Chemical dynamic approach to synergetics and instability in biological systems

Based on Haken's theory, self-organization or synergetics is discussed using chemical dynamics to represent an autocatalytic reaction. In a simple case the changes in a self-organizing system are given by a set of two rate equations for a primary and a partial system. When these systems mutually form a feedback loop under the adiabatic condition, the rate equation of self-organization is described by a generalized Gibbs' free energy change delta U (delta x) followed by the reaction. The sign of the parameter k'3 (k0-kex; k0, kex: rate constants with or without an external stimulus) determines the instability of the coupled system in quasi-equilibrium (k'3 approximately greater than 0; k0 greater than kex). When the product exceeds the threshold (k'3 less than 0; k0 less than kex), the system transfers into a new state, or a phase transition appears. Considering the Boltzmann distribution, the transition parameter k'3 is evaluated by an average distribution of the states and the instability is discussed using the reaction velocities vqe and vqe in the quasi-equilibrium state. As an example of this model membrane excitation is discussed briefly.     

Theory of the rotational contribution to facilitated diffusion

Gros and others have recently shown experimentally that the facilitated diffusion of protons carried by a form of haemoglobin is enhanced by rotational diffusion of the carrier, whereas facilitated diffusion of oxygen by the same carrier is not. In this paper the theory of facilitated transport by rotating carriers is developed from first principles. The theory confirms Gros's findings that (i) the rotational contribution appears only when the angle of rotational diffusion over the average time the proton remains bound is small and (ii) under these conditions rotation enhances the normal translational contribution by a factor 1/2 at the lowest carrier concentrations. The theory also shows that there must be a rotational boundary layer.     

Evidence for facilitated diffusion of urea across the gill basolateral membrane of the rainbow trout (Oncorhynchus mykiss)

Recent in vivo evidence suggests that the mechanism of branchial urea excretion in the ammoniotelic rainbow trout (Oncorhynchus mykiss) is carrier-mediated. Further characterization of this proposed mechanism was achieved by using an in vitro isolated basolateral membrane vesicle (BLMV) preparation in which isolated gill membranes were used to determine a variety of physiological properties of the transporter. BLMV demonstrated two components of urea uptake, a linear component at concentrations up to 17.5 mmol x l(-1) and a saturable component (K(0.5)=0.35+/-0.01 mmol x l(-1); V(max)=0.14+/-0.02 micromol mg protein(-1) h(-1)) with a Hill constant of 1.35+/-0.18 at low, physiologically relevant urea concentrations (<2 mmol x l(-1)). Saturable uptake of urea at 1 mmol x l(-1) by BLMV was reduced by 88.5% when incubated with 0.25 mmol x l(-1) phloretin, a potent blocker of UT-type facilitated diffusion urea transport mechanisms. BLMV also demonstrated differential handling of urea versus urea analogues at 1 mmol x l(-1) concentrations and total analogue/total urea uptake ratios were 32% for acetamide and 84% for thiourea. Saturable urea uptake at 1 mmol x l(-1) was significantly reduced by almost 100% in the presence of 5 mmol x l(-1) thiourea but was not affected by 5 mmol x l(-1) acetamide or 5 mmol x l(-1) N-methylurea. Lastly, total urea uptake at 1 mmol x l(-1) by BLMV was sensitive to temperatures above and below the temperature of acclimation with a Q(10)>2 suggesting a protein carrier-mediated process. Combined, this evidence indicates that a facilitated diffusion urea transport mechanism is likely present in the basolateral membrane of the rainbow trout gill.     

Oxygen diffusion-concentration product in rhodopsin as observed by a pulse ESR spin labeling method.

