Molecular shape as a key source of prebiotic information.

One of the most striking features of a living system is the self-sustaining functional inner organization, which is only possible when a source of internal references is available from which the system is able to self-organize components and processes. Internal references are intrinsically related to biological information, which is typically understood as genetic information. However, the organization in living systems supports a diversity of intricate processes that enable life to endure, adapt and reproduce because of this organization. In a biological context, information refers to a complex relationship between internal architecture and system functionality. Nongenetic processes, such as conformational recognition, are not considered biological information, although they exert important control over cell processes. In this contribution, we discuss the informational nature in the recognition of molecular shape in living systems. Thus, we highlight supramolecular matching as having a theoretical key role in the origin of life. Based on recent data, we demonstrate that the transfer of molecular conformation is a very likely dynamic of prebiotic information, which is closely related to the origin of biological homochirality and biogenic systems. In light of the current hypothesis, we also revisit the central dogma of molecular biology to assess the consistency of the proposal presented here. We conclude that both spatial (molecular shape) and sequential (genetic) information must be represented in this biological paradigm.

Multiwall and bamboo-like carbon nanotubes from the Allende chondrite: A probable source of asymmetry.

This study presents multiwall and bamboo-like carbon nanotubes found in samples from the Allende carbonaceous chondrite using high-resolution transmission electron microscopy (HRTEM). A highly disordered lattice observed in this material suggests the presence of chiral domains in it. Our results also show amorphous and poorly-graphitized carbon, nanodiamonds, and onion-like fullerenes. The presence of multiwall and bamboo-like carbon nanotubes have important implications for hypotheses that explain how a probable source of asymmetry in carbonaceous chondrites might have contributed to the enantiomeric excess in soluble organics under extraterrestrial scenarios. This is the first study proving the existence of carbon nanotubes in carbonaceous chondrites.

Rank ordered beta distributions of nonlinear map symbolic dynamics families with a first-order transition between dynamical regimes.

Rank-ordered distributions have been a matter of intense study. Often Zipf type invariant scaling is invoked; however, in the last decade the ubiquity of a Discrete Generalized Beta Distribution, DGBD, with two scaling exponents has been established. This distribution incorporates deviations from the power law at the extremes. A proper understanding of the meaning of these exponents is still lacking. Here, using two families of unimodal maps on the [0,1] interval, we construct binary sequences via standard symbolic dynamics. In both cases, the tent map, which is at the convex-concave border of the mapping families, separates intermittent regimes from chaotic dynamics. We show that the frequencies of n-tuples of the generated symbolic sequences are remarkably well fitted by the DGBD. We argue that in the underlying dynamics an order-disorder competition takes place and that one of the exponents is related to multiple range correlations, while the other is sensitive to disorder. In our study, we implement thermodynamic formalisms with which we can readily calculate n-tuple frequencies, in some particular cases, analytically. We show that for the convex mappings there is a first-order thermodynamic phase transition, while concave mappings have smooth free energy densities. Within our DGBD study, the transition between these two regimes coincides with a zero value for both exponents; in this sense, they may even be considered as indicators of the transition. An analysis of the difference between the exponents reinforces the interpretation we have assigned to them. Furthermore, the two regimes can be identified by the sign of such a difference. We also show that divergences in the invariant densities are responsible for the first order phase transitions observed in a range of the rank-frequency distributions. Our findings give further support to previous studies based on expansion-modification algorithms, birth-death processes, and random variable subtraction dynamics.

Cancer growth and metastasis as a metaphor of Go gaming: An Ising model approach.

This work aims for modeling and simulating the metastasis of cancer, via the analogy between the cancer process and the board game Go. In the game of Go, black stones that play first could correspond to a metaphor of the birth, growth, and metastasis of cancer. Moreover, playing white stones on the second turn could correspond the inhibition of cancer invasion. Mathematical modeling and algorithmic simulation of Go may therefore benefit the efforts to deploy therapies to surpass cancer illness by providing insight into the cellular growth and expansion over a tissue area. We use the Ising Hamiltonian, that models the energy exchange in interacting particles, for modeling the cancer dynamics. Parameters in the energy function refer the biochemical elements that induce cancer birth, growth, and metastasis; as well as the biochemical immune system process of defense.

