How environment geometry affects grid cell symmetry and what we can learn from it

The mammalian hippocampal formation provides neuronal representations of environmental location but the underlying mechanisms are unclear. The majority of cells in medial entorhinal cortex and parasubiculum show spatially periodic firing patterns. Grid cells exhibit hexagonal symmetry and form an important subset of this more general class. Occasional changes between hexagonal and non-hexagonal firing patterns imply a common underlying mechanism. Importantly, the symmetrical properties are strongly affected by the geometry of the environment. Here, we introduce a field–boundary interaction model where we demonstrate that the grid cell pattern can be formed from competing place-like and boundary inputs. We show that the modelling results can accurately capture our current experimental observations.     

Phase equilibria in four lysophosphatidylcholine/water systems. Exceptional behaviour of 1-palmitoyl-glycerophosphocholine

The phase equilibria in four lysophosphatidylcholine/water systems were investigated at different temperatures. Each of the 1-palmitoyl-, 1-stearoyl-, 1-oleoyl- and 1-linoleoyl-sn-glycero-3-phosphocholines was dispersed in heavy water at different concentrations. The phase structures were determined by 2H-, 14N- and 31P-NMR, polarization microscopy and low-angle X-ray diffraction. The phase diagrams of the oleoyl and linoleoyl systems were quite similar. At room temperature and with decreasing water content the isotropic micellar solution was followed by a hexagonal phase and then a cubic phase. Finally the lamellar phase appeared before the region of hydrated crystals. The same sequence of phases was observed in the stearoyl system at elevated temperatures. The palmitoyl system differed from the others: here a cubic phase followed after the micellar solution, then came a hexagonal phase and after this a lamellar phase. In general the lysophosphatidylcholines seem to behave similarly to the many soaps and detergents as they show the same sequence of isotropic micellar solution, hexagonal phase, lamellar phase with interspersed cubic phases. The presently established phase diagrams demonstrate that the major lysophosphatidylcholines which may be generated by phospholipase A2 in mammalian cell membranes, viz. 1-palmitoyl- and 1-stearoyl-glycerophosphocholines differ greatly in their packing properties. The extraordinary ability of 1-palmitoyl-glycerophosphocholine to form a cubic phase in equilibrium with a micellar solution is of particular interest with regard to the possible occurrence of cubic structures in biomembranes during the process of fusion.     

The crystal and molecular structure of VH amylose by electron diffraction analysis

The crystal and molecular structures of VH amylose were determined by a constrained linked-atom least-squares refinement, utilizing intensities measured from electron diffraction patterns and stereochemical restraints. Hexagonal platelet single crystals were grown from dilute aqueous ethanol solution and their electron diffraction diagrams analysed. These data indicated that the amylose chains were crystallized in a hexagonal lattice with a = b = 13.65 A, c (chain axis) = 8.05 A and space group P6(5)22. The best model obtained using the base plane data coupled with a stereochemical refinement yielded R = 0.24 (R' = 0.25). It corresponded to a system of left-handed 6-fold helices packed on an hexagonal net but with statistically random up/down chain disorder. A column of six water molecules was present within each helical repeat. Additionally, the gap between each pair of adjacent helices was bridged by two water molecules positioned so as to allow hydrogen bonding with chains of either sense. This proposed crystal structure differs somewhat from previous reports which invoked orthorhombic lattices and requires a regularly alternating arrangement of up and down chains to account for the intensity. Suggestions are made to account for these differences.     

Wave pattern analyses for cold vaso-oscillation

By immersion of rabbit's earlobes into a cold liquid at –5 to –10C, the blood vessels begin to constrict or dilate alternately. This is reflected in the vessel temperature: temperatures were recorded and the patterns analyzed. In each unit wave, the height and the period were designated as X and Y. From a series of about 10 waves, the standard deviation SD, coefficient of variation CV and correlation coefficient R for X and/or Y were obtained. These were considered as three fundamental parameters describing the characteristics of scatter diagrams for X and Y. The successive changes of RXY for the diagrams indicated in most cases the periodic tendency. In such cases, it can be regarded as a pantograph-like change of the successive scattered diagrams. The time course of CV also showed a similar tendency but nonperiodic time courses sometimes appeared. For weaker stimuli above 0C, the wave patterns tended to become more irregular.     

