time constants τ _d and τ _f respectively. The analysis indicates that the measuredf _∞ agrees with the theoreticalf _∞, but the measuredd _∞ differs from the theoreticald _∞ by a factor which depends on τ _d . The peak tension can be made to correlate closely with the theoreticald _∞ after a correction factor is applied to the raw measurements of activation. It can be shown that experiments designed to measure τ _f can also be used to determine τ _d with greater accuracy.     

Characterization of excitation beam on second-harmonic generation in fibrillous type I collagen

Following our established theoretical model to deal with the second-harmonic generation (SHG) excited by a linearly polarized focused beam in type I collagen, in this paper, we further quantitatively characterize the differences between SHG emissions in type I collagen excited by collimated and focused beams. The effects of the linear polarization angle (α) and the fibril polarity characterized by the hyperpolarizability ratio ρ on SHG emission has been compared under collimated and focused beam excitation, respectively. In particular, SHG emission components along the i axis ( I_2w,i )\left( {I_{2\omega {,}i} } \right) (i = x,y,z), the induced SHG emission deviation angle γ _ij , and the detected SHG signals (I _2ω,ij ) in the ij plane by rotating the applied polarizer angle φ _ij have been investigated (i = x, x, y; j = y, z, z). Results show that under our simulation model, SHG emission in the xy plane, such as I _2ω,x ,I _2ω,y ,γ _xy and I _2ω,xy varying as polarization angle (α) under collimated and focused light, presents no significant difference. The reverse of the fibril polarity has induced great impact on I _2ω,x ,γ _xy and I _2ω,xy in both collimated and focused light. I _2ω,x and γ _xy show similarity, but I _2ω,xy at α = 30° demonstrates a slight difference in focused light to that in collimated light. Under focused light, the reverse of fibril polarity causes obvious changes of the collected SHG intensity I _2ω,xz and I _2ω,yz at a special polarization angle α = 60° and γ _xz , γ _yz along α.     

Bayesian image processing of data from constrained source distributions—I. non-valued,uncorrelated and correlated constraints

A series of Bayesian image processing algorithms which incorporate various classes ofa priori source information in treating data which obeys Poisson and Gaussian statistics is derived using maximum entropy considerations. The standard maximum likelihood equations are shown to be a special case of Bayesian image processing when thea priori information about a source distribution φ _j is solely that a non-vanishing probability for each element value φ _j exists only in some finite interval,a _j ≤φ _j ≤φ _j . Bayesian image processing equations for thea priori source information that all φ _j are finite -∞<φ _j <∞ and each φ _j distribution has a defined mean φ _j and a defined variance σ _j are derived. The Bayesian image processing equations are also derived when thea priori source information is that all φ _j ≥0 and that each φ _j distribution has a defined mean φ _j and a defined variance σ _j . The a priori source distribution constraint that a correlation exists among nearby elements is also considered. The results indicate improvement over standard methods.     

Four-frequency polarizing microscope for recording plasma images in the wavelength range 0.4–1.1 μm

The optical scheme and design of a four-frequency polarizing microscope intended for simultaneous recording of plasma images in the wavelength range 0.4–1.1 μm with the spatial resolution 12 μm in the entire spectral range are described. The effectiveness of such a microscope in studies of plasmas produced on interaction of laser radiation with a target is demonstrated. The plasma images are obtained at the frequencies ω₀, (3/2)ω₀, 2ω₀, and (5/2)ω₀, where ω₀ corresponds to the frequency of heating radiation. The transformation coefficient that characterizes the efficiency of conversion of heating radiation into the 2ω₀, (3/2)ω₀, and (5/2)ω₀ harmonics generated in the plasma is determined.     

