PeerJ Preprints: Mathematical Biologyhttps://peerj.com/preprints/index.atom?journal=peerj&subject=1900Mathematical Biology articles published in PeerJ PreprintsApproach for numerically describing and classifying benthic animals’ polymorphic cells morphologyhttps://peerj.com/preprints/272712018-10-112018-10-11Yura A KaretinEduardas Cicinskas
Describing cell morphology is a tricky task, prone to misinterpretation due to subjective nature of the human observer and his vocabulary limitations. Consequently, these limitations actuate prevalence of non-formalized, statistically unverifiable language use. This determines the reason for overlooking cell shape as a viable parameter for describing cell's functional state intricacies. In this study we demonstrate the use of mathematical parameters set for describing two-dimensional fractals, such as: convex hull, density, roundness and asymmetry, for comparative in vitro morphological analysis of sprawled starfishes' Aphelasterias japonica and Patiria pectinifera (Echinodermata: Asteroidea) coelomocytes, and bivalve's Callista brevisiphonata (Mollusca: Bivalvia) hemocytes. We found that these parameters allow us to describe visually distinguishable but verbally indescribable "chaotic" sprawled cell shapes. Furthermore, resulting numerical cell descriptions differs significantly, enabling for their species-specific grouping and classification. We argue that presented morphometric methodology can be used for describing and classifying cells of any arbitrary morphology, as well as compiling "cell shape - cell functional state" match library for later use in in vitro analysis, potentially for cells of any animal.
Describing cell morphology is a tricky task, prone to misinterpretation due to subjective nature of the human observer and his vocabulary limitations. Consequently, these limitations actuate prevalence of non-formalized, statistically unverifiable language use. This determines the reason for overlooking cell shape as a viable parameter for describing cell's functional state intricacies. In this study we demonstrate the use of mathematical parameters set for describing two-dimensional fractals, such as: convex hull, density, roundness and asymmetry, for comparative in vitro morphological analysis of sprawled starfishes' Aphelasterias japonica and Patiria pectinifera (Echinodermata: Asteroidea) coelomocytes, and bivalve's Callista brevisiphonata (Mollusca: Bivalvia) hemocytes. We found that these parameters allow us to describe visually distinguishable but verbally indescribable "chaotic" sprawled cell shapes. Furthermore, resulting numerical cell descriptions differs significantly, enabling for their species-specific grouping and classification. We argue that presented morphometric methodology can be used for describing and classifying cells of any arbitrary morphology, as well as compiling "cell shape - cell functional state" match library for later use in in vitro analysis, potentially for cells of any animal.Alpha shapes: Determining 3D shape complexity across morphologically diverse structureshttps://peerj.com/preprints/272702018-10-102018-10-10James D GardinerJulia BehnsenCharlotte A Brassey
Background. Following recent advances in bioimaging, high-resolution 3D models of biological structures are now generated rapidly and at low-cost. To utilise this data to address evolutionary and ecological questions, an array of tools has been developed to conduct 3D shape analysis and quantify topographic complexity. Here we focus particularly on shape techniques applied to irregular-shaped objects lacking clear homologous landmarks, and propose the new ‘alpha-shapes’ method for quantifying 3D shape complexity.
Methods. We apply alpha-shapes to quantify shape complexity in the mammalian baculum as an example of a morphologically disparate structure. Micro- computed-tomography (μCT) scans of bacula were conducted. Bacula were binarised and converted into point clouds. Following application of a scaling factor to account for absolute differences in size, a suite of alpha-shapes was fitted to each specimen. An alpha shape is a formed from a subcomplex of the Delaunay triangulation of a given set of points, and ranges in refinement from a very coarse mesh (approximating convex hulls) to a very fine fit. ‘Optimal’ alpha was defined as the degree of refinement necessary in order for alpha-shape volume to equal CT voxel volume, and was taken as a metric of overall shape ‘complexity’.
Results Our results show that alpha-shapes can be used to quantify interspecific variation in shape ‘complexity’ within biological structures of disparate geometry. The ‘stepped’ nature of alpha curves is informative with regards to the contribution of specific morphological features to overall shape ‘complexity’. Alpha-shapes agrees with other measures of topographic complexity (dissection index, Dirichlet normal energy) in identifying ursid bacula as having low shape complexity. However, alpha-shapes estimates mustelid bacula as possessing the highest topographic complexity, contrasting with other shape metrics. 3D fractal dimension is found to be an inappropriate metric of complexity when applied to bacula.
