Measurement scale in maximum entropy models of species abundance

The consistency of the species abundance distribution across diverse communities has attracted widespread attention. In this paper, I argue that the consistency of pattern arises because diverse ecological mechanisms share a common symmetry with regard to measurement scale. By symmetry, I mean that different ecological processes preserve the same measure of information and lose all other information in the aggregation of various perturbations. I frame these explanations of symmetry, measurement, and aggregation in terms of a recently developed extension to the theory of maximum entropy. I show that the natural measurement scale for the species abundance distribution is log-linear: the information in observations at small population sizes scales logarithmically and, as population size increases, the scaling of information grades from logarithmic to linear. Such log-linear scaling leads naturally to a gamma distribution for species abundance, which matches well with the observed patterns. Much of the variation between samples can be explained by the magnitude at which the measurement scale grades from logarithmic to linear. This measurement approach can be applied to the similar problem of allelic diversity in population genetics and to a wide variety of other patterns in biology.     

Informational symmetry breaking between proteins and nucleic acids.

Anti-symmetry of the information-processing mechanisms between proteins and nucleic acids is generalized to informational symmetry breaking between a genetic polymer and an anti-genetic polymer so as not to depend on particular chemical species. In a genetic polymer, e.g. nucleic acids, any sequence can form a closed double-stranded structure with a specific partner sequence. On the other hand, in an anti-genetic polymer, e.g. proteins, a chain could fold to an open multi-stranded structure and reinterpretation of the genetic information through slides or shifts between stacked strands could be induced by external perturbations. The possibility of the informational symmetry breaking by hierarchical organization of a single chemical species, i.e. polypeptides as a genetic polymer and nucleic acids as an anti-genetic polymer, is examined. The informational functions of genetic polymers and anti-genetic polymers in a complex mixture of macromolecules are characterized.     

Assessing mate size in the red swamp crayfish Procambarus clarkii: effects of visual versus chemical stimuli

1. Mate assessment requires an efficient system of information exchange between the sexes and often relies on several forms of communication. Both sexes of the crayfish, Procambarus clarkii , select a mate on the basis of its body size, independently of chelar size/symmetry and dominance status, large size being a proxy for a high quality partner. Here, we explored the effects that visual and chemical stimuli, emitted alone or in combination, exert on the assessment of size of a potential mate.
2. We followed a binary choice test paradigm, in which two male or female 'targets', of either large or small size, were simultaneously presented to a female or a male 'chooser'. We recorded the first target visited, the total duration of the visits per target, and the behaviour of the chooser when approaching the target area.
3. Our results show that females require a combination of visual and chemical stimuli to select the larger male. A more complex pattern was found when males were the choosers. While visual and chemical cues together rendered them willing to mate with the larger female, their initial choice and the total time spent near her depended only on smell. In mate assessment by P. clarkii , visual and chemical information seem to act as 'non-redundant signals'.     

Thermodynamics and muscle contraction. II. Consequences of the principle of maximization of the rate of entropy production]

For non-elastic irreversible mechanochemical machines of the muscular type, the above-mentioned principle (by H. Ziegler) leads to the following results. The velocity of shortening, v, decreases when the force F increases. The mechanical power of the system Fv, is active when 0 greater than v greater than vF=0 or 0 greater than F greater than Fv=0. At F=0 the rate of chemical reaction has the maximum and dQ/dF = -v greater than 0 (where Q is the rate of heat production). At v = 0 the rate of entropy production has the minimum and d/dv = F/A greater than 0 (where A is an affinity of the chemical reaction). The Onsager symmetry relation holds at v=0 only.     

Synthetic Turing protocells: vesicle self-reproduction through symmetry-breaking instabilities

The reproduction of a living cell requires a repeatable set of chemical events to be properly coordinated. Such events define a replication cycle, coupling the growth and shape change of the cell membrane with internal metabolic reactions. Although the logic of such process is determined by potentially simple physico-chemical laws, modelling of a full, self-maintained cell cycle is not trivial. Here we present a novel approach to the problem that makes use of so-called symmetry breaking instabilities as the engine of cell growth and division. It is shown that the process occurs as a consequence of the breaking of spatial symmetry and provides a reliable mechanism of vesicle growth and reproduction. Our model opens the possibility of a synthetic protocell lacking information but displaying self-reproduction under a very simple set of chemical reactions.     