Permeation of molecular oxygen in rhodopsin, an integral membrane protein, has been investigated by monitoring the bimolecular collision rate between molecular oxygen and the nitroxide spin label using a pulse electron spin resonance (ESR) T1 method. Rhodopsin was labeled by regeneration with the spin-labeled 9-cis retinal analogue in which the beta-ionone ring of retinal is replaced by the nitroxide tetramethyl-oxypyrrolidine ring. The bimolecular collision rate was evaluated in terms of an experimental parameter W(x), defined as T1(-1)(air,x)--T1(-1)(N2,x) where T1's are the spin-lattice relaxation times of the nitroxide in samples equilibrated with atmospheric air and nitrogen respectively, which is proportional to the product of local oxygen concentration and local diffusion coefficient (transport). W-values at the beta-ionone binding site in spin-labeled rhodopsin are in the range of 0.02-0.13 microseconds-1, which are 10-60 times smaller than W's in water and 1.1-20 times smaller than in model membranes in the gel phase, indicating that membrane proteins create significant permeation resistance to transport of molecular oxygen inside and across the membrane. W(thereby the oxygen diffusion-concentration product) is larger in the meta II-enriched sample than in rhodopsin, indicating light-induced conformational changes of opsin around the beta-ionone binding site. W decreases with increase of temperature for both rhodopsin and meta II-enriched samples, suggesting that temperature-induced conformational changes take place in both samples. These changes were not observable using conventional ESR spectroscopy. It is concluded that W is a sensitive monitor of conformational changes of proteins.     

The steady-state transport of oxygen through hemoglobin solutions

The steady-state transport of oxygen through hemoglobin solutions was studied to identify the mechanism of the diffusion augmentation observed at low oxygen tensions. A novel technique employing a platinum-silver oxygen electrode was developed to measure the effective diffusion coefficient of oxygen in steady-state transport. The measurements were made over a wider range of hemoglobin and oxygen concentrations than previously reported. Values of the Brownian motion diffusion coefficient of oxygen in hemoglobin solution were obtained as well as measurements of facilitated transport at low oxygen tensions. Transport rates up to ten times greater than ordinary diffusion rates were found. Predictions of oxygen flux were made assuming that the oxyhemoglobin transport coefficient was equal to the Brownian motion diffusivity which was measured in a separate set of experiments. The close correlation between prediction and experiment indicates that the diffusion of oxyhemoglobin is the mechanism by which steady-state oxygen transport is facilitated.     

Steady-State, Hemoglobin-Facilitated O2 Transport in Human Erythrocytes

We measured the rate of oxygen transport through thin (165 µ) films of packed erythrocytes (Hb concentration = 30 g/100 ml). Under optimal conditions steady-state O₂ diffusion was nearly three times that found when the hemoglobin was prevented from acting as a carrier molecule by carbon monoxide binding or high oxygen back pressure. After each experiment we measured hemolysis and found that it averaged less than 1%. Hemolysis could not account for the facilitation, thus proving that facilitated transport of O₂ by hemoglobin can occur in red blood cells. The rate of facilitated transport was identical for Hb solutions of equal concentration to the cells. We interpret this to mean that under the conditions of our experiments the red cell membrane offers no detectable diffusion resistance to O₂ and that the mobility of Hb in intact red cells is the same as in concentrated Hb solution.     

Spontaneous, intervesicular transfer rates of fluorescent, acyl chain-labeled phosphatidylcholine analogs

It was recently shown that the structure of the fluorophore attached to the acyl chain of phosphatidylcholine analogs determines their mechanism of transport across the plasma membrane of yeast cells (Elvington et al., J. Biol Chem. 280:40957, 2005). In order to gain further insight into the physical properties of these fluorescent phosphatidylcholine (PC) analogs, the rate and mechanism of their intervesicular transport was determined. The rate of spontaneous exchange was measured for PC analogs containing either NBD (7-nitrobenz-2-oxa-1,3-diazol-4-yl), Bodipy FL (4,4-difluoro-5,7-dimethyl-4-bora-3a,4a-diaza-s-indacene), Bodipy 530 (4,4-difluoro-5,7-diphenyl-4-bora-3a,4a-diaza-s-indacene), or Bodipy 581 (4,4-difluoro-5-(4-phenyl-1,3-butadienyl)-4-bora-3a,4a-diaza-s-indacene) attached to a five or six carbon acyl chain in the sn-2 position. The rate of transfer between phospholipid vesicles was measured by monitoring the increase in fluorescence as the analogs transferred from donor vesicles containing self-quenching concentrations to unlabeled acceptor vesicles. Kinetic analysis indicated that the transfer of each analog occurred by diffusion through the water phase as opposed to transfer during vesicle collisions. The vesicle-to-monomer dissociation rate constants differed by over four orders of magnitude: NBD-PC (k(dis)=0.115 s(-1); t(1/2)=6.03 s); Bodipy FL-PC (k(dis)=5.2x10(-4); t(1/2)=22.2 min); Bodipy 530-PC (k(dis)=1.52x10(-5); t(1/2)=12.6 h); and Bodipy 581-PC (k(dis)=5.9x10(-6); t(1/2)=32.6 h). The large differences in spontaneous rates of transfer through the water measured for these four fluorescent PC analogs reflect their hydrophobicity and may account for their recognition by different mechanisms of transport across the plasma membrane of yeast.     

