PeerJ Preprints: Mathematical Biologyhttps://peerj.com/preprints/index.atom?journal=peerj&subject=1900Mathematical Biology articles published in PeerJ PreprintsCoccolith 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.Cancer growth, metastasis and control likewise Go gaming: an Ising model approachhttps://peerj.com/preprints/34342017-11-292017-11-29Didier Barradas-BautistaMatías AlvaradoGerminal CochoMark Agostino
This work aims for modeling and simulating the metastasis of cancer, via the analogy between the cancer process and the board game Go. In the game of Go, black stones play first, could correspond to metastasis of cancer. Moreover, playing white stones on the second turn would correspond to the inhibition of cancer invasion. Mathematical modeling and algorithmic simulation of Go may, therefore, benefit the efforts to deploy therapies to surpass cancer illness by providing insight into the cellular growth and expansion over a tissue area. In this paper, we use the Ising Hamiltonian, an energy model to describe the energy exchange in interacting particles, to propose the modeling of cancer dynamics. Parameters in the energy function refer the biochemical elements that induce cancer metastasis; as well as, the biochemical immune system process of response.
This work aims for modeling and simulating the metastasis of cancer, via the analogy between the cancer process and the board game Go. In the game of Go, black stones play first, could correspond to metastasis of cancer. Moreover, playing white stones on the second turn would correspond to the inhibition of cancer invasion. Mathematical modeling and algorithmic simulation of Go may, therefore, benefit the efforts to deploy therapies to surpass cancer illness by providing insight into the cellular growth and expansion over a tissue area. In this paper, we use the Ising Hamiltonian, an energy model to describe the energy exchange in interacting particles, to propose the modeling of cancer dynamics. Parameters in the energy function refer the biochemical elements that induce cancer metastasis; as well as, the biochemical immune system process of response.The mathematics of extinction across scales: from populations to the biospherehttps://peerj.com/preprints/33672017-10-242017-10-24Colin 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 a new 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 a new example using data on Spix's macaw (Cyanopsitta spixii), the "rarest bird in the world," to demonstrate the challenges associated with extinction date research.On the exponent in the von Bertalanffy growth modelhttps://peerj.com/preprints/33032017-09-292017-09-29Katharina Renner-MartinNorbert BrunnerManfred KühleitnerGeorg NowakKlaus Scheicher
Bertalanffy proposed the differential equation m´(t) = p × m (t) a –q × m (t) for the description of the mass growth of animals as a function m(t) of time t. He suggested that the solution using the metabolic scaling exponent a = 2/3 (von Bertalanffy growth function VBGF) would be universal for vertebrates. Several authors questioned universality, as for certain species other models would provide a better fit. This paper reconsiders this question. Using the Akaike information criterion it proposes a testable definition of ‘weak universality’ for a taxonomic group of species. (It roughly means that a model has an acceptable fit to most data sets of that group.) This definition was applied to 60 data sets from literature (37 about fish and 23 about non-fish species) and for each dataset an optimal metabolic scaling exponent 0 ≤ a opt < 1 was identified, where the model function m(t) achieved the best fit to the data. Although in general this optimal exponent differed widely from a = 2/3 of the VBGF, the VBGF was weakly universal for fish, but not for non-fish. This observation supported the conjecture that the pattern of growth for fish may be distinct. The paper discusses this conjecture.
Bertalanffy proposed the differential equation m´(t) = p × m (t) a –q × m (t) for the description of the mass growth of animals as a function m(t) of time t. He suggested that the solution using the metabolic scaling exponent a = 2/3 (von Bertalanffy growth function VBGF) would be universal for vertebrates. Several authors questioned universality, as for certain species other models would provide a better fit. This paper reconsiders this question. Using the Akaike information criterion it proposes a testable definition of ‘weak universality’ for a taxonomic group of species. (It roughly means that a model has an acceptable fit to most data sets of that group.) This definition was applied to 60 data sets from literature (37 about fish and 23 about non-fish species) and for each dataset an optimal metabolic scaling exponent 0 ≤ a opt < 1 was identified, where the model function m(t) achieved the best fit to the data. Although in general this optimal exponent differed widely from a = 2/3 of the VBGF, the VBGF was weakly universal for fish, but not for non-fish. This observation supported the conjecture that the pattern of growth for fish may be distinct. The paper discusses this conjecture.Genome rearrangements and phylogeny reconstruction in Yersinia pestishttps://peerj.com/preprints/32232017-09-052017-09-05Olga O BochkarevaNatalia O DranenkoElena S OcheredkoGerman M KanevskyYaroslav N LozinskyVera A KhalaychevaIrena I ArtamonovaMikhail S Gelfand
Genome rearrangements have played an important role in the evolution of Yersinia pestis from its progenitor Yersinia pseudotuberculosis. Traditional phylogenetic trees for Y. pestis based on sequence comparison have short internal branches and low bootstrap supports as only a small number of nucleotide substitutions have occurred. On the other hand, even a small number of genome rearrangements may resolve topological ambiguities in a phylogenetic tree.