Parameters Estimation in Phase-Space Landscape Reconstruction of Cell Fate: A Systems Biology Approach.

The thermodynamical formalism of irreversible processes offers a theoretical framework appropriate to explain the complexity observed at the macroscopic level of dynamic systems. In this context, together with the theory of complex systems and systems biology, the thermodynamical formalism establishes an appropriate conceptual framework to address the study of biological systems, in particular cancer.The Chapter is organized as follows: In Subheading 1, an integrative view of these disciplines is offered, for the characterization of the emergence and evolution of cancer, seen as a self-organized dynamic system far from the thermodynamic equilibrium. Development of a thermodynamic framework, based on the entropy production rate, is presented in Subheading 2. Subheading 3 is dedicated to all tumor growth, as seen through a "phase transitions" far from equilibrium. Subheading 4 is devoted to complexity of cancer glycolysis. Finally, some concluding remarks are presented in Subheading 5.

Protein surface roughness accounts for binding free energy of Plasmepsin II-ligand complexes.

The calculation of absolute binding affinities for protein-inhibitor complexes remains as one of the main challenges in computational structure-based ligand design. The present work explored the calculations of surface fractal dimension (as a measure of surface roughness) and the relationship with experimental binding free energies of Plasmepsin II complexes. Plasmepsin II is an attractive target for novel therapeutic compounds to treat malaria. However, the structural flexibility of this enzyme is a drawback when searching for specific inhibitors. Concerning that, we performed separate explicitly solvated molecular dynamics simulations using the available high-resolution crystal structures of different Plasmepsin II complexes. Molecular dynamics simulations allowed a better approximation to systems dynamics and, therefore, a more reliable estimation of surface roughness. This constitutes a novel approximation in order to obtain more realistic values of fractal dimension, because previous works considered only x-ray structures. Binding site fractal dimension was calculated considering the ensemble of structures generated at different simulation times. A linear relationship between binding site fractal dimension and experimental binding free energies of the complexes was observed within 20 ns. Previous studies of the subject did not uncover this relationship. Regression model, coined FD model, was built to estimate binding free energies from binding site fractal dimension values. Leave-one-out cross-validation showed that our model reproduced accurately the absolute binding free energies for our training set (R2  = 0.76; <|error|> =0.55 kcal/mol; SDerror  = 0.19 kcal/mol). The fact that such a simple model may be applied raises some questions that are addressed in the article.

Population patterns in World's administrative units.

Whereas there has been an extended discussion concerning city population distribution, little has been said about that of administrative divisions. In this work, we investigate the population distribution of second-level administrative units of 150 countries and territories and propose the discrete generalized beta distribution (DGBD) rank-size function to describe the data. After testing the balance between the goodness of fit and number of parameters of this function compared with a power law, which is the most common model for city population, the DGBD is a good statistical model for 96% of our datasets and preferred over a power law in almost every case. Moreover, the DGBD is preferred over a power law for fitting country population data, which can be seen as the zeroth-level administrative unit. We present a computational toy model to simulate the formation of administrative divisions in one dimension and give numerical evidence that the DGBD arises from a particular case of this model. This model, along with the fitting of the DGBD, proves adequate in reproducing and describing local unit evolution and its effect on the population distribution.

Beyond Zipf's Law: The Lavalette Rank Function and Its Properties.

Although Zipf's law is widespread in natural and social data, one often encounters situations where one or both ends of the ranked data deviate from the power-law function. Previously we proposed the Beta rank function to improve the fitting of data which does not follow a perfect Zipf's law. Here we show that when the two parameters in the Beta rank function have the same value, the Lavalette rank function, the probability density function can be derived analytically. We also show both computationally and analytically that Lavalette distribution is approximately equal, though not identical, to the lognormal distribution. We illustrate the utility of Lavalette rank function in several datasets. We also address three analysis issues on the statistical testing of Lavalette fitting function, comparison between Zipf's law and lognormal distribution through Lavalette function, and comparison between lognormal distribution and Lavalette distribution.

