Dominant ionic mechanisms explored in spiking and bursting using local low-dimensional reductions of a biophysically realistic model neuron

The large number of variables involved in many biophysical models can conceal potentially simple dynamical mechanisms governing the properties of its solutions and the transitions between them as parameters are varied. To address this issue, we extend a novel model reduction method, based on “scales of dominance,” to multi-compartment models. We use this method to systematically reduce the dimension of a two-compartment conductance-based model of a crustacean pyloric dilator (PD) neuron that exhibits distinct modes of oscillation—tonic spiking, intermediate bursting and strong bursting. We divide trajectories into intervals dominated by a smaller number of variables, resulting in a locally reduced hybrid model whose dimension varies between two and six in different temporal regimes. The reduced model exhibits the same modes of oscillation as the 16 dimensional model over a comparable parameter range, and requires fewer ad hoc simplifications than a more traditional reduction to a single, globally valid model. The hybrid model highlights low-dimensional organizing structure in the dynamics of the PD neuron, and the dependence of its oscillations on parameters such as the maximal conductances of calcium currents. Our technique could be used to build hybrid low-dimensional models from any large multi-compartment conductance-based model in order to analyze the interactions between different modes of activity.     

An approach to the residence time distribution for stochastic multi-compartment models

Stochastic compartmental models are widely used in modeling processes such as drug kinetics in biological systems. This paper considers the distribution of the residence times for stochastic multi-compartment models, especially systems with non-exponential lifetime distributions. The paper first derives the moment generating function of the bivariate residence time distribution for the two-compartment model with general lifetimes and approximates the density of the residence time using the saddlepoint approximation. Then, it extends the distributional approach to the residence time for multi-compartment semi-Markov models combining the cofactor rule for a single destination and the analytic approach to the two-compartment model. This approach provides a complete specification of the residence time distribution based on the moment generating function and thus facilitates an easier calculation of high-order moments than the approach using the coefficient matrix. Applications to drug kinetics demonstrate the simplicity and usefulness of this approach.     

Stochastic modelling of prey depletion processes

The modelling of prey-predator interactions is of major importance for the understanding of population dynamics. Classically, these interactions are modelled using ordinary differential equations, but this approach has the drawbacks of assuming continuous population variables and of being deterministic. We propose a general approach to stochastic modelling based on the concept of functional response for a prey depletion process with a constant number of predators. Our model could involve any kind of functional response, and permits a likelihood-based approach to statistical modelling and stable computation using matrix exponentials. To illustrate the method we use the Holling-Juliano functional response and compare the outcomes of our model with a deterministic counterpart considered by Schenk and Bacher [2002. Functional response of a generalist insect predator to one of its prey species in the field. Journal of Animal Ecology 71 (3), 524-531], who observed the depletion of Cassida rubiginosa due to its exclusive predator, Polistes dominulus. The predation was found to be Holling type III, reflecting the ability of the predator to regulate its prey. Our approach corroborates this result, but suggests that the prey depletion census should have been performed more often, and that predation features were significantly different between the two years for which data are available.     

Timing of simulated aboveground herbivory influences population dynamics of root-feeding nematodes

Aims

A soil-plant-atmosphere continuum (SPAC) model for simulating tree transpiration (Ep) with variable water stress and water distribution in the soil is presented. The model couples a sun/shade approach for the canopy with a discrete representation of the soil in different layers and compartments.

Methods

To test its performance, the outputs from the simulations are compared to those from an experiment using trees of olive ‘Picual’ and almond ‘Marinada’ with the root system split into two. Trees are subjected to different irrigation phases in which one side of the root system is dried out while the other is kept wet.

Results

The model is able to accurately predict Ep (R² and the efficiency factor (EF) around 0.9) in the two species studied. The use of a function that modulates the uptake capacity of a root according to the soil water content was necessary to track the fluxes observed from each split part. It was also appropriate to account for root clumping to match the measured and modelled leaf water potential.

Conclusions

Coupling the sun/shade approach with the soil multi-compartment solution provides a useful tool to explore tree Ep for different degrees of water availability and distribution.

