A mathematical model of the carbon metabolism in photosynthesis. Difficulties in explaining oscillations by fructose 2, 6-bisphosphate regulation

1989 ◽  
Vol 237 (1289) ◽  
pp. 389-415 ◽  
Keyword(s):  
Mathematical Model ◽  
Active Sites ◽  
Starch Synthesis ◽  
Standard Free Energy ◽  
Atp Synthesis ◽  
Rate Equations ◽  
Standard Free Energy Change ◽  
Sucrose Synthesis ◽  
Carbon Reduction ◽  
Fructose 2

A mathematical model of the pentosephosphate carbon reduction (PCR) cycle is presented. The internal structure of the model is consistent with and complements the known biochemical pathways in the PCR cycle, together with starch and sucrose synthesis. Individual enzymes are described by maximum rate ( V m ), standard free energy change (Δ G´ 0 ) and Michaelis constant ( K m ) values as parameters and rate-equations, sym­metrical for the direct and reverse reactions. Enzymic control is included in the starch synthesis pathway (activation by phosphoglycerate (PGA)), inhibition by inorganic phosphate) and in the reactions of sucrose synthesis based on fructose 2, 6-bisphosphate (F2, 6BP) as a metabolite con­trolling the cytosolic fructose bisphosphatase (FBPase) activity. The phosphate translocator carries out the exchange of triose phosphates, orthophosphate and PGA. Ionic forms of metabolites are calculated in relation to pH and assumed to be the actual reacting substances. The significant concentration of the active sites of ribulose 1, 5-bisphosphate (RuBP) carboxylase is taken into account. Light reactions are included only in the form of an ATPase the Δ G´ 0 of which is shifted towards ATP synthesis by the existing proton gradient. The behaviour of the model was studied with the aim of reproducing oscillations in photosynthesis. It is concluded that oscillations in photosynthesis cannot be caused by the fructose 2, 6-bisphosphate control of sucrose synthesis alone, but that an additional control of photosynthetic rate must also be involved.

Control of phosphate turnover as a rate-limiting factor and possible cause of oscillations in photosynthesis: a mathematical model

1986 ◽  
Vol 227 (1248) ◽  
pp. 281-302 ◽  
Keyword(s):  
Mathematical Model ◽  
Time Lag ◽  
Photon Flux ◽  
Limiting Factor ◽  
Sucrose Synthesis ◽  
Carbon Reduction ◽  
Reduction Cycle ◽  
Primary Reactions ◽  
Rate Of Photosynthesis ◽  
Carbon Reduction Cycle

A mathematical model of photosynthetic processes, comprising the primary reactions, the carbon reduction cycle, the phosphate translocator and sucrose synthesis, has been constructed and solved by computer. The aim was to simulate oscillations in photosynthesis generated by changes in CO 2 concentration and light intensity. The activation of sucrose synthesis by organic phosphates and its inactivation by orthophosphate was taken into account. Slowly dampening oscillations could be generated only if modulation of sucrose synthesis was assumed to proceed with a time-lag of about 15–20 s. It is concluded that the rate of phosphate turnover, as determined by the activity of sucrose synthesis, may be a limiting factor in determining the maximum rate of photosynthesis in saturating CO 2 concentrations and photon flux densities. The model demonstrates an absolute need for a lag in the feedback loop controlling the rate of photosynthesis if oscillations are to be generated. It also accommodates the possibility that the rate of photosynthesis may be controlled by accumulating sucrose, through modulation of the activity of the sucrose synthesizing system.

The Equilibrium and the Determination of D00 (H—CN)

1975 ◽  
Vol 53 (16) ◽  
pp. 2365-2370 ◽  
Author(s):  
Don Betowski ◽  
Gervase Mackay ◽  
John Payzant ◽  
Diethard Bohme
Keyword(s):  
Free Energy ◽  
Standard Enthalpy ◽  
Transfer Reaction ◽  
Standard Free Energy ◽  
Proton Transfer Reaction ◽  
Enthalpy Change ◽  
Standard Free Energy Change ◽  
Flowing Afterglow ◽  
Standard Enthalpy Change

The rate constants and equilibrium constant for the proton transfer reaction [Formula: see text] have been measured at 296 ± 2 K using the flowing afterglow technique: kforward = (2.9 ± 0.6) × 10−9 cm3molecule−1s−1, kreverse = (1.8 ± 0.4) × 10−10 cm3 molecule1 s−1, and K = 16 ± 2. The measured value of K corresponds to a standard free energy change, ΔG296°, of −1.6 ± 0.1 kcal mol−1 which provides values for the standard enthalpy change, ΔH298°= −1.0 ± 0.2 kcal mol−1, the bond dissociation energy, D00(H—CN) = 124 ± 2 kcal mol−1, and the proton affinity, p.a.(CN−) = 350 ± 1 kcal mol−1.

