What Are the New Implications of Chaos for Unpredictability?

Werndl, Charlotte

doi:10.1093/bjps/axn053

Cited by 155 publications

(71 citation statements)

References 45 publications

(47 reference statements)

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“…It is possible that such a phase transition involves a large amount of energy (a dissipative system) accompanied by fluctuations, chaos, and/or self-organization processes with the presence of emergent variables, in agreement with other authors [5,[35][36][37][38][40][41][42][43][44][45][46].…”

Section: New Predictions and Hypothesis For Tgksupporting

confidence: 87%

“…It is interesting that our model reveals that SI is highly non linear, a fact that could be associated with the presence of chaos [5,42,43], in agreement with other authors [5,42,43]. This corresponds with established non-equilibrium thermodynamics, in which systems driven out of equilibrium (as solid tumors and biological systems generally are) often exhibit fluctuations or phase transitions [35,44].…”

Section: New Predictions and Hypothesis For Tgksupporting

confidence: 85%

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Modified Gompertz Equation for Electrotherapy Murine Tumor Growth Kinetics: Predictions and New Hypotheses

Cabrales¹,

Nava²,

Aguilera³

et al. 2015

IFMBE Proceedings

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Background: Electrotherapy effectiveness at different doses has been demonstrated in preclinical and clinical studies; however, several aspects that occur in the tumor growth kinetics before and after treatment have not yet been revealed. Mathematical modeling is a useful instrument that can reveal some of these aspects. The aim of this paper is to describe the complete growth kinetics of unperturbed and perturbed tumors through use of the modified Gompertz equation in order to generate useful insight into the mechanisms that underpin this devastating disease. Methods: The complete tumor growth kinetics for control and treated groups are obtained by interpolation and extrapolation methods with different time steps, using experimental data of fibrosarcoma Sa-37. In the modified Gompertz equation, a delay time is introduced to describe the tumor's natural history before treatment. Different graphical strategies are used in order to reveal new information in the complete kinetics of this tumor type.

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Section: New Predictions and Hypothesis For Tgksupporting

confidence: 87%

Section: New Predictions and Hypothesis For Tgksupporting

confidence: 85%

Modified Gompertz Equation for Electrotherapy Murine Tumor Growth Kinetics: Predictions and New Hypotheses

Cabrales¹,

Nava²,

Aguilera³

et al. 2015

IFMBE Proceedings

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“…1B) (Werndl 2009). Multiple enzymes likely compete for common intermediates, referred to as "hub" metabolites ( Fig.…”

Section: Homeostasis and Dynamics In Specialized Metabolismmentioning

confidence: 99%

The Remarkable Pliability and Promiscuity of Specialized Metabolism

Weng

Noel

2012

Cold Spring Harbor Symposia on Quantitative Biology

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Metabolic pathways are often considered "perfected" or at least predictable as substrates efficiently rearrange into products through the intervention of an optimized enzyme. Moreover, single catalytic steps link up, forming a myriad of metabolic circuits that are often modeled with a high degree of certainty. However, on closer examination, most enzymes are not precise with respect to their activity, using not just one substrate but often a variety and producing not just one product but a diversity. Hence, the metabolic systems assembled from enzymes possessing varying degrees of what can be termed catalytic promiscuity are not clear-cut and restrictive; rather, they may at times operate stochastically in the intracellular milieu. This "messiness" complicates our understanding of normal and aberrant cellular behavior, while paradoxically sowing the seeds for future advantageous metabolic adaptations for host organisms. Catalytic promiscuity is intrinsically associated with the dynamic nature of enzyme structures and their chemical mechanisms, both key to enzyme and metabolic evolvability. In addition to primary (core) metabolism, which is essential for survival, organisms also possess highly elaborated secondary (specialized) metabolic systems. These specialized enzymes and pathways often provide unique adaptive strategies for a myriad of organisms and their populations in challenging and changing ecosystems. Generally, enzymes of specialized metabolism show attenuated kinetic activities and expanded catalytic promiscuity compared with their phylogenetic relatives rooted in primary metabolism. We propose that evolvability may be a selected trait in many specialized metabolic systems spread across populations of organisms exposed to continually fluctuating biotic and abiotic environmental pressures. As minor metabolites arising from catalytic messiness provided enhanced population fitness, specificity relaxed, and catalytic efficiency was attenuated. This updated view provides a mechanistic basis for reaching a deeper understanding of the evolutionary underpinnings of the explosion of chemodiversity in nature.Fundamentally, metabolism is a chemical property of living organisms, defined as the collection of enzymecatalyzed chemical reactions that synthesize or deconstruct metabolic chemicals necessary to sustain life and contribute to the reproductive success of host populations in the face of ever-changing environmental pressures. Similarly to other catalysts, enzymes do not alter the equilibrium of the chemical reactions but enhance the rate of the reactions by lowering their activation energies (Cook and Cleland 2007). Reactions catalyzed by enzymes are generally precise and efficient, involving specific metabolic substrates transformed into predictable metabolic products using defined catalytic mechanisms. This ordered view of one enzyme -one mechanism -one product comes from seminal discoveries made by many investigators during the last century, focused for excellent practical reasons on the phylogenetically...

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“…There are many dynamical systems, including the tent map (Example 1) and the logistic map (Example 2) and generally all chaotic systems, which are ergodic/epsilon-ergodic (cf. Aligood, Sauer and Yorke 1996;Werndl 2009b). Hence for these systems Theorem 3/Theorem 4 shows that the typicality measure is unique/unique from a pragmatic perspective.…”

Section: Uniqueness Resultsmentioning

confidence: 86%

Justifying typicality measures of Boltzmannian statistical mechanics and dynamical systems

Werndl

2013

Studies in History and Philosophy of Science Part B: Studies in

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A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measuretheoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a justification why these measures are a good choice of typicality measures is missing, and the paper attempts to fill this gap. The paper first argues that Pitowsky's (2012) justification of typicality measures does not fit the bill. Then a first proposal of how to justify typicality measures is presented. The main premises are that typicality measures are invariant and are related to the initial probability distribution of interest (which are translationcontinuous or translation-close). The conclusion are two theorems which show that the standard measures of statistical mechanics and dynamical systems are typicality measures. There may be other typicality measures, but they agree about judgements of typicality. Finally, it is proven that if systems are ergodic or epsilon-ergodic, there are uniqueness results about typicality measures.

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What Are the New Implications of Chaos for Unpredictability?

Cited by 155 publications

References 45 publications

Modified Gompertz Equation for Electrotherapy Murine Tumor Growth Kinetics: Predictions and New Hypotheses

Modified Gompertz Equation for Electrotherapy Murine Tumor Growth Kinetics: Predictions and New Hypotheses

The Remarkable Pliability and Promiscuity of Specialized Metabolism

Justifying typicality measures of Boltzmannian statistical mechanics and dynamical systems

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