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arXiv2017

Application of Fractional Derivatives in Characterization of ECG graphs of Right Ventricular Hypertrophy Patients

There are many functions which are continuous everywhere but non-differentiable at some or all points such functions are termed as unreachable functions. Graphs representing such unreachable functions are called unreachable graphs. For example, ECG is such an unreachable graph. Classical calculus fails in their characterization as derivatives do not exist at the unreachable points. Such unreachable functions can be characterized by fractional calculus as fractional derivatives exist at those unreachable points where classical derivatives do not exist. Definition of fractional derivatives has been proposed by several mathematicians like Grunwald-Letinikov, Riemann-Liouville, Caputo, and Jumarie to develop the theory of fractional calculus. In this paper, we have used Jumarie type fractional derivative and consequently the phase transition (P.T.) which is the difference between left fractional derivative and right fractional derivatives to characterize those points. A comparative study has been done between normal ECG sample and problematic ECG sample (Right Ventricular Hypertrophy) by the help of the above mentioned mathematical tool.

q-bio.OT↗
arXiv2026

Physics of the Propagating Action Potential

We analyze the Rosenthal--Bezanilla experimental action potential waveforms using a charge-conserving phase-space formulation of the cable equation for a steadily propagated action potential. Each measured waveform determines the axial Ohmic current $J_z$, its geometry-converted divergence $J_m$, the capacitive current, and the total ionic current without requiring voltage-clamp currents as independent inputs. The current balance is expressed branchwise through $V$, $Φ(V)=dV/dt$, and $dΦ(V)/dV$; laboratory time remains recoverable from $dt=dV/Φ(V)$. At points where $Φ(V)\neq0$, the total ionic current vanishes when $dΦ/dV=k$, producing one zero crossing on each branch. Both crossings are present in the Rosenthal--Bezanilla data. The reconstructed currents remain continuous through the action-potential peak, while their state-dependent decomposition changes, supporting a continuous $M\rightarrow H$ transition between sodium-channel regimes. The second crossing occurs shortly after the peak on the recovery branch, after which the total ionic current is outward. Its effective reversal potential, channel-completion kinetics, and temperature dependence support a sodium-dominated interpretation. Quasilinear phase-space regions yield effective conductances, reversal potentials, and characteristic time rates. Channel completion follows a modified Avrami relation with nearly temperature-independent exponents and Arrhenius time rates. The fitted processes share an approximately invariant dimensionless prefactor, numerically close to the fine-structure constant, whose physical origin remains undetermined. This framework provides a unified charge-conserving, clock-free relational description of propagated action potentials and reveals current and channel-state structure not resolved by stationary voltage-clamp measurements.

q-bio.OT↗
arXiv2017

On the Mathematics of Fraternal Birth Order Effect and the Genetics of Homosexuality

Mathematicians have always been attracted to the field of genetics. I am especially interested in the mathematical aspects of research on homosexuality. Certain studies show that male homosexuality may have a genetic component that is correlated with female fertility. Other studies show the existence of the fraternal birth order effect, that is the correlation of homosexuality with the number of older brothers. This paper is devoted to the mathematical aspects of how these two phenomena are interconnected. In particular, I show that the fraternal birth order effect produces a correlation between homosexuality and maternal fecundity. Vice versa, I show that the correlation between homosexuality and female fecundity implies the increase of the probability of the younger brothers being homosexual.

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arXiv2017

The evolution and structure of biomedical knowledge on cytochrome P450

Cytochrome P450 are fundamental proteins to the metabolism of drugs and other relevant processes. through a combination of text mining and network analysis of the P450 literature we mapped the emergence and evolution of the biomedical research communities working on this family of proteins. Our results suggest that the historical research communities that worked on P450 emerged and were organized mainly around methodological achievements like the induction of animal liver microsomal P450 by drugs, the use of chemical inhibitors of P450 enzymes in in-vitro metabolism studies and the development of E. coli expression systems. We found clear evidence that P450 research indeed constitutes a material scientific culture, as we discuss in the text.

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arXiv2018

Screening of Fungi for the Application of Self-Healing Concrete

Concrete is susceptible to cracking owing to drying shrinkage, freeze-thaw cycles, delayed ettringite formation, reinforcement corrosion, creep and fatigue, etc. Since maintenance and inspection of concrete infrastructure require onerous labor and high costs, self-healing of harmful cracks without human interference or intervention could be of great attraction. The goal of this study is to explore a new self-healing approach in which fungi are used as a self-healing agent to promote calcium carbonate precipitation to fill the cracks in concrete structures. Recent research results in the field of geomycology have shown that many species of fungi could play an important role in promoting calcium carbonate mineralization, but their application in self-healing concrete has not been reported. Therefore, a screening of different species of fungi has been conducted in this study. Our results showed that, despite the drastic pH increase owing to the leaching of calcium hydroxide from concrete, Aspergillus nidulans (MAD1445), a pH regulatory mutant, could grow on concrete plates and promote calcium carbonate precipitation.