Solid-state NMR investigation of indomethacin-cyclodextrin complexes in PEG 6000 carrier

Various solid dispersions of alpha-, beta- and gamma-cyclodextrin (CD) in PEG 6000 with and without the addition of 5% w/w indomethacin were prepared by the melting method using the original components. The samples were investigated by solid-state (13)C NMR, and the interactions between the drug and the cyclodextrins were evaluated. The indomethacin-gamma-CD phase with tetragonal symmetry found in a previous X-ray study gave chemical shifts which suggested that this phase is a complex between indomethacin and gamma-CD. Evidence of an indomethacin-beta-CD complex were found. A distribution of the chemical shifts for beta-CD was attributed to the possible formation of different types of complexes between indomethacin and beta-CD. No complex formation was found in the alpha-CD system. The degree of relative crystallinity of the samples in the gamma-CD system was measured by (1)H NMR, X-ray powder diffraction (XRD), differential scanning calorimetry (DSC), and modulated-temperature DSC (MTDSC). The results obtained by the NMR, XRD, and DSC techniques showed that the dispersions were less crystalline than the pure polymer carrier, and the dispersion containing the indomethacin-gamma-CD complex had the lowest degree of crystallinity. By the MTDSC method a deviation was found for the PEG 6000/indomethacin dispersion. This emphasizes that the different techniques give specific information on the crystallinity.     

Heteronuclear NMR assignments and secondary structure of the coiled coil trimerization domain from cartilage matrix protein in oxidized and reduced forms.

The C-terminal oligomerization domain of chicken cartilage matrix protein is a trimeric coiled coil comprised of three identical 43-residue chains. NMR spectra of the protein show equivalent magnetic environments for each monomer, indicating a parallel coiled coil structure with complete threefold symmetry. Sequence-specific assignments for 1H-, 15N-, and 13C-NMR resonances have been obtained from 2D 1H NOESY and TOCSY spectra, and from 3D HNCA, 15N NOESY-HSQC, and HCCH-TOCSY spectra. A stretch of alpha-helix encompassing five heptad repeats (35 residues) has been identified from intra-chain HN-HN and HN-H alpha NOE connectivities. 3JHNH alpha coupling constants, and chemical shift indices. The alpha-helix begins immediately downstream of inter-chain disulfide bonds between residues Cys 5 and Cys 7, and extends to near the C-terminus of the molecule. The threefold symmetry of the molecule is maintained when the inter-chain disulfide bonds that flank the N-terminus of the coiled coil are reduced. Residues Ile 21 through Glu 36 show conserved chemical shifts and NOE connectivities, as well as strong protection from solvent exchange in the oxidized and reduced forms of the protein. By contrast, residues Ile 10 through Val 17 show pronounced chemical shift differences between the oxidized and reduced protein. Strong chemical exchange NOEs between HN resonances and water indicate solvent exchange on time scales faster than 10 s, and suggests a dynamic fraying of the N-terminus of the coiled coil upon reduction of the disulfide bonds. Possible roles for the disulfide crosslinks of the oligomerization domain in the function of cartilage matrix protein are proposed.     

The portal protein of bacteriophage SPP1: a DNA pump with 13-fold symmetry.

Electron microscopy in combination with image processing is a powerful method for obtaining structural information on non-crystallized biological macromolecules at the 10-50 A resolution level. The processing of noisy microscopical images requires advanced data processing methodologies in which one must carefully avoid the introduction of any form of bias into the data set. Using a novel multivariate statistical approach to the analysis of symmetry, we studied the structure of the bacteriophage SPP1 portal protein oligomer. This portal structure, ubiquitous in icosahedral bacteriophages which package dsDNA, is located at the site of symmetry mismatch between a 5-fold vertex of the icosahedral shell and the 6-fold symmetric (helical) tail. From previous studies such 'head-to-tail connector' structures were generally accepted to be homododecamers assembled in a 12-fold symmetric ring around a central channel. Using a new analysis methodology we have found that the phage SPP1 portal structure exhibits 13-fold cyclical symmetry: a new point group organization for oligomeric proteins. A model for the DNA packaging mechanism by 13-fold symmetric portal protein assemblies is presented which attributes a coherent functional meaning to their unusual symmetry.     

Integrating Cross-Linking Experiments with Ab Initio Protein–Protein Docking

Ab initio protein–protein docking algorithms often rely on experimental data to identify the most likely complex structure. We integrated protein–protein docking with the experimental data of chemical cross-linking followed by mass spectrometry. We tested our approach using 19 cases that resulted from an exhaustive search of the Protein Data Bank for protein complexes with cross-links identified in our experiments. We implemented cross-links as constraints based on Euclidean distance or void-volume distance. For most test cases, the rank of the top-scoring near-native prediction was improved by at least twofold compared with docking without the cross-link information, and the success rate for the top 5 predictions nearly tripled. Our results demonstrate the delicate balance between retaining correct predictions and eliminating false positives. Several test cases had multiple components with distinct interfaces, and we present an approach for assigning cross-links to the interfaces. Employing the symmetry information for these cases further improved the performance of complex structure prediction.     

