scholarly journals Short relaxation times but long transient times in both simple and complex reaction networks

2016 ◽  
Vol 13 (120) ◽  
pp. 20160388 ◽  
Author(s):  
Adrien Henry ◽  
Olivier C. Martin
Keyword(s):  
Relaxation Time ◽  
Linear Chain ◽  
Relaxation Times ◽  
Relevant Information ◽  
Reaction Rates ◽  
Mass Action ◽  
Reaction Networks ◽  
Complex Reaction ◽  
Linear Chains ◽  
Simple Systems

When relaxation towards an equilibrium or steady state is exponential at large times, one usually considers that the associated relaxation time τ , i.e. the inverse of the decay rate, is the longest characteristic time in the system. However, that need not be true, other times such as the lifetime of an infinitesimal perturbation can be much longer. In the present work, we demonstrate that this paradoxical property can arise even in quite simple systems such as a linear chain of reactions obeying mass action (MA) kinetics. By mathematical analysis of simple reaction networks, we pin-point the reason why the standard relaxation time does not provide relevant information on the potentially long transient times of typical infinitesimal perturbations. Overall, we consider four characteristic times and study their behaviour in both simple linear chains and in more complex reaction networks taken from the publicly available database ‘Biomodels’. In all these systems, whether involving MA rates, Michaelis–Menten reversible kinetics, or phenomenological laws for reaction rates, we find that the characteristic times corresponding to lifetimes of tracers and of concentration perturbations can be significantly longer than τ .

Non-Equilibrium Dynamics in Untying Knots

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4242-4246
Author(s):  
Pik-Yin Lai ◽  
Y.-J. Sheng ◽  
H.-K. Tsao
Keyword(s):  
Relaxation Time ◽  
Linear Chain ◽  
Relaxation Times ◽  
Characteristic Relaxation Time ◽  
Topological Information ◽  
Topological Constraint ◽  
Equilibrium Dynamics ◽  
Average Relaxation Time ◽  
Bond Fluctuation ◽  
Equal Spacing

Flexible closed knots with strict topological constraint of no segment crossing are studied in our simulations using the bond-fluctuation model for polymers. A well-equilibrated polymer knot is cut at a randomly chosen segment and allow to relax to it new equilibrium state, which is the indistinguishable from the free linear chain. In the course of the relaxation, the topological information of the original knot is lost and the characteristic relaxation time measures its rate. The average relaxation time is the typical time scale needed to untie the cut knot by random Brownian motion. Some knot is found to have a longer relaxation time than other knots having more crossings. Remarkably, when all the knots are arranged into homologous groups with a common parametrization in terms of their Alexander polynomials, the relaxation times increase monotonically and linearly with C for all the four groups we studied. Our observation indicates that conventional labelling of knots can further be parametrized naturally into groups in a way that has a direct physical meaning in terms of the topological interactions in a knot. The linear stepwise increase of the relaxation time with the essential crossing suggests that the topological energy spectrum has equal spacing of for knots within a group.

scholarly journals Inferring Reaction Networks using Perturbation Data

2018 ◽  
Author(s):  
Kiri Choi ◽  
Joesph Hellerstein ◽  
H. Steven Wiley ◽  
Herbert M. Sauro
Keyword(s):  
Linear Chain ◽  
Mass Action ◽  
Evolutionary Strategy ◽  
Reaction Networks ◽  
Second Phase ◽  
Mass Action Kinetics ◽  
Rate Laws ◽  
Perturbation Data ◽  
Parameter Values ◽  
The Impact

AbstractIn this paper we examine the use of perturbation data to infer the underlying mechanistic dynamic model. The approach uses an evolutionary strategy to evolve networks based on a fitness criterion that measures the difference between the experimentally determined set of perturbation data and proposed mechanistic models. At present we only deal with reaction networks that use mass-action kinetics employing uni-uni, bi-uni, uni-bi and bi-bi reactions. The key to our approach is to split the algorithm into two phases. The first phase focuses on evolving network topologies that are consistent with the perturbation data followed by a second phase that evolves the parameter values. This results in almost an exact match between the evolved network and the original network from which the perturbation data was generated from. We test the approach on four models that include linear chain, feed-forward loop, cyclic pathway and a branched pathway. Currently the algorithm is implemented using Python and libRoadRunner but could at a later date be rewritten in a compiled language to improve performance. Future studies will focus on the impact of noise in the perturbation data on convergence and variability in the evolved parameter values and topologies. In addition we will investigate the effect of nonlinear rate laws on generating unique solutions.