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arXiv2017

Sequencing single-stranded libraries on the Illumina NextSeq 500 platform

Single-stranded libraries generated from ancient DNA extracts have specific sequencing requirements. The short library molecules typically associated with ancient DNA templates are expected to behave differently during the annealing to the flow cell and subsequent cluster generation (bridge PCR), requiring optimisation of loading amounts to obtain optimal and consistent cluster densities. For the past 3 years, we have carried out sequencing of single-stranded libraries on the Illumina NextSeq 500 sequencing platform at the Institute for Biochemistry and Biology, University of Potsdam. We report our optimisations here. This document may be useful for other researchers wishing to sequence single-stranded libraries on the NextSeq 500 platform. It does not replace the excellent documentation provided by Illumina (links provided below), but rather serves as additional information specific to single-stranded libraries. The original papers describing the library protocol should also be studied in detail, and complement the information presented here.

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arXiv2017

Encoding DNA sequences by integer chaos game representation

DNA sequences are fundamental for encoding genetic information. The genetic information may not only be understood by symbolic sequences but also from the hidden signals inside the sequences. The symbolic sequences need to be transformed into numerical sequences so the hidden signals can be revealed by signal processing techniques. All current transformation methods encode DNA sequences into numerical values of the same length. These representations have limitations in the applications of genomic signal compression, encryption, and steganography. We propose an integer chaos game representation (iCGR) of DNA sequences and a lossless encoding method DNA sequences by the iCGR. In the iCGR method, a DNA sequence is represented by the iterated function of the nucleotides and their positions in the sequence. Then the DNA sequence can be uniquely encoded and recovered using three integers from iCGR. One integer is the sequence length and the other two integers represent the accumulated distributions of nucleotides in the sequence. The integer encoding scheme can compress a DNA sequence by 2 bits per nucleotide. The integer representation of DNA sequences provides a prospective tool for sequence compression, encryption, and steganography. The Python programs in this study are freely available to the public at https://github.com/cyinbox/iCGR

cs.CE↗
arXiv2018

Nobel Symposium 162 - Microfluidics

The Nobel Foundation's Symposium programme was initiated in 1965 and since then over 160 symposia have taken place. With the Nobel symposium summarized in this proceedings volume, we had the ambition to cover the past, current and future developments of microfluidics; a highly challenging task as there are many excellent researchers in this area and only thirty slots in the program. We tried to cover the early breakthrough contributions to the field, important developments over the years and applications of microfluidics that now propagate in vastly different directions both as industrial components or processes and as tools and methods supporting fundamental research. To give the entire research community an opportunity to sample the science presented at the symposium we have compiled a symposium volume that reflects the major messages conveyed by our invited speakers. We are deeply grateful to the effort that our participants put into writing their lecture notes/abstracts.

physics.flu-dyn↗
arXiv2019

Mean squared displacement and sinuosity of three-dimensional random search movements

Correlated random walks (CRW) have been used for a long time as a null model for animal's random search movement in two dimensions (2D). An increasing number of studies focus on animals' movement in three dimensions (3D), but the key properties of CRW, such as the way the mean squared displacement is related to the path length, are well known only in 1D and 2D. In this paper I derive such properties for 3D CRW, in a consistent way with the expression of these properties in 2D. This should allow 3D CRW to act as a null model when analyzing actual 3D movements similarly to what is done in 2D

q-bio.OT↗
arXiv2018

Thermodynamic Mechanism of Life and Aging

Life is a complex biological phenomenon represented by numerous chemical, physical and biological processes performed by a biothermodynamic system/cell/organism. Both living organisms and inanimate objects are subject to aging, a biological and physicochemical process characterized by changes in biological and thermodynamic state. Thus, the same physical laws govern processes in both animate and inanimate matter. All life processes lead to change of an organism's state. The change of biological and thermodynamic state of an organism in time underlies all of three kinds of aging (chronological, biological and thermodynamic). Life and aging of an organism both start at the moment of fertilization and continue through entire lifespan. Fertilization represents formation of a new organism. The new organism represents a new thermodynamic system. From the very beginning, it changes its state by changing thermodynamic parameters. The change of thermodynamic parameters is observed as aging and can be related to change in entropy. Entropy is thus the parameter that is related to all others and describes aging in the best manner. In the beginning, entropy change appears as a consequence of accumulation of matter (growth). Later, decomposition and configurational changes dominate, as a consequence of various chemical reactions (free radical, decomposition, fragmentation, accumulation of lipofuscin-like substances...).

q-bio.OT↗
arXiv2018

Nerve impulse propagation and wavelet theory

A luminous stimulus which penetrates in a retina is converted to a nerve message. Ganglion cells give a response that may be approximated by a wavelet. We determine a function PSI which is associated with the propagation of nerve impulses along an axon. Each kind of channel (inward and outward) may be open or closed, depending on the transmembrane potential. The transition between these states is a random event. Using quantum relations, we estimate the number of channels susceptible to switch between the closed and open states. Our quantum approach was first to calculate the energy level distribution in a channel. We obtain, for each kind of channel, the empty level density and the filled level density of the open and closed conformations. The joint density of levels provides the transition number between the closed and open conformations. The algebraic sum of inward and outward open channels is a function PSI of the normalized energy E. The function PSI verifies the major properties of a wavelet. We calculate the functional dependence of the axon membrane conductance with the transmembrane energy.

