Macroscopic Organization Research Articles

Constructal theory: from thermodynamic and geometric optimization to predicting shape in nature

This is a review of recent theoretical developments toward predicting macroscopic organization (the occurrence of shape and structure) in natural flow systems, animate and inanimate. The starting point is the question of how to optimize the access between one point and a finite volume (i.e., an infinite number of points). If the volume is an electronic device that generates heat uniformly, then access optimization means minimum thermal resistance between the volume and a point-size heat sink. Similarly, if the volume must be bathed at every point by a flow (e.g., air flow in the lung, or blood flow in a capillary bed), optimal access means minimum flow resistance between the volume and a source or sink. The main discovery is purely geometric: any finite-size portion of this composite can have its shape optimized such that its overall resistance to flow is minimal. Consequently, the optimal-access solution for the total volume is obtained by optimizing volume shape at every length scale, in a sequence that begins with the smallest building block (elemental system), and proceeds toward larger building blocks (assemblies, constructs). The solution is constructed, hence the “constructal” name of the associated theory. The paths form a tree network in which every single geometric detail is determined theoretically. The tree network cannot be determined theoretically when the time direction is reversed, from large elements toward smaller elements. The constructal principle is further illustrated for fluid flow between a volume and one point, for minimum-time travel between an area and one point, and for minimum-cost economics structures.

Multipolar Symmetry Patterns in Molecular Nonlinear Optics

Organic materials for quadratic nonlinear optics generally follow the basic pattern of strongly dipolar quasi one-dimensional intramolecular charge transfer molecules organized in macroscopic crystalline or statistical polar lattices. This restriction has been lifted by the introduction of the much broader class of multipolar materials whereby efficient two- and three-dimensional molecules can be fruitfully exploited in self assembled or externally engineered multipolar macroscopic structures. At the molecular level, polarized harmonic scattering permits to evaluate the invariant irreducible components of the molecular quadratic tensor. Its anisotropy and dispersion can be accounted for by a three-quantum model in agreement with linear spectroscopy on poled samples, whereas the validity of the two-level model is restricted to one-dimensional systems. Permanent macroscopic multipolar organization can be implemented by purely optical photoinduced processes. Adequate choice of the polarization of "write" beams permits to imprint any desired symmetry pattern onto the (non)linear material. Photonic engineering thus complements and considerably broadens the more traditional scope of molecular engineering.

Equipartition, optimal allocation, and the constructal approach to predicting organization in nature

This is a review of recent engineering developments in thermodynamic optimization, which shed light on a universal design principle that accounts for macroscopic organization in nature. It is shown that the optimal performance of a finite-size system with purpose is always characterized by the equipartition of driving forces or the optimal allocation of material subject to overall constraints. Examples are drawn from natural inanimate systems (river basins, turbulent flow) and animate systems (living trees). It is shown that this principle also governs the architecture of tree networks. Tree networks can be obtained in purely deterministic fashion by minimizing the flow resistance (or the time of travel) between one point and a finite area or a finite volume (an infinite number of points). The shape of each volume element can be optimized for minimal flow resistance. The network is ‘constructed’ by assembling the shape-optimized building blocks, and proceeding in time from the smallest volume element toward larger constructs. In constructal theory small size and shapeless flow (diffusion) come first, and larger sizes and geometrical form (channels, streams) come later.

Spontaneous chiral domains in the nematic phase of achiral trans-4-alkylcyclohexanecarboxylic acids

