PeerJ Preprints: Mathematical Biologyhttps://peerj.com/preprints/index.atom?journal=peerj&subject=1900Mathematical Biology articles published in PeerJ PreprintsComparing enzyme activity modifier equations through the development of global data fitting templates in Excelhttps://peerj.com/preprints/30942018-08-062018-08-06Ryan Walsh
The classical way of defining enzyme inhibition has obscured the distinction between inhibitory effect and the inhibitor binding constant. This article examines the relationship between the simple binding curve used to define biomolecular interactions and the standard inhibitory term (1+([I]/Ki)). By understanding how this term relates to binding curves which are ubiquitously used to describe biological processes, a modifier equation which distinguishes between inhibitor binding and the inhibitory effect, is examined. This modifier equation which can describe both activation and inhibition is compared to standard inhibitory equations with the development of global data fitting templates in Excel and via the global fitting of these equations to simulated and previously published datasets. In both cases, this modifier equation was able to match or outperform the other equations by providing superior fits to the datasets. The ability of this single equation to outperform the other equations suggests an over-complication of the field. This equation and the template developed in this article should prove to be useful tools in the study of enzyme inhibition and activation.
The classical way of defining enzyme inhibition has obscured the distinction between inhibitory effect and the inhibitor binding constant. This article examines the relationship between the simple binding curve used to define biomolecular interactions and the standard inhibitory term (1+([I]/Ki)). By understanding how this term relates to binding curves which are ubiquitously used to describe biological processes, a modifier equation which distinguishes between inhibitor binding and the inhibitory effect, is examined. This modifier equation which can describe both activation and inhibition is compared to standard inhibitory equations with the development of global data fitting templates in Excel and via the global fitting of these equations to simulated and previously published datasets. In both cases, this modifier equation was able to match or outperform the other equations by providing superior fits to the datasets. The ability of this single equation to outperform the other equations suggests an over-complication of the field. This equation and the template developed in this article should prove to be useful tools in the study of enzyme inhibition and activation.Choice of choice models: Theory of signal detectability outperforms Bradley-Terry-Luce choice modelhttps://peerj.com/preprints/269782018-06-052018-06-05Diana E KornbrotGeorge J GeorgiouMike Page
Identifying the best framework for two-choice decision-making has been a goal of psychology theory for many decades (Bohil, Szalma, & Hancock, 2015; Macmillan & Creelman, 1991). There are two main candidates: the theory of signal detectability (TSD) (Swets, Tanner Jr, & Birdsall, 1961; Thurstone, 1927) based on a normal distribution/probit function, and the choice-model theory (Link, 1975; Luce, 1959) that uses the logistic distribution/logit function. A probit link function, and hence TSD, was shown to have a better Bayesian Goodness of Fit than the logit function for every one of eighteen diverse psychology data sets (Open-Science-Collaboration, 2015a), conclusions having been obtained using Generalized Linear Mixed Models (Lindstrom & Bates, 1990; Nelder & Wedderburn, 1972) . These findings are important, not only for the psychology of perceptual, cognitive and social decision-making, but for any science that use binary proportions to measure effectiveness, as well as the meta-analysis of such studies.
Identifying the best framework for two-choice decision-making has been a goal of psychology theory for many decades (Bohil, Szalma, & Hancock, 2015; Macmillan & Creelman, 1991). There are two main candidates: the theory of signal detectability (TSD) (Swets, Tanner Jr, & Birdsall, 1961; Thurstone, 1927) based on a normal distribution/probit function, and the choice-model theory (Link, 1975; Luce, 1959) that uses the logistic distribution/logit function. A probit link function, and hence TSD, was shown to have a better Bayesian Goodness of Fit than the logit function for every one of eighteen diverse psychology data sets (Open-Science-Collaboration, 2015a), conclusions having been obtained using Generalized Linear Mixed Models (Lindstrom & Bates, 1990; Nelder & Wedderburn, 1972) . These findings are important, not only for the psychology of perceptual, cognitive and social decision-making, but for any science that use binary proportions to measure effectiveness, as well as the meta-analysis of such studies.Mathematical modelling and analysis of elite athletes’ sprint data to study the rate and regulation of ATP during a maximal exercise of short durationhttps://peerj.com/preprints/269192018-05-092018-05-09Dineshen ChuckravanenLaila AhlimaleSujan Rajbhandari
According to the energy supply/energy depletion model, it is not clear how the depletion of substrates (adenosine triphosphate) affects sprint performance. Therefore, this research was conducted to find out how the human organism regulates the amount and the rate of adenosine triphosphate to observe how these factors affect performance specifically during a maximal exercise of short duration.It was found there was a causal relationship between percentage of PCr and speed which might affect sprint performance.The percentage of chemical energy derived from the anaerobic energy system was found to be 95% for 100-m sprint running. The rate constant for the PCr anaerobic metabolic energy process (0.31s-1) was found to be greater than that of the oxygen-independent glycolysis metabolic process (0.11s-1) and these rate constants affect sprint performance.