Kinetic modelling of microalgal growth and fucoxanthin synthesis in photobioreactor

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Xiaojuan Zhang ◽  
Junru Zhao ◽  
Jie Zhang ◽  
Shijing Su ◽  
Luqiang Huang ◽  
...  
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Kinetic Parameters ◽  
Kinetic Modelling ◽  
Inhibitory Effect ◽  
Rate Equations ◽  
Phosphorus Concentration ◽  
Model Output ◽  
Nitrogen And Phosphorus ◽  
Nitrogen Phosphorus

Abstract This paper presented a mathematical model to describe the production of fucoxanthin by alga Thalassiosira weissflogi ND-8 in photobioreactor. Our interest was focused on characterizing the effects of nitrogen and phosphorus on the growth of microalgae and on the synthesis of fucoxanthin. The rate equations of microalgal growth, fucoxanthin synthesis and substrate consumptions were formulated. Kinetic parameters of the model and their sensitivities with respect to model output were estimated. The predicted results were compared with experimental data, which showed that this model closely agrees with actual experiment and is able to reflect the growth and metabolism characteristics of microalgae. Our results also indicated that nitrogen plays a major role in the synthesis of fucoxanthin, and the synthesis of fucoxanthin is partially linearly related to the consumption of nitrogen. Phosphorus is primarily consumed in the growth and metabolism of microalgal cells, while excessive phosphorus concentration has an inhibitory effect on the growth of microalgae.

scholarly journals Mathematical Modeling and Analysis of Multirobot Cooperative Hunting Behaviors

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Yong Song ◽  
Yibin Li ◽  
Caihong Li ◽  
Xin Ma
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Numerical Solutions ◽  
Rate Equations ◽  
Ratio Analysis ◽  
Hunting Behavior ◽  
Modeling And Analysis ◽  
Cooperative Hunting ◽  
Model Equations ◽  
The Mathematical Model

This paper presents a mathematical model of multirobot cooperative hunting behavior. Multiple robots try to search for and surround a prey. When a robot detects a prey it forms a following team. When another “searching” robot detects the same prey, the robots form a new following team. Until four robots have detected the same prey, the prey disappears from the simulation and the robots return to searching for other prey. If a following team fails to be joined by another robot within a certain time limit the team is disbanded and the robots return to searching state. The mathematical model is formulated by a set of rate equations. The evolution of robot collective hunting behaviors represents the transition between different states of robots. The complex collective hunting behavior emerges through local interaction. The paper presents numerical solutions to normalized versions of the model equations and provides both a steady state and a collaboration ratio analysis. The value of the delay time is shown through mathematical modeling to be a strong factor in the performance of the system as well as the relative numbers of the searching robots and the prey.

scholarly journals The reversibility of adenosine triphosphate cleavage by myosin

1973 ◽  
Vol 133 (2) ◽  
pp. 323-328 ◽  
Author(s):  
C. R. Bagshaw ◽  
D. R. Trentham
Keyword(s):  
Muscle Contraction ◽  
Active Site ◽  
Energy Exchange ◽  
Atp Hydrolysis ◽  
Mechanical Energy ◽  
Standard Free Energy ◽  
Standard Free Energy Change ◽  
Heavy Meromyosin ◽  
Cleavage Step ◽  
Hydrolysis Of

For the simplest kinetic model the reverse rate constants (k−1 and k−2) associated with ATP binding and cleavage on purified heavy meromyosin and heavy meromyosin subfragment 1 from rabbit skeletal muscle in the presence of 5mm-MgCl2, 50mm-KCl and 20mm-Tris–HCl buffer at pH8.0 and 22°C are: k−1<0.02s−1 and k−1=16s−1. Apparently, higher values of k−1 and k−2 are found with less-purified protein preparations. The values of k−1 and k−2 satisfy conditions required by previous 18O-incorporation studies of H218O into the Pi moiety on ATP hydrolysis and suggest that the cleavage step does involve hydrolysis of ATP or formation of an adduct between ATP and water. The equilibrium constant for the cleavage step at the myosin active site is 9. If the cycle of events during muscle contraction is described by the model proposed by Lymn & Taylor (1971), the fact that there is only a small negative standard free-energy change for the cleavage step is advantageous for efficient chemical to mechanical energy exchange during muscle contraction.