Bending, hydration and interstitial energies quantitatively account for the hexagonal-lamellar-hexagonal reentrant phase transition in dioleoylphosphatidylethanolamine.

We have accounted for the unusual structural change wherein dioleoylphosphatidylethanolamine undergoes a hexagonal-lamellar-hexagonal transition sequence as the water content is reduced systematically. We describe the role played by the energies of bending, hydration, voids in hexagonal interstices, and van der Waals interaction in this transition sequence. We have used the X-ray diffraction and osmotic stress experiments on the two phases to derive the structural parameters and all of the force constants defining the energetics of the hexagonal and lamellar phases. We have calculated the chemical potentials of lipid and water in both phases and derived the phase diagram of the lipid with no free, adjustable parameters. The calculated temperature/osmotic stress and temperature/composition diagrams quantitatively agree with experiment. The reentrant transition appears to be driven by a delicate balance between the hydration energy in the lamellar phase and bending energy in the hexagonal phase, whereas the energy of voids in hexagonal interstices defines its energy scale and temperature range. Van der Waals attraction between the bilayers in the lamellar phase does not appear to be important in this transition.     

Flagellar root maps allow speculative comparisons of root patterns and of their ontogeny

A method of mapping the patterns of origin of flagellar roots around basal bodies in two-dimensional diagrams is suggested, making allowance for the varied orientations of members of a pair or quartet of basal bodies in a cell. The method is used to compare flagellar root patterns in a wide range of protistan groups, and appears to demonstrate similarities in many areas. Comparison of such patterns in three published examples shows that during the ontogeny of a basal body it may display first one root pattern and then another, so that the root array of a given basal body is not fixed but changes with the position and role of that basal body in the cell.     

The conformation of the mucopolysaccharides. Hyaluronates

X-ray-diffraction patterns of hyaluronate fibres from a variety of sources were obtained. Sodium hyaluronate gives well-defined patterns which index on a hexagonal unit cell with dimensions a=1.17+/-nm and a fibre repeat-distance of 2.85+/-0.03nm. A further form of sodium hyaluronate is produced by annealing at 60 degrees C in 75% relative humidity. This stable state indexes on a hexagonal unit cell of unchanged fibre repeat-distance but with a=1.87nm. The chain conformation is a threefold helix. Analysis of these diffraction patterns led to two tentative structures for sodium hyaluronate, involving different packing of the polysaccharide chains. The significance of side-chain interaction is discussed. Hyaluronic acid produces an X-ray pattern different from that obtained with the sodium salt. The fibre repeat-distance is 1.96+/-0.02nm and the unit cell appears to be monoclinic. The chain conformation is a twofold helix and conformational change between free acid and monovalent salt is discussed. These findings, together with model-building experiments, are interpreted as indicating a highly ordered structure, and the physical properties of hyaluronate solutions with regard to molecular shape and polyelectrolyte behaviour are rationalized.     

Expected utility violations evolve under status-based selection mechanisms

The expected utility theory of decision making under uncertainty, a cornerstone of modern economics, assumes that humans linearly weight “utilities” for different possible outcomes by the probabilities with which these outcomes occur. Despite the theory's intuitive appeal, both from normative and from evolutionary perspectives, many experiments demonstrate systematic, though poorly understood, patterns of deviation from EU predictions. This paper offers a novel theoretical account of such patterns of deviation by demonstrating that EU violations can emerge from evolutionary selection when individual “status” affects inclusive fitness. In humans, battles for resources and social standing involve high-stakes decision making, and assortative mating ensures that status matters for fitness outcomes. The paper therefore proposes grounding the study of decision making under uncertainty in an evolutionary game-theoretic framework.     