     

Simulation of neurocomputing based on the photophobic reactions of Euglena with optical feedback stimulation

To explore possible forms of unconventional computers that have high capacities for adaptation and exploration, we propose a new approach to developing a biocomputer based on the photophobic reactions of microbes (Euglena gracilis), and perform the Monte-Carlo simulation of Euglena-based neural network computing, involving virtual optical feedback to the Euglena cells. The photophobic reactions of Euglena are obtained experimentally, and incorporated in the simulation, together with a feedback algorithm with a modified Hopfield–Tank model for solving a 4-city traveling salesman problem. The simulation shows high performances in terms of (1) reaching one of the best solutions of the problem, and (2) searching for a number of solutions via dynamic transition among the solutions. This dynamic transition is attributed to the fluctuation of state variables, global oscillation through feedback instability, and the one-by-one change of state variables.     

Kinetic modeling of rhamnolipid production by Pseudomonas aeruginosa PAO1 including cell density-dependent regulation

The production of rhamnolipid biosurfactants by Pseudomonas aeruginosa is under complex control of a quorum sensing-dependent regulatory network. Due to a lack of understanding of the kinetics applicable to the process and relevant interrelations of variables, current processes for rhamnolipid production are based on heuristic approaches. To systematically establish a knowledge-based process for rhamnolipid production, a deeper understanding of the time-course and coupling of process variables is required. By combining reaction kinetics, stoichiometry, and experimental data, a process model for rhamnolipid production with P. aeruginosa PAO1 on sunflower oil was developed as a system of coupled ordinary differential equations (ODEs). In addition, cell density-based quorum sensing dynamics were included in the model. The model comprises a total of 36 parameters, 14 of which are yield coefficients and 7 of which are substrate affinity and inhibition constants. Of all 36 parameters, 30 were derived from dedicated experimental results, literature, and databases and 6 of them were used as fitting parameters. The model is able to describe data on biomass growth, substrates, and products obtained from a reference batch process and other validation scenarios. The model presented describes the time-course and interrelation of biomass, relevant substrates, and products on a process level while including a kinetic representation of cell density-dependent regulatory mechanisms.     

Biological treatment of saline wastewater in a rotating biodisc contactor by using halophilic organisms

Biological treatment of saline wastewater presents unique difficulties as a result of plasmolysis of microorganisms in the presence of salt. Removal of salt from wastewater before biological treatment by reverse osmosis or ion exchange operations are rather expensive. Inclusion of halophilic organisms in activated sludge culture seems to be a more practical approach in biological treatment of saline wastewater. A synthetic wastewater composed of diluted molasses, urea, KH₂PO₄, MgSO₄ and various concentrations of salt (0–5% NaCl) was treated in a rotating biodisc contactor (RBC). A salt tolerant organism Halobacter halobium was added onto activated sludge culture (50%) and used as inoculum. Effects of important process variables such as A/Q ratio, COD loading rate, feed COD concentration, salt concentration and liquid phase aeration on system performance were investigated. An empirical mathematical model describing the system's performance as a function of important process variables was developed and constants were determined by using the experimental data.     

Development and Internal Validation of a Predictive Model for Individual Cancer Risk Assessment for Thyroid Nodules

Objective: The objective of this study was to develop and validate a predictive model for the assessment of the individual risk of malignancy of thyroid nodules based on clinical, ultrasound, and analytic variables.Methods: A retrospective case-control study was carried out with 542 patients whose thyroid nodules were analyzed at our endocrinology department between 2013 and 2018 while undergoing treatment for thyroidectomy. Starting with a multivariate logistic regression analysis, which included clinical, analytic, and ultrasound variables, a predictive model for thyroid cancer (TC) risk was devised. This was then subjected to a cross-validation process, using resampling techniques.Results: In the final model, the independent predictors of the risk of malignancy were: being male, age of the extremes, family history of TC, thyroid-stimulating hormone level >4.7 μU/L, presence of autoimmune thyroiditis, solid consistency, hypoechogenicity, irregular or microlobed borders, nodules that are taller than they are wide, microcalcifications, and suspicious adenopathy. With a cut-off point of 50% probability of thyroid cancer, the predictive model had an area under the receiver operating characteristic curve of 0.925 (95% confidence interval 0.898 to 0.952). Finally, using the 10-fold cross-validation method, the accuracy of the model was found to be 88.46%, with a kappa correlation coefficient of 0.62.Conclusion: A predictive model for the individual risk of malignancy of thyroid nodules was developed and validated using clinical, analytic, and ultrasound variables. An online calculator was developed from this model to be used by clinicians to improve decision-making in patients with thyroid nodules.     