Bidirectional transport of glutamine across the cell membrane in rat liver.

Hepatocytes isolated from fed rats were used to investigate glutamine transport. Glutamine transport appears as a composite process involving at least two saturable components. The Na+-dependent component probably represents the entry through the N system. The Na+-independent component was also inhibited by histidine and exhibited trans-stimulation, suggestive of a facilitated diffusion process. Kinetic parameters for both systems suggest that facilitated diffusion only plays a minor role in glutamine influx. In contrast, the Km for glutamine efflux was consistent with a physiological role of the facilitated-diffusion component in glutamine release. In Na+ medium, relatively constant distribution ratios (about 8) between intra- and extra-cellular concentrations were observed, with external glutamine ranging from 0.5 to 5 mM. The present observations suggest that glutamine influx might largely be mediated by the N system, whereas facilitated diffusion allows hepatocytes to release glutamine when intracellular concentrations are elevated. The physiological consequences of this bidirectional transfer of glutamine across the liver cell membrane is discussed.     

Distinction of three types of D-glucose transport systems in animal cells

Immunoblotting of plasma membrane fractions from rat kidney cortex with antibody to human erythrocyte glucose transporter showed a single major cross-reacting material of 48K in basolateral membrane fractions possessing a facilitated diffusion system for D-glucose, but not in brush border membrane fractions which have a Na-dependent active transport system. Cytochalasin B inhibited D-glucose uptake in basolateral membrane vesicles but not in brush border vesicles. Cross-reacting materials of 44-55K were detected in several animal cells exhibiting facilitated diffusion systems, including a hormone dependent system. These results indicate molecular difference between glucose transporters of facilitated diffusion systems and active transport systems.     

Regulation of the lateral diffusion of WGA-labeled glycoconjugates in human leukocytes. Comparison between adult granulocytes and differentiating promyelocytic HL60 cells

The regulation of the membrane mobility of glycoconjugates in human polymorphonuclear leukocytes (PMNL) was studied by comparing adult PMNL with promyelocytic HL60 cells before and after stimulation of differentiation in HL60 cells with phorbol-myristate acetate (PMA) with respect to lateral diffusion of wheat germ agglutinin (WGA)-labeled glycoconjugates. For this purpose we developed a novel variant of microscope equipment for the study of fluorescence recovery after photobleaching (FRAP) and continuous fluorescence microphotolysis (CFM) using a mini-computer for handling of shutters, data acquisition, and calculations. This equipment is presented in the report. We found that PMA-induced differentiation in HL60 cells reduced the lateral diffusion coefficient (D) of WGA-labeled membrane entities from about 1.5 to 1.0 x 10(-10) cm2/s, which was close to that found for adult blood PMNL, i.e., 1-1.2 x 10(-10) cm2/s. The lateral mobility (D x 10(10)) of succinylated WGA (S-WGA) was 2.3 and 1.7 cm2/s in undifferentiated and PMA-differentiated HL60 cells, respectively, indicating that WGA might have cross-linked membrane receptors, resulting in the slower diffusion. The results are discussed in relation to the effect of phagocyte maturation on the mobility of membrane components.     

