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arXiv2008

Towards an unifying perspective of the fundamental properties and structural principles governing the immune system

In the study of the basic properties observed in the immune system and, in a broader view, in biological systems, several concepts have already been mathematically formulated or treated in an analytical perspective, such as degeneracy, robustness, noise, and bow tie architecture. These properties, among others, seem to rule many aspects of the system functioning, and share among themselvesseveral characteristics, intersecting each other, and often becoming one the indivisible part of the other. According to Kitano, systems biology needs solid theoretical and methodological foundation of principles and properties, able to lead towards a unified perspective. An effort in unifying the formalization and analysis of these principles can be now timely attempted.

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arXiv2008

Within-host HIV models with periodic antiretroviral therapy

This paper investigates the effect of drug treatment on the standard within-host HIV model, assuming that therapy occurs periodically. It is shown that eradication is possible under these periodic regimes, and we quantitatively characterize successful drugs or drug combinations, both theoretically and numerically. We also consider certain optimization problems, motivated for instance, by the fact that eradication should be achieved at acceptable toxicity levels to the patient. It turns out that these optimization problems can be simplified considerably, and this makes calculations of the optima a fairly straightforward task. All our results will be illustrated by means of numerical examples based on up-to-date knowledge of parameter values in the model.

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arXiv2010

The degeneracy of the genetic code and Hadamard matrices

The matrix form of the presentation of the genetic code is described as the cognitive form to analyze structures of the genetic code. A similar matrix form is utilized in the theory of signal processing. The Kronecker family of the genetic matrices is investigated, which is based on the genetic matrix [C A; U G], where C, A, U, G are the letters of the genetic alphabet. This matrix in the third Kronecker power is the (8*8)-matrix, which contains 64 triplets. Peculiarities of the degeneracy of the vertebrate mitochondria genetic code are reflected in the symmetrical black-and-white mosaic of this genetic (8*8)-matrix. This mosaic matrix is connected algorithmically with Hadamard matrices unexpectedly, which are famous in the theory of signal processing, spectral analysis, quantum mechanics and quantum computers. A special decomposition of numeric genetic matrices reveals their close relations with a family of 8-dimensional hypercomplex numbers (not Cayley's octonions). Some hypothesis and thoughts are formulated on the basis of these phenomenological facts.

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arXiv2008

A microstructurally informed model for the mechanical response of three-dimensional actin networks

We propose a class of microstructurally informed models for the linear elastic mechanical behavior of cross-linked polymer networks such as the actin cytoskeleton. Salient features of the models include the possibility to represent anisotropic mechanical behavior resulting from anisotropic filament distributions, and a power-law scaling of the mechanical properties with the filament density. Mechanical models within the class are parameterized by seven different constants. We demonstrate a procedure for determining these constants using finite element models of three-dimensional actin networks. Actin filaments and cross-links were modeled as elastic rods, and the networks were constructed at physiological volume fractions and at the scale of an image voxel. We show the performance of the model in estimating the mechanical behavior of the networks over a wide range of filament densities and degrees of anisotropy.

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arXiv2008

Vortices in brain waves

Interactions by mutual excitation in neural populations in human and animal brains create a mesoscopic order parameter that is recorded in brain waves (electroencephalogram, EEG). Spatially and spectrally distributed oscillations are imposed on the background activity by inhibitory feedback in the gamma range (30-80 Hz). Beats recur at theta rates (3-7 Hz), at which the order parameter transiently approaches zero and microscopic activity becomes disordered. After these null spikes, the order parameter resurges and initiates a frame bearing a mesoscopic spatial pattern of gamma amplitude modulation that governs the microscopic activity, and that is correlated with behavior. The brain waves also reveal a spatial pattern of phase modulation in the form of a cone. Using the formalism of the dissipative many-body model of brain, we describe the null spikes and the accompanying phase cones as vortices.