Phenotypic assortment mediates the effect of social selection in a wild beetle population

Social interactions often have major fitness consequences, but little is known about how specific interacting phenotypes affect the strength of natural selection. Social influences on the evolutionary process can be assessed using a multilevel selection approach that partitions the effects of social partner phenotypes on fitness (referred to as social or group selection) from those of the traits of a focal individual (nonsocial or individual selection). To quantify the contribution of social selection to total selection affecting a trait, the patterns of phenotypic association among interactants must also be considered. We estimated selection gradients on male body size in a wild population of forked fungus beetles (Bolitotherus cornutus). We detected positive nonsocial selection and negative social selection on body size operating through differences in copulation success, indicating that large males with small social partners had highest fitness. In addition, we found that, in low-density demes, the phenotypes of focal individuals were negatively correlated with those of their social partners. This pattern reversed the negative effect of group selection on body size and led to stronger positive selection for body size. Our results demonstrate multilevel selection in nature and stress the importance of considering social selection whenever conspecific interactions occur nonrandomly.     

Robustness to noise in gene expression evolves despite epistatic constraints in a model of gene networks

Stochastic noise in gene expression causes variation in the development of phenotypes, making such noise a potential target of stabilizing selection. Here, we develop a new simulation model of gene networks to study the adaptive landscape underlying the evolution of robustness to noise. We find that epistatic interactions between the determinants of the expression of a gene and its downstream effect impose significant constraints on evolution, but these interactions do allow the gradual evolution of increased robustness. Despite strong sign epistasis, adaptation rarely proceeds via deleterious intermediate steps, but instead occurs primarily through small beneficial mutations. A simple mathematical model captures the relevant features of the single‐gene fitness landscape and explains counterintuitive patterns, such as a correlation between the mean and standard deviation of phenotypes. In more complex networks, mutations in regulatory regions provide evolutionary pathways to increased robustness. These results chart the constraints and possibilities of adaptation to reduce expression noise and demonstrate the potential of a novel modeling framework for gene networks.     

Method for the quantitative evaluation of the distribution pattern of nuclei in normal and malignant endometrial epithelia

A quantitative method of evaluating the pattern of distribution of nuclei within a cell cluster was developed and applied to endometrial cytology. The distribution pattern (DP) is mathematically expressed using a "DP index," which can be determined as a product of the square root of the nuclear density, square root of n0, and the mean distance between the two nearest nuclei, r. The DP index has a limited range of decreasing values from 1.074 to 0.5 to 0, indicative of regular, random and aggregated patterns of nuclear distribution, respectively. The estimated DP index was 0.831 +/- 0.031 (mean +/- standard deviation) in the clusters of normal endometrial epithelial cells from 16 nonneoplastic cases, but 0.638 +/- 0.041 in malignant epithelia from 19 cases of well-differentiated adenocarcinoma. The index of normal epithelia was close to 0.877 of the regular hexagonal distribution pattern. Contrary to this, the DP index was significantly smaller in well-differentiated adenocarcinoma (P less than .001), approaching 0.5, the theoretical value of a random distribution pattern. These findings suggest that quantitative analysis of the distribution pattern of nuclei can be a useful aid in the cytodiagnosis of endometrial lesions.     

Polygonal planforms and phyllotaxis on plants

We demonstrate how phyllotaxis (the arrangement of leaves on plants) and the ribbed, hexagonal, or parallelogram planforms on plants can be understood as the energy-minimizing buckling pattern of a compressed sheet (the plant's tunica) on an elastic foundation. The key idea is that the elastic energy is minimized by configurations consisting of special triads of periodic deformations. We study the conditions that lead to continuous or discontinuous transitions between patterns, state testable predictions, and suggest experiments to test the theory.     

The crystal structure of Bombyx mori silk fibroin at the air–water interface

A new crystalline polymorph of Bombyx mori silk, which forms at the air–water interface, has been characterized. A previous study found this structure to be trigonal, and to be distinctly different than the two previously observed silk crystal structures, silk I and silk II. This new structure was named silk III. Identification of this new silk polymorph was based on evidence from transmission electron microscopy and electron diffraction, coupled with molecular modeling. In the current paper, additional data enables us to refine our model of the silk III structure. Some single crystal electron diffraction patterns indicate a deviation in symmetry away from a perfect trigonal unit cell to monoclinic unit cell. The detailed shape of the powder diffraction peaks also supports a monoclinic cell. The monoclinic crystal structure has an nonprimitive unit cell incorporating a slightly distorted hexagonal packing of silk molecular helices. The chains each assume a threefold helical conformation, resulting in a crystal structure similar to that observed for polyglycine II, but with some additional sheet-like packing features common to the threefold helical crystalline forms of many glycine-rich polypeptides. © 1997 John Wiley & Sons, Inc. Biopoly 42: 705–717, 1997     