According to the energy supply/energy depletion model, it is not clear how the depletion of substrates (adenosine triphosphate) affects sprint performance. Therefore, this research was conducted to find out how the human organism regulates the amount and the rate of adenosine triphosphate to observe how these factors affect performance specifically during a maximal exercise of short duration.It was found there was a causal relationship between percentage of PCr and speed which might affect sprint performance.The percentage of chemical energy derived from the anaerobic energy system was found to be 95% for 100-m sprint running. The rate constant for the PCr anaerobic metabolic energy process (0.31s-1) was found to be greater than that of the oxygen-independent glycolysis metabolic process (0.11s-1) and these rate constants affect sprint performance.Analysis of relative abundances on environmental gradientshttps://peerj.com/preprints/269082018-05-022018-05-02Fiona ChongMatthew Spencer
Ecologists often analyze relative abundances, which are compositions (sets of non-negative numbers with a fixed sum). However, they have made surprisingly little use of recent advances in the field of compositional data analysis. Compositions form a vector space in which addition and scalar multiplication are replaced by operations known as perturbation and powering. This algebraic structure makes it easy to understand how relative abundances change along environmental gradients. We illustrate this with an analysis of changes in hard-substrate marine communities along a depth gradient. We show how the algebra of compositions can be used to understand patterns in dissimilarity. We use the calculus of simplex-valued functions to estimate rates of change, and to summarize the structure of the community over a vertical slice. We discuss the benefits of the compositional approach in the interpretation and visualization of relative abundance data.
Ecologists often analyze relative abundances, which are compositions (sets of non-negative numbers with a fixed sum). However, they have made surprisingly little use of recent advances in the field of compositional data analysis. Compositions form a vector space in which addition and scalar multiplication are replaced by operations known as perturbation and powering. This algebraic structure makes it easy to understand how relative abundances change along environmental gradients. We illustrate this with an analysis of changes in hard-substrate marine communities along a depth gradient. We show how the algebra of compositions can be used to understand patterns in dissimilarity. We use the calculus of simplex-valued functions to estimate rates of change, and to summarize the structure of the community over a vertical slice. We discuss the benefits of the compositional approach in the interpretation and visualization of relative abundance data.A thermodynamic description for physiological transmembrane transporthttps://peerj.com/preprints/13122018-04-162018-04-16Marco A Herrera-Valdez
Physiological mechanisms for passive and active transmembrane transport have been theoretically described using many different approaches. A generic formulation for both passive and active transmembrane transport, is derived from basic thermodynamical principles taking into account macroscopic forward and backward molecular fluxes, relative to a source compartment, respectively. Electrogenic fluxes also depend on the transmembrane potential and can be readily converted into currents. Interestingly, the conductance-based formulation for current is the linear approximation of the generic formulation for current, around the reversal potential. Also, other known formulas for current based on electrodiffusion turn out to be particular examples of the generic formulation. The applicability of the generic formulations is illustrated with models of transmembrane potential dynamics for cardiocytes and neurons. The generic formulations presented here provide a common ground for the biophysical study of physiological phenomena that depend on transmembrane transport.