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arXiv2013

Matrix genetics, part 1: permutations of positions in triplets and symmetries of genetic matrices

The Kronecker family of the genetic matrices is investigated, which is based on the genetic matrix [C T; A G], where C, T, A, G are the letters of the genetic alphabet. The matrix [C T; A G] in the second Kronecker power is the (4*4)-matrix of 16 duplets. The matrix [C T; A G] in the third Kronecker power is the (8*8)-matrix of 64 triplets. It is significant that peculiarities of the degeneracy of the genetic code are reflected in the symmetrical black-and-white mosaic of these genetic matrices. The article represents interesting mathematical properties of these mosaic matrices, which are connected with positional permutations inside duplets and triplets; with projector operators; with unitary matrices and cyclic groups, etc. Fractal genetic nets are proposed as a new effective tool to study long nucleotide sequences. Some results about revealing new symmetry principles of long nucleotide sequences are described.

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arXiv2008

Matrix genetics, part 2: the degeneracy of the genetic code and the octave algebra with two quasi-real units (the genetic octave Yin-Yang-algebra)

Algebraic properties of the genetic code are analyzed. The investigations of the genetic code on the basis of matrix approaches ("matrix genetics") are described. The degeneracy of the vertebrate mitochondria genetic code is reflected in the black-and-white mosaic of the (8*8)-matrix of 64 triplets, 20 amino acids and stop-signals. This mosaic genetic matrix is connected with the matrix form of presentation of the special 8-dimensional Yin-Yang-algebra and of its particular 4-dimensional case. The special algorithm, which is based on features of genetic molecules, exists to transform the mosaic genomatrix into the matrices of these algebras. Two new numeric systems are defined by these 8-dimensional and 4-dimensional algebras: genetic Yin-Yang-octaves and genetic tetrions. Their comparison with quaternions by Hamilton is presented. Elements of new "genovector calculation" and ideas of "genetic mechanics" are discussed. These algebras are considered as models of the genetic code and as its possible pre-code basis. They are related with binary oppositions of the Yin-Yang type and they give new opportunities to investigate evolution of the genetic code. The revealed fact of the relation between the genetic code and these genetic algebras is discussed in connection with the idea by Pythagoras: "All things are numbers". Simultaneously these genetic algebras can be utilized as the algebras of genetic operators in biological organisms. The described results are related with the problem of algebraization of bioinformatics. They take attention to the question: what is life from the viewpoint of algebra?

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arXiv2008

Reverse Engineering of Proteasomal Translocation Rates

We address the problem of proteasomal protein translocation and introduce a new stochastic model of the proteasomal digestion (cleavage) of proteins. In this model we account for the protein translocation and the positioning of cleavage sites of a proteasome from first principles. We show by test examples and by processing experimental data that our model allows reconstruction of the translocation and cleavage rates from mass spectroscopy data on digestion patterns and can be used to investigate the properties of transport in different experimental set-ups. Detailed investigation with this model will enable theoretical quantitative prediction of the proteasomal activity.

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arXiv2008

Run and tumble chemotaxis in a shear flow: the effect of temporal comparisons and other complications

Escherichia coli is a motile bacterium that moves up a chemoattractant gradient by performing a biased random walk composed of alternating runs and tumbles. This paper presents calculations of the chemotactic drift velocity vd (the mean velocity up the chemoattractant gradient) of an E. coli cell performing chemotaxis in a uniform, steady shear flow, with a weak chemoattractant gradient at right angles to the flow. Extending earlier models, a combined analytic and numerical approach is used to assess the effect of several complications, namely (i) a cell cannot detect a chemoattractant gradient directly but rather makes temporal comparisons of chemoattractant concentration, (ii) the tumbles exhibit persistence of direction, meaning that the swimming directions before and after a tumble are correlated, (iii) the cell suffers random re-orientations due to rotational Brownian motion, and (iv) the non-spherical shape of the cell affects the way that it is rotated by the shear flow. These complications influence the dependence of vd on the shear rate gamma. When they are all included, it is found that (a) shear disrupts chemotaxis and shear rates beyond gamma = 2/second cause the cell to swim down the chemoattractant gradient rather than up it, (b) in terms of maximising drift velocity, persistence of direction is advantageous in a quiescent fluid but disadvantageous in a shear flow, and (c) a more elongated body shape is advantageous in performing chemotaxis in a strong shear flow.