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arXiv2018

Hierarchical evolutive systems, fuzzy categories and the living single cell

In this article, the theory of hierarchical evolutive systems of Ehresmann and Vandremeersch [Bull. Math. Bio. 49, 13-50 (1987)] is improved by considering the categories of the theory as fuzzy sets whose elements are the composite objects formed by the arrows and corresponding vertices of their embedded graphs. This way each category can be represented as a point in the states space [0.1]**N. The introduction of a diffeomorphism, that acts in this context as a functor between categories, allows to define a measure preserving dynamical system. In particular, we apply this formalism to describe a living single cell. We propose for its state at a given time a hirerchical category with three levels (molecular, coarse-grained and cellular levels) related by adequate colimits. Each level involves the main functional and structural modules in which the cell can be partitioned. The time evolution of the cell is drived by a transformation which is a N-dimensional generalization of the Ricker map whose parameters we propose to be determined by requiring that, as hallmark of its behavior, the living cell to evolve at the edge of chaos. From the dynamical point of view this property manifests in the fact that the largest Lyapunov exponent is equal to zero. Since in a rather complete model of the living cell the huge number of involved parameters can make of the calculations a hard task, we also propose a toy model, with fewer parameters to be determined, which emphasizes the cellular fission.

q-bio.OT↗
arXiv2018

A mathematical model of the metabolism of a cell. Self-organization and chaos

Using the classical tools of nonlinear dynamics, we study the process of self-organization and the appearance of the chaos in the metabolic process in a cell with the help of a mathematical model of the transformation of steroids by a cell Arthrobacter globiformis. We constructed the phase-parametric diagrams obtained under a variation of the dissipation of the kinetic membrane potential. The oscillatory modes obtained are classified as regular and strange attractors. We calculated the bifurcations, by which the self-organization and the chaos occur in the system, and the transitions "chaos-order", "order-chaos", "order-order", and "chaos-chaos" arise. Feigenbaum's scenarios and the intermittences are found. For some selected modes, the projections of the phase portraits of attractors, Poincaré sections, and Poincaré maps are constructed. The total spectra of Lyapunov indices for the modes under study are calculated. The structural stability of the attractors is demonstrated. A general scenario of the formation of regular and strange attractors in the given metabolic process in a cell is found. The physical nature of their appearance in the metabolic process is studied.

q-bio.OT↗
arXiv2018

Hamiltonian dynamics and distributed chaos in DNA

It is shown that distributed chaos, generated by Hamiltonian DNA dynamics with spontaneously broken time translational symmetry, imprints itself on the DNA sequence of Arabidopsis thaliana (a model plant for genetic sequencing and mapping) and of the NRXN1 and BRCA2 human genes (as an example). The base-stacking interactions in the DNA duplex and degenerate codon groups have been discussed in this context.

q-bio.OT↗
arXiv2018

Microfluidics in Late Adolescence

George Whitesides is a Woodford L. and Ann A. Flowers Professor at Harvard University. In this contribution he describes the development of microfluidic techniques, from the spark that ignited this branch of academic research and its industrial sibling, to potential future application within medicine, security and organic synthesis. The diversity in technologies as well as in applications makes this an intriguing story, but it is in the simplest of materials - paper - that we find some of the most successful applications so far.

physics.flu-dyn↗
arXiv2018

Order and Chaos: Collective Behavior of Crowded Drops in Microfluidic Systems

Sindy Tang is assistant professor at in the Department of Mechanical Engineering at Stanford University. In this contribution she describes how her team uses droplet microfluidics to identify bacteria that could increase the efficiency of generation of bioplastics, and how this work motivated them to investigate the physics and design criteria necessary for further up-scaling of the droplet technology.

physics.flu-dyn↗
arXiv2018

Theoretical aspects of microscale acoustofluidics

Henrik Bruus is professor of lab-chip systems and theoretical physics at the Technical University of Denmark. In this contribution, he summarizes some of the recent results within theory and simulation of microscale acoustofluidic systems that he has obtained in collaboration with his students and international colleagues. The main emphasis is on three dynamical effects induced by external ultrasound fields acting on aqueous solutions and particle suspensions: The acoustic radiation force acting on suspended micro- and nanoparticles, the acoustic streaming appearing in the fluid, and the newly discovered acoustic body force acting on inhomogeneous solutions.

physics.flu-dyn↗