Conclusions. The alpha-shapes methodology can be used to calculate ‘optimal’ alpha refinement as a proxy for shape ‘complexity’ without identifying landmarks. The implementation of alpha-shapes is straightforward, and is automated to process large datasets quickly. Beyond genital shape, we consider the alpha-shapes technique to hold considerable promise for new applications across evolutionary, ecological and palaeoecological disciplines.
Background. Following recent advances in bioimaging, high-resolution 3D models of biological structures are now generated rapidly and at low-cost. To utilise this data to address evolutionary and ecological questions, an array of tools has been developed to conduct 3D shape analysis and quantify topographic complexity. Here we focus particularly on shape techniques applied to irregular-shaped objects lacking clear homologous landmarks, and propose the new ‘alpha-shapes’ method for quantifying 3D shape complexity.Methods. We apply alpha-shapes to quantify shape complexity in the mammalian baculum as an example of a morphologically disparate structure. Micro- computed-tomography (μCT) scans of bacula were conducted. Bacula were binarised and converted into point clouds. Following application of a scaling factor to account for absolute differences in size, a suite of alpha-shapes was fitted to each specimen. An alpha shape is a formed from a subcomplex of the Delaunay triangulation of a given set of points, and ranges in refinement from a very coarse mesh (approximating convex hulls) to a very fine fit. ‘Optimal’ alpha was defined as the degree of refinement necessary in order for alpha-shape volume to equal CT voxel volume, and was taken as a metric of overall shape ‘complexity’.Results Our results show that alpha-shapes can be used to quantify interspecific variation in shape ‘complexity’ within biological structures of disparate geometry. The ‘stepped’ nature of alpha curves is informative with regards to the contribution of specific morphological features to overall shape ‘complexity’. Alpha-shapes agrees with other measures of topographic complexity (dissection index, Dirichlet normal energy) in identifying ursid bacula as having low shape complexity. However, alpha-shapes estimates mustelid bacula as possessing the highest topographic complexity, contrasting with other shape metrics. 3D fractal dimension is found to be an inappropriate metric of complexity when applied to bacula.Conclusions. The alpha-shapes methodology can be used to calculate ‘optimal’ alpha refinement as a proxy for shape ‘complexity’ without identifying landmarks. The implementation of alpha-shapes is straightforward, and is automated to process large datasets quickly. Beyond genital shape, we consider the alpha-shapes technique to hold considerable promise for new applications across evolutionary, ecological and palaeoecological disciplines.Seasonality in ecology: Progress and prospects in theoryhttps://peerj.com/preprints/272352018-09-212018-09-21Easton R WhiteAlan Hastings
Seasonality is an important feature of essentially all natural systems but the consequences of seasonality have been vastly underappreciated. Early work emphasized the role of seasonality in driving cyclic population dynamics, but the consequences of seasonality for ecological processes are far broader. In ecological systems, seasonality may include variations in temperature, precipitation, or other processes. Seasonality is typically not explicitly included in either empirical or theoretical studies. However, many aspects of ecological dynamics can only be understood when seasonality is included, ranging from the oscillations in the incidence of childhood diseases to the coexistence of species. Further, studies of phenology and global climate change only make sense in the context of seasonal dynamics. Our goal is to outline what is now known about seasonality and to set the stage for future efforts. We review the effects of seasonality on ecological systems in both laboratory and field settings. We then discuss approaches for incorporating seasonality in mathematical models, including Floquet theory. We argue, however, that these tools are still limited in scope and more approaches need to be developed. We demonstrate the range of impacts of seasonality on ecological systems and show the necessity of incorporating seasonality to understand ecological dynamics.