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arXiv2008

Developing a Theoretical Framework for Optofluidic Device Designing for System Identification in Systems Biology: the EGFR Study Case

Identification of dynamics underlying biochemical pathways of interest in oncology is a primary goal in current systems biology. Understanding structures and interactions that govern the evolution of such systems is believed to be a cornerstone in this research. Systems theory and systems identification theory are primary resources for this task since they both provide a self consistent framework for modelling and manipulating models of dynamical systems that are best suited for the problem under investigation. We address herein the issue of obtaining an informative dataset ZN to be used as starting point for identification of EGFR pathway dynamics. In order to match experimental identifiability criteria we propose a theoretical framework for input stimulus design based on dynamical properties of the system under investigation. A feasible optofluidic design has been designed on the basis of the spectral properties of the driving inputs that maximize information content after the theoretical studies.

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arXiv2008

Dynamic origin of species

A simple model of species origin resulted from dynamic features of a population, solely, is developed. The model is based on the evolution optimality in space distribution, and the selection is gone over the mobility. Some biological issues are discussed.

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arXiv2008

Analytical Equations to the Chromaticity Cone: Algebraic Methods for Describing Color

We describe an affine transformation on the (CIE) color matching functions and map the spectral locus as a circle. We then homogenize the right circular cylinder erected by the circle, with respect to a normalizing plane and develop an analytical equation to the chromaticity cone, for the spectral colors. In the interior of the (CIE) chromaticity diagram, by homogenizing elliptic cylinders with respect to the normalizing planes, analytical equations to subsets (also cones) of the chromaticity cone are developed. These equations provide an algebraic method for describing color perception. As an application of the interior chromaticity cones, we demonstrate that by sectioning homogenized cones with planes and projecting, analytical equations to the Macadam ellipses may be derived. Further, the cone equations are used to propose new types of color order systems.

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arXiv2008

Prey-predator modeling of CO2 atmospheric concentration

In this work we propose a mathematical model, based in a modified version of the Lotka-Volterra prey-predator equations, to predict the increasing in CO2 atmospheric concentration. We consider how the photosynthesis rate has changed with the increase of CO2 and how this affects plant reproduction and CO2 absorptions rates. Total CO2 emissions (natural and manmade) and biomass numerical parameter changes are considered. It is shown that the atmospheric system can be in equilibrium under some specific conditions, and also some comparisons with historical are done.

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arXiv2008

Human-Robot Biodynamics

This paper presents the scientific body of knowledge behind the Human Biodynamics Engine (HBE), a human motion simulator developed on the concept of Euclidean motion group SE(3), with 270 active degrees of freedom, force-velocity-time muscular mechanics and two-level neural control - formulated in the fashion of nonlinear humanoid robotics. The following aspects of the HBE development are described: geometrical, dynamical, control, physiological, AI, behavioral and complexity, together with several simulation examples. Keywords: Human Biodynamics Engine, Euclidean SE(3)-group, Lagrangian/Hamiltonian biodynamics, Lie-derivative control, muscular mechanics, fuzzy-topological coordination, biodynamical complexity, validation, application

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arXiv2008

Anapedesis: Implications and Applications of Bio-Structural Robustness

Here we develop an approach to bio-structural robustness integrated with structure-function relationship in a unified conceptual and methodological framework, and envision its study using adequate computational and experimental methods. To distinguish this structural robustness from the abstract organizational robustness of systems, we call it anapedesis, and define it as the scale-independent property of biological objects, from biomolecules to organisms, to deform and recover while minimizing and/or repairing the damage produced by stretch. We propose to study the consequences of deformation of biological objects closer to their structural and/or functional failure than previously considered relevant. We show that structural robustness is present as a basic principle in many facets of biomedicine: many pathological conditions may derive from the failure of molecules, cells and their higher-order assemblies to maintain robustness against deformation. Furthermore, structural robustness could have been the key selective criterion during pre-biotic evolution and afterwards, and its universality can be demonstrated by modeling using genetic algorithms. Thus, the specific investigation of bio-structural robustness as anapedesis could help the solving of fundamental problems of biology and medicine.