We reconstructed the evolutionary history of genome rearrangements in Y. pestis. We also reconciled phylogenetic trees for each of the three CRISPR-loci to obtain an integrated scenario of the CRISPR-cassette evolution. We detected numerous parallel inversions and gain/loss events by the analysis of contradictions between the obtained evolutionary trees. We also tested the hypotheses that large within-replichore inversions tend to be balanced by subsequent reversal events and that the core genes less frequently switch the chain by inversions. Both predictions were not confirmed.
Our data indicate that an integrated analysis of sequence-based and inversion-based trees enhances the resolution of phylogenetic reconstruction. In contrast, reconstructions of strain relationships based on solely CRISPR loci may not be reliable, as the history is obscured by large deletions, obliterating the order of spacer gains. Similarly, numerous parallel gene losses preclude reconstruction of phylogeny based on gene content.
Genome rearrangements have played an important role in the evolution of Yersinia pestis from its progenitor Yersinia pseudotuberculosis. Traditional phylogenetic trees for Y. pestis based on sequence comparison have short internal branches and low bootstrap supports as only a small number of nucleotide substitutions have occurred. On the other hand, even a small number of genome rearrangements may resolve topological ambiguities in a phylogenetic tree.We reconstructed the evolutionary history of genome rearrangements in Y. pestis. We also reconciled phylogenetic trees for each of the three CRISPR-loci to obtain an integrated scenario of the CRISPR-cassette evolution. We detected numerous parallel inversions and gain/loss events by the analysis of contradictions between the obtained evolutionary trees. We also tested the hypotheses that large within-replichore inversions tend to be balanced by subsequent reversal events and that the core genes less frequently switch the chain by inversions. Both predictions were not confirmed.Our data indicate that an integrated analysis of sequence-based and inversion-based trees enhances the resolution of phylogenetic reconstruction. In contrast, reconstructions of strain relationships based on solely CRISPR loci may not be reliable, as the history is obscured by large deletions, obliterating the order of spacer gains. Similarly, numerous parallel gene losses preclude reconstruction of phylogeny based on gene content.Integrating ecology and evolution to study hypothetical dynamics of algal blooms and Muller’s ratchet using Evolvixhttps://peerj.com/preprints/32182017-09-012017-09-01Sarah NortheyCourtney HoveJustine KaoJon IdeJanel McKinneyLaurence Loewe
Algal blooms have been the subject of considerable research as they occur over various spatial and temporal scales and can produce toxins that disrupt their ecosystem. Algal blooms are often governed by nutrient availability however other limitations exist. Algae are primary producers and therefore subject to predation which can keep populations below levels supported by nutrient availability. If algae as prey mutate to gain the ability to produce toxins deterring predators, they may increase their survival rates and form blooms unless other factors counter their effective increase in growth rate. Where might such mutations come from? Clearly, large populations of algae will repeatedly experience mutations knocking-out DNA repair genes, increasing mutation rates, and with them the chance of acquiring de-novo mutations producing a toxin against predators. We investigate this hypothetical scenario by simulation in the Evolvix modeling language. We modeled a sequence of steps that in principle can allow a typical asexual algal population to escape predation pressure and form a bloom with the help of mutators. We then turn our attention to the unavoidable side effect of generally increased mutation rates, many slightly deleterious mutations. If these accumulate at sufficient speed, their combined impact on fitness might place upper limits on the duration of algal blooms. These steps are required: (1) Random mutations result in the loss of DNA repair mechanisms. (2) Increased mutation rates make it more likely to acquire the ability to produce toxins by altering metabolism. (3) Toxins deter predators providing algae with growth advantages that can mask linked slightly deleterious mutational effects. (4) Reduced predation pressure enables blooms if algae have sufficient nutrients. (5) Lack of recombination results in the accumulation of slightly deleterious mutations as predicted by Muller’s ratchet. (6) If fast enough, deleterious mutation accumulation eventually leads to mutational meltdown of toxic blooming algae. (7) Non-mutator algal populations are not affected due to ongoing predation pressure. Our simulation models integrate ecological continuous-time dynamics of predator-prey systems with the population genetics of a simplified Muller’s ratchet model using Evolvix. Evolvix maps these models to Continuous-Time Markov Chain models that can be simulated deterministically or stochastically depending on the question. The current model is incomplete; we plan to investigate many parameter combinations to produce a more robust model ensemble with stable links to reasonable parameter estimates. However, our model already has several intriguing features that may allow for the eventual development of observation methods for monitoring ecosystem health. Our work also highlights a growing need to simulate integrated models combining ecological processes, multi-level population dynamics, and evolutionary genetics in a single computational run.