We have discovered a spontaneous chiral ordering in thermotropic nematic liquid crystals forming hydrogen bonds, namely in trans -4-alkylcyclohexanecarboxylic acids, which do not contain any chiral group in the molecular structure, and have suggested a possible explanation of this phenomenon. The investigation was performed by polarizing light microscopy, using cells with glass substrates treated to give a uniform planar alignment in the nematic phase. On cooling from the isotropic phase, two types of nematic domains with different alignment were found to grow: some possessing a unidirectional planar orientation as expected, and others with a spontaneous twisted molecular arrangement. The appearance of the twisted domains and the sense of their twist were random, i.e. they always emerged in various regions of the cell with different twist sense: thus, they cannot be regarded as induced by stable defects in the surface aligning film. With the coalescence of the nematic droplets, the number of the domains with the spontaneous twist very quickly characterized by different handedness transformed into a racemic domain with uniform planar alignment. Here the explanation of the macroscopic texture is given in terms of molecular structure, based upon the ability of the carboxylic acids to organize through hydrogen bonds into not only dimers, but also trimers and oligomers. The microscopic structure influences the macroscopic twisted organization of the director inside the domains, and the surface lies normally to the helix axis. A brief review is given of work done in the fields of hydrogen bonded liquid crystals and of order transitions, together with a Landau-de Gennes model describing the mechanism of the spontaneous chiral ordering. decreased, since two chiral domains

Spatial evolutionary game theory: Hawks and Doves revisited

We consider a spatial generalization of evolutionary game theory in which strategies are distributed over a spatial array of sites. We assume that the strategy corresponding to a given site has local interactions with the strategies sitting on neighbouring sites, and that the strategies change if neighbouring strategies are doing better. After briefly setting the stage with a formal definition of spatial evolutionary game theory, we consider the spatial extension of the Hawk-Dove game, and we show that the results are qualitatively different from those obtained from classical evolutionary game theory. For example, the proportion of Hawks in the population is in general lower in the spatial game than in the classical one. We also consider spatial generalizations of the extensions of the Hawk-Dove game obtained by including strategies such as Retaliator and Bully. Here, too, the results from the spatial game are very different from the classical results. In particular, with space Retaliator is a much more successful strategy than one would expect from classical considerations. This suggests that, in general, spatial structure may facilitate the evolution of strategies such as Retaliator, which do not necessarily prosper classically, and which are reminiscent of the \`nice', \`provokable' and `forgiving' strategies which seem to play a central role in the evolution of cooperation. The results indicate that including spatial structure in evolutionary game theory is a fruitful extension.

PATTERNS IN THIN LIQUID CRYSTAL FILMS AND THE DIVERGENCE (“SURFACELIKE”) ELASTICITY

Thin submicron and micron films of liquid crystals placed between two isotropic media represent a particular example of confined systems. Such films can be prepared on the surface of glycerin or other liquids, In comparison with Langmuir monolayers, these films are macroscopically thick to involve the liquid crystalline order in the interplay between molecular structure and macroscopic organization. At the same time, the films are thin enough for such a strong competition between surface and bulk properties that transitional in-plane symmetry is spontaneously violated and a number of patterns appear: stripe domains, square lattices, strings, high strength defects and so on. We show that these structures are governed by the divergence (or “sufacelike”) K13 and K24 terms in the nematic free energy which have been ignored for decades. We also show that both terms can be included in the standard elasiticty theory without contradictions with the basic idea of the nematic phase. The one-dimensional confinement makes the films a unique object of investigation: although the phenomena observed are attributed to the vertical confinement, their manifestation is detected in a non-restricted film plane.

Dendritic arbors of spiny neurons in the primate striatum are directionally polarized.

Despite the relatively unfeatured cytoarchitecture of the striatum, this large subcortical region has been found to have a modular macroscopic substructure comprising the neurochemically distinct striosomes and matrix, and, within the matrix, patchy input and output arrangements called matrisomes. In the study reported here, we explored the possibility that the cellular architecture of the striatum is also more specialized than previously suspected. We injected medium spiny neurons in lightly fixed slices of the squirrel monkey caudate nucleus, reconstructed their dendritic arbors, and analyzed the orientations of these arbors with respect to the cardinal planes of the striatum. The data were unequivocal in suggesting that many spiny neurons, whether near striosomes or not, have dendritic arbors with preferred orientations along a diagonal axis running from rostral, dorsal, and medial to caudal, ventral, and lateral. This axis corresponds to the orientations of many striosomes and matrisomes in the squirrel monkey's caudate nucleus. We therefore suggest that the primate striatum is characterized not only by a macroscopic organization dividing it into striosomes and matrisomes, but also by a microscopic architecture observed by the dendritic arbors of many of its projection neurons. We obtained comparable supplementary observations for the ferret caudate nucleus, suggesting that such spatial alignment of spiny dendritic arbors may be a general feature of striatal organization. These polarized dendritic arrangements could provide a cellular framework for compartmental input-output processing within the striatum.