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arXiv2008

Phase Transitions, Chaos and Joint Action in the Life Space Foam

This paper extends our recently developed Life Space Foam (LSF) model of motivated cognitive dynamics \cite{IA}. LSF uses adaptive path integrals to generate Lewinian force--fields on smooth manifolds, in order to characterize the dynamics of individual goal--directed action. According to explanatory theories growing in acceptance in cognitive neuroscience, one of the key properties of this dynamics, capable of linking it to microscopic-level cortical neurodynamics, is its meta-stability and the resulting phase transitions. Our extended LSF model incorporates the notion of phase transitions and complements it with embedded geometrical chaos. To describe this LSF phase transition, a general path--integral is used, along the corresponding LSF topology change. As a result, our extended LSF model is able to rigorously represent co-action by two or more actors in the common LSF--manifold. The model yields substantial qualitative differences in geometrical properties between bilateral and multi-lateral co-action due to intrinsic chaotic coupling between $n$ actors when $n\geq 3$. Keywords: cognitive dynamics, adaptive path integrals, phase transitions, chaos, topology change, human joint action, function approximation

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arXiv2008

Failure of antibiotic treatment in microbial populations

The tolerance of bacterial populations to biocidal or antibiotic treatment has been well documented in both biofilm and planktonic settings. However, there is still very little known about the mechanisms that produce this tolerance. Evidence that small, non-mutant subpopulations of bacteria are not affected by antibiotic challenge has been accumulating and provides an attractive explanation for the failure of typical dosing protocols. Although a dosing challenge can kill all the susceptible bacteria, the remaining persister cells can serve as a source of population regrowth. We give a robust condition for the failure of a periodic dosing protocol for a general chemostat model, which supports the mathematical conclusions and simulations of an earlier, more specialized batch model. Our condition implies that the treatment protocol fails globally, in the sense that a mixed bacterial population will ultimately persist above a level that is independent of the initial composition of the population. We also give a sufficient condition for treatment success, at least for initial population compositions near the steady state of interest, corresponding to bacterial washout. Finally, we investigate how the speed at which the bacteria are wiped out depends on the duration of administration of the antibiotic. We find that this dependence is not necessarily monotone, implying that optimal dosing does not necessarily correspond to continuous administration of the antibiotic. Thus, genuine periodic protocols can be more advantageous in treating a wide variety of bacterial infections.

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arXiv2008

Unifying Theories of Molecular, Community and Network Evolution

The origin of diversification and coexistence of genes and species have been traditionally studied in isolated biological levels. Ecological and evolutionary views have focused on the mechanisms that enable or constrain species coexistence, genetic variation and the genetics of speciation, but a unified theory linking those approaches is still missing. Here we introduce evolutionary graphs in the context of neutral theories of molecular evolution and biodiversity to provide a framework that simultaneously addresses speciation rate and joint genetic and species diversities. To illuminate this question we also study two models of evolution on graphs with fitness differences, which provide insights on how genetic and ecological dynamics drive the speed of diversification. Neutral evolution generates the highest speed of speciation, species richness (i.e. five times and twice as many species as compared to genetic and ecological graphs, respectively) and genetic--species diversity (i.e., twice as many as genetic and ecological graphs, respectively). Thus the speed of speciation, the genetic--species diversity and coexistence can differ dramatically depending on whether genetic factors versus ecological factors drive the evolution of the system. By linking molecular, sexual and trophic behavior at ecological and evolutionary scales, interacting graphs can illuminate the origin and evolution of diversity and organismal coexistence.

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