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  1. Abdul Latif NS, Wake GC, Reglinski T, Elmer PA
    J Theor Biol, 2014 Apr 21;347:144-50.
    PMID: 24398025 DOI: 10.1016/j.jtbi.2013.12.023
    Plant disease control has traditionally relied heavily on the use of agrochemicals despite their potentially negative impact on the environment. An alternative strategy is that of induced resistance (IR). However, while IR has proven effective in controlled environments, it has shown variable field efficacy, thus raising questions about its potential for disease management in a given crop. Mathematical modelling of IR assists researchers with understanding the dynamics of the phenomenon in a given plant cohort against a selected disease-causing pathogen. Here, a prototype mathematical model of IR promoted by a chemical elicitor is proposed and analysed. Standard epidemiological models describe that, under appropriate environmental conditions, Susceptible plants (S) may become Diseased (D) upon exposure to a compatible pathogen or are able to Resist the infection (R) via basal host defence mechanisms. The application of an elicitor enhances the basal defence response thereby affecting the relative proportion of plants in each of the S, R and D compartments. IR is a transient response and is modelled using reversible processes to describe the temporal evolution of the compartments. Over time, plants can move between these compartments. For example, a plant in the R-compartment can move into the S-compartment and can then become diseased. Once in the D-compartment, however, it is assumed that there is no recovery. The terms in the equations are identified using established principles governing disease transmission and this introduces parameters which are determined by matching data to the model using computer-based algorithms. These then give the best match of the model with experimental data. The model predicts the relative proportion of plants in each compartment and quantitatively estimates elicitor effectiveness. An illustrative case study will be given; however, the model is generic and will be applicable for a range of plant-pathogen-elicitor scenarios.
  2. Fernando WJ
    J Theor Biol, 2009 Jul 21;259(2):297-303.
    PMID: 19336237 DOI: 10.1016/j.jtbi.2009.03.026
    Chemical inactivation of microorganisms is a common process widely employed in many fields such as in treatment of water, preservation in food industry and antimicrobial treatments in healthcare. For economy of applications and efficiency of treatment establishment the minimum dosage of breakpoint in the chemical application becomes essential. Even though experimental investigations have been extensive, theoretical understanding of such processes are demanding. Commonly employed theoretical analyses for the inactivation of microorganisms and depletion of chemicals include kinetics expressing the rates of depletion of chemical and microorganisms. The terms chemical demand (x) and specific disinfectant demand (alpha) are often used in theoretical modeling of inactivation. The value of specific disinfectant demand (alpha) has always been assumed to be a constant in these models. Intracellular concentration built up within the cells of the microorganisms during inactivation could lead to possible weakening effects of microorganisms thereby requiring lower doses as disinfection proceeds makes the assumption of constant alpha inaccurate. Model equations are formulated based on these observations co-relating the parameters alpha and x with a progressive inactivation (N/N(0)). The chemical concentration (C) is also presented in terms of the inactivation time (t) and the survival ratio (N/N(0)) for given pH and temperature conditions. The model is examined using experimentally verified Ct data of Giardia Cysts/chlorine system. The respective values of x for different survival ratios were evaluated from the data using MatLab software. Proposed model correlating for the disinfectant demand (x) with the survival ratio (N/N(0)) fits satisfactorily with those evaluated from data. The rate constants for different pH and temperature conditions are evaluated which showed compatibility with the Arrhenius model. The dependence of frequency factors with pH indicated compatibility with accepted models. The Ct values regenerated with the kinetic data shows a very accurate fit with published data.
  3. Mohamed Hashim EK, Abdullah R
    J Theor Biol, 2015 Dec 21;387:88-100.