An Observer for Mass-action Chemical Reaction Networks

2009 ◽  
Vol 15 (5) ◽  
pp. 578-597
Author(s):  
Marcello Farina ◽  
Sergio Bittanti
Keyword(s):  
Chemical Reaction ◽  
Chemical Reaction Networks ◽  
Mass Action ◽  
Reaction Networks

scholarly journals Non-normality and non-monotonic dynamics in complex reaction networks

2020 ◽  
Vol 2 (4) ◽  
Author(s):  
Zachary G. Nicolaou ◽  
Takashi Nishikawa ◽  
Schuyler B. Nicholson ◽  
Jason R. Green ◽  
Adilson E. Motter
Keyword(s):  
Reaction Networks ◽  
Complex Reaction

scholarly journals T2 mapping of the peritumoral infiltration zone of glioblastoma and anaplastic astrocytoma

2021 ◽  
pp. 197140092198932
Author(s):  
Timo Alexander Auer ◽  
Maike Kern ◽  
Uli Fehrenbach ◽  
Yasemin Tanyldizi ◽  
Martin Misch ◽  
...  
Keyword(s):  
Relaxation Time ◽  
Isocitrate Dehydrogenase ◽  
Anaplastic Astrocytoma ◽  
T2 Mapping ◽  
Relaxation Times ◽  
Region Of Interest ◽  
World Health ◽  
High Grade ◽  
High Grade Gliomas ◽  
Health Organization

Purpose To characterise peritumoral zones in glioblastoma and anaplastic astrocytoma evaluating T2 values using T2 mapping sequences. Materials and methods In this study, 41 patients with histopathologically confirmed World Health Organization high grade gliomas and preoperative magnetic resonance imaging examinations were retrospectively identified and enrolled. High grade gliomas were differentiated: (a) by grade, glioblastoma versus anaplastic astrocytoma; and (b) by isocitrate dehydrogenase mutational state, mutated versus wildtype. T2 map relaxation times were assessed from the tumour centre to peritumoral zones by means of a region of interest and calculated pixelwise by using a fit model. Results Significant differences between T2 values evaluated from the tumour centre to the peritumoral zone were found between glioblastoma and anaplastic astrocytoma, showing a higher decrease in signal intensity (T2 value) from tumour centre to periphery for glioblastoma ( P = 0.0049 – fit-model: glioblastoma –25.02± 19.89 (–54–10); anaplastic astrocytoma –5.57±22.94 (–51–47)). Similar results were found when the cohort was subdivided by their isocitrate dehydrogenase profile, showing an increased drawdown from tumour centre to periphery for wildtype in comparison to mutated isocitrate dehydrogenase ( P = 0.0430 – fit model: isocitrate dehydrogenase wildtype –10.35±16.20 (–51) – 0; isocitrate dehydrogenase mutated 12.14±21.24 (–15–47)). A strong statistical proof for both subgroup analyses ( P = 0.9987 – glioblastoma R2 0.93±0.08; anaplastic astrocytoma R2 0.94±0.15) was found. Conclusion Peritumoral T2 mapping relaxation time tissue behaviour of glioblastoma differs from anaplastic astrocytoma. Significant differences in T2 values, using T2 mapping relaxation time, were found between glioblastoma and anaplastic astrocytoma, capturing the tumour centre to the peritumoral zone. A similar curve progression from tumour centre to peritumoral zone was found for isocitrate dehydrogenase wildtype high grade gliomas in comparison to isocitrate dehydrogenase mutated high grade gliomas. This finding is in accordance with the biologically more aggressive behaviour of isocitrate dehydrogenase wildtype in comparison to isocitrate dehydrogenase mutated high grade gliomas. These results emphasize the potential of mapping techniques to reflect the tissue composition of high grade gliomas.

