scholarly journals Bifurcation analysis of metabolic pathways: an illustration from yeast glycolysis

2017 ◽  
Author(s):  
Gosse Overal ◽  
Bas Teusink ◽  
Frank J. Bruggeman ◽  
Josephus Hulshof ◽  
Robert Planqué
Keyword(s):  
Steady State ◽  
Metabolic Pathways ◽  
Coarse Graining ◽  
State Equations ◽  
Analytical Treatment ◽  
Small Core ◽  
Biological Phenomena ◽  
Tightly Coupled ◽  
Biological Interpretation ◽  
Small Models

AbstractIn microorganisms such as bacteria or yeasts, metabolic rates are tightly coupled to growth rate, and therefore to fitness. Although the topology of central pathways are largely conserved across organisms, the enzyme kinetics and their parameters generally vary. This prevents us to understand and predict (changes in) metabolic dynamics. The analytical treatment of metabolic pathways is generally restricted to small models, containing maybe two to four equations. Since such small core models involve much coarse graining, their biological interpretation is often hampered. In this paper we aim to bridge the gap between analytical, more in-depth treatment of small core models and biologically more realistic and detailed models by developing new methods. We illustrate these methods for a model of glycolysis in Saccharo-myces cerevisiae yeast, arguably the best characterised metabolic pathway in the literature. The model is more involved than in previous studies, and involves both ATP/ADP and NADH/NAD householding.A detailed analysis of the steady state equations sheds new light on two recently studied biological phenomena in yeast glycolysis: whether it is to be expected that fructose-1,6-biphosphate (FBP) parameterises all steady states, and the occurrence of bistability between a regular steady state and imbalanced steady state in which glycolytic intermediates keep accumulating.This work shows that the special structure of metabolic pathways does allow for more in-depth bifurcation analyses than is currently the norm. We especially emphasise which of the techniques developed here scale to larger pathways, and which do not.

Validation of a new method for determination of free fatty acid turnover

1987 ◽  
Vol 252 (3) ◽  
pp. E431-E438 ◽  
Author(s):  
J. M. Miles ◽  
M. G. Ellman ◽  
K. L. McClean ◽  
M. D. Jensen
Keyword(s):  
Steady State ◽  
Fatty Acid ◽  
Free Fatty Acid ◽  
Clearance Rate ◽  
Experimental Period ◽  
Metabolic Clearance ◽  
Metabolic Clearance Rate ◽  
State Equations ◽  
Tracer Methods

The accuracy of tracer methods for estimating free fatty acid (FFA) rate of appearance (Ra), either under steady-state conditions or under non-steady-state conditions, has not been previously investigated. In the present study, endogenous lipolysis (traced with 14C palmitate) was suppressed in six mongrel dogs with a high-carbohydrate meal 10 h before the experiment, together with infusions of glucose, propranolol, and nicotinic acid during the experimental period. Both steady-state and non-steady-state equations were used to determine oleate Ra ([3H]oleate) before, during, and after a stepwise infusion of an oleic acid emulsion. Palmitate Ra did not change during the experiment. Steady-state equations gave the best estimates of oleate inflow approximately 93% of the known oleate infusion rate overall, while errors in tracer estimates of inflow were obtained when non-steady-state equations were used. The metabolic clearance rate of oleate was inversely related to plasma concentration (P less than 0.01). In conclusion, accurate estimates of FFA inflow were obtained when steady-state equations were used, even under conditions of abrupt and recent changes in Ra. Non-steady-state equations, in contrast, may provide erroneous estimates of inflow. The decrease in metabolic clearance rate during exogenous infusion of oleate suggests that FFA transport may follow second-order kinetics.

The basic equations for a supplemented GSMP and its applications to queues

1988 ◽  
Vol 25 (03) ◽  
pp. 565-578 ◽  
Author(s):  
Masakiyo Miyazawa ◽  
Genji Yamazaki
Keyword(s):  
Stochastic Process ◽  
Steady State ◽  
Queueing Networks ◽  
General Setting ◽  
Main Concern ◽  
Stationary Condition ◽  
State Equations ◽  
Semi Markov Process ◽  
Basic Equations ◽  
Stieltjes Transforms

A supplemented GSMP (generalized semi-Markov process) is a useful stochastic process for discussing fairly general queues including queueing networks. Although much work has been done on its insensitivity property, there are only a few papers on its general properties. This paper considers a supplemented GSMP in a general setting. Our main concern is with a system of Laplace–Stieltjes transforms of the steady state equations called the basic equations. The basic equations are derived directly under the stationary condition. It is shown that these basic equations with some other conditions characterize the stationary distribution. We mention how to get a solution to the basic equations when the solution is partially known or inferred. Their applications to queues are discussed.