Detecting local adaptation using the joint sampling of polymorphism data in the parental and derived populations

When a local colonization in a new niche occurs, the new derived population should be subject to different selective pressures from that in the original parental population; consequently it is likely that many loci will be subject to directional selection. In such a quick adaptation event through environmental changes, it is reasonable to consider that selection utilizes genetic variations accumulated in the precolonization phase. This mode of selection from standing variation would play an important role in the evolution of new species. Here, we developed a coalescent-based simulation algorithm to generate patterns of DNA polymorphism in both parental and derived populations. Our simulations demonstrate that selection causes a drastic change in the pattern of polymorphism in the derived population, but not in the parental population. Therefore, for detecting the signature of local adaptation in polymorphism data, it is important to evaluate the data from both parental and derived populations simultaneously.     

ON THE OPPORTUNITY FOR SEXUAL SELECTION, THE BATEMAN GRADIENT AND THE MAXIMUM INTENSITY OF SEXUAL SELECTION

Bateman's classic paper on fly mating systems inspired quantitative study of sexual selection but also resulted in much debate and confusion. Here, I consider the meaning of Bateman's principles in the context of selection theory. Success in precopulatory sexual selection can be quantified as a "mating differential," which is the covariance between trait values and relative mating success. The mating differential is converted into a selection differential by the Bateman gradient, which is the least squares regression of relative reproductive success on relative mating success. Hence, a complete understanding of precopulatory sexual selection requires knowledge of two equally important aspects of mating patterns: the mating differential, which requires a focus on mechanisms generating covariance between trait values and mating success, and the Bateman gradient, which requires knowledge of the genetic mating system. An upper limit on the magnitude of the selection differential on any sexually selected trait is given by the product of the standard deviation in relative mating success and the Bateman gradient. This latter view of the maximum selection differential provides a clearer focus on the important aspects of precopulatory sexual selection than other methods and therefore should be an important part of future studies of sexual selection.     

Maintenance of clinal variation for shell colour phenotype in the flat periwinkle Littorina obtusata

Clines can signal spatially varying selection and therefore have long been used to investigate the role of environmental heterogeneity in maintaining genetic variation. However, clinal patterns alone are not sufficient to reject neutrality or to establish the mechanism of selection. Indirect, inferential methods can be used to address neutrality and mechanism, but fully understanding the adaptive significance of clinal variation ultimately requires a direct approach. Ecological model systems such as the rocky intertidal provide a useful context for direct experimentation and can serve as a complement to studies in more traditional genetic model systems. In this study, we use indirect and direct approaches to investigate the role of environmental heterogeneity in the maintenance of shell colour polymorphism in the flat periwinkle snail, Littorina obtusata. We document replicated clines in shell colour morph frequencies over thermal gradients at two spatial scales, contrasting with patterns at previously reported microsatellite loci. In addition, experimental results demonstrate that that shell colour has predictable effects on shell temperature and that these differences in temperature, in turn, coincide with patterns of survivorship under episodic thermal stress. Direct manipulation of shell colour revealed that shell colour, and not a correlated character, was the target of selection. Our study provides evidence that spatially varying selection via thermal regime contributes to the maintenance of shell colour phenotype variation in L. obtusata in the sampled areas of the Gulf of Maine.     

Heterogeneous patterns of variation among multiple human x-linked Loci: the possible role of diversity-reducing selection in non-africans

Studies of human DNA sequence polymorphism reveal a range of diversity patterns throughout the genome. This variation among loci may be due to natural selection, demographic influences, and/or different sampling strategies. Here we build on a continuing study of noncoding regions on the X chromosome in a panel of 41 globally sampled humans representing African and non-African populations by examining patterns of DNA sequence variation at four loci (APXL, AMELX, TNFSF5, and RRM2P4) and comparing these patterns with those previously reported at six loci in the same panel of 41 individuals. We also include comparisons with patterns of noncoding variation seen at five additional X-linked loci that were sequenced in similar global panels. We find that, while almost all loci show a reduction in non-African diversity, the magnitude of the reduction varies substantially across loci. The large observed variance in non-African levels of diversity results in the rejection of a neutral model of molecular evolution with a multi-locus HKA test under both a constant size and a bottleneck model. In non-Africans, some loci harbor an excess of rare mutations over neutral equilibrium predictions, while other loci show no such deviation in the distribution of mutation frequencies. We also observe a positive relationship between recombination rate and frequency spectra in our non-African, but not in our African, sample. These results indicate that a simple out-of-Africa bottleneck model is not sufficient to explain the observed patterns of sequence variation and that diversity-reducing selection acting at a subset of loci and/or a more complex neutral model must be invoked.     