Seasonality is an important feature of essentially all natural systems but the consequences of seasonality have been vastly underappreciated. Early work emphasized the role of seasonality in driving cyclic population dynamics, but the consequences of seasonality for ecological processes are far broader. In ecological systems, seasonality may include variations in temperature, precipitation, or other processes. Seasonality is typically not explicitly included in either empirical or theoretical studies. However, many aspects of ecological dynamics can only be understood when seasonality is included, ranging from the oscillations in the incidence of childhood diseases to the coexistence of species. Further, studies of phenology and global climate change only make sense in the context of seasonal dynamics. Our goal is to outline what is now known about seasonality and to set the stage for future efforts. We review the effects of seasonality on ecological systems in both laboratory and field settings. We then discuss approaches for incorporating seasonality in mathematical models, including Floquet theory. We argue, however, that these tools are still limited in scope and more approaches need to be developed. We demonstrate the range of impacts of seasonality on ecological systems and show the necessity of incorporating seasonality to understand ecological dynamics.The mathematics of extinction across scales: from populations to the biospherehttps://peerj.com/preprints/33672018-09-112018-09-11Colin CarlsonKevin BurgioTad DallasWayne Getz
The sixth mass extinction poses an unparalleled quantitative challenge to conservation biologists. Mathematicians and ecologists alike face the problem of developing models that can scale predictions of extinction rates from populations to the level of a species, or even to an entire ecosystem. We review some of the most basic stochastic and analytical methods of calculating extinction risk at different scales, including population viability analysis, stochastic metapopulation occupancy models, and the species area relationship. We also consider two major extensions of theory: the possibility of evolutionary rescue from extinction in a changing environment, and the posthumous assignment of an extinction date from sighting records. In the case of the latter, we provide an example using data on Spix's macaw (Cyanopsitta spixii), the "rarest bird in the world," to demonstrate the challenges associated with extinction date research.
The sixth mass extinction poses an unparalleled quantitative challenge to conservation biologists. Mathematicians and ecologists alike face the problem of developing models that can scale predictions of extinction rates from populations to the level of a species, or even to an entire ecosystem. We review some of the most basic stochastic and analytical methods of calculating extinction risk at different scales, including population viability analysis, stochastic metapopulation occupancy models, and the species area relationship. We also consider two major extensions of theory: the possibility of evolutionary rescue from extinction in a changing environment, and the posthumous assignment of an extinction date from sighting records. In the case of the latter, we provide an example using data on Spix's macaw (Cyanopsitta spixii), the "rarest bird in the world," to demonstrate the challenges associated with extinction date research.Synchronization, oscillator death, and frequency modulation in a class of biologically inspired coupled oscillatorshttps://peerj.com/preprints/264472018-09-112018-09-11Alessio FranciMarco A Herrera-ValdezMiguel Lara-AparicioPablo Padilla-Longoria
The general purpose of this paper is to build up on our understanding of the basic mathematical principles that underlie the emergence of synchronous biological rhythms, in particular, the circadian clock. To do so, we study the role that the coupling strength, coupling type, and noise play in the synchronization of a system of coupled, nonlinear oscillators. First, we study a deterministic model based on Van der Pol coupled oscillators, modeling a population of diffusively coupled cells, to find regions in the parameter space for which synchronous oscillations emerge and to provide conditions under which diffusive coupling kills the synchronous oscillation. Second, we study how noise and coupling interact and lead to synchronous oscillations in linearly coupled oscillators, modeling the interaction between various pacemaker populations, each having an endogenous circadian clock. To do so, we use the Fokker-Planck equation associated to the system. We show how coupling can tune the frequency of the emergent synchronous oscillation, which provides a general mechanism to make fast (ultradian) pacemakers slow (circadian) and synchronous via coupling. The basic mechanisms behind the generation of oscillations and the emergence of synchrony that we describe here can be used to guide further studies of 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 synchronous biological rhythms, in particular, the circadian clock. To do so, we study the role that the coupling strength, coupling type, and noise play in the synchronization of a system of coupled, nonlinear oscillators. First, we study a deterministic model based on Van der Pol coupled oscillators, modeling a population of diffusively coupled cells, to find regions in the parameter space for which synchronous oscillations emerge and to provide conditions under which diffusive coupling kills the synchronous oscillation. Second, we study how noise and coupling interact and lead to synchronous oscillations in linearly coupled oscillators, modeling the interaction between various pacemaker populations, each having an endogenous circadian clock. To do so, we use the Fokker-Planck equation associated to the system. We show how coupling can tune the frequency of the emergent synchronous oscillation, which provides a general mechanism to make fast (ultradian) pacemakers slow (circadian) and synchronous via coupling. The basic mechanisms behind the generation of oscillations and the emergence of synchrony that we describe here can be used to guide further studies of coupledoscillations in biophysical nonlinear models.The time distribution of biological phenomena – illustrated with the London marathonhttps://peerj.com/preprints/271752018-09-062018-09-06Miguel Franco