    PMID: 26427337 DOI: 10.1016/j.jtbi.2015.09.014
    Empirical analysis on k-mer DNA has been proven as an effective tool in finding unique patterns in DNA sequences which can lead to the discovery of potential sequence motifs. In an extensive study of empirical k-mer DNA on hundreds of organisms, the researchers found unique multi-modal k-mer spectra occur in the genomes of organisms from the tetrapod clade only which includes all mammals. The multi-modality is caused by the formation of the two lowest modes where k-mers under them are referred as the rare k-mers. The suppression of the two lowest modes (or the rare k-mers) can be attributed to the CG dinucleotide inclusions in them. Apart from that, the rare k-mers are selectively distributed in certain genomic features of CpG Island (CGI), promoter, 5' UTR, and exon. We correlated the rare k-mers with hundreds of annotated features using several bioinformatic tools, performed further intrinsic rare k-mer analyses within the correlated features, and modeled the elucidated rare k-mer clustering feature into a classifier to predict the correlated CGI and promoter features. Our correlation results show that rare k-mers are highly associated with several annotated features of CGI, promoter, 5' UTR, and open chromatin regions. Our intrinsic results show that rare k-mers have several unique topological, compositional, and clustering properties in CGI and promoter features. Finally, the performances of our RWC (rare-word clustering) method in predicting the CGI and promoter features are ranked among the top three, in eight of the CGI and promoter evaluations, among eight of the benchmarked datasets.
  4. Luczkovich JJ, Borgatti SP, Johnson JC, Everett MG
    J Theor Biol, 2003 Feb 07;220(3):303-21.
    PMID: 12468282
    We present a graph theoretic model of analysing food web structure called regular equivalence. Regular equivalence is a method for partitioning the species in a food web into "isotrophic classes" that play the same structural roles, even if they are not directly consuming the same prey or if they do not share the same predators. We contrast regular equivalence models, in which two species are members of the same trophic group if they have trophic links to the same set of other trophic groups, with structural equivalence models, in which species are equivalent if they are connected to the exact same other species. Here, the regular equivalence approach is applied to two published food webs: (1) a topological web (Malaysian pitcher plant insect food web) and (2) a carbon-flow web (St. Marks, Florida seagrass ecosystem food web). Regular equivalence produced a more satisfactory set of classes than did the structural approach, grouping basal taxa with other basal taxa and not with top predators. Regular equivalence models provide a way to mathematically formalize trophic position, trophic group and trophic niche. These models are part of a family of models that includes structural models used extensively by ecologists now. Regular equivalence models uncover similarities in trophic roles at a higher level of organization than do the structural models. The approach outlined is useful for measuring the trophic roles of species in food web models, measuring similarity in trophic relations of two or more species, comparing food webs over time and across geographic regions, and aggregating taxa into trophic groups that reduce the complexity of ecosystem feeding relations without obscuring network relationships. In addition, we hope the approach will prove useful in predicting the outcome of predator-prey interactions in experimental studies.
  5. Wan Ab Naim WN, Mohamed Mokhtarudin MJ, Chan BT, Lim E, Ahmad Bakir A, Nik Mohamed NA
    J Theor Biol, 2021 01 21;509:110527.
    PMID: 33096094 DOI: 10.1016/j.jtbi.2020.110527
    Reperfusion of the blood flow to ischemic myocardium is the standard treatment for patients suffering myocardial infarction. However, the reperfusion itself can also induce myocardial injury, in which the actual mechanism and its risk factors remain unclear. This work aims to study the mechanism of ischemia-reperfusion treatment using a three-dimensional (3D) oxygen diffusion model. An electrical model is then coupled to an oxygen model to identify the possible region of myocardial damage. Our findings show that the value of oxygen exceeds its optimum (>1.0) at the ischemic area during early reperfusion period. This complication was exacerbated in a longer ischemic period. While a longer reperfusion time causes a continuous excessive oxygen supply to the ischemic area throughout the reperfusion time. This work also suggests the use of less than 0.8 of initial oxygen concentration in the reperfusion treatment to prevent undesired upsurge at the early reperfusion period and further myocardial injury. We also found the region at risk for myocardial injury is confined in the ischemic vicinity revealed by its electrical conductivity impairment. Although there is a risk that reperfusion leads to myocardial injury for excessive oxygen accumulation, the reperfusion treatment is helpful in reducing the infarct size.
