Mathematical modelling of the anaerobic digestion process: Application of dynamic mass-energy balance

The method of mass and energy balance was used in the design of a dynamic model of anaerobic digestion of complex organic substrates with production of methane. Distribution of mass flow, represented by the most abundant elements (C, H, N, O), and energy flow, represented by redoxons (available electrons), into gas and liquid output streams is influenced by environmental conditions in a continuous flow digester. Two pathways of methane generation,via cleavage of acetate andvia carbon dioxide reduction by hydrogen, are described in the model. The model was compared with experimental data from laboratory and pilot-plant experiments     

Thermodynamic equilibrium model in anaerobic digestion process

Catabolic reactions provide the chemical energy necessary for the maintenance of living microorganisms. The catabolic reactions in anaerobic digestion process may progress close to the equilibrium state (ΔG = 0) depending strongly on the microorganisms in the digester. The thermodynamic equilibrium of catabolic reactions in the anaerobic digestion process was modelled under isothermal and isobaric conditions. Three thermodynamic models were considered; the ideal, the Debye-Hückel–Praunitz, and the Pitzer–Praunitz. The models in this paper concentrate on the methanogenic equilibrium of the anaerobic digestion process. The thermodynamic equilibrium model shows that the methanogenesis step requires thermal energy and electrons, so that anaerobic digestion may achieve high substrate degradation and high conversion to methane. Some thermodynamic recommendations are suggested for the future development of the methanogenic phase of anaerobic digestion.     

Mathematical model of anaerobic digestion in a chemostat: effects of syntrophy and inhibition

Three of the four main stages of anaerobic digestion: acidogenesis, acetogenesis, and methanogenesis are described by a system of differential equations modelling the interaction of microbial populations in a chemostat. The microbes consume and/or produce simple substrates, alcohols and fatty acids, acetic acid, and hydrogen. Acetogenic bacteria and hydrogenotrophic methanogens interact through syntrophy. The model also includes the inhibition of acetoclastic and hydrogenotrophic methanogens due to sensitivity to varying pH-levels. To examine the effects of these interactions and inhibitions, we first study an inhibition-free model and obtain results for global stability using differential inequalities together with conservation laws. For the model with inhibition, we derive conditions for existence, local stability, and bistability of equilibria and present a global stability result. A case study illustrates the effects of inhibition on the regions of stability. Inhibition introduces regions of bistability and stabilizes some equilibria.     

A mathematical model and computer simulation study of insulin receptor regulation

A homeomorphic mathematical model of cell surface insulin receptor regulation is developed. The overall structure of the model is based on molecular mechanisms suggested by in vivo and in vitro experimental evidence from many different cell types. Model parameters correspond to cellular processes which are constrained by known boundry value conditions. As an example, computer simulation results are compared with published data from BC3H-1 myocytes in culture. With appropriate parameter choice, this model is able to simulate data from other cell types. Cellular processes which are explicitly represented in the model include: bound and unbound receptor endocytosis, receptor recycling, intracellular receptor degradation, and state-dependent receptor synthesis. Most of these processes are represented as first-order events. Using more complex representations of the model structure with higher order rate constants or saturable pathways does not qualitatively improve simulation results. Simulations are able to reproduce ligand-induced down and up regulation of receptors as well as the initial spontaneous display of surface insulin receptors. To demonstrate the behavior of our model and illustrate its utility for explaining insulin receptor regulation for a variety of conditions, simulations for which experimental data is unavailable for direct comparison are also shown. We believe the structure of our model is sufficient to explain insulin receptor regulation in a wide variety of cell types. In addition our model may aid in understanding the receptor component of insulin resistance (decreased sensitivity or responsiveness to insulin) seen in pathological states such as obesity and diabetes mellitus. Finally, this model may be applicable to the study of the regulation of other polypeptide hormone receptors.     