Theory of transport in linear biological systems: I. Fundamental integral equation

The conditions under which the output,γ _b (t), of a biological system is related to the input,γ _a (t), by an integral equation of the typeγ _b (t) = ∫ ₀ ^t γ _a (ω)w(t−ω)dω, where ω(t) is a transport functioncharacteristic of the system, are analyzed in detail. Methods of solving this type of integral equation are briefly discussed. The theory is then applied to problems in tracer kinetics in which input and output are sums of exponentials, and explicit formulae, which are applicable whether or not the pool is uniformly mixed, are derived for “turnover time” and “pool” size.     

Electric potential in three-dimensional electrically syncytial tissues

The problem of calculating the potential induced in an electrical syncytium by a point source of current is studied. The interiors of the many interconnected cells are treated as one continuum with resistivity ρ _i . The interdigitated extracellular space is treated as a second continuum of resistivity ρ _e , occupying the same overall volume, coupled to the first via the resistanceR _m and capacitanceC _m of the cell membranes. The intra- and extracellular potentials are then solutions to a pair of coupled partial differential equations. The equations are uncoupled, yielding a cable equation for the transmembrane potential and a Poisson equation for a second auxiliary potential. For an unbounded syncytium the potential for a step function source is obtained in terms of error functions. For a spherical syncytium of radiusa, bounded by a membrane with surface resistanceR _a, and capacitanceC _a, expansions are obtained in spherical harmonics and spherical Bessel functions. For ɛ=ρ _{ia/R a} and β=ρ _i /ρ _e small, an asymptotic expansion of the potential is developed. The results are compared to earlier results for a spherical cell as well as to microelectrode measurements of the lens of the eye.     

Nonquasineutral current equilibria as elementary structures of plasma dynamics

A study is made of the fundamental features of current filaments with a nonzero electron vorticity Ω _e ≡ B − (c/e) ▿ × p _ee ≠ 0 and the corresponding Lagrangian invariant I _e . Such current structures can exist on spatial scales of up to ω _pi ⁻¹. It is shown that the dissipative stage of the plasma evolution and the violation of Thomson’s theorem on vorticity conservation in an electron fluid are of fundamental importance for the onset of electron current structures. A key role of the screening of electric and magnetic fields at distances on the order of the magnetic Debye radius r _B = B/(4πen _e )—the main property of such current structures in a Hall medium with σB/(en _e c) ≫ 1—is stressed. Since the minimum size of a vortex structure is the London length c/ω _pe , the structures under consideration correspond to the condition r _B > c/ω _pe or B ² > 4πn _e m _e c ², which leads to strong charge separation in the filament and relativistic electron drift. It is demonstrated that the specific energy content in current structures is high at a filament current of 10–15 kA: from 100 J/cm³ at a plasma density of 10¹⁴ cm⁻³ (the parameters of a lightning leader) to 10⁷ J/cm³ for a fully ionized atmospheric-pressure air. Estimates are presented showing that the Earth’s ionosphere, circumsolar space, and interstellar space are all Hall media in which current vortex structures can occur. A localized cylindrical equilibrium with a magnetic field reversal is constructed—an equilibrium that correlates with the magnetic structures observed in intergalactic space. It is shown that a magnetized plasma can be studied by using evolutionary equations for the electron and ion Lagrangian invariants I _e and I _i . An investigation is carried out of the evolution of a current-carrying plasma in a cylinder with a strong external magnetic field and with a longitudinal electron current turned on in the initial stage—an object that can serve as the simplest electrodynamic model of a tokamak. In this case, it is assumed that the plasma conductivity is low in the initial stage and then increases substantially with time. Based on the conservation of the integral momentum of the charged particles and electromagnetic field in a plasma cylinder within a perfectly conducting wall impenetrable by particles, arguments are presented in support of the generation of a radial electric field in a plasma cylinder and the production of drift ion fluxes along the cylinder axis. A hypothesis is proposed that the ionized intergalactic gas expands under the action of electromagnetic forces.     