The macroscopic organization of reconstituted M13 coat protein-phospholipid systems. An EPR spectroscopy and polarizing microscope study

The coat protein of the bacteriophage M13 in the α-helical state is reconstituted in macroscopically oriented systems of dioleoylphosphatidylcholine that are prepared by squeezing the reconstituted material between glass plates. The coat protein dramatically influences the macroscopic orientation of the multibilayers, as is investigated by polarizing microscopy and EPR spectroscopy of the cholestane spin label embedded in the bilayers. It is found that with increasing amounts of protein the spontaneous macroscopic orientation of the reconstituted system decreases. This effect is proposed to be due to an increase of the apparent viscosity of the lipid-protein systems with increasing amounts of protein. This is assumed to arise from a sticky effect of the C- and N-terminal protein parts that extend into the aqueous phase between the bilayers.

Effects of temperature variation and phenethyl alcohol addition on acyl chain order and lipid organization in Escherichia coli derived membrane systems. A 2H- and 31P-NMR study

Using 2H- and 31P-NMR techniques the effects of temperature variation and phenethyl alcohol addition were investigated on lipid acyl chain order and on the macroscopic lipid organization of membrane systems derived from cells of the Escherichia coli fatty acid auxotrophic strain K1059, which has grown in the presence of [11,11- 2H 2]oleic acid. Membranes of intact cells showed a gel to liquid-crystalline phase transition in the range of 4–20°C, which was similar to that observed for the total lipid extract and for the dominant lipid species phosphatidylethanolamine (PE). Phosphatidylglycerol (PG) remained in a fluid bilayer throughout the whole temperature range (4–70°C). At 30°C acyl chain order was highest in PE, followed by the total lipid extract, PG, intact cells, and isolated inner membrane vesicles. Acyl chain order in E. coli PE and PG was much higher than in the corresponding dioleoylphospholipids. E. coli PE was found to maintain a bilayer organization up to about 60°C, whereas in the total lipid extract as well as in intact E. coli cells bilayer destabilization occurred already at about 42°C. It is proposed that the regulation of temperature at which the bilayer-to-non-bilayer transition occurs may be important for membrane functioning in E. coli. Addition of phenethyl alcohol did not affect the macroscopic lipid organization in E. coli cells or in the total lipid extract, but caused a large reduction in chain order of about 70% at 1 mol% of the alcohol in both membrane systems. It is concluded that while both increasing temperature and addition of phenethyl alcohol can affect membrane integrity, in the former case this is due to the induction of non-bilayer lipid structures, whereas in the latter case this is caused by an increase in membrane fluidity.

Ultraweak photon emission in germinating seeds: A signal of biological order

Photon emission from germinating gram seeds at various stages of growth exhibits a definite pattern. The pattern of emission changes when a seed is disrupted by physical processes, e.g. mechanical crushing, cooling or heating. The disrupted seeds do not grow. The change in the biological order responsible for seed growth and the observed changes in the pattern of photo emission suggest a link between the macroscopic spatio-temporal organization and metabolic processes.

Stability of the two-way memory effect during thermal cycling of a high- Ms temperature CuAlNi alloy : Rodriguez, P. and Guenin, G. Mater. Sci. Forum 1990 56–58 Pt. II, 541–546

Heusler alloy Ni48Mn39.5Sn12.5−xAlx (x = 0, 1, 2,3) ribbons were prepared by melt spinning. The cross section of ribbons reveals a typical heterogeneous microstructure consisting of small equi-axed and columnar grains. The top and bottom ribbons sides are homogenous in composition but they differ in terms of surface structure. The wheel ribbon side appears smoother and shows some degree of macroscopic organization. On the other hand the free ribbon surface regardless of composition shows a more complex morphology consisting of small equi-axed grains, larger grains forming clusters and conical sub crystal structures. A characteristic twinned plate like microstructure confirming the presence of an increased amount of martensite has been observed for the Ni48Mn39.5Sn9.5Al3 ribbon. The martensitic plates are 70–100 nm in size. The phase shift of 0.5° was detected, while scanning the latter ribbon sample in magnetic force microscope mode, indicating the existence of a magnetic multi-domain structure in this sample.