Genomic signatures in viral sequences by in-frame and out-frame mutual information.

In order to understand the unique biology of viruses, we use the Mutual Information Function (MIF) to characterize 792 viral sequences comprising 458 viral whole genomes. A 3-base periodicity (3-bp) was observed only in DNA-viruses whereas RNA-viruses showed irregular patterns. The correlation of MIF values at frequencies of 3-bp (in-frame) with frequencies of 4 and 5bps (out-frame), turned out to be useful to distinguish viruses according to their respective taxonomic order, and whether they pertain to any of the three different kingdoms, Eubacteria, Archaea and Eukarya. The clustering of viruses was carried out by the use of a new statistics, namely, the pair of in- and out-frame values of the MIF. The clustering thus obtained turned out to be entirely consistent with the current viral taxonomy. As a result we were able to compare in a single plot both viral and cellular genomes unlike any given phylogenetic reconstruction.

Statistical correlation of nonconservative substitutions of HIV gp41 variable amino acid residues with the R5X4 HIV-1 phenotype.

BACKGROUND: The interaction of the envelope glycoprotein of HIV-1 (gp120/gp41) with coreceptor molecules has important implications for specific cellular targeting and pathogenesis. Experimental and theoretical evidences have shown a role for gp41 in coreceptor tropism, although there is no consensus about the positions involved. Here we analyze the association of physicochemical properties of gp41 amino acid residues with viral tropism (X4, R5, and R5X4) using a large set of HIV-1 sequences. Under the assumption that conserved regions define the complex structural features essential for protein function, we focused our search only on amino acids in the gp41 variable regions. METHODS: Gp41 amino acid sequences of 2823 HIV-1 strains from all clades with known coreceptor tropism were retrieved from Los Alamos HIV Database. Consensus sequences were constructed for homologous sequences (those obtained from the same patient and having the same tropism) in order to avoid bias due to sequence overrepresentation, and the variability (entropy) per site was determined. Comparisons of hydropathy index (HI) and charge (Q) of amino acid residues at highly variable positions between coreceptor groups were performed using two non-parametrical tests and Benjamini-Hochberg correction. Pearson's correlation analysis was performed to determine covariance of HI and Q values. RESULTS: Calculation of variability per site rendered 58 highly variable amino acid positions. Of these, statistical analysis rendered significantly different HI or Q only for the R5 vs. R5X4 comparison at twelve positions: 535, 602, 619, 636, 640, 641, 658, 662, 667, 723, 756 and 841. The largest differences in particular amino acid frequencies between coreceptor groups were found at 619, 636, 640, 641, 662, 723 and 756. A hydrophobic tendency of residues 619, 640, 641, 723 and 756, along with a hydrophilic/charged tendency at residues 636 and 662 was observed in R5X4 with respect to R5 sequences. HI of position 640 covariated with that of 602, 619, 636, 662, and 756. CONCLUSIONS: Variability and significant correlations of physicochemical properties with viral phenotype suggest that substitutions at residues in the loop (602 and 619), the HR2 (636, 640, 641, 662), and the C-terminal tail (723, 756) of gp41 may contribute to phenotype of R5X4 strains.

Rank diversity of languages: generic behavior in computational linguistics.

Statistical studies of languages have focused on the rank-frequency distribution of words. Instead, we introduce here a measure of how word ranks change in time and call this distribution rank diversity. We calculate this diversity for books published in six European languages since 1800, and find that it follows a universal lognormal distribution. Based on the mean and standard deviation associated with the lognormal distribution, we define three different word regimes of languages: "heads" consist of words which almost do not change their rank in time, "bodies" are words of general use, while "tails" are comprised by context-specific words and vary their rank considerably in time. The heads and bodies reflect the size of language cores identified by linguists for basic communication. We propose a Gaussian random walk model which reproduces the rank variation of words in time and thus the diversity. Rank diversity of words can be understood as the result of random variations in rank, where the size of the variation depends on the rank itself. We find that the core size is similar for all languages studied.