Physiological mechanisms for passive and active transmembrane transport have been theoretically described using many different approaches. A generic formulation for both passive and active transmembrane transport, is derived from basic thermodynamical principles taking into account macroscopic forward and backward molecular fluxes, relative to a source compartment, respectively. Electrogenic fluxes also depend on the transmembrane potential and can be readily converted into currents. Interestingly, the conductance-based formulation for current is the linear approximation of the generic formulation for current, around the reversal potential. Also, other known formulas for current based on electrodiffusion turn out to be particular examples of the generic formulation. The applicability of the generic formulations is illustrated with models of transmembrane potential dynamics for cardiocytes and neurons. The generic formulations presented here provide a common ground for the biophysical study of physiological phenomena that depend on transmembrane transport.Moving sclerochronology to shell growth morphodynamics: A comprehensive approachhttps://peerj.com/preprints/268272018-04-052018-04-05Jennifer Coston-Guarini
Sclerochronology is presented as an approach to reconstruct, from linear growth records, environmental conditions. This was proposed by analogy with dendrochronology, but shells differ from trees since shells increase in size by terminal, instead of radial, growth. However, variability in the accretion process is being disregarded since it is minimized by the calculations of the “average individual”, a non-existent concept in theoretical ecology because this theoretical individual would possess all characteristics averaged at the same time. Furthermore, growth models are assumed to be static representations of dynamic processes, hypothesized to change under the influence of local disturbances. We have revised this, describing growth by incrementation in a morphodynamic model of the shell, permitting exploration of growth variability. We replaced the "average individual" by a concept of "time-varying covariance", establishing similarities within groups of individuals submitted to the same environmental conditions, even with high variability in their growth patterns. We believe that these approaches to growth and form linking mathematics, biology and ecology have potential to make profound changes across many disciplines, including oncology, by emphasizing the multidimensionality of growth processes, supplanting the current correlations with environmental variables by global analyses of biological and morphological dynamic patterns.
Sclerochronology is presented as an approach to reconstruct, from linear growth records, environmental conditions. This was proposed by analogy with dendrochronology, but shells differ from trees since shells increase in size by terminal, instead of radial, growth. However, variability in the accretion process is being disregarded since it is minimized by the calculations of the “average individual”, a non-existent concept in theoretical ecology because this theoretical individual would possess all characteristics averaged at the same time. Furthermore, growth models are assumed to be static representations of dynamic processes, hypothesized to change under the influence of local disturbances. We have revised this, describing growth by incrementation in a morphodynamic model of the shell, permitting exploration of growth variability. We replaced the "average individual" by a concept of "time-varying covariance", establishing similarities within groups of individuals submitted to the same environmental conditions, even with high variability in their growth patterns. We believe that these approaches to growth and form linking mathematics, biology and ecology have potential to make profound changes across many disciplines, including oncology, by emphasizing the multidimensionality of growth processes, supplanting the current correlations with environmental variables by global analyses of biological and morphological dynamic patterns.Coccolith arrangement follows Eulerianmathematics in the coccolithophore Emiliania huxleyihttps://peerj.com/preprints/34572018-03-072018-03-07Kai XuDavid HutchinsKunshan Gao
Background. The globally abundant coccolithophore, Emiliania huxleyi, plays an importantecological role in oceanic carbon biogeochemistry by forming a cellularcovering of plate-like CaCO 3 crystals (coccoliths) and fixing CO 2 .It is unknown how the cells arrange different-size of coccoliths to maintainfull coverage, as the cell surface area of the cell changes during daily cycle.
Methods. We used Euler’s polyhedron formula and CaGe simulationsoftware, validated with the geometries of coccoliths, to analze and simulatethe coccolith topology of the coccosphere and to explore the arrangementmechanisms.
Results. There were only small variations in the geometries ofcoccoliths, even when the cells were cultured under variable light conditions.Because of geometric limits, small coccoliths tended to interlock with fewerand larger coccoliths, and vice versa. Consequently, to sustain a full coverageon the surface of cell, each coccolith was arranged to interlock with four tosix others, which in turn led to each coccosphere contains at least 6coccoliths.
Conclusions. The number of coccoliths per coccosphere must keep pacewith changes on the cell surface area as a result of photosynthesis,respiration and cell division. This study is an example of natural selectionfollowing Euler’s polyhedral formula, in response to the challenge ofmaintaining a CaCO 3 covering on coccolithophore cells as cell sizechanges.