scholarly journals Theoretical Effect of Temperature on Threshold in the Hodgkin-Huxley Nerve Model

1966 ◽  
Vol 49 (5) ◽  
pp. 989-1005 ◽  
Author(s):  
Richard Fitzhugh
Keyword(s):  
Relaxation Time ◽  
Relaxation Times ◽  
Giant Axon ◽  
Temperature Curve ◽  
Effect Of Temperature ◽  
Threshold Temperature ◽  
Ionic Conductances ◽  
And Shifts ◽  
The Right ◽  
Increasing Temperature

In the squid giant axon, Sjodin and Mullins (1958), using 1 msec duration pulses, found a decrease of threshold with increasing temperature, while Guttman (1962), using 100 msec pulses, found an increase. Both results are qualitatively predicted by the Hodgkin-Huxley model. The threshold vs. temperature curve varies so much with the assumptions made regarding the temperature-dependence of the membrane ionic conductances that quantitative comparison between theory and experiment is not yet possible. For very short pulses, increasing temperature has two effects. (1) At lower temperatures the decrease of relaxation time of Na activation (m) relative to the electrical (RC) relaxation time favors excitation and decreases threshold. (2) For higher temperatures, effect (1) saturates, but the decreasing relaxation times of Na inactivation (h) and K activation (n) factor accommodation and increased threshold. The result is a U-shaped threshold temperature curve. R. Guttman has obtained such U-shaped curves for 50 µsec pulses. Assuming higher ionic conductances decreases the electrical relaxation time and shifts the curve to the right along the temperature axis. Making the conductances increase with temperature flattens the curve. Using very long pulses favors effect (2) over (1) and makes threshold increase monotonically with temperature.

scholarly journals Longer T2relaxation time is a marker of hypothalamic gliosis in mice with diet-induced obesity

2013 ◽  
Vol 304 (11) ◽  
pp. E1245-E1250 ◽  
Author(s):  
Donghoon Lee ◽  
Joshua P. Thaler ◽  
Kathryn E. Berkseth ◽  
Susan J. Melhorn ◽  
Michael W. Schwartz ◽  
...  
Keyword(s):  
Relaxation Time ◽  
High Field ◽  
Relaxation Times ◽  
Quantitative Mri ◽  
Human Studies ◽  
Mri Findings ◽  
Diet Induced Obesity ◽  
Magnetic Resonance Imaging Mri ◽  
The Right ◽  
Mr Brain

A hallmark of brain injury from infection, vascular, neurodegenerative, and other disorders is the development of gliosis, which can be detected by magnetic resonance imaging (MRI). In rodent models of diet-induced obesity (DIO), high-fat diet (HFD) consumption rapidly induces inflammation and gliosis in energy-regulating regions of the mediobasal hypothalamus (MBH), and recently we reported MRI findings suggestive of MBH gliosis in obese humans. Thus, noninvasive imaging may obviate the need to assess MBH gliosis using histopathological end points, an obvious limitation to human studies. To investigate whether quantitative MRI is a valid tool with which to measure MBH gliosis, we performed analyses, including measurement of T2relaxation time from high-field MR brain imaging of mice fed HFD and chow-fed controls. Mean bilateral T2relaxation time was prolonged significantly in the MBH, but not in the thalamus or cortex, of HFD-fed mice compared with chow-fed controls. Histological analysis confirmed evidence of increased astrocytosis and microglial accumulation in the MBH of HFD-fed mice compared with controls, and T2relaxation times in the right MBH correlated positively with mean intensity of glial fibrillary acidic protein staining (a marker of astrocytes) in HFD-fed animals. Our findings indicate that T2relaxation time obtained from high-field MRI is a useful noninvasive measurement of HFD-induced gliosis in the mouse hypothalamus with potential for translation to human studies.

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