KINETIC EQUATIONS FOR ENZYME REACTIONS IN THE PRESENCE OF POWERFUL INHIBITORS

1959 ◽  
Vol 37 (8) ◽  
pp. 1268-1271 ◽  
Author(s):  
Richard M. Krupka ◽  
Keith J. Laidler
Keyword(s):  
Steady State ◽  
Kinetic Equations ◽  
Competitive Inhibitor ◽  
Graphical Analysis ◽  
Rate Data ◽  
State Equations ◽  
Enzyme Reactions ◽  
Simple Addition

Steady-state equations are worked out for the case of a competitive inhibitor that is present in concentrations comparable with that of the enzyme; allowance is made for the inhibitor attached to the enzyme. Two cases are considered: in case 1 the enzyme and inhibitor form a simple addition complex, while in case 2 a molecule is split off. Methods of graphical analysis of rate data are described.

Hopf Bifurcation in the Double-Glazing Problem With Conducting Boundaries

1987 ◽  
Vol 109 (4) ◽  
pp. 894-898 ◽  
Author(s):  
K. H. Winters
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Gravity Waves ◽  
Traveling Waves ◽  
Critical Rayleigh Number ◽  
Boussinesq Approximation ◽  
Time Dependent ◽  
Oscillatory Convection ◽  
Extended System ◽  
State Equations

Oscillatory convection has been observed in recent experiments in a square, air-filled cavity with differentially heated sidewalls and conducting horizontal surfaces. We show that the onset of the oscillatory convection occurs at a Hopf bifurcation in the steady-state equations for free convection in the Boussinesq approximation. The location of the bifurcation point is found by solving an extended system of steady-state equations. The predicted critical Rayleigh number and frequency at the onset of oscillations are in excellent agreement with the values measured recently and with those of a time-dependent simulation. Four other Hopf bifurcation points are found near the critical point and their presence supports a conjectured resonance between traveling waves in the boundary layers and interior gravity waves in the stratified core.

The influence of pH and inhibitors on the kinetics of enzyme reactions involving two intermediates

1967 ◽  
Vol 45 (5) ◽  
pp. 539-546 ◽  
Author(s):  
Harvey Kaplan ◽  
Keith J. Laidler
Keyword(s):  
Steady State ◽  
Ph Dependence ◽  
Free Enzyme ◽  
State Equations ◽  
Enzyme Reactions ◽  
Substrate Complex ◽  
Rate Determining Step ◽  
Enzyme Substrate ◽  
Special Cases ◽  
Influence Of Ph

General steady-state equations are worked out for enzyme reactions which occur according to the scheme [Formula: see text]Equations showing the pH dependence of the kinetic parameters are developed in a form which distinguishes between essential and nonessential ionizing groups. The pK dependence of [Formula: see text], the second-order constant extrapolated to zero substrate constant, gives pK values for groups which ionize on the free enzyme, but reveals such a pK only if the corresponding group is also involved in the breakdown of the Michaelis complex. General steady-state equations are also developed for the case in which an inhibitor can combine with the free enzyme, the enzyme–substrate complex, and also a second intermediate (e.g. an acyl enzyme). The equations are given in a form that is convenient for analyzing the experimental results, and a number of special cases are considered. It is shown how the type of inhibition depends not only on the nature of the inhibitor but also on that of the substrate, an important factor being the rate-determining step of the reaction. Examples of the various kinds of behavior are given.

scholarly journals Walking dynamics are symmetric (enough)

2015 ◽  
Vol 12 (108) ◽  
pp. 20150209 ◽  
Author(s):  
M. Mert Ankaralı ◽  
Shahin Sefati ◽  
Manu S. Madhav ◽  
Andrew Long ◽  
Amy J. Bastian ◽  
...  
Keyword(s):  
Steady State ◽  
Dynamical Systems ◽  
Cross Validation ◽  
Sagittal Plane ◽  
Bilateral Symmetry ◽  
Human Locomotion ◽  
Human Walking ◽  
Biological Phenomena ◽  
Systems Modelling ◽  
Walking Dynamics