Background. The globally abundant coccolithophore, Emiliania huxleyi, plays an importantecological role in oceanic carbon biogeochemistry by forming a cellularcovering of plate-like CaCO 3 crystals (coccoliths) and fixing CO 2 .It is unknown how the cells arrange different-size of coccoliths to maintainfull coverage, as the cell surface area of the cell changes during daily cycle. Methods. We used Euler’s polyhedron formula and CaGe simulationsoftware, validated with the geometries of coccoliths, to analze and simulatethe coccolith topology of the coccosphere and to explore the arrangementmechanisms. Results. There were only small variations in the geometries ofcoccoliths, even when the cells were cultured under variable light conditions.Because of geometric limits, small coccoliths tended to interlock with fewerand larger coccoliths, and vice versa. Consequently, to sustain a full coverageon the surface of cell, each coccolith was arranged to interlock with four tosix others, which in turn led to each coccosphere contains at least 6coccoliths. Conclusions. The number of coccoliths per coccosphere must keep pacewith changes on the cell surface area as a result of photosynthesis,respiration and cell division. This study is an example of natural selectionfollowing Euler’s polyhedral formula, in response to the challenge ofmaintaining a CaCO 3 covering on coccolithophore cells as cell sizechanges.Biochemical conversion of fruit rind of Telfairia occidentalis (Fluted Pumpkin) and poultry manurehttps://peerj.com/preprints/265642018-02-222018-02-22Olatunde Samuel DahunsiSolomon U OranusiVincent E EfeovbokhanMunachi EnyinnayaSoraya ZahediJohn OjediranPeter OluyoriJohn Izebere
This study evaluated the potentials of Fluted pumpkin fruit rind and poultry manure for biogas generation. Mechanical and thermo-alkaline pre-treatments were applied to two samples labelled ‘O’ and ‘P’ while the third sample (Q) had no thermo-alkaline treatment. The physicochemical characteristics of the substrates revealed richness in nutrients and mineral elements. The modelling was done using the Response Surface Methodology and Artificial Neural Networks and statistical prediction showed the process optimal conditions to be 30.02 o C, 7.90, 20.03 days, 5.94 g/kg and 4.01 g/kg for temperature, pH, retention time, total solids and volatile solids. Using the above set values, the biogas yield was predicted to be 2614.1, 2289.9 and 1003.3 10-3m3/kg VS for digestions ‘O’, ‘P’ and ‘Q’ respectively. The results showed that use of combination of pre-treatment methods enhanced the biogas yield in the pre-treated substrates. Analysis of the gas composition showed 66.5 ± 2.5 % Methane, 25 ± 1% Carbon dioxide; 58.5 ± 2.5 % Methane, 26 ± 1% Carbon dioxide; 54.5 ± 1.5 % Methane, 28 ± 2% Carbon dioxide for the three experiments respectively. All the obtained values show the models had a high predictive ability. However, the coefficient of determination (R2) for RSM was lower compared to that of ANN which is an indication that ANNs model is more accurate than RSM model in predicting biogas generation from the anaerobic co-digestion of rind of Fluted pumpkin and poultry manure. The substrates should be further used for energy generation.