Effect of alkyl chain unsaturation and cholesterol intercalation on oxygen transport in membranes: a pulse ESR spin labeling study.

Transport and diffusion of molecular oxygen in phosphatidylcholine (PC)-cholesterol membranes and their molecular mechanism were investigated. A special attention was paid to the molecular interaction involving unsaturated alkyl chains and cholesterol. Oxygen transport was evaluated by monitoring the bimolecular collision rate of molecular oxygen and the lipid-type spin labels, tempocholine phosphatidic acid ester, 5-doxylstearic acid, and 16-doxylstearic acid. The collision rate was determined by measuring the spin-lattice relaxation times (T1's) in the presence and absence of molecular oxygen with long-pulse saturation-recovery ESR techniques. In the absence of cholesterol, incorporation of either a cis or trans double bond at the C9-C10 position of the alkyl chain decreases oxygen transport at all locations in the membrane. The activation energy for the translational diffusion of molecular oxygen in the absence of cholesterol is 3.7-6.5 kcal/mol, which is comparable to the activation energy theoretically estimated for kink migration or C-C bond rotation of alkyl chains [Tr?uble, H. (1971) J. Membr. Biol. 4, 193-208; Pace, R. J., & Chan, S. I. (1982) J. Chem. Phys. 76, 4241-4247]. Intercalation of cholesterol in saturated PC membranes reduces oxygen transport in the headgroup region and the hydrophobic region near the membrane surface but little affects the transport in the central part of the bilayer. In unsaturated PC membranes, intercalation of cholesterol also reduces oxygen transport in and near the headgroup regions. In contrast, it increases oxygen transport in the middle of the bilayer. On the basis of these observations, a model for the mechanism of oxygen transport in the membrane is proposed in which oxygen molecules reside in vacant pockets created by gauche-trans isomerization of alkyl chains and the structural nonconformability of neighboring lipids, unsaturated PC and cholesterol in particular, and oxygen molecules jump from one pocket to the adjacent one or move along with the movement of the pocket itself. The presence of cholesterol decreases oxygen permeability across the membrane in all membranes used in this work in spite of the increase in oxygen transport in the central part of unsaturated PC-cholesterol membranes because cholesterol decreases oxygen transport in and near the headgroup regions, where the major barriers for oxygen permeability are located. Oxygen gradients across the membranes of the cells and the mitochondria are evaluated. Arguments are advanced that oxygen permeation across the protein-rich mitochondrial membranes can be a rate-limiting step for oxygen consumption under hypoxic conditions in vivo.     

Facilitated transport of oxygen in the presence of membranes in the diffusion path.

Most of the experimental observations on facilitated transport have been done with millipore filters, and all the theoretical studies have assumed homogeneous spatial properties. In striated muscle there exist membranes that may impede the diffusion of the carrier myoglobin. In this paper a theoretical study is undertaken to analyze the transport in the presence of membranes in the diffusion path. For the numerical computations physiologically relevant values of the parameters were chosen. The numerical results indicate that the presence of membranes tends to decrease the facilitation. For the nonlinear chemical kinetics of the reaction of oxygen with the carrier, this decrement also depends on the location of the membranes. At the higher oxygen concentration side of each membrane the flow of combined oxygen is transferred to the flow of dissolved oxygen. The reverse process occurs at the lower concentration side. Jump discontinuities of the concentration of the oxygen-carrier compound at each membrane are associated with these transfers. The decrement of facilitation is due to the cumulative effect of these jump discontinuities.     