Examining and elucidation of human weight cycle model adopting e-cell simulation system

Cellular rhythms regulate various physiological functions in circadian oscillatory mechanisms. Weight cycling or ‘yo-yo’ dieting is an evitable process in human, because of subsequent loss and regain of body weight due to irregular diet. Human weight cycle (HWC) is the major factor for causing global epidemic diseases in human beings. Understanding the HWC process would provide potent additional knowledge to prevent obesity. However till date, there is no study dealing with examine the HWC model using virtual cell simulation based on system biological approach. Therefore, the present study was designed to develop a computational HWC model, which was simulated using E-cell system v3.0. The developed model has the cyclic feedback reactions of three significant variables (the consecutive cycles of weight loss in continuous food intake (Q) and regain of body weight (P) at highest threshold point of cognitive restraint (R)) which are obtained by mathematical modelling. The dynamic plot results supported that the PQR variables depicted sustained oscillation with reversible modification due to protein diet. By contrast, the virtual model simulation would provide extensive information on HWC, which might provide knowledge to develop HWC linked with obesity pathway. The presents study concludes that optimization of body weight is essential to prevent the obesity based diseases.     

On dependency properties of the ISIs generated by a two-compartmental neuronal model

One-dimensional leaky integrate and fire neuronal models describe interspike intervals (ISIs) of a neuron as a renewal process and disregarding the neuron geometry. Many multi-compartment models account for the geometrical features of the neuron but are too complex for their mathematical tractability. Leaky integrate and fire two-compartment models seem a good compromise between mathematical tractability and an improved realism. They indeed allow to relax the renewal hypothesis, typical of one-dimensional models, without introducing too strong mathematical difficulties. Here, we pursue the analysis of the two-compartment model studied by Lansky and Rodriguez (Phys D 132:267–286, 1999), aiming of introducing some specific mathematical results used together with simulation techniques. With the aid of these methods, we investigate dependency properties of ISIs for different values of the model parameters. We show that an increase of the input increases the strength of the dependence between successive ISIs.     

Estimating linear causality in the presence of latent variables

Learning causality from data is known as the causal discovery problem, and it is an important and relatively new field. In many applications, there often exist latent variables, if such latent variables are completely ignored, which can lead to the estimation results seriously biased. In this paper, a method of combining exploratory factor analysis and path analysis (EFA-PA) is proposed to infer the causality in the presence of latent variables. Our method expands latent variables as well as their linear causal relationships with observed variables, which enhances the accuracy of causal models. Such model can be thought of as the simplest possible causal models for continuous data. The EFA-PA is very similar to that of structural equation model, but the theoretical model established by the structural equation model needs to be modified in the process of data fitting until the ideal model is established.The model gained by EFA-PA not only avoids subjectivity but also reduces estimation complexity. It is found that the EFA-PA estimation model is superior to the other models. EFA-PA can provides a basis for the correct estimation of the causal relationship between the observed variables in the presence of latent variables. The experiment shows that EFA-PA is better than the structural equation model.     

Tumour angiogenesis: the gap between theory and experiments

A common experimental technique for viewing in vivo angiogenesis utilises tumours implanted into a test animal cornea. The cornea is avascular but the tumour promotes vascularisation from the limbus and the new blood vessels can be readily observed through the transparent cornea. Many of the early mathematical models for tumour angiogenesis used this scenario as their experimental template and as such assumed that there is a large gap, of the order of 2 mm, between the tumour and neighbouring vasculature at the onset of angiogenesis. In this work we consider whether the assumption that there is a significant gap between the tumour and neighbouring vasculature is unique to intra-cornea tumour implants, or whether this characterises avascular tumour growth more generally. To do this we utilise a simple scaling argument, derive a multi-compartment model for tumour growth, and consider in vivo images. This analysis demonstrates that the corneal implant experiments and the corresponding mathematical models cannot generally be applied to a clinical setting.     

Lutzomyia longipalpis Presence and Abundance Distribution at Different Micro-spatial Scales in an Urban Scenario