Contribution to the probabilistic theory of neural nets: III. Specific inhibition

The input-output formula is derived for a neuron upon which converge the axones of two other neurons (one excitatory, the other inhibitory) which are themselves subjected to a “Poisson shower” of excitatory stimuli. If the period of latent inhibition, σ, does not exceed one half the refractory period, δ, the input-output curve has no maximum. If, however, σ>δ/2, a maximum exists in the input-output curve. As the outside frequencyx increases without bound, the output frequencyx ₃ approaches an asymptotic value which ranges from 1/δ to 0, depending on the ratio σ/δ. The maximum output (if it exists) is also derived as a function of σ and δ.     

Mathematical biosociology of beliefs and prejudices

Following a suggestion made previously (Bull. Math. Biophysics,13, 61, 1951), it is assumed that every individual has both a tendency to behavearationally, by accepting everything on faith, and rationally, by subjecting everything to rational analysis. Arational behavior is characterized by various beliefs, prejudices, etc., which are considered to be conditioned reactions, learned by the individual before he completely develops his faculties for rational thinking. The two tendencies are assumed to be due to excitations of two different regions of the central nervous system, and are measured by the intensities ɛ _f and ɛ _r of those excitations. Those intensities are further assumed to increase linearly with time, the increases of the two beginning, in general, at different ages. The rates of increase are considered as normally distributed in the population. The relative frequency of arational and rational behavior is determined by the difference φ=ɛ _f =ɛ _r according to equations 0 developed previously (Bull. Math. Biophysics,11, 255, 1949). It is shown that with the above assumptions the majority of the population, which starts with arational behavior, will, within two or three of generations, either change to rational behavior or continue indefinitely to behave arationally. This will hold as long as imitative factors are present. Expressions for the numbers of individuals who behave rationally and arationally are derived. If the intensity of conditioning toward an arational behavior decreases with increasing size of the rationally behaving minority, or, if the rationally behaving individuals are not influenced by imitation, then a slow secular trend toward rational behavior may be present. An expression is also derived for the fraction of individuals who behave rationally as a function of age. This fraction increases with increase of the age at which the beginning conditioning toward any beliefs or prejudices begins.     

Primary sequence dependence of conformation in oligomannose oligosaccharides

The oligomannose series of oligosaccharides from bovine thyroglobulin (BTG) and the variant surface glycoprotein (VSG) ofTrypanosoma brucei have been isolated and sequenced by¹H NMR. The structure of Man₉GlcNAc₂, the parent molecule of the series, is shown below. Structural isomerism occurs within this series through the removal of residues D1, D2, D3, and C. Using spin-spin coupling and chemical shift data the rotamer distributions about the dihedral angle ω for the Manα1-6Man\ and Manα1-6Manα linkages were determined for each member of the series. It is shown that the dihedral angle ω of the Manα1-6Man\ linkage exhibits low flexibility with a preference for the ω = 180° conformation when residue D2 is present and high flexibility when this residue is absent. Flexibility of ω for the Manα1-6Manα is largely independent of primary sequence and is intermediate between the two Manoα1-6Man\ extremes, again with a preference for the ω = 180° conformation. There are, however, data which indicate that removal of residue D3 may confer additional flexibility upon the dihedral angle ω of the Manα1-6Manα linkage. Molecular graphics modelling, together with chemical and enzymatic modification studies, suggest that the origin of the observed primary sequence dependence of the Manα1-6Man\ linkage arises from steric factors. On the basis of these observations taken together with previous work, it is postulated that recognition of individual oligomannose conformations may play a role in the control of N-linked oligosaccharide biosynthesis. Offprint requests to: T W Rademacher     

Fatty acid composition as an indicator of physiological condition of the cyanobacterium Microcystis aeruginosa