The binding of a neutral aromatic molecule to a negatively-charged lipid membrane. II. Kinetics and mechanism

The kinetics of the binding of the fluorescence indicator N-phenyl naphthylamine to bilayer vesicles of C12-methyl-phosphatidic acid have been investigated by means of the temperature-jump relaxation technique utilizing fluorescence light detection. Single-exponential relaxation curves were observed, with time constants in the range 0.2-3 ms. The concentration dependence of the relaxation time yielded an apparent association rate constant (expressed in terms of monomeric phospholipid) of k(on) = 5 x 10(6) M(-1) s(-1) in aqueous solution at 25 degrees . The activation energy and viscosity dependence associated with the binding rate show that this process is actually diffusion-controlled. The theory of diffusion-controlled reactions then allows a determination of the average size of the bilayer vesicles and of the true rate constant for the association of the indicator molecules with the vesicles. Assuming spherical geometry for the vesicles, the values are: r(ves) = 190 A, which corresponds to 20000 lipid molecules per vesicle and k'(on) = 1 x 10(11) M(-1) s(-1) (25 degrees). The correctness of this size-determination was confirmed semi-quantitatively by electron microscopy. Since in fact a distribution of vesicle sizes must be present, a discussion is included of the relaxation function which the system is expected to take in the general case. Biological implications of diffusion control for the transport of non-polar substances and for lipid mixing are indicated.     

Formation of compound I and compound II ferryl species in the reaction of hemoglobin I from Lucina pectinata with hydrogen peroxide

The formation of ferryl heme (Fe(IV) = O) species, i.e., compound I and compound II, has been identified as the main intermediates in heme protein peroxidative reactions. We report stopped-flow kinetic measurements which illustrate that the reaction of hemoglobin I (HbI) from Lucina pectinata with hydrogen peroxide produce ferryl intermediates compound I and compound II. Compound I appears relatively stable displaying an absorption at 648 nm. The rate constant value (k'(2)) for the conversion of compound I to compound II is 3.0 x 10(-2) s(-1), more than 100 times smaller than that reported for myoglobin. The rate constant value for the oxidation of the ferric heme (k'(12) + k'(13)) is 2.0 x 10(2) M(-1) s(-1). These values suggest an alternate route for the formation of compound II (by k'(13)) avoiding the step from compound I to compound II (k'(2)). In HbI from L. pectinata the stabilization of compound I is attribute to the unusual collection of amino acids residues (Q64, F29, F43, F68) in the heme pocket active site of the protein.     

A note on the nonautonomous delay Beverton-Holt model

It is well known that the periodic cycle {x(n)} of a periodically forced nonlinear difference equation is attenuant (resonant) if av(x(n)) < av(K(n))(av(x(n)) > av(K(n))),where {K ( n )} is the carrying capacity of the environment and av(t(n)) = (1/p)∑(p?1) (i=0) ti (arithmetic mean of the p-periodic cycle {t ( n )}). In this article, we extend the concept of attenuance and resonance of periodic cycles using the geometric mean for the average of a periodic cycle. We study the properties of the periodically forced nonautonomous delay Beverton-Holt model x(n+1) = r(n)x(n)/1 + (r(n?l) ? 1)x(n?k)/K(n?k), n= 0, 1, . . . , where {K ( n )} and {r ( n )} are positive p-periodic sequences; (K ( n )>0, r ( n )>1) as well as k and l are nonnegative integers. We will show that for all positive solutions {x ( n )} of the previous equation lim sup (n→∞) (∏(n?1)(i=0)xi)(1/n) ≤ ((∏(p?1)(i=0)ri)(1/p) ? 1)(∏(p?1)(i=0)(ri ? 1))(?1/p)(∏(p?1)(i=0)Ki)(1/p). In particular, in the case where {x(n)} is a p-periodic solution of the above equation (assuming that such solution exists) and r ( n )=r>1, the periodic cycle is g-attenuant, that is (∏(p?1)(i=0)x(i))(1/p)<(∏(p?1)(i=0)K(i))(p?1) Surprisingly, the obtained results show that the delays k and l do not play any role.     

Pyruvate transport across the plasma membrane of the bloodstream form of Trypanosoma brucei is mediated by a facilitated diffusion carrier.