Nucleotide hydrolysis in cytoskeletal assembly

Two major polymers of the cytoskeleton, actin filaments and microtubules, are assembled with expenditure of energy: the ATP/GTP tightly bound to actin/tubulin is irreversibly hydrolyzed to ADP/GTP during the assembly process, and liberation of P i in the medium occurs subsequent to the incorporation of subunits in the polymer. P i release acts as a switch, causing the destabilization of protein-protein interactions in the polymer, therefore regulating the dynamics of these fibres. An understanding of this regulation in vivo requires that progress be made in four areas: the chemistry of the NTPase reaction; the structure of the intermediates in nucleotide hydrolysis and the nature of the conformational switch; the regulation of parameters involved in dynamic instability of microtubules; and the possible involvement of nucleotide hydrolysis in the macroscopic organization of these polymers in highly concentrated solutions, compared with the simple case of a equilibrium polymers. Progress made along these lines will define trends for future investigation.

Proton NMR dipolar echo decay spectroscopy: a sensitive probe of membrane structure

The structural and motional properties of membrane lipids in various physical states and macroscopic organizations are elucidated by 1H NMR dipolar echo decay spectroscopy (DECODE). Multilamellar lipid dispersions in the gel (L beta') and liquid-crystalline (L alpha) states and a nonbilayer, hexagonal (HII) phase are readily distinguished, a dynamic profile within these phases is identified, and dipolar order parameters are obtained in the fluid phases. The method is suitable for any pulsed NMR spectrometer. DECODE provides the first depth-dependent assay of lipid order that does not rely on isotopic labeling or exogenous probe.

Phospholipase-induced modulation of dolichyl-phosphomannose synthase activity.

Rat liver dolichyl-phosphomannose synthase is optimally active when the enzyme is reconstituted with lipids that prefer a nonlamellar macroscopic organization in isolation, such as phosphatidylethanolamine (PE), but the enzyme is only negligibly active in the presence of lipids that normally form stable bilayers, such as phosphatidylcholine (PC) [Jensen, J.W., & Schutzbach, J.S. (1985) Eur. J. Biochem. 153, 41-48]. We now report that the activity of the synthase can be modulated by incorporating diacylglycerol and lysophosphatidylcholine into the lipid matrix. Enzyme activity in PC bilayers was stimulated by the presence of diacylglycerol, a lipid that has a conical dynamic molecular shape and disrupts bilayer stability. In PC/diacylglycerol mixtures the apparent Km for dolichyl-P was 30-fold lower than the apparent Km for the polyprenol acceptor in PC membranes. Enzyme activity was also stimulated when diacylglycerol was generated in situ by incubation of PC vesicles with phospholipase C. In contrast, the activity of enzyme reconstituted in PE dispersions, or in PE/PC bilayers, was markedly inhibited by the presence of lysophospholipids. Enzyme activity was also reduced by the in situ generation of lysophospholipids in PE/PC vesicles by incubation with phospholipase A2. Since lysophospholipids and diacylglycerols arise in vivo as products of phospholipid metabolism, modulation of enzyme activity by these compounds may represent a potential regulatory mechanism for the synthesis of oligosaccharide lipids.

Amplification of intrinsic fluctuations along the center manifold

AbstractWe consider a dissipative system sustaining a center manifold beyond a hard‐mode instability. The evolution towards the far‐from‐equilibrium organization is shown to be caused by the correlation of subsystems with a common coarse‐grained phase space. Critical induction periods are calculated for the onset of macroscopic organization.