Mathematical model of the development of an epidemic process with aerosol transmission

A model of a pathogenic system with respiratory transmission was proposed. The internal regulation mechanism and the conditions for the onset of seasonal rise in morbidity were studied. The role of asymptomatic carriers in the formation of the virulence potential of the pathogen was shown.     

Mathematical model for the androgenic regulation of the prostate in intact and castrated adult male rats

The testicular-hypothalamic-pituitary axis regulates male reproductive system functions. Understanding these regulatory mechanisms is important for assessing the reproductive effects of environmental and pharmaceutical androgenic and antiandrogenic compounds. A mathematical model for the dynamics of androgenic synthesis, transport, metabolism, and regulation of the adult rodent ventral prostate was developed on the basis of a model by Barton and Anderson (1997). The model describes the systemic and local kinetics of testosterone (T), 5alpha-dihydrotestosterone (DHT), and luteinizing hormone (LH), with metabolism of T to DHT by 5alpha-reductase in liver and prostate. Also included are feedback loops for the positive regulation of T synthesis by LH and negative regulation of LH by T and DHT. The model simulates maintenance of the prostate as a function of hormone concentrations and androgen receptor (AR)-mediated signal transduction. The regulatory processes involved in prostate size and function include cell proliferation, apoptosis, fluid production, and 5alpha-reductase activity. Each process is controlled through the occupancy of a representative gene by androgen-AR dimers. The model simulates prostate dynamics for intact, castrated, and intravenous T-injected rats. After calibration, the model accurately captures the castration-induced regression of the prostate compared with experimental data that show that the prostate regresses to approximately 17 and 5% of its intact weight at 14 and 30 days postcastration, respectively. The model also accurately predicts serum T and AR levels following castration compared with data. This model provides a framework for quantifying the kinetics and effects of environmental and pharmaceutical endocrine active compounds on the prostate.     

Decidual activin: its role in the apoptotic process and its regulation by prolactin

Successful pregnancy requires profound differentiation and reorganization of the uterine tissues including, as pregnancy progresses, extensive apoptosis of decidual tissue to accommodate the developing conceptus. We have previously shown a positive correlation between expression of activin A and apoptosis in the decidua and have also shown that expression of activin A occurs at the time when prolactin (PRL) receptors disappear from decidual cells. The goals of this study were to examine whether activin A plays a role in decidual apoptosis and whether expression of activin A in the decidua is regulated by PRL and placental lactogens. Studies were carried out using primary rat decidual cells, a decidual cell line (GG-AD), and PRL null mice. Treatment of decidual cells with activin A significantly increased DNA degradation, caspase 3 activity, and caspase 3 mRNA expression. However, this effect was observed only in the absence of endogenous activin production by these cells. Addition of follistatin to decidual cells that were producing activin A decreased both caspase 3 activity and mRNA expression. Similarly, addition of activin-blocking antibodies to cultures of GG-AD cells, which also produce activin A, caused a reduction in both DNA degradation and caspase 3 activity. PRL and placental lactogens caused an inhibition of activin A mRNA expression in primary decidual cells. Even more convincingly, decidua of PRL null mice expressed abundant activin A at a time when no expression of this hormone is detected in wild-type mice and treatment of PRL null mice with PRL caused a profound inhibition of activin A mRNA expression. In summary, our investigations into the role and regulation of decidual activin have revealed that activin A can induce cell death in the decidua and that its expression is under tight regulation by PRL and placental lactogens.     

A mathematical model and computer simulation study of insulin sensitive glucose transporter regulation