Mimetic butterflies support Wallace's model of sexual dimorphism

Theoretical and empirical observations generally support Darwin's view that sexual dimorphism evolves due to sexual selection on, and deviation in, exaggerated male traits. Wallace presented a radical alternative, which is largely untested, that sexual dimorphism results from naturally selected deviation in protective female coloration. This leads to the prediction that deviation in female rather than male phenotype causes sexual dimorphism. Here I test Wallace's model of sexual dimorphism by tracing the evolutionary history of Batesian mimicry-an example of naturally selected protective coloration-on a molecular phylogeny of Papilio butterflies. I show that sexual dimorphism in Papilio is significantly correlated with both female-limited Batesian mimicry, where females are mimetic and males are non-mimetic, and with the deviation of female wing colour patterns from the ancestral patterns conserved in males. Thus, Wallace's model largely explains sexual dimorphism in Papilio. This finding, along with indirect support from recent studies on birds and lizards, suggests that Wallace's model may be more widely useful in explaining sexual dimorphism. These results also highlight the contribution of naturally selected female traits in driving phenotypic divergence between species, instead of merely facilitating the divergence in male sexual traits as described by Darwin's model.     

Smart skin patterns protect springtails

Springtails, arthropods who live in soil, in decaying material, and on plants, have adapted to demanding conditions by evolving extremely effective and robust anti-adhesive skin patterns. However, details of these unique properties and their structural basis are still unknown. Here we demonstrate that collembolan skin can resist wetting by many organic liquids and at elevated pressures. We show that the combination of bristles and a comb-like hexagonal or rhombic mesh of interconnected nanoscopic granules distinguish the skin of springtails from anti-adhesive plant surfaces. Furthermore, the negative overhang in the profile of the ridges and granules were revealed to be a highly effective, but as yet neglected, design principle of collembolan skin. We suggest an explanation for the non-wetting characteristics of surfaces consisting of such profiles irrespective of the chemical composition. Many valuable opportunities arise from the translation of the described comb-like patterns and overhanging profiles of collembolan skin into man-made surfaces that combine stability against wear and friction with superior non-wetting and anti-adhesive characteristics.     

Staying cool in a changing landscape: the influence of maximum daily ambient temperature on grizzly bear habitat selection

To fulfill their needs, animals are constantly making trade-offs among limiting factors. Although there is growing evidence about the impact of ambient temperature on habitat selection in mammals, the role of environmental conditions and thermoregulation on apex predators is poorly understood. Our objective was to investigate the influence of ambient temperature on habitat selection patterns of grizzly bears in the managed landscape of Alberta, Canada. Grizzly bear habitat selection followed a daily and seasonal pattern that was influenced by ambient temperature, with adult males showing stronger responses than females to warm temperatures. Cutblocks aged 0–20 years provided an abundance of forage but were on average 6 °C warmer than mature conifer stands and 21- to 40-year-old cutblocks. When ambient temperatures increased, the relative change (odds ratio) in the probability of selection for 0- to 20-year-old cutblocks decreased during the hottest part of the day and increased during cooler periods, especially for males. Concurrently, the probability of selection for 21- to 40-year-old cutblocks increased on warmer days. Following plant phenology, the odds of selecting 0- to 20-year-old cutblocks also increased from early to late summer while the odds of selecting 21- to 40-year-old cutblocks decreased. Our results demonstrate that ambient temperatures, and therefore thermal requirements, play a significant role in habitat selection patterns and behaviour of grizzly bears. In a changing climate, large mammals may increasingly need to adjust spatial and temporal selection patterns in response to thermal constraints.