Background. The time distribution of biological phenomena (phenology) is a subject of wide interest, but a general statistical distribution to describe and quantify its essential properties is lacking. Existing distributions are limiting, if not entirely inappropriate, because their parameters do not in general correlate with biologically relevant attributes of the organism and the conditions under which they find themselves. Methods. A distribution function that allows quantification of three essential properties of a biological dynamic process occurring over a continuous timescale was derived from first principles. The distribution turned out to have three parameters with clear meanings and units: (i) a scaled rate of completion (dimensionless), (ii) a measure of temporal concentration of the process (units: time-1), and (iii) an overall measure of temporal delay (units: time). Its performance as an accurate description of the process was tested with completion data for the London Marathon employing non-linear regression. Results. The parameters of the distribution correlated with biological attributes of the runners (gender and age) and with the maximum temperature on the day of the race. These relationships mirrored known differences in morphology and physiology of participants and the deterioration of these biological attributes with age (senescence), as well as the known effects of hypo- and hyperthermia. Discussion. By relating the variation in parameter values to possible biological and environmental variables, the marathon example demonstrates the ability of the distribution to help identify possible triggers and drivers of the duration, shape and temporal shift of its temporal distribution. This more detailed account of the effect of biological and environmental variables would provide a deeper insight into the drivers of a wide variety of phenological phenomena of high current interest, such as the shifting patterns of leafing, flowering, growth, migration, etc. of many organisms worldwide.
Background. The time distribution of biological phenomena (phenology) is a subject of wide interest, but a general statistical distribution to describe and quantify its essential properties is lacking. Existing distributions are limiting, if not entirely inappropriate, because their parameters do not in general correlate with biologically relevant attributes of the organism and the conditions under which they find themselves. Methods. A distribution function that allows quantification of three essential properties of a biological dynamic process occurring over a continuous timescale was derived from first principles. The distribution turned out to have three parameters with clear meanings and units: (i) a scaled rate of completion (dimensionless), (ii) a measure of temporal concentration of the process (units: time-1), and (iii) an overall measure of temporal delay (units: time). Its performance as an accurate description of the process was tested with completion data for the London Marathon employing non-linear regression. Results. The parameters of the distribution correlated with biological attributes of the runners (gender and age) and with the maximum temperature on the day of the race. These relationships mirrored known differences in morphology and physiology of participants and the deterioration of these biological attributes with age (senescence), as well as the known effects of hypo- and hyperthermia. Discussion. By relating the variation in parameter values to possible biological and environmental variables, the marathon example demonstrates the ability of the distribution to help identify possible triggers and drivers of the duration, shape and temporal shift of its temporal distribution. This more detailed account of the effect of biological and environmental variables would provide a deeper insight into the drivers of a wide variety of phenological phenomena of high current interest, such as the shifting patterns of leafing, flowering, growth, migration, etc. of many organisms worldwide.Optimal exponent-pairs for the Bertalanffy-Pütter growth modelhttps://peerj.com/preprints/271522018-08-282018-08-28Katharina Renner-MartinNorbert BrunnerManfred KühleitnerWerner-Georg NowakKlaus Scheicher
The Bertalanffy-Pütter growth model describes mass m at age t by means of the differential equation dm/dt = p⋅ma−q⋅mb. The special case using the Bertalanffy exponent-pair a=2/3 and b=1 is most common (it corresponds to the von Bertalanffy growth function VBGF for length in fishery literature). For data fitting using general exponents, five model parameters need to be optimized, the pair a<b of non-negative exponents, the non-negative constants p and q, and a positive initial value m0 for the differential equation. For the case b=1 it is known that for most fish data any exponent a<1 could be used to model growth without affecting the fit to the data significantly (when the other parameters p, q, m0 were optimized). Thereby, data fitting used the method of least squares, minimizing the sum of squared errors (SSE). It was conjectured that the optimization of both exponents would result in a significantly better fit of the optimal growth function to the data and thereby reduce SSE. This conjecture was tested for a data set for the mass-growth of Walleye (Sander vitreus), a fish from Lake Erie, USA. Compared to the Bertalanffy exponent-pair the optimal exponent-pair achieved a reduction of SSE by 10%. However, when the optimization of additional parameters was penalized, using the Akaike information criterion (AIC), then the optimal exponent-pair model had a higher (worse) AIC, when compared to the Bertalanffy exponent-pair. Thereby SSE and AIC are different ways to compare models. SSE is used, when predictive power is needed alone, and AIC is used, when simplicity of the model and explanatory power are needed.