A mathematical model of insulin sensitive glucose transporter regulation is developed. Model structure is based on experimental evidence from adipocytes and myocytes. Model parameters correspond with known cellular processes. As an example, computer simulation results are compared with data from rat adipocytes. Cellular processes explicitly represented in the model include state-dependent glucose transporter synthesis and degradation rates, insulin sensitive glucose transporter translocation rates, and a glucose transporter endocytosis rate. Most of these processes are represented as first-order events. Using more complex representations of the model structure (e.g. higher order rate constants or saturable pathways) or alternative structures did not result in qualitatively better results. The model is able to accurately simulate the insulin sensitive, insulin concentration dependent, reversible translocation of glucose transporters observed in normal adipocytes. The model is also able to accurately simulate the changes in regulation of glucose transporter translocation observed with increases in cell surface area. Finally, the model can simulate pathogenic states which induce impairment of glucose transporter regulation (e.g. altered glucose transporter regulation in adipocytes from rats on high fat diets, rats with streptozotocin induced diabetes, and fasted rats). Since the structure of our model is sufficient to explain glucose transporter regulation in both normal and pathological states, it may aid in understanding the post-receptor components of insulin resistance (decreased sensitivity or responsiveness to insulin) seen in pathological states such as obesity and diabetes mellitus.     

大优角蚱卵块外型的数学模型研究及其生态学意义

【目的】探究大优角蚱Eucriotettix grandis独特的卵块形态的生态学意义。【方法】在大量野外调查大优角蚱卵块生态学特征的基础上, 通过对卵块图片的三维数据点进行截面线抽取, 获得卵块截面曲线的拟合方程, 并用线条拟合法建立相应的数学模型。依据拟合曲线的曲率图和二阶导数值图对数据拟合曲线的几何特性进行分析。【结果】大优角蚱多以完整卵块的形式产卵, 卵块为约六边形的橘子瓣状结构, 且卵块顶部有一明显的半球形凹槽, 底部则中间略隆起。利用线条拟合理论, 构造出既能够有效满足拟合优度, 又能够满足光滑度的核函数, 通过对函数取值得到模型曲线非常近似拟合于真值曲线。【结论】凹槽很可能是便于存水, 保持卵块的湿润, 利于卵的存活和孵化; 棱角有利于缓解卵块的远距离滚动和破散, 紧密结合的卵块结构利于卵的保温保湿。     

Degradation of aflatoxin B1 during anaerobic digestion and its effect on process stability

The effect of aflatoxin B1 (AFB1) on an anaerobic digestion process (AD) was studied. Batch anaerobic digestion trials were performed with both non-contaminated AFB1 corn grain (Control A) and contaminated-AFB1 corn grain at different doses (AFB1 contents of 0.54, 66.2, and 110 μg kg⁻¹ wet weight). Both cumulative biogas production and the degradation rate of AFB1 were studied. Results indicated that no adverse effects on AD were detected during the processes which could be attributed to the presence of AFB1. AFB1 degradation ranged from 69% to 87% of the total initial AFB1 content.Anaerobic digestion trials using Completely Stirred Tank Reactors (CSTR) were also carried out, comparing the biogas production of a mix of contaminated corn grain plus pig slurry (AFB1 content of 7.2 μg kg⁻¹ wet weight) with a mix of non-contaminated corn grain plus pig slurry (Control B). No adverse effect of AFB1 on biogas production was detected. The CSTR trial resulted in an average degradation of AFB1 of 42%. The further storage of the digestate for 30 days resulted in an overall degradation (CSTR plus storage) of AFB1 of 61% of the starting content.     

Hydrogen-dependent control of the continuous anaerobic digestion process

Summary Membrane inlet mass spectrometry was used to directly measure the concentrations of CH₄ and H₂ in a mesophilic (37°C) completely mixed, laboratory scale, anaerobic digester, continuously fed at a retention time of 7 days with a glucose (50 mM) mineral salts medium. When the digester was overloaded by an increase in the influent substrate concentration, equivalent to 15.5 kg (COD) m^-3 (digester) day^-1 the concentrations of H₂ and short chain fatty acids increased with a concomitant decline in the pH: following an initial stimulation methanogenesis was inhibited. Regulation of the H₂ signal from the mass spectrometer in a closed feedback loop by controlled addition of carbon source under a potential overload condition, enabled the H₂ concentration to the controlled around 1M and a high steady state rate of methanogenesis of 42 M min^-1 to be maintained; this is equivalent to 1.4 volumes of CH₄ per culture volume per day. The hydrogen-dependent control system was also used to prevent inhibition of methanogenesis when the digester was subject to volumetric overloading potentially equivalent to a retention time of 1 day.     