A comparison of symmetry and flatness measurements in small electron fields by different dosimeters in electron beam radiotherapy

BackgroundSymmetry and flatness are two quantities which should be evaluated in the commissioning and quality control of an electron beam in electron beam radiotherapy. The aim of this study is to compare symmetry and flatness obtained using three different dosimeters for various small and large fields in electron beam radiotherapy with linac.Materials and methodsBeam profile measurements were performed in a PTW water phantom for 10, 15 and 18 MeV electron beams of an Elekta Precise linac for small and large beams (1.5 × 1.5 cm² to 20 × 20 cm² field sizes). A Diode E detector and Semiflex-3D and Advanced Markus ionization chambers were used for dosimetry.ResultsBased on the obtained results, there are minor differences between the responses from different dosimeters (Diode E detector and Semiflex-3D and Advanced Markus ionization chambers) in measurement of symmetry and flatness for the electron beams. The symmetry and flatness values increase with increasing field size and electron beam energy for small and large field sizes, while the increases are minor in some cases.ConclusionsThe results indicate that the differences between the symmetry and flatness values obtained from the three dosimeter types are not practically important.     

Action in Perception: Prominent Visuo-Motor Functional Symmetry in Musicians during Music Listening

Musical training leads to sensory and motor neuroplastic changes in the human brain. Motivated by findings on enlarged corpus callosum in musicians and asymmetric somatomotor representation in string players, we investigated the relationship between musical training, callosal anatomy, and interhemispheric functional symmetry during music listening. Functional symmetry was increased in musicians compared to nonmusicians, and in keyboardists compared to string players. This increased functional symmetry was prominent in visual and motor brain networks. Callosal size did not significantly differ between groups except for the posterior callosum in musicians compared to nonmusicians. We conclude that the distinctive postural and kinematic symmetry in instrument playing cross-modally shapes information processing in sensory-motor cortical areas during music listening. This cross-modal plasticity suggests that motor training affects music perception.     

Resource value and communication strategy in the hermit crab Pagurus bernhardus (L.)

The prediction of Maynard Smith & Parker (1976) that increases in symmetry of resourceholding potential should be associated with reduced levels of information transmission by displays was tested in the hermit crab Pagurus bernhardus. Equalization of the gastropod shell resource value within groups of crabs was followed by a reduction of inter-individual transmission of information, but only in medium-sized crabs and not in small crabs.     

Chiral Symmetry Breaking in Peptide Systems During Formation of Life on Earth

Chiral symmetry breaking in complex chemical systems with a large number of amino acids and a large number of similar reactions was considered. It was shown that effective averaging over similar reaction channels may result in very weak effective enantioselectivity of forward reactions, which does not allow most of the known models to result in chiral symmetry breaking during formation of life on Earth. Models with simple and catalytic synthesis of a single amino acid, formation of peptides up to length five, and sedimentation of insoluble pair of substances were considered. It was shown that depending on the model and the values of the parameters, chiral symmetry breaking may occur in up to about 10% out of all possible unique insoluble pair combinations even in the absence of any catalytic synthesis and that minimum total number of amino acids in the pair is 5. If weak enantioselective forward catalytic synthesis of amino acids is present, then the number of possible variants, in which chiral symmetry breaking may occur, increases substantially. It was shown that that the most interesting catalysts have zero or one amino acid of “incorrect” chirality. If the parameters of the model are adjusted in such a way to result in an increase of concentration of longer peptides, then catalysts with two amino acids of incorrect chirality start to appear at peptides of length five. Models of chiral symmetry breaking in the presence of epimerization were considered for peptides up to length three. It was shown that the range of parameters in which chiral symmetry breaking could occur significantly shrinks in comparison to previously considered models with peptides up to length two. An experiment of chiral symmetry breaking was proposed. The experiment consists of a three-step cycle: reversible catalytic synthesis of amino acids, reversible synthesis of peptides, and irreversible sedimentation of insoluble substances.     

Information transformations in molecular evolution

The prebiotic evolution of chemical systems is characterized by their development of increasingly complex levels of molecular organization. This development is dependent upon the capacity of these systems to acquire and transform chemical information. The informational content of a chemical system can be divided into configurational, energetic, and thermal contributions. The thermal information is specifically related to the number of molecules in the system, and is therefore a function of molecular size or complexity. The molecular complexity of a chemical system can be increased through reactions in which reductions in configurational or energetic information are coupled to increases in thermal information, as limited by the second law of thermodynamics.     

Selection of molecular chirality by extremely weak chiral interactions under far-from-equilibrium conditions

A general formalism for chiral symmetry breaking in far-from-equilibrium chemical systems is presented. It is pointed out that slow passage through the transition point makes the system sensitive to very weak, but systematic, chiral influences. The general implications of this process for the origin of biomolecular chirality is discussed.     