The Bertalanffy-Pütter growth model describes mass m at age t by means of the differential equation dm/dt = p⋅ma−q⋅mb. The special case using the Bertalanffy exponent-pair a=2/3 and b=1 is most common (it corresponds to the von Bertalanffy growth function VBGF for length in fishery literature). For data fitting using general exponents, five model parameters need to be optimized, the pair a<b of non-negative exponents, the non-negative constants p and q, and a positive initial value m0 for the differential equation. For the case b=1 it is known that for most fish data any exponent a<1 could be used to model growth without affecting the fit to the data significantly (when the other parameters p, q, m0 were optimized). Thereby, data fitting used the method of least squares, minimizing the sum of squared errors (SSE). It was conjectured that the optimization of both exponents would result in a significantly better fit of the optimal growth function to the data and thereby reduce SSE. This conjecture was tested for a data set for the mass-growth of Walleye (Sander vitreus), a fish from Lake Erie, USA. Compared to the Bertalanffy exponent-pair the optimal exponent-pair achieved a reduction of SSE by 10%. However, when the optimization of additional parameters was penalized, using the Akaike information criterion (AIC), then the optimal exponent-pair model had a higher (worse) AIC, when compared to the Bertalanffy exponent-pair. Thereby SSE and AIC are different ways to compare models. SSE is used, when predictive power is needed alone, and AIC is used, when simplicity of the model and explanatory power are needed.Modelling of the SDF-1/CXCR4 regulated in vivo homing of therapeutic mesenchymal stem/stromal cells in micehttps://peerj.com/preprints/271442018-08-272018-08-27Wang JinXiaowen LiangAnastasia BrooksKathryn FutregaXin LiuMichael R. DoranMatthew J. SimpsonMichael S. RobertsHaolu Wang
Background. Mesenchymal stem/stromal cells (MSCs) are a promising tool for cell-based therapies in the treatment of tissue injury. The stromal cell-derived factor-1 (SDF-1)/CXC chemokine receptor 4 (CXCR4) axis plays a significant role in directing MSC homing to sites of injury. However in vivo MSC distribution following intravenous transplantation remains poorly understood, potentially hampering the precise prediction and evaluation of therapeutic efficacy.
Methods. A murine model of partial ischemia/reperfusion (I/R) is used to induce liver injury, increase the hepatic levels of SDF-1, and study in vivo MSC distribution. Hypoxia-preconditioning increases the expression of CXCR4 in human bone marrow-derived MSCs. Quantitative assays for human DNA allow us to examine the in vivo kinetics of intravenously infused human MSCs in mouse blood and liver. A mathematical model-based system is developed to characterize in vivo homing of human MSCs in mouse models with SDF-1 levels in liver and CXCR4 expression on the transfused MSCs. The model is calibrated to experimental data to provide novel estimates of relevant parameter values.
Results. Images of immunohistochemistry for SDF-1 in the mouse liver with I/R injury show a significantly higher SDF-1level in the I/R injured liver than that in the control. Correspondingly, the ELISA results illustrate a higher MSC dose in the I/R injured liver than the normal liver. CXCR4 is overexpressed in hypoxia-preconditioned MSCs. An increased number of hypoxia-preconditioned MSCs in the I/R injured liver is observed from the ELISA results. The model simulations align with the experimental data of control and hypoxia-preconditioned human MSC distribution in normal and injured mouse livers, and accurately predict the experimental outcomes with different MSC doses.
Discussion. The modelling results suggest that SDF-1 in organs is an effective in vivo attractant for MSCs through the SDF-1/CXCR4 axis and reveals the significance of the SDF-1/CXCR4 chemotaxis on in vivo homing of MSCs, especially under hypoxic preconditioning. The impact of the liver and MSC conditions on passive homing is small. This in vivo modelling approach allows qualitative characterization and prediction of the MSC homing to normal and injured organs on the basis of clinically accessible variables, such as the MSC dose and SDF-1 concentration in blood. This model could also be adapted to abnormal conditions and/or other types of circulating cells to predict in vivo homing patterns.