The present study examined the fatty acid composition of Microcystis aeruginosa grown in a batch culture and that of Microcystis-dominated plankton collected in an experimental enclosure in a shallow, eutrophic embayment of Lake Biwa (Akanoi Bay). In pure culture, we detected 16 : 0, 18 : 2ω6, 18 : 3ω3, 18 : 3ω6, and 18 : 4ω3 acids as major fatty acids of M. aeruginosa, with trace amounts of C₂₀ polyunsaturated fatty acids. In both pure culture and the field enclosure, the ratio of total fatty acid weight to dry weight decreased with decreasing availability of dissolved inorganic nitrogen. The ω3/ω6 ratios of C₁₈ polyunsaturated fatty acids [(18 : 3ω3 + 18 : 4ω3)/(18 : 2ω6 + 18 : 3ω6)] varied greatly (range, 2–5) in response to the changes in physical and chemical conditions for Microcystis growth. Most notably, the ω3/ω6 fatty acid ratios were significantly positively correlated with the growth rate of cells in a batch culture. We suggest that the fatty acid composition is a useful indicator of the physiological state of Microcystis in freshwater lakes. Received: March 2, 2001/ Accepted: December 19, 2001     

Coordination between ventilatory pressure oscillations and venous return in the cephalopod <Emphasis Type="Italic">Sepia officinalis</Emphasis> under control conditions,spontaneous exercise and recovery

Venous blood flow was measured for the first time in a cephalopod. Blood velocity was determined in the anterior vena cava (AVC) of cuttlefish S. officinalis with a Doppler, while simultaneously, ventilatory pressure oscillations were recorded in the mantle cavity. In addition, magnetic resonance imaging (MRI) was employed to investigate pulsatile flow in other major vessels. Blood pulses in the AVC are obligatorily coupled to ventilatory pressure pulses, both in frequency and phase. AVC peak blood velocity (v_AVC) in animals of 232 (± 30 SD) g wet mass at 15°C was found to be 14.2 (± 7.1) cm s⁻¹, AVC stroke volume (SV_AVC) was 0.2 (± 0.1) ml stroke⁻¹, AVC minute volume (MV_AVC) amounted to 5.5 (± 2.8) ml min⁻¹. Intense exercise bouts of 1–2 min resulted in 2.2-fold increases in MV_AVC, enabled by 1.6-fold increments in both, AVC pulse frequency (f _AVC) and v_AVC. As increases in blood flow occurred delayed in time by 1.7 min with regard to exercise periods, we concluded that it is not direct mantle cavity pressure conveyance that drives venous return in this cephalopod blood vessel. However, during jetting at high pressure amplitude (> 1 kPa), AVC blood flow and mantle cavity pressure pulse shapes completely overlap, suggesting that under these conditions, blood transport must be driven passively by mantle cavity pressure. MRI measurements at 15°C also revealed that under resting conditions, f _AVC and ventilation frequency (f _V) match at 31.6 (± 2.1) strokes min⁻¹. In addition, rates of pulsations in the cephalic artery and in afferent branchial vessels did not significantly differ from f _AVC and f _V. It is suggested that these adaptations are beneficial for high rates of oxygen extraction observed in S. officinalis and the energy conserving mode of life of the cuttlefish ecotype in general.     

The influence of extremely weak alternating magnetic fields on the regeneration of planarians and the gravitropic response of plants

The influence of extremely weak alternating magnetic fields (EW AMF) directed collinearly to the static Earth magnetic field on the rate of regeneration of planarians and the rate of gravitropic response in the stem segments of flax has been studied. The value of bioeffects of EW AMF is determined by the parameter γB _AC/f, where γ is the gyromagnetic ratio of the magnetic moments induced by the orbital movements of electrons in atoms, and B _AC and f correspond to magnetic induction and frequency of the alternating magnetic component. It was shown that the magnitude of bioeffects depends on the amplitude (at fixed 1000 Hz — frequency) and frequency (at fixed 192 nT — amplitude) of the alternating component. Maxima of bioeffects are observed at γB _AC/f = 0.9; 2.75, and minor maxima γB _AC/f = 4.5; 6.1. The bioeffects are absent at γB _AC/f =1.8, 3.8, 5.3, 6.7. The positions of the maxima and minima of bioeffects correspond to the theoretical prediction (at γ = 14000 Hz/μT). Primary targets for the EW AMF of this type are the magnetic moments induced by the orbital movements of electrons in atoms.