  6. Hassan M, Abbasi MA, Aziz-Ur-Rehman, Siddiqui SZ, Hussain G, Shah SAA, et al.
    J Theor Biol, 2018 12 07;458:169-183.
    PMID: 30243565 DOI: 10.1016/j.jtbi.2018.09.018
    A new series of multifunctional amides has been synthesized having moderate enzyme inhibitory potentials and mild cytotoxicity. 2-Furyl(1-piperazinyl)methanone (1) was coupled with 3,5-dichloro-2-hydroxybenzenesulfonyl chloride (2) to form {4-[(3,5-dichloro-2-hydroxyphenyl)sulfonyl]-1-piperazinyl}(2-furyl)methanone (3). Different elecrophiles were synthesized by the reaction of various un/substituted anilines (4a-o) with 2-bromoacetylbromide (5), 2‑bromo‑N-(un/substituted-phenyl)acetamides (6a-o). Further, equimolar ratios of 3 and 6a-o were allowed to react in the presence of K2CO3 in acetonitrile to form desired multifunctional amides (7a-o). The structural confirmation of all the synthesized compounds was carried out by their EI-MS, IR, 1H NMR and 13C NMR spectral data. Enzyme inhibition activity was performed against acetyl and butyrylcholinestrase enzymes, whereby 7e showed very good activity having IC50 value of 5.54 ± 0.03 and 9.15 ± 0.01 μM, respectively, relative to eserine, a reference standard. Hemolytic activity of the molecules was checked to asertain their cytotoxicity towards red blood cell membrance and it was observed that most of the compounds were not toxic up to certain range. Moreover, chemoinformatic protepties and docking simulation results also showed the significance of 7e as compared to other compounds. Based on in vitro and in silico analysis 7e could be used as a template for the development of new drugs against Alzheimer's disease.
  7. Tay CJ, Mohd MH, Teh SY, Koh HL
    J Theor Biol, 2022 01 07;532:110913.
    PMID: 34562459 DOI: 10.1016/j.jtbi.2021.110913
    Internal phosphorus recycling in lakes is an important nutrient source that promotes algal growth. Its persistence impedes the effort to improve water quality and thus poses a challenge to the management of eutrophication in lakes, especially in shallow lakes where the occurrence of internal phosphorus recycling is reportedly more common. This paper aims to provide crucial insights on the effects of internal phosphorus recycling on eutrophication dynamics for effective management of lake eutrophication. For this purpose, a mathematical model for lake eutrophication, comprising two compartments of algae and phosphorus, is first formulated for application to a eutrophic tropical lake named Tasik Harapan in Universiti Sains Malaysia. Numerical bifurcation analysis of the model is then performed to assess the combined influences of internal phosphorus recycling, algal mortality and external phosphorus loading on Tasik Harapan eutrophication dynamics. Specifically, co-dimension one bifurcation analysis of algal mortality rate is carried out by means of XPPAUT for various external phosphorus loading rates. The emergence of limit cycle for a certain range of algal mortality rate could be related to the hydra effect (i.e., algal concentration increases in response to greater algal mortality) and the paradox of enrichment (i.e., destabilization of algae in nutrient rich environment). To trace the locus of co-dimension one bifurcation, co-dimension two bifurcation analysis is performed by means of MatCont. The analysis demonstrated that the inclusion of the internal phosphorus recycling term induces rich and complex dynamics of the model. These dynamics include saddle-node bifurcation, cusp, Bogdanov-Takens bifurcation, Generalized Hopf bifurcation and limit point bifurcation of cycles. The results suggest that high internal phosphorus recycling rate promotes bistability and catastrophic shift in a shallow and tropical lake like Tasik Harapan. Hence, the key to effective management of eutrophication in shallow and tropical lakes is the control of internal phosphorus recycling.
  8. Mokhtar NH, Abas A, Razak NA, Hamid MNA, Teong SL
    J Theor Biol, 2017 11 21;433:73-84.