Bacterial genomes lacking long-range correlations may not be modeled by low-order Markov chains: the role of mixing statistics and frame shift of neighboring genes.

We examine the relationship between exponential correlation functions and Markov models in a bacterial genome in detail. Despite the well known fact that Markov models generate sequences with correlation function that decays exponentially, simply constructed Markov models based on nearest-neighbor dimer (first-order), trimer (second-order), up to hexamer (fifth-order), and treating the DNA sequence as being homogeneous all fail to predict the value of exponential decay rate. Even reading-frame-specific Markov models (both first- and fifth-order) could not explain the fact that the exponential decay is very slow. Starting with the in-phase coding-DNA-sequence (CDS), we investigated correlation within a fixed-codon-position subsequence, and in artificially constructed sequences by packing CDSs with out-of-phase spacers, as well as altering CDS length distribution by imposing an upper limit. From these targeted analyses, we conclude that the correlation in the bacterial genomic sequence is mainly due to a mixing of heterogeneous statistics at different codon positions, and the decay of correlation is due to the possible out-of-phase between neighboring CDSs. There are also small contributions to the correlation from bases at the same codon position, as well as by non-coding sequences. These show that the seemingly simple exponential correlation functions in bacterial genome hide a complexity in correlation structure which is not suitable for a modeling by Markov chain in a homogeneous sequence. Other results include: use of the (absolute value) second largest eigenvalue to represent the 16 correlation functions and the prediction of a 10-11 base periodicity from the hexamer frequencies.

Differences in HIV-1 viral loads between male and female antiretroviral-untreated Mexican patients.

BACKGROUND AND AIMS: HIV-1 viral load is used to monitor AIDS progression and effect of antiretroviral therapy (ART). Several reports have indicated that the HIV-1 viral load of infected individuals is lower in females than in males. There are no reports exploring this issue in the Mexican population. We analyzed the relationship between sex and viral load in Mexican patients differing in CD4 T-cell count, age and treatment status. METHODS: A retrospective study was performed in 3949 male and 696 female HIV-1-infected individuals. Statistical distributions were compared using the Mann-Whitney U nonparametric test. RESULTS: Among the antiretroviral-untreated group, females had a significantly lower viral load than males (0.52 female/male median viral load ratio, p = 0.008). When classified according to different ranges of CD4⁺ T cell counts, females had consistently lower viral loads than males, although statistical significance was achieved only for the group in the range of 201-350 (p = 0.014). Patients with the lowest CD4⁺ T-cell counts showed similar viral loads for both sexes. No differences were observed in the ART group. CONCLUSIONS: This study demonstrates a baseline difference in viral load between male and female ART-untreated Mexican patients. The overall tendency indicating a lower viral load in females in the same ranges of CD4⁺ T-cell counts than males, suggests that the lower viral load in females is not indicative of a lower risk of developing AIDS. These observations suggest a significant influence of sex on viral dynamics and immune response despite variations in demographic factors.

An epigenetic model for pigment patterning based on mechanical and cellular interactions.