The principal objective of this study was to assess a modeling approach to Lu. longipalpis distribution in an urban scenario, discriminating micro-scale landscape variables at microhabitat and macrohabitat scales and the presence from the abundance of the vector. For this objective, we studied vectors and domestic reservoirs and evaluated different environmental variables simultaneously, so we constructed a set of 13 models to account for micro-habitats, macro-habitats and mixed-habitats. We captured a total of 853 sandflies, of which 98.35% were Lu. longipalpis. We sampled a total of 197 dogs; 177 of which were associated with households where insects were sampled. Positive rK39 dogs represented 16.75% of the total, of which 47% were asymptomatic. Distance to the border of the city and high to medium density vegetation cover ended to be the explanatory variables, all positive, for the presence of sandflies in the city. All variables in the abundance model ended to be explanatory, trees around the trap, distance to the stream and its quadratic, being the last one the only one with negative coefficient indicating that the maximum abundance was associated with medium values of distance to the stream. The spatial distribution of dogs infected with L. infantum showed a heterogeneous pattern throughout the city; however, we could not confirm an association of the distribution with the variables assessed. In relation to Lu. longipalpis distribution, the strategy to discriminate the micro-spatial scales at which the environmental variables were recorded allowed us to associate presence with macrohabitat variables and abundance with microhabitat and macrohabitat variables. Based on the variables associated with Lu. longipalpis, the model will be validated in other cities and environmental surveillance, and control interventions will be proposed and evaluated in the microscale level and integrated with socio-cultural approaches and programmatic and village (mesoscale) strategies.     

Assessment and improvement of the appropriateness of an LCI data set on a system level – application to textile manufacturing

Purpose

This paper aims at assessing the appropriateness at the system level of different Life Cycle Inventory (LCI) data sets (including default models) selected by the Life Cycle Assessment (LCA) practitioner. This means that the uncertainty measurements are applied on some specific main parameters of the LCI data set instead of measured input values. This approach aims at providing a pragmatic method to approximate and reduce the uncertainties resulting from a lack of information on a specific step.

Methods

The method proposed in this paper to assess the percentage errors on appropriateness includes three main steps. First, different systems including different versions of the same process with technological or geographical changes are assessed. Second, a hierarchical cluster analysis (HCA) or a principal component analysis (PCA) is performed to identify the main variables influencing the results. Third, a multivariate analysis of variances (MANOVA) assesses the significance of the main variables on the results. An appropriate default model can be developed by setting the variables introducing high variations in results.

Results and discussion

When comparing the same spinning process located in different countries, the HCA enabled us to identify the electricity mix as the main variable influencing the results. The “world average default models” has proven inappropriate to represent country specific locations. When comparing spinning technologies, the PCAs identified the electricity and the cotton input required as the main variables influencing the results and explained the variations in results due to technological changes. The HCA performed on different yarn manufacturing procedures identified the location and the yarn thickness as the two main variables influencing the results. The MANOVA assessed the percentage marginal variance (PMV) explained by the variable location between 85 and 92 % for four impact categories. The MANOVA performed on different fabric manufacturing systems assessed the PMV explained by the variables harvest, spinning, and weaving locations above 68 % for all impact categories. The HCA and MANOVA analyses helped design an appropriate “technological average default model.”

Conclusions

From the identification of the main influencing variables (HCA and PCA) to the quantitative appropriateness assessment (MANOVA) and the development of appropriate default models, the method has proven effective in assisting the LCA practitioner in the modeling of textile manufacturing systems, and for other worldwide multi-step manufacturing systems.     

A Two-Stage System for the Large-Scale Cultivation of Biomass: a Design and Operation Analysis Based on a Simple Steady-State Model Tuned on Laboratory Measurements

The optimal design and operation at large scale of a continuous fermentation process including a biological reactor/photobioreactor and a gravity settler with partial recycle and purge of the biomass are addressed. The proposed method is developed with reference to microalgae (Scenedesmus obliquus) cultivation, but it can be applied to any fermentation process as well as to activated sludge wastewater treatment. A procedure is developed to predict the effect of process variables, mainly the recycle ratio (R), the solid retention time (θ _c ), the reactor residence time (θ), and the ratio between feed and purge flow rates (F _I /F _W ). It includes a simple steady-state model of the two units coupled in the process and the experimental measurement of basic kinetic data, in both the bioreactor and the settler, for the tuning of model parameters. The bioreactor is assumed as perfectly mixed, and a rigorous gravity-flux approach is used for the settler. The process model is solved in terms of dimensionless variables, and plots are given to allow sensitivity analyses and optimization of operating conditions. A discussion about washout is presented, and a simple method is outlined for the calculation of the minimum values of residence time (θ _min ) and recycle ratio (R _min ) and of the maximum allowed recycle ratio (R _{max,operating} ) and biomass purge rate (F _Wmax ). In particular, it is shown that the system is sensitive to the concentration of biomass lost from the top of the settler (C _X ^S ). The proposed method can be useful for the design and analysis of large-scale processes of this type.     