    PMID: 28844907 DOI: 10.1016/j.jtbi.2017.08.016
    Proper design of stent for application at specific aneurysm effect arteries could help to reduce the issues with thrombosis and aneurysm. In this paper, four types of stent configuration namely half-Y (6 mm), half-Y (4 mm), cross-bar, and full-Y configuration will implanted on real 3D artery bifurcation aneurysm effected arteries. Comparisons were then conducted based on the flow patterns after stent placement using both LBM-based solver and PIV experimental findings. According to the data obtained from all 4 stent designs, the flow profiles and the computed velocity from both methods were in agreement with each other. Both methods found that half-Y (6 mm) stent configuration is by far the best configuration in reducing the blood velocity at the vicinity of the aneurysm sac. The analysis also show that the half-Y (6 mm) stent configuration recorded the highest percentage of velocity reduction and managed to substantially reduce the pressure at the bifurcation region. This high flow velocity reduction through the use of half-Y stent could consequently promote the formation of thrombus thereby reducing the risk of rupture in the aneurysm sac.
  9. Oroji A, Omar M, Yarahmadian S
    J Theor Biol, 2016 10 21;407:128-137.
    PMID: 27457094 DOI: 10.1016/j.jtbi.2016.07.035
    In this paper, a new mathematical model is proposed for studying the population dynamics of breast cancer cells treated by radiotherapy by using a system of stochastic differential equations. The novelty of the model is essentially in capturing the concept of the cell cycle in the modeling to be able to evaluate the tumor lifespan. According to the cell cycle, each cell belongs to one of three subpopulations G, S, or M, representing gap, synthesis and mitosis subpopulations. Cells in the M subpopulation are highly radio-sensitive, whereas cells in the S subpopulation are highly radio-resistant. Therefore, in the process of radiotherapy, cell death rates of different subpopulations are not equal. In addition, since flow cytometry is unable to detect apoptotic cells accurately, the small changes in cell death rate in each subpopulation during treatment are considered. Subsequently, the proposed model is calibrated using experimental data from previous experiments involving the MCF-7 breast cancer cell line. Consequently, the proposed model is able to predict tumor lifespan based on the number of initial carcinoma cells. The results show the effectiveness of the radiation under the condition of stability, which describes the decreasing trend of the tumor cells population.
  10. Dodd J, Sweby PK, Mayes S, Murchie EH, Karunaratne AS, Massawe F, et al.
    J Theor Biol, 2023 Mar 07;560:111373.
    PMID: 36509139 DOI: 10.1016/j.jtbi.2022.111373
    A principal objective in agriculture is to maximise food production; this is particularly relevant with the added demands of an ever increasing population, coupled with the unpredictability that climate change brings. Further improvements in productivity can only be achieved with an increased understanding of plant and crop processes. In this respect, mathematical modelling of plants and crops plays an important role. In this paper we present a two-scale mathematical model of crop yield that accounts for plant growth and canopy interactions. A system of nonlinear ordinary differential equations (ODEs) is formulated to describe the growth of each individual plant, where equations are coupled via a term that describes plant competition via canopy-canopy interactions. A crop of greenhouse plants is then modelled via an agent based modelling approach in which the growth of each plant is described via our system of ODEs. The model is formulated for the African drought tolerant legume bambara groundnut (Vigna subterranea), which is currently being investigated as a food source in light of climate change and food insecurity challenges. Our model allows us to account for plant diversity and also investigate the effect of individual plant traits (e.g. plant canopy size and planting distance) on the yield of the overall crop. Informed with greenhouse data, model results show that plant positioning relative to other plants has a large impact on individual plant yield. Variation in physiological plant traits from genetic diversity and the environmental effects lead to experimentally observed variations in crop yield. These traits include plant height, plant carrying capacity, leaf accumulation rate and canopy spread. Of these traits plant height and ground cover growth rates are found to have the greatest impact on crop yield. We also consider a range of different planting arrangements (uniform grid, staggered grid, circular rings and random allocation) and find that the staggered grid leads to the greatest crop yield (6% more compared to uniform grid). Whilst formulated specifically for bambara groundnut, the generic formulation of our model means that with changes to certain parameter's, it may be extended to other crop species that form a canopy.
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