Nonlinear Mass Action Research Articles

Exponential trajectories, cell size fluctuations, and the adder property in bacteria follow from simple chemical dynamics and division control.

Experiments on steady-state bacterial cultures have uncovered several quantitative regularities at the system level. These include, first, the exponential growth of cell size with time and the balanced growth of intracellular chemicals between cell birth and division, which are puzzling given the nonlinear and decentralized chemical dynamics in the cell. We model a cell as a set of chemical populations undergoing nonlinear mass action kinetics in a container whose volume is a linear function of the chemical populations. This turns out to be a special class of dynamical systems that generically has attractors in which all populations grow exponentially with time at the same rate. This explains exponential balanced growth of bacterial cells without invoking any regulatory mechanisms and suggests that this could be a robust property of protocells as well. Second, we consider the hypothesis that cells commit themselves to division when a certain internal chemical population reaches a threshold of N molecules. We show that this hypothesis leads to a simple explanation of some of the variability observed across cells in a bacterial culture. In particular, it reproduces the adder property of cell size fluctuations observed recently in E. coli; the observed correlations among interdivision time, birth volume, and added volume in a generation; and the observed scale of the fluctuations (CV ≈ 10-30%) when N is between 10 and 100. Third, upon including a suitable regulatory mechanism that optimizes the growth rate of the cell, the model reproduces the observed bacterial growth laws including the dependence of the growth rate and ribosomal protein fraction on the medium. Thus, the models provide a framework for unifying diverse aspects of bacterial growth physiology under one roof. They also suggest new questions for experimental and theoretical enquiry.

Assessing inference of the basic reproduction number in an SIR model incorporating a growth‐scaling parameter

The standard mass action, which assumes that infectious disease transmission occurs in well-mixed populations, is popular for formulating compartmental epidemic models. Compartmental epidemic models often follow standard mass action for simplicity and to gain insight into transmission dynamics as it often performs well at reproducing disease dynamics in large populations. In this work, we formulate discrete time stochastic susceptible-infected-removed models with linear (standard) and nonlinear mass action structures to mimic varying mixing levels. Using simulations and real epidemic data, we demonstrate the sensitivity of the basic reproduction number to these mathematical structures of the force of infection. Our results suggest the need to consider nonlinear mass action in order to generate more accurate estimates of the basic reproduction number although its uncertainty increases due to the addition of one growth scaling parameter.

Geochemical modeling of cyanide in tailing dam gold processing plant

This research is aimed at investigating possible neutralization of cyanide in tailing dam of Muteh gold processing plant in Isfahan, Iran at various conditions such as pH and temperature using USEPA Visual MINTEQ geochemical model simulation. The model is based on geochemical equilibrium which uses the simultaneous solution of the non-linear mass action expressions and linear mass balance relationships to formulate and solve the multiple-component chemical equilibrium problems. In this study the concentration of aqueous species in tailing dam as an aqueous, solid and gaseous were used as input in the model. Temperature and pH variation were simulated. The results of the model indicated that cyanide may be complexes in 10 < pH < 5. In other pH values complexation is not important. The results also indicated that cyanide reduction mechanism in acidic pH and temperature above 30°C is due to cyanide acid formation which is vaporized.

Modelling Copper (II) Liquid–Liquid Extraction: The System Acorga M5640-Exxsol D100–CuSO4–H2SO4

A predictive model, which consists in a set of non-linear mass action and mass balance equations solved by using a taylor-made equation-solving program, is used as a basis to predict experimentally measured distribution coefficients for the Acorga M5640-Exxsol D100–CuSO4–H2SO4 liquid–liquid extraction system at 20°C and aqueous copper concentrations in the range 0.0016–0.0032 mol l−1. The model is also used to obtain the copper loading isotherm at various equilibrium aqueous pH values.

Liquid–liquid Extraction Equilibrium in the CuSO4–H2SO4–MOC 80TD–Iberfluid system

A predictive model, which consists of a set of non-linear mass action and mass balance equations solved by using a tailor-made equation-solving program, is used as a basis to predict experimentally measured distribution coefficients for the CuSO4–H2SO4–MOC 80TD-Iberfluid liquid–liquid extraction system at 20°C and aqueous copper concentrations in the range 0.1-1.0 g l−1. The model is also used to obtain the copper loading isotherm at various initial aqueous pH values.

Modeling of solvent extraction equilibrium of Cu(II) from sulphuric Acid solution with MOC-55TD

The extraction of Cu(II) from acidic sulphate aqueous solutions using the commercial MOC-55TD extractant is studied. A predictive model, which consists in a set of non-linear mass action and mass balance equations is proposed. The model was solved using a tailor-made equation-solving program. The extraction of copper can be described by the formation of CuR 2 species (log K ext = 0.717 ± 0.03) in the organic phase. The copper equilibrium isotherm was also obtained at 20°C.

Modelling copper solvent extraction from acidic sulphate solutions using MOC 45

A mathematical model to predict the extraction has been developed for the Cu-MOC 45 system. The model consists of sets of nonlinear mass action and mass balance equations where the dimerization of the oxime was also considered. The predictive model calculated the equilibrium concentrations from the total oxime concentration, total copper concentration, initial pH value and the O/A volume phase ratio. The model suggests that the extraction of copper can be defined by the existence of two species into the organic solution: CuR 2 ( k ext = 4.2) and Cu(HR 2 ) 2 ( k ext = 10.000)- The initial oxime concentration defines the predominancy in the organic solution of both species. The model can be used to predict copper extraction isotherm as well as copper stripping with sulphuric acid.

MODELING Cu EXTRACTION FROM ACIDIC SOLUTIONS USING P5100, PT5050, AND LIX 84

ABSTRACT The Bureau of Mines studied the extraction of copper (II) from acidic sulfate solutions using commercial extractants LIX 84, P5100, and PT5050. Mathematical models, consisting of sets of nonlinear mass action and mass balance equations, were solved using a commercial equation-solving program on a personal computer. The models suggest that LIX 84 is a mixture of monomelic and dimeric extractant with an extraction equilibrium constant of 145 and a dimerization constant of 65 L/mol; PT5050 appears to be a monomeric extractant with an extraction equilibrium constant of 53; and P5100 shows more complex characteristics, with a monomeric extraction equilibrium constant of 400, a dimer formation constant of 3.7 L/mol, and a modifier-complex formation constant of 5.8 L/mol. For all models, the relative error of fit was less than 6%.

Computer-aided assessment of receptor status in human breast cancer

Computer-aided analysis of simulated cytosolic estradiol-17β receptor binding data using Scatchard and nonlinear Mass Action models showed the latter to be superior. Simulation studies of binding data, incorporating the magnitude and uncertainties associated with inefficiencies of separating free from bound hormone, nonspecific and specific binding, allowed the prediction of uncertainties associated with estimates of receptor content. Realistic values for the minimum detectable receptor concentration that can be distinguished from zero with a given probability were also obtained and may be used as a cutoff value for selection of patients for hormone therapy. This improved reliability in quantification should more clearly define the prognostic value of these receptor assays with respect to adjuvant therapy for primary cancer following surgery or anti-estrogen treatment for recurrent disease, thereby improving the management of breast cancer. Computer simulations and regression analyses were performed on a PDP11 34 using programs written in FORTRAN IV.