Interrelationships between tyrocidine and gramicidin A′ in their interaction with phospholipids in model membranes

(1) The interaction of tyrocidine with different lipids is studied in model membranes and the results are compared to the gramicinid-lipid interaction. (2) The tyrocidine-dielaidoylphosphatidylethanolamine interaction gives rise to a population of phospholipids with a lower gel to liquid-crystalline transition temperature and to an abolition of the bilayer to H II phase transition, resulting in a macroscopic organization with dynamic and structural properties different from those of the pure lipid. (3) Tyrocidine has a strong fluidizing effect on the acyl chains of phosphatidylcholines, manifested by a decrease in enthalpy of the main thermotropic transition. (4) No evidence of a gramicidin A′-like lipid-structure modulating activity was found. However, tyrocidine inhibits the formation by gramicidin of an H II phase in dioleoylphosphatidylcholine model membranes. Instead, a cubic type of lipid organization is observed. (5) Tyrocidine greatly perturbs the barrier properties of dioleoylphosphatidylcholine model membrane. (6) Gramicidin A′ reverses the effect of tyrocidine on membrane permeability by forming a complex in the model membrane with an apparent 1:1 stoichiometry. (7) The results suggest that both peptide antibiotics, which are produced by Bacillus brevis ATC 8185 prior to sporulation, show antagonism in their effect on membrane structure similar to their effect on superhelical DNA (Bogh, A. and Ristow, H. (1986) Eur. J. Biochem. 160, 587–591. The possible underlying basic mechanism is indicated.

Phase separation and hexagonal H II phase formation by gramicidins A, B and C in dioleoylphosphatidylcholine model membranes. A study on the role of the tryptophan residues

The role of the tryptophan-residues in gramicidin-induced H II phase formation was investigated in dioleoylphosphatidylcholine (DOPC) model membranes. 31P-NMR and small angle X-ray diffraction measurements showed, that gramicidin A and C (in which tryptophan-11 is replaced by tyrosine) induce a similar extent of H II phase formation, whereas for gramicidin B and synthetic analogs in which one tryptophan, either at position 9 or 11 is replaced by phenylalanine, a dramatic decrease of the H II phase inducing activity can be observed. Modification of all four tryptophans by means of formylation of the indole NH group leads to a complete block of H II phase formation. Sucrose density centrifugation experiments on the various peptide/lipid samples showed a quantitative incorporation of the peptide into the lipid. For all samples in a 1 10 molar ratio of peptide to lipid distinct bands were found, indicative of a phase separation. For the gramicidin A′/DOPC mixture these bands were analyzed and the macroscopic organization was determined by 31P-NMR and small-angle X-ray diffraction. The results demonstrate that a quantitative phase separation had occurred between a lamellar phase with a gramicidin/lipid ratio of 1 15 and a hexagonal H II phase, which is highly enriched in gramicidin. A study on the hydration properties of tryptophan- N-formylated gramicidin in mixtures with DOPC showed that this analog has a similar dehydrating effect on the lipid headgroup as the unmodified gramicidin. In addition both the hydration study and sucrose density centrifugation experiments showed that, like gramicidin also its analogs have a tendency to aggregate, but with differences in aggregation behaviour which seemed related to their H II phase inducing activity. It is proposed (i) that the main driving force for H II phase formation is the tendency of gramicidin molecules to self-associate and organize into tubular structures such as found in the H II phase and (ii) that whether gramicidin (analogs) form these or other types of aggregates depends on their tertiary structure, which is determined by intra- as well as intermolecular aromatic-aromatic stacking interactions.

Opioid antagonist-induced modulation of cerebral and hippocampal development: histological and morphometric studies.