Many biological phenomena such as locomotion, circadian cycles and breathing are rhythmic in nature and can be modelled as rhythmic dynamical systems. Dynamical systems modelling often involves neglecting certain characteristics of a physical system as a modelling convenience. For example, human locomotion is frequently treated as symmetric about the sagittal plane. In this work, we test this assumption by examining human walking dynamics around the steady state (limit-cycle). Here, we adapt statistical cross-validation in order to examine whether there are statistically significant asymmetries and, even if so, test the consequences of assuming bilateral symmetry anyway. Indeed, we identify significant asymmetries in the dynamics of human walking, but nevertheless show that ignoring these asymmetries results in a more consistent and predictive model. In general, neglecting evident characteristics of a system can be more than a modelling convenience—it can produce a better model.

Combined cycle dynamics

2003 ◽  
Vol 217 (3) ◽  
pp. 247-258 ◽  
Author(s):  
F. M. Mansour ◽  
A. M. Abdul Aziz ◽  
S. M. Abdel-Ghany ◽  
H. M. El-shaer
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Combined Cycle ◽  
Stable Operation ◽  
Algebraic Equations ◽  
State Equations ◽  
Combined Cycle Plant ◽  
Fast Settling ◽  
Operational Data ◽  
Good Agreement

A mathematical model describing the dynamic behaviour of each major component of the combined cycle is presented. The formulae are deduced from continuity, momentum, energy, and state equations. Partial differential equations (PDEs) are discretized to algebraic equations by using the implicit backward-central finite difference scheme and then solved by iteration. Explicit-Euler's integration method is applied to other differential equations (DEs). A multi-element control system is implemented to investigate its effect on the combined cycle's dynamic response. The simulation results are compared with the design and steady-state operational data of the unit number 4 in Cairo South Combined Cycle Power Plant, showing good agreement. The dynamic results prove the effectiveness of the multi-element control strategy to control the combined cycle plant with fast settling time, neglected steady-state error, and moderate overshoot or undershoot while assuring a stable operation under sudden changes of load.

scholarly journals Divergent Regulation of Protein Synthesis in the Cytosol and Endoplasmic Reticulum Compartments of Mammalian Cells

2008 ◽  
Vol 19 (2) ◽  
pp. 623-632 ◽  
Author(s):  
Samuel B. Stephens ◽  
Christopher V. Nicchitta
Keyword(s):  
Endoplasmic Reticulum ◽  
Protein Synthesis ◽  
Steady State ◽  
Mammalian Cells ◽  
Signal Sequence ◽  
Integral Membrane Protein ◽  
Cellular Protein ◽  
Eukaryotic Cells ◽  
Global Protein Synthesis ◽  
Tightly Coupled

In eukaryotic cells, mRNAs encoding signal sequence-bearing proteins undergo translation-dependent trafficking to the endoplasmic reticulum (ER), thereby restricting secretory and integral membrane protein synthesis to the ER compartment. However, recent studies demonstrating that mRNAs encoding cytosolic/nucleoplasmic proteins are represented on ER-bound polyribosomes suggest a global role for the ER in cellular protein synthesis. Here, we examined the steady-state protein synthesis rates and compartmental distribution of newly synthesized proteins in the cytosol and ER compartments. We report that ER protein synthesis rates exceed cytosolic protein synthesis rates by 2.5- to 4-fold; yet, completed proteins accumulate to similar levels in the two compartments. These data suggest that a significant fraction of cytosolic proteins undergo synthesis on ER-bound ribosomes. The compartmental differences in steady-state protein synthesis rates correlated with a divergent regulation of the tRNA aminoacylation/deacylation cycle. In the cytosol, two pathways were observed to compete for aminoacyl-tRNAs—protein synthesis and aminoacyl-tRNA hydrolysis—whereas on the ER tRNA deacylation is tightly coupled to protein synthesis. These findings identify a role for the ER in global protein synthesis, and they suggest models where compartmentalization of the tRNA acylation/deacylation cycle contributes to the regulation of global protein synthesis rates.

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