Random Forest model and TRIX used in combination to assess and diagnose the trophic status of Bizerte Lagoon,southern Mediterranean

A combined multimetric trophic index (TRIX) and the Random Forest (RF) model were used to characterize the trophic status of Bizerte Lagoon. The RF model was used to build a predictive model of chlorophyll a using physicochemical variables (nitrite, nitrate, ammonium, phosphate, oxygen, temperature and salinity) as predictors. The approach is based on physicochemical and biological parameters measured in samples collected twice weekly from January to December 2012 at one representative sampling station located at the lagoon center.The observed TRIX values vary from 5.18 to 6.12, reflecting waters ranging from moderate to poor quality with a high trophic level. The results of the RF model show that the most important predictor of chlorophyll a variation appears to be dissolved oxygen, followed by nitrate and temperature, suggesting a reduced model for this variable. The link between chlorophyll a and observed variables was also studied using numerical models, analyzing the linear statistical correlations and a recently proposed non linear model, the Random Forest. Both methods highlight a high correlation between chlorophyll a and dissolved oxygen as opposed to chlorophyll a and nitrate.     

A model of thymocyte proliferation.

A steady-state model, based upon an analytical approach to the interpretation pf thymic radioautographic data is presented. In the model the process of cellular proliferation is represented by a feedback amplifier. It is shown by computer simulation that a model based on this conception, in which cellular flow through G₁ compartments is treated as a stochastic process and that through the S, G2 and M compartments by a sequential unidirectional process, is in reasonable agreement with the experimental data.     

Modelling habitat use of Tetrao urogallus L. in Austria for conservation issues

Loss and deterioration of habitats are major threats for Tetrao urogallus in central Europe, where forests are highly fragmented and forest practices have distinctly changed during the last decades. Habitat models are important tools for conservation planning, often relying on presence–absence data. We mapped indirect signs of Tetrao urogallus presence as well as habitat variables over a series of seven study areas in the Austrian Alps, situated on limestone and on silicate rock. We modelled habitat use of Tetrao urogallus with one parametric approach (binary logistic regression) and two machine learning classification algorithms (classification trees and random forests) for both geological substrata separately. All three modelling approaches performed equally well in terms of accuracy or predictive power, but differed in model calibration. Three variables significantly contributed to all three habitat models on limestone and on silicate substrate, respectively, i.e. the cover of field-layer, the cover of dwarf shrubs and the proportion of deciduous trees in forest stands on limestone and the cover of field-layer, the canopy cover and the occurrence of Abies alba and/or Pinus sylvestris in forest stands on silicate rock. Some variables like the cover of Rubus sp. appeared in several models, which are not frequently mentioned in other studies. There have been some explanatory variables, which would have been missed, when applying just one single modelling approach, for example the occurrence of forest edges, the availability of canopy gaps and the supply of ant hills. Our results suggest differing habitat management strategies on limestone and on silicate rock. Considering the large spatial requirements of Tetrao urogallus the necessity of active habitat management for Tetrao urogallus becomes obvious.     

Review and Model-Based Analysis of Factors Influencing Soil Carbon Sequestration Beneath Switchgrass (Panicum virgatum)

A multi-compartment model was developed to summarize existing data and predict soil carbon sequestration beneath switchgrass (Panicum virgatum) in the southeastern USA. Soil carbon sequestration is an important part of sustainable switchgrass production for bioenergy because soil organic matter promotes water retention, nutrient supply, and soil properties that minimize erosion. A literature review was undertaken for the purpose of model parameterization. A sensitivity analysis of the model indicated that predictions of soil carbon sequestration were affected most by changes in aboveground biomass production, the ratio of belowground-to-aboveground biomass production, and mean annual temperature. Simulations indicated that the annual rate of soil carbon sequestration approached steady state after a decade of switchgrass growth while predicted mineral soil carbon stocks were still increasing. A model-based experiment was performed to predict rates of soil carbon sequestration at different levels of nitrogen fertilization and initial soil carbon stocks (to a 30-cm depth). At a mean annual temperature of 13°C, the predicted rate of soil carbon sequestration varied from ?28 to 114?g?C?m^?2?year^?1 (after 30?years) and was greater than zero in 11 of 12 simulations that varied initial surface soil carbon stocks from 1 to 5?kg?C?m^?2 and nitrogen fertilization from 0 to 18?g?N?m^?2?year^?1. The modeling indicated that more research is needed on the process of biomass allocation and on nitrogen loss from mature plantations, respectively, to improve our understanding of carbon and nitrogen dynamics in switchgrass agriculture.