Experimental and theoretical studies of proton removal from propene

1978 ◽  
Vol 56 (1) ◽  
pp. 131-140 ◽  
Author(s):  
Gervase I. Mackay ◽  
Min H. Lien ◽  
Alan C. Hopkinson ◽  
Diethard K. Bohme
Keyword(s):  
Proton Affinity ◽  
Electron Affinity ◽  
Rate Constants ◽  
Equilibrium Constants ◽  
Standard Free Energy ◽  
Proton Transfer Reaction ◽  
Heat Of Formation ◽  
Molecular Orbital Calculations ◽  
Standard Free Energy Change ◽  
Methyl Proton

The kinetics and energetics of proton removal from propene, which contains several sites of different acidities, were investigated both theoretically and experimentally. Rate and equilibrium constants were measured for the proton-transfer reaction [Formula: see text]at 296 ± 2 K using the flowing afterglow technique. The rate constants were determined to be kforward = (1.1 ± 0.3) × 10−9 cm3 molecule−1 s−1 and kreverse = (5.4 ± 1.9) × 10−10 cm3 molecule−1 s−1. The ratio of rate constants, kf/kr = 2.1 ± 0.7, was found to be in agreement with the equilibrium constant, K = 2.2 ± 0.8, determined from equilibrium concentrations. Abinitio molecular orbital calculations predicted the removal of a methyl proton from propene to yield the allyl anion to be energetically favoured. This prediction was supported by measurements of deuteron removal from CD3CHCH2. The measured value of K corresponds to a standard free energy change, ΔG0298, of −0.44 ± 0.14 kcal mol−1 which provided values for the standard enthalpy change ΔH0298 = +0.5 ± 0.4 kcal mol−1, the proton affinity, PA298(C3H5−) = 391 ± 1 kcal mol−1, the heat of formation, ΔH0f,298(C3H5−) = 29.0 ± 0.8 kcal mol−1, and the electron affinity EA(CH2CHCH2) = 12.4 ± 1.9 kcal mol−1. The experimentally established value for the proton affinity of the allyl anion was in reasonable accord with the value of 422.3 kcal mol−1 determined by calculation. The electron affinity of the allyl radical derived in this study is supported by previous calculations and several limiting values obtained experimentally.

Hydrogen concentrations in methane-forming cells probed by the ratios of reduced and oxidized coenzyme F420

Microbiology ◽  
2005 ◽  
Vol 151 (5) ◽  
pp. 1697-1705 ◽  
Author(s):  
Linda M. I. de Poorter ◽  
Wim J. Geerts ◽  
Jan T. Keltjens
Keyword(s):  
Gas Phase ◽  
Thermodynamic Equilibrium ◽  
Standard Free Energy ◽  
Methanosarcina Barkeri ◽  
Standard Free Energy Change ◽  
Partial Pressures ◽  
Batch Fermenter ◽  
Dissolved Hydrogen ◽  
Methanothermobacter Thermautotrophicus

Coenzyme F420 is the central low-redox-potential electron carrier in methanogenic metabolism. The coenzyme is reduced under hydrogen by the action of F420-dependent hydrogenase. The standard free-energy change at pH 7 of F420 reduction was determined to be −15 kJ mol−1, irrespective of the temperature (25–65 °C). Experiments performed with methane-forming cell suspensions of Methanothermobacter thermautotrophicus incubated under various conditions demonstrated that the ratios of reduced and oxidized F420 were in thermodynamic equilibrium with the gas-phase hydrogen partial pressures. During growth in a fed-batch fermenter, ratios changed in connection with the decrease in dissolved hydrogen. For most of the time, the changes were as expected for thermodynamic equilibrium between the oxidation state of F420 inside the cells and extracellular hydrogen. Also, methanol-metabolizing, but not acetate-converting, cells of Methanosarcina barkeri maintained the ratios of reduced and oxidized coenzyme F420 in thermodynamic equilibrium with external hydrogen. The results of the study demonstrate that F420 is a useful probe to assess in situ hydrogen concentrations in H2-metabolizing methanogens.

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