The characteristics of pyruvate transport across the plasma membrane in the bloodstream form of Trypanosoma brucei were studied using [14C]pyruvate in combination with the silicone-oil centrifugation technique. We present evidence for the existence of a facilitated diffusion carrier in the plasma membrane of T. brucei which specifically mediates the translocation of pyruvate. The uptake of pyruvate followed saturation kinetics (Km 1.96 +/- 0.28 mM; Cmax 36.61 +/- 1.15 nmol pyruvate/30 sec.mg protein), after correction of the data for a nonsaturable diffusion component. The uptake of pyruvate was competitively inhibited by a number of (oxo)monocarboxylic acids, including pyruvate analogs and metabolically related substances, but not by L-lactate. The transport exhibited the phenomenon of transacceleration, indicative for the involvement of a facilitated diffusion carrier. The carrier is highly specific for pyruvate and differs from other known monocarboxylate carriers present in the mitochondrial and/or plasma membrane of other eukaryotic cells in that it does not transport L-lactate.     

Deoxygenation affects fluorescence photobleaching recovery measurements of red cell membrane protein lateral mobility.

We have used the fluorescence photobleaching recovery technique to study the dependence on oxygen tension of the lateral mobility of fluorescently labeled band 3, the phospholipid analogue fluorescein phosphatidylethanolamine, and glycophorins in normal red blood cell membranes. Band 3 protein and sialic acid moieties on glycophorins were labeled specifically with eosin maleimide and fluorescein thiosemicarbazide, respectively. The band 3 diffusion rate increased from 1.7 x 10(-11) cm2 s-1 to 6.0 x 10(-11) cm2 s-1 as oxygen tension was decreased from 156 to 2 torr, and a further increase to 17 x 10(-11) cm2 s-1 occurred as oxygen tension was decreased from 2 to 0 torr. The fractional mobility of band 3 decreased from 58 to 32% as oxygen tension was decreased from 156 to 0 torr. The phospholipid diffusion coefficient remained constant as oxygen tension was decreased from 156 to 20 torr, but increased from 2.3 x 10(-9) cm2 s-1 to 7.1 x 10(-9) cm2 s-1 as oxygen tension was decreased from 20 to 0 torr. Neither the diffusion coefficient nor the fractional mobility of glycophorins changed significantly at low oxygen tension. Under non-bleaching excitation conditions, intensities of fluorescence emission were identical for oxygenated and deoxygenated eosin-labeled RBCs. Deoxygenated eosin-labeled RBCs required 160-fold greater laser intensities than did oxygenated RBCs to achieve comparable extents of photobleaching, however. Oxygen seems to act as a facilitator of fluorophore photobleaching and may thereby protect the fluorescently labeled red cell membrane from photodamage.(ABSTRACT TRUNCATED AT 250 WORDS)     

The survival of chloroplasts in vitro: Particle volume distribution patterns as a criterion for assessing the degree of integrity of isolated chloroplasts

Summary Volume distribution patterns of chloroplast suspensions obtained electronically with a Coulter counter have been compared with the corresponding diameter measurements and with the appearance of chloroplasts observed by phase-contrast microscopy. It was found that the Coulter counter pattern could be used to detect gross morphological changes of chloroplasts in isolation, but could not be used for the quantitative determination of the properties of chloroplasts in different morphological states. The pattern for a suspension containing both intact and damaged chloroplasts in approximately equal numbers has only one maximum. Two maxima are present if the proportion of intact chloroplasts is considerably greater than 50%. Chloroplasts which have lost both their outer limiting membrane and also their stroma (i.e. naked, but intact, lamellae systems) make only a very small contribution to the size distribution pattern in the region recording apparent volumes between 0 and 11.2 µ³.Previous workers have described intact chloroplasts as Class I, and damaged chloroplasts lacking limiting membrane and stroma as Class II. We suggest that a third Intermediate Class should be recognized for chloroplasts devoid of their limiting membrane, but still retaining stroma. Such chloroplasts can be distinguished from Class II chloroplasts by their less clearly visible grana, and slightly lighter appearance under phase contrast, and also by their considerable contribution to Coulter counter volume distribution patterns with a peak maximum between 35 and 55 µ³. Such Intermediate Class chloroplasts would also be expected to have biochemical properties differing considerably from those of both Class I and Class II chloroplasts.Salters' Scholar 1967/68.