Polarity determination in the Drosophila eye.

In the Drosophila eye, photoreceptor clusters are arranged with mirror-image symmetry about the dorso-ventral midline. Recent work indicates critical r?les for Wingless and JAK/STAT signalling in setting up long-range gradients of positional information that determine this symmetry. Furthermore, important functions have been elucidated for Notch signalling in specifying the position of the axis of symmetry and then later in development in interpreting gradient information.     

Unilateral Auditory Cortex Lesions Impair or Improve Discrimination Learning of Amplitude Modulated Sounds,Depending on Lesion Side

A fundamental principle of brain organization is bilateral symmetry of structures and functions. For spatial sensory and motor information processing, this organization is generally plausible subserving orientation and coordination of a bilaterally symmetric body. However, breaking of the symmetry principle is often seen for functions that depend on convergent information processing and lateralized output control, e.g. left hemispheric dominance for the linguistic speech system. Conversely, a subtle splitting of functions into hemispheres may occur if peripheral information from symmetric sense organs is partly redundant, e.g. auditory pattern recognition, and therefore allows central conceptualizations of complex stimuli from different feature viewpoints, as demonstrated e.g. for hemispheric analysis of frequency modulations in auditory cortex (AC) of mammals including humans. Here we demonstrate that discrimination learning of rapidly but not of slowly amplitude modulated tones is non-uniformly distributed across both hemispheres: While unilateral ablation of left AC in gerbils leads to impairment of normal discrimination learning of rapid amplitude modulations, right side ablations lead to improvement over normal learning. These results point to a rivalry interaction between both ACs in the intact brain where the right side competes with and weakens learning capability maximally attainable by the dominant left side alone.     

Synaptic Symmetry Increases Coherence in a Pair of Excitable Electronic Neurons

We study how the synaptic connections in a pair of excitable electronic neurons affect the coherence of their spike trains when the neurons are submitted to noise from independent sources. The coupling is provided by electronic circuits which mimic the dynamics of chemical AMPA synapses. In particular, we show that increasing the strength of an unidirectional synapse leads to a decrease of coherence in the post-synaptic neuron. More interestingly, we show that the decrease of coherence can be reverted if we add a synapse of sufficient strength in the reverse direction. Synaptic symmetry plays an important role in this process and, under the right choice of parameters, increases the network coherence beyond the value achieved at the resonance due to noise alone in uncoupled neurons. We also show that synapses with a longer time scale sharpen the dependency of the coherence on the synaptic symmetry. The results were reproduced by numerical simulations of a pair of synaptically coupled FitzHugh-Nagumo models.     

Survey of chemical speciation of trace elements using synchrotron radiation

Information concerning the chemical state of trace elements in biological systems generally has not been available. Such information for toxic elements and metals in metalloproteins could prove extremely valuable in the elucidation of their metabolism and other biological processes. The shielding of core electrons by binding electrons affect the energy required for creating inner-shell holes. Furthermore, the molecular binding and symmetry of the local environment of an atom affect the absorption spectrum in the neighborhood of the absorption edge. X-ray absorption near-edge structure (XANES) using synchrotron radiation excitation can be used to provide chemical speciation information for trace elements at concentrations as low as 10 ppm. The structure and position of the absorption curve in the region of an edge can yield vital data about the local structure and oxidation state of the trace element in question. Data are most easily interpreted by comparing the observed edge structure and position with those of model compounds of the element covering the entire range of possible oxidation states. Examples of such analyses will be reviewed.     

Symmetry and entropy of biological patterns: discrete Walsh functions for 2D image analysis

To quantify symmetry and entropy inherent in the discrete patterns such as spatial self-organization in cell sorting and mussel bed ecosystems, we introduce the discrete Walsh analysis. This analysis enables us to estimate the degree of the complicated symmetry, and to extract the symmetry from the pattern that seems to be asymmetric. The results obtained in this paper are summarized as follows. (I) The geometrical patterns of the cell sorting become systematic with the predominance of the particular symmetry. This implies that not only the entropy but also the particular symmetry can decrease in the biological process. (II) The magnitude of the symmetry is related to the absolute value of the adhesion, and the type of the symmetry is related to the sign of the adhesion. That is, centro-symmetry dominates in the cell sorting pattern caused by large negative adhesion, and double symmetry dominates in the pattern caused by large positive adhesion. (III) Spatial self-organization in mussel bed is accompanied by the decreasing of the centro-symmetry. This implies that the positive "adhesion" between mussel individuals increases with time. (IV) In the biological process, the Curie symmetry breaking occurs at intervals.