This study evaluated the potentials of Fluted pumpkin fruit rind and poultry manure for biogas generation. Mechanical and thermo-alkaline pre-treatments were applied to two samples labelled ‘O’ and ‘P’ while the third sample (Q) had no thermo-alkaline treatment. The physicochemical characteristics of the substrates revealed richness in nutrients and mineral elements. The modelling was done using the Response Surface Methodology and Artificial Neural Networks and statistical prediction showed the process optimal conditions to be 30.02 o C, 7.90, 20.03 days, 5.94 g/kg and 4.01 g/kg for temperature, pH, retention time, total solids and volatile solids. Using the above set values, the biogas yield was predicted to be 2614.1, 2289.9 and 1003.3 10-3m3/kg VS for digestions ‘O’, ‘P’ and ‘Q’ respectively. The results showed that use of combination of pre-treatment methods enhanced the biogas yield in the pre-treated substrates. Analysis of the gas composition showed 66.5 ± 2.5 % Methane, 25 ± 1% Carbon dioxide; 58.5 ± 2.5 % Methane, 26 ± 1% Carbon dioxide; 54.5 ± 1.5 % Methane, 28 ± 2% Carbon dioxide for the three experiments respectively. All the obtained values show the models had a high predictive ability. However, the coefficient of determination (R2) for RSM was lower compared to that of ANN which is an indication that ANNs model is more accurate than RSM model in predicting biogas generation from the anaerobic co-digestion of rind of Fluted pumpkin and poultry manure. The substrates should be further used for energy generation.Discrete stochastic marine metapopulation disease modelhttps://peerj.com/preprints/264542018-01-232018-01-23Gorka BidegainTal Ben-Horin
Some marine microparasitic pathogens can survive several months outside the host in the water column to make contact with hosts or to be absorbed or filtered by hosts. Once inside, pathogens invade the host if they find suitable conditions for reproduction within the host. This transmission from the environment occurs via pathogens released from infected animals and dead infected animals. Some recent modeling studies concentrated on the disease dynamic imposed by this complex interaction between population and water column at the host-pathogen level in single populations. However, only when a marine disease can be understood at the metapopulation scale effective approaches to management will become routinely achievable. In this paper we explore the disease dynamics at the metapopulation applying a stochastic version. The discrete-time disease model in this paper investigates both spatial and temporal dynamics of hosts and waterborne pathogens in a three patch system. This metapopulation with a patch providing infective particles and susceptible and infected individuals by dispersal tries to imitate the effect of current forces in the ocean on the passive dispersal of organisms. The model detects system behaviors that are not present in single population continuous-time and deterministic models.
Some marine microparasitic pathogens can survive several months outside the host in the water column to make contact with hosts or to be absorbed or filtered by hosts. Once inside, pathogens invade the host if they find suitable conditions for reproduction within the host. This transmission from the environment occurs via pathogens released from infected animals and dead infected animals. Some recent modeling studies concentrated on the disease dynamic imposed by this complex interaction between population and water column at the host-pathogen level in single populations. However, only when a marine disease can be understood at the metapopulation scale effective approaches to management will become routinely achievable. In this paper we explore the disease dynamics at the metapopulation applying a stochastic version. The discrete-time disease model in this paper investigates both spatial and temporal dynamics of hosts and waterborne pathogens in a three patch system. This metapopulation with a patch providing infective particles and susceptible and infected individuals by dispersal tries to imitate the effect of current forces in the ocean on the passive dispersal of organisms. The model detects system behaviors that are not present in single population continuous-time and deterministic models.Coupling and noise in the circadian clock synchronizationhttps://peerj.com/preprints/264472018-01-192018-01-19Marco A Herrera-ValdezPablo Padilla-LongoriaAlessio FranciMiguel Lara-Aparicio
The general purpose of this paper is to build up on our understanding of the basic mathematical principles that underlie the emergence of biological rhythms, in particular, the circadian clock. To do so, we study the role that the coupling strength and noise play in the synchronization of a system of nonlinear, linearly coupled oscillators. First, we study a deterministic version of the model to find plausible regions in the parameter space for which synchronization is observed. Second, we focus on studying how noise and coupling interact in determining the synchronized behavior. To do so, we leverage the Fokker-Planck equation associated with the system. The basic mechanisms behind the generation of oscillations and the emergence of synchrony that we describe here can be used as a guide to further study coupled oscillations in biophysical nonlinear models.
The general purpose of this paper is to build up on our understanding of the basic mathematical principles that underlie the emergence of biological rhythms, in particular, the circadian clock. To do so, we study the role that the coupling strength and noise play in the synchronization of a system of nonlinear, linearly coupled oscillators. First, we study a deterministic version of the model to find plausible regions in the parameter space for which synchronization is observed. Second, we focus on studying how noise and coupling interact in determining the synchronized behavior. To do so, we leverage the Fokker-Planck equation associated with the system. The basic mechanisms behind the generation of oscillations and the emergence of synchrony that we describe here can be used as a guide to further study coupled oscillations in biophysical nonlinear models.