The role of endogenous opioid systems in preweaning cerebral and hippocampal development was explored in rats utilizing naltrexone, a potent opioid antagonist. Sprague-Dawley rats were given daily injections (s.c.) of either 1 or 50 mg/kg naltrexone to invoke a temporary or complete blockade, respectively, of opioid receptors throughout the first 3 weeks of postnatal life; animals injected with sterile water served as controls. At weaning (Day 21), macroscopic, morphometric, and histological assessments were undertaken. In general, 50 mg/kg naltrexone had a stimulatory action on brain development, whereas 1 mg/kg naltrexone had an inhibitory influence. In most cases, both males and females were affected comparably. Opioid antagonist action was especially directed at cellular and tissue differentiation, with marked changes in macroscopic and areal dimensions and histotypic organization observed in the cerebrum. A prominent effect on the cerebrum of the 1 mg/kg naltrexone group was a substantial increase in packing density of the neural cells, reflecting a reduced area for accommodating neural elements. Changes in the hippocampus were largely restricted to the 1 mg/kg group. However, the number of granule cells was increased in the dentate gyrus of the 50 mg/kg group, suggesting that opioid receptor blockade affects cell types undergoing postnatal proliferation. Cellular elements derived prior to naltrexone treatment (e.g., pyramidal neurons) were capable of being influenced in only differentiative capacity. Our results show that endogenous opioids are natural trophic factors in brain development and provide evidence for the crucial role of endogenous opioid-opioid receptor interaction in neuro-ontogeny.

Dolichyl phosphate induces non-bilayer structures, vesicle fusion and transbilayer movement of lipids: a model membrane study

The effect of dolichol and dolichyl phosphate on fusion between large unilamellar vesicles comprised of 1,2-dioleoyl- sn-glycero-3-phosphocholine (DOPC) and 1,2-dioleoyl- sn-glycero-3-phosphoethanolamine (DOPE) was studied using a fluorescence resonance energy transfer assay. The influence of dolichyl phosphate on the transbilayer movement of DOPC in multilamellar vesicles (MLV) and large unilamellar vesicles (LUV) composed of DOPC and DOPE (1:2) was investigated by using the phosphatidylcholine-specific transfer protein. 31P-NMR and freeze-fracture electron microscopy were employed to study the macroscopic organization of DOPC and DOPE containing model membranes in the absence or presence of dolichyl phosphate. The results indicate that (1) both dolichol and dolichyl phosphate enhance vesicle fusion in a comparable and concentration-dependent way; (2) the amount of exchangeable PC from MLVs is increased by dolichyl phosphate, probably as a result of fusion processes; (3) dolichyl phosphate destabilizes the bilayer organization in MLVs comprised of DOPE and DOPC, resulting in the formation of hexagonal (H II) phase and ‘lipidic’ particles.

Influence of trinitrophenylation on the structure and dynamics of phosphatidylethanolamine-containing model membranes

The influence of trinitrophenylation on hydration, acyl chain melting characteristics, and polymorphism of phosphatidylethanolamine- (PE-) containing model membranes has been investigated. 2H nuclear magnetic resonance spectroscopy (NMR) was used to study the hydration properties of (trinitro- pheny1)phosphatidylethanolamine (TNPPE). 31P NMR techniques, including saturation transfer and the use of phosphatidylcholine thio analogues, were employed to investigate the TNPPE head-group conformation. The thermotropic behavior of PE/TNPPE mixtures was studied by means of differential scanning calorimetry. The macroscopic organization of the phospholipids was monitored by 31P NMR, small-angle X-ray diffraction, and freeze-fracture electron microscopy. The results indicate that TNPPE is anhydrous in character and does not form ordered structures by itself. Furthermore, even in excess of water, the phosphate region of the fluid TNPPE molecules cannot undergo long-axis rotation, presumably due to intermolecular ring interactions. On the other hand, in aqueous dispersions TNPPE molecules are to a limited extent ( N 20 mol 7%) soluble in PE. From the decrease in enthalpy of the gel to liquid-crystalline phase transition the TNPPE molecules appear to interact with PE molecules in a 1 :4 stoichiometry. In hydrated mixtures with phosphatidylcholine (PC) or PE, the phosphate moiety of the TNPPE molecule undergoes long-axis rotation. However, by comparison with PC and PE in these samples, TNPPE has a different head-group conformation. This is possibly caused by a trinitrophenyl ring orientation either at the bilayer/water interface or per- pendicular to the plane of the bilayer. TNPPE hardly influences the temperature of the gel to liquid-crystalline phase transition in PE bilayers. In contrast, TNPPE strongly destabilizes the bilayer organization in both PE and PC model membranes, most likely due to dehydration effects and interbilayer trinitrophenyl ring interactions.