scholarly journals Differential equation based minimal model describing metabolic oscillations in Bacillus subtilis biofilms

2019 ◽  
Author(s):  
Ravindra Garde ◽  
Bashar Ibrahim ◽  
Ákos T. Kovács ◽  
Stefan Schuster
Keyword(s):  
Bacillus Subtilis ◽  
Reaction System ◽  
Theoretical Work ◽  
State Approximation ◽  
Steady State Approximation ◽  
Spatial Oscillations ◽  
Feedback Structure ◽  
Chemical Reaction System ◽  
Metabolic Oscillations ◽  
Temporal And Spatial

AbstractBiofilms offer an excellent example of ecological interaction among bacteria. Temporal and spatial oscillations in biofilms are an emerging topic. In this paper we describe the metabolic oscillations in Bacillus subtilis biofilms by applying the smallest theoretical chemical reaction system showing Hopf bifurcation proposed by Wilhelm and Heinrich in 1995. The system involves three differential equations and a single bilinear term. We perform computer simulations and a detailed analysis of the system including bifurcation analysis and quasi-steady-state approximation. We also discuss the feedback structure of the system and the correspondence of the simulations to biological observations. We also specifically select parameters that are more suitable for the biological scenario of biofilm oscillations. Our theoretical work suggests potential scenarios about the oscillatory behaviour of biofilms and also serves as an application of a previously described chemical oscillator to a biological system.

scholarly journals Differential equation-based minimal model describing metabolic oscillations in Bacillus subtilis biofilms

2020 ◽  
Vol 7 (2) ◽  
pp. 190810 ◽  
Author(s):  
Ravindra Garde ◽  
Bashar Ibrahim ◽  
Ákos T. Kovács ◽  
Stefan Schuster
Keyword(s):  
Bacillus Subtilis ◽  
Reaction System ◽  
Theoretical Work ◽  
State Approximation ◽  
Steady State Approximation ◽  
Spatial Oscillations ◽  
Feedback Structure ◽  
Chemical Reaction System ◽  
Metabolic Oscillations ◽  
Temporal And Spatial

Biofilms offer an excellent example of ecological interaction among bacteria. Temporal and spatial oscillations in biofilms are an emerging topic. In this paper, we describe the metabolic oscillations in Bacillus subtilis biofilms by applying the smallest theoretical chemical reaction system showing Hopf bifurcation proposed by Wilhelm and Heinrich in 1995. The system involves three differential equations and a single bilinear term. We specifically select parameters that are suitable for the biological scenario of biofilm oscillations. We perform computer simulations and a detailed analysis of the system including bifurcation analysis and quasi-steady-state approximation. We also discuss the feedback structure of the system and the correspondence of the simulations to biological observations. Our theoretical work suggests potential scenarios about the oscillatory behaviour of biofilms and also serves as an application of a previously described chemical oscillator to a biological system.

Synthesis and Kinetics of Highly Substituted Piperidines in the Presence of Tartaric Acid as a Catalyst

2018 ◽  
Vol 21 (4) ◽  
pp. 302-311
Author(s):  
Younes Ghalandarzehi ◽  
Mehdi Shahraki ◽  
Sayyed M. Habibi-Khorassani
Keyword(s):  
Ambient Temperature ◽  
Tartaric Acid ◽  
Aromatic Aldehydes ◽  
One Pot ◽  
Rate Determining Step ◽  
State Approximation ◽  
Solvent Free Conditions ◽  
Steady State Approximation ◽  
Absorbance Changes ◽  
The One

Aim & Scope: The synthesis of highly substituted piperidine from the one-pot reaction between aromatic aldehydes, anilines and β-ketoesters in the presence of tartaric acid as a catalyst has been investigated in both methanol and ethanol media at ambient temperature. Different conditions of temperature and solvent were employed for calculating the thermodynamic parameters and obtaining an experimental approach to the kinetics and mechanism. Experiments were carried out under different temperature and solvent conditions. Material and Methods: Products were characterized by comparison of physical data with authentic samples and spectroscopic data (IR and NMR). Rate constants are presented as an average of several kinetic runs (at least 6-10) and are reproducible within ± 3%. The overall rate of reaction is followed by monitoring the absorbance changes of the products versus time on a Varian (Model Cary Bio- 300) UV-vis spectrophotometer with a 10 mm light-path cell. Results: The best result was achieved in the presence of 0.075 g (0.1 M) of catalyst and 5 mL methanol at ambient temperature. When the reaction was carried out under solvent-free conditions, the product was obtained in a moderate yield (25%). Methanol was optimized as a desirable solvent in the synthesis of piperidine, nevertheless, ethanol in a kinetic investigation had none effect on the enhancement of the reaction rate than methanol. Based on the spectral data, the overall order of the reaction followed the second order kinetics. The results showed that the first step of the reaction mechanism is a rate determining step. Conclusion: The use of tartaric acid has many advantages such as mild reaction conditions, simple and readily available precursors and inexpensive catalyst. The proposed mechanism was confirmed by experimental results and a steady state approximation.

scholarly journals Enzyme kinetics and metabolic control. A method to test and quantify the effect of enzymic properties on metabolic variables

1990 ◽  
Vol 269 (3) ◽  
pp. 697-707 ◽  
Author(s):  
L Acerenza ◽  
H Kacser
Keyword(s):  
Enzyme Concentration ◽  
Time Dependent ◽  
Experimental Systems ◽  
State Approximation ◽  
Metabolic Systems ◽  
Steady State Approximation ◽  
Before And After ◽  
Factor Alpha ◽  
Metabolic Variables ◽  
Time Invariant

It is usual to study the sensitivity of metabolic variables to small (infinitesimal) changes in the magnitudes of individual parameters such as an enzyme concentration. Here, the effect that a simultaneous change in all the enzyme concentrations by the same factor alpha (Co-ordinate-Control Operation, CCO) has on the variables of time-dependent metabolic systems is investigated. This factor alpha can have any arbitrary large value. First, we assume, for each enzyme measured in isolation, the validity of the steady-state approximation and the proportionality between reaction rate and enzyme concentration. Under these assumptions, any time-invariant variable may behave like a metabolite concentration, i.e. S alpha = Sr (S-type), or like a flux, i.e. J alpha = alpha Jr (J-type). The subscripts r and alpha correspond to the values of the variable before and after the CCO respectively. Similarly, time-dependent variables may behave according to S alpha (t/alpha) = Sr (t) (S-type) or to J alpha (t/alpha) = alpha J r (t) (J-type). A method is given to test these relationships in experimental systems, and to quantify deviations from the predicted behaviour. A positive test for deviations proves the violation of some of the assumptions made. However, the breakdown of the assumptions in an enzyme-catalysed reaction, studied in isolation, may or may not affect significantly the behaviour of the system when the component reaction is embedded in the metabolic network.

The Quasi-Steady-State Approximation: Numerical Validation

1998 ◽  
Vol 75 (9) ◽  
pp. 1158 ◽  
Author(s):  
Richard A. B. Bond ◽  
Bice S. Martincigh ◽  
Janusz R. Mika ◽  
Reuben H. Simoyi
Keyword(s):  
Steady State ◽  
Quasi Steady State ◽  
Numerical Validation ◽  
State Approximation ◽  
Steady State Approximation

Ergodic Approximation to Chemical Reaction System with Delay

2019 ◽  
Vol 57 (1) ◽  
pp. 70-95 ◽  
Author(s):  
Chuchu Chen ◽  
Di Liu
Keyword(s):  
Chemical Reaction ◽  
Reaction System ◽  
System With Delay ◽  
Chemical Reaction System
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