Algal blooms have been the subject of considerable research as they occur over various spatial and temporal scales and can produce toxins that disrupt their ecosystem. Algal blooms are often governed by nutrient availability however other limitations exist. Algae are primary producers and therefore subject to predation which can keep populations below levels supported by nutrient availability. If algae as prey mutate to gain the ability to produce toxins deterring predators, they may increase their survival rates and form blooms unless other factors counter their effective increase in growth rate. Where might such mutations come from? Clearly, large populations of algae will repeatedly experience mutations knocking-out DNA repair genes, increasing mutation rates, and with them the chance of acquiring de-novo mutations producing a toxin against predators. We investigate this hypothetical scenario by simulation in the Evolvix modeling language. We modeled a sequence of steps that in principle can allow a typical asexual algal population to escape predation pressure and form a bloom with the help of mutators. We then turn our attention to the unavoidable side effect of generally increased mutation rates, many slightly deleterious mutations. If these accumulate at sufficient speed, their combined impact on fitness might place upper limits on the duration of algal blooms. These steps are required: (1) Random mutations result in the loss of DNA repair mechanisms. (2) Increased mutation rates make it more likely to acquire the ability to produce toxins by altering metabolism. (3) Toxins deter predators providing algae with growth advantages that can mask linked slightly deleterious mutational effects. (4) Reduced predation pressure enables blooms if algae have sufficient nutrients. (5) Lack of recombination results in the accumulation of slightly deleterious mutations as predicted by Muller’s ratchet. (6) If fast enough, deleterious mutation accumulation eventually leads to mutational meltdown of toxic blooming algae. (7) Non-mutator algal populations are not affected due to ongoing predation pressure. Our simulation models integrate ecological continuous-time dynamics of predator-prey systems with the population genetics of a simplified Muller’s ratchet model using Evolvix. Evolvix maps these models to Continuous-Time Markov Chain models that can be simulated deterministically or stochastically depending on the question. The current model is incomplete; we plan to investigate many parameter combinations to produce a more robust model ensemble with stable links to reasonable parameter estimates. However, our model already has several intriguing features that may allow for the eventual development of observation methods for monitoring ecosystem health. Our work also highlights a growing need to simulate integrated models combining ecological processes, multi-level population dynamics, and evolutionary genetics in a single computational run.An invitation to modeling: building a community with shared explicit practiceshttps://peerj.com/preprints/32152017-09-012017-09-01Kam D DahlquistMelissa L AikensJoseph T DauerSamuel S DonovanCarrie Diaz EatonHannah Callender HighlanderKristin P JenkinsJohn R JungckM Drew LaMarGlenn LedderRobert L MayesRichard C Schugart
Models and the process of modeling are fundamental to the discipline of biology, and therefore should be incorporated into undergraduate biology courses. In this essay, we draw upon the literature and our own teaching experiences to provide practical suggestions for how to introduce models and modeling to introductory biology students. We begin by demonstrating the ubiquity of models in biology, including representations of the process of science itself. We advocate for a model of the process of science that highlights parallel tracks of mathematical and experimental modeling investigations. With this recognition, we suggest ways in which instructors can call students’ attention to biological models more explicitly by using modeling language, facilitating metacognition about the use of models, and employing model-based reasoning. We then provide guidance on how to begin to engage students in the process of modeling, encouraging instructors to scaffold a progression to mathematical modeling. We use the Hardy-Weinberg Equilibrium model to provide specific pedagogical examples that illustrate our suggestions. We propose that by making even a small shift in the way models and modeling are discussed in the classroom, students will gain understanding of key biological concepts, practice realistic scientific inquiry, and build quantitative and communication skills.
Models and the process of modeling are fundamental to the discipline of biology, and therefore should be incorporated into undergraduate biology courses. In this essay, we draw upon the literature and our own teaching experiences to provide practical suggestions for how to introduce models and modeling to introductory biology students. We begin by demonstrating the ubiquity of models in biology, including representations of the process of science itself. We advocate for a model of the process of science that highlights parallel tracks of mathematical and experimental modeling investigations. With this recognition, we suggest ways in which instructors can call students’ attention to biological models more explicitly by using modeling language, facilitating metacognition about the use of models, and employing model-based reasoning. We then provide guidance on how to begin to engage students in the process of modeling, encouraging instructors to scaffold a progression to mathematical modeling. We use the Hardy-Weinberg Equilibrium model to provide specific pedagogical examples that illustrate our suggestions. We propose that by making even a small shift in the way models and modeling are discussed in the classroom, students will gain understanding of key biological concepts, practice realistic scientific inquiry, and build quantitative and communication skills.