Background. Mesenchymal stem/stromal cells (MSCs) are a promising tool for cell-based therapies in the treatment of tissue injury. The stromal cell-derived factor-1 (SDF-1)/CXC chemokine receptor 4 (CXCR4) axis plays a significant role in directing MSC homing to sites of injury. However in vivo MSC distribution following intravenous transplantation remains poorly understood, potentially hampering the precise prediction and evaluation of therapeutic efficacy.Methods. A murine model of partial ischemia/reperfusion (I/R) is used to induce liver injury, increase the hepatic levels of SDF-1, and study in vivo MSC distribution. Hypoxia-preconditioning increases the expression of CXCR4 in human bone marrow-derived MSCs. Quantitative assays for human DNA allow us to examine the in vivo kinetics of intravenously infused human MSCs in mouse blood and liver. A mathematical model-based system is developed to characterize in vivo homing of human MSCs in mouse models with SDF-1 levels in liver and CXCR4 expression on the transfused MSCs. The model is calibrated to experimental data to provide novel estimates of relevant parameter values.Results. Images of immunohistochemistry for SDF-1 in the mouse liver with I/R injury show a significantly higher SDF-1level in the I/R injured liver than that in the control. Correspondingly, the ELISA results illustrate a higher MSC dose in the I/R injured liver than the normal liver. CXCR4 is overexpressed in hypoxia-preconditioned MSCs. An increased number of hypoxia-preconditioned MSCs in the I/R injured liver is observed from the ELISA results. The model simulations align with the experimental data of control and hypoxia-preconditioned human MSC distribution in normal and injured mouse livers, and accurately predict the experimental outcomes with different MSC doses.Discussion. The modelling results suggest that SDF-1 in organs is an effective in vivo attractant for MSCs through the SDF-1/CXCR4 axis and reveals the significance of the SDF-1/CXCR4 chemotaxis on in vivo homing of MSCs, especially under hypoxic preconditioning. The impact of the liver and MSC conditions on passive homing is small. This in vivo modelling approach allows qualitative characterization and prediction of the MSC homing to normal and injured organs on the basis of clinically accessible variables, such as the MSC dose and SDF-1 concentration in blood. This model could also be adapted to abnormal conditions and/or other types of circulating cells to predict in vivo homing patterns.An improved tree-based statistical method for genome-wide association studyhttps://peerj.com/preprints/271182018-08-202018-08-20Dwueng-Chwuan Jhwueng
In genetic studies, quantitative traits are found possibly associated with genetic data. Due to advanced sequencing technology, many methods have been proposed in genome wide association study (GWAS) to search the single nucleotide polymorphism (SNP) associated with the traits. Currently several methods that account for the evolutionary relatedness among individuals were developed. When comparing with conventional methods without evolutionary relatedness among individuals, tree based methods are found to have better performance when the population structure increases. In this work, we extend a couple of methods in previous studies by varying the magnitude of relatedness. The magnitude of relatedness of the evolutionary history is controlled by an Ornstein-Uhlenbeck (OU) process through its parameters. Our method combines a pertinent process and phylogenetic comparative method where the incorporated evolutionary history is built by SNP data. We perform simulation as well as analyze drosophila longevity data set.
In genetic studies, quantitative traits are found possibly associated with genetic data. Due to advanced sequencing technology, many methods have been proposed in genome wide association study (GWAS) to search the single nucleotide polymorphism (SNP) associated with the traits. Currently several methods that account for the evolutionary relatedness among individuals were developed. When comparing with conventional methods without evolutionary relatedness among individuals, tree based methods are found to have better performance when the population structure increases. In this work, we extend a couple of methods in previous studies by varying the magnitude of relatedness. The magnitude of relatedness of the evolutionary history is controlled by an Ornstein-Uhlenbeck (OU) process through its parameters. Our method combines a pertinent process and phylogenetic comparative method where the incorporated evolutionary history is built by SNP data. We perform simulation as well as analyze drosophila longevity data set.Comparing 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.