Pigment patterning in animals generally occurs during early developmental stages and has ecological, physiological, ethological, and evolutionary significance. Despite the relative simplicity of color patterns, their emergence depends upon multilevel complex processes. Thus, theoretical models have become necessary tools to further understand how such patterns emerge. Recent studies have reevaluated the importance of epigenetic, as well as genetic factors in developmental pattern formation. Yet epigenetic phenomena, specially those related to physical constraints that might be involved in the emergence of color patterns, have not been fully studied. In this article, we propose a model of color patterning in which epigenetic aspects such as cell migration, cell-tissue interactions, and physical and mechanical phenomena are central. This model considers that motile cells embedded in a fibrous, viscoelastic matrix-mesenchyme-can deform it in such a way that tension tracks are formed. We postulate that these tracks act, in turn, as guides for subsequent cell migration and establishment, generating long-range phenomenological interactions. We aim to describe some general aspects of this developmental phenomenon with a rather simple mathematical model. Then we discuss our model in the context of available experimental and morphological evidence for reptiles, amphibians, and fishes, and compare it with other patterning models. We also put forward novel testable predictions derived from our model, regarding, for instance, the localization of the postulated tension tracks, and we propose new experiments. Finally, we discuss how the proposed mechanism could constitute a dynamic patterning module accounting for pattern formation in many animal lineages.

Universality of rank-ordering distributions in the arts and sciences.

Searching for generic behaviors has been one of the driving forces leading to a deep understanding and classification of diverse phenomena. Usually a starting point is the development of a phenomenology based on observations. Such is the case for power law distributions encountered in a wealth of situations coming from physics, geophysics, biology, lexicography as well as social and financial networks. This finding is however restricted to a range of values outside of which finite size corrections are often invoked. Here we uncover a universal behavior of the way in which elements of a system are distributed according to their rank with respect to a given property, valid for the full range of values, regardless of whether or not a power law has previously been suggested. We propose a two parameter functional form for these rank-ordered distributions that gives excellent fits to an impressive amount of very diverse phenomena, coming from the arts, social and natural sciences. It is a discrete version of a generalized beta distribution, given by f(r) = A(N+1-r)(b)/r(a), where r is the rank, N its maximum value, A the normalization constant and (a, b) two fitting exponents. Prompted by our genetic sequence observations we present a growth probabilistic model incorporating mutation-duplication features that generates data complying with this distribution. The competition between permanence and change appears to be a relevant, though not necessary feature. Additionally, our observations mainly of social phenomena suggest that a multifactorial quality resulting from the convergence of several heterogeneous underlying processes is an important feature. We also explore the significance of the distribution parameters and their classifying potential. The ubiquity of our findings suggests that there must be a fundamental underlying explanation, most probably of a statistical nature, such as an appropriate central limit theorem formulation.

Scale-free foraging by primates emerges from their interaction with a complex environment.

Scale-free foraging patterns are widespread among animals. These may be the outcome of an optimal searching strategy to find scarce, randomly distributed resources, but a less explored alternative is that this behaviour may result from the interaction of foraging animals with a particular distribution of resources. We introduce a simple foraging model where individual primates follow mental maps and choose their displacements according to a maximum efficiency criterion, in a spatially disordered environment containing many trees with a heterogeneous size distribution. We show that a particular tree-size frequency distribution induces non-Gaussian movement patterns with multiple spatial scales (Lévy walks). These results are consistent with field observations of tree-size variation and spider monkey (Ateles geoffroyi) foraging patterns. We discuss the consequences that our results may have for the patterns of seed dispersal by foraging primates.

HIV-1 dynamics at different time scales under antiretroviral therapy.

We exploit a model that considers three compartments: blood plasma (BP), lymphoid tissue-interstitial spaces (LT-IS), and follicular dendritic cells (FDC), for the HIV-1 dynamics under the application of highly active antiretroviral therapy (HAART) which allowed us to unravel distinct viral dynamics occurring in short- (2 days), middle- (21 days), and long-term (183 days) time scales. The different time scales are determined by the viral clearance rate, the ratio of productively infected CD4(+) T cells to chronically infected cells, and the dissociation rate of HIV-1 complexes from FDC. This generates a scenario in which, after an initial transient stage, the viral BP dynamics decouples and becomes governed by the lymphoid tissue (LT) dynamics; in a later stage, a new decoupling occurs in which the LT-IS dynamics is slaved to that of the FDC dynamics. We observed an initial increase in the viremia after HAART in a patient who did not receive protease inhibitors (PI). By means of the above-mentioned model we were able to highlight the relevant parameters which need to be estimated at three different time scales after HAART.