Biodegradability and toxicity of styrene in the anaerobic digestion process

Start-up and operation of an Upflow Anaerobic Sludge Blanket (UASB) reactor fed with an industrial effluent from a polymer synthesis plant containing 6 mg styrene l^–1 was unstable. In batch assays with 200 mg styrene l^–1, 74% of styrene was degraded at a rate of 7 ml methane g^–1 volatile suspended solids.day, without a lag phase. The toxicity limit (IC₅₀) of styrene was 1.4 mM for the acetoclastic activity, 0.45 and 1.6 mM for the methanogenic activity in the presence of 30 mM of propionate and ethanol respectively. Instability of UASB operation was attributed to other compounds such as acrylates or detergents present in the industrial effluent.     

Competitive regulation of plant allometry and a generalized model for the plant self-thinning process

Taking into account the individual growth form (allometry) in a plant population and the effects of intraspecific competition on allometry under the population self-thinning condition, and adopting Ogawa's allometric equation 1/y = 1/axb + 1/c as the expression of complex allometry, the generalized model describing the change mode of r (the self-thinning exponential in the self-thinning equation, log M = K + log N, where M is mean plant mass, K is constant, and N is population density) was constructed. Meanwhile, with reference to the changing process of population density to survival curve type B, the exponential, r, was calculated using the software MATHEMATICA 4.0. The results of the numerical simulation show that (1) the value of the self-thinning exponential, r, is mainly determined by allometric parameters; it is most sensitive to change of b of the three allometric parameters, and a and c take second place; (2) the exponential, r, changes continuously from about -3 to the asymptote -1; the slope of -3/2 is a transient value in the population self-thinning process; (3) it is not a 'law' that the slope of the self-thinning trajectory equals or approaches -3/2, and the long-running dispute in ecological research over whether or not the exponential, r, equals -3/2 is meaningless. So future studies on the plant self-thinning process should focus on investigating how plant neighbor competition affects the phenotypic plasticity of plant individuals, what the relationship between the allometry mode and the self-thinning trajectory of plant population is and, in the light of evolution, how plants have adapted to competition pressure by plastic individual growth.     

Mathematical model of nucleotide regulation on airway epithelia. Implications for airway homeostasis

In the airways, adenine nucleotides support a complex signaling network mediating host defenses. Released by the epithelium into the airway surface liquid (ASL) layer, they regulate mucus clearance through P2 (ATP) receptors, and following surface metabolism through P1 (adenosine; Ado) receptors. The complexity of ASL nucleotide regulation provides an ideal subject for biochemical network modeling. A mathematical model was developed to integrate nucleotide release, the ectoenzymes supporting the dephosphorylation of ATP into Ado, Ado deamination into inosine (Ino), and nucleoside uptake. The model also includes ecto-adenylate kinase activity and feed-forward inhibition of Ado production by ATP and ADP. The parameters were optimized by fitting the model to experimental data for the steady-state and transient concentration profiles generated by adding ATP to polarized primary cultures of human bronchial epithelial (HBE) cells. The model captures major aspects of ATP and Ado regulation, including their >4-fold increase in concentration induced by mechanical stress mimicking normal breathing. The model also confirmed the independence of steady-state nucleotide concentrations on the ASL volume, an important regulator of airway clearance. An interactive approach between simulations and assays revealed that feed-forward inhibition is mediated by selective inhibition of ecto-5'-nucleotidase. Importantly, the model identifies ecto-adenylate kinase as a key regulator of ASL ATP and proposes novel strategies for the treatment of airway diseases characterized by impaired nucleotide-mediated clearance. These new insights into the biochemical processes supporting ASL nucleotide regulation illustrate the potential of this mathematical model for fundamental and clinical research.