Solitary waves in biology

Scott, Alwyn C.

doi:10.1007/978-3-662-08994-1_19

Cited by 7 publications

(6 citation statements)

References 40 publications

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“…Indications for this were recently supported by direct evidence [94]. A much more complex type of soliton is the action potential [91, 95], a well-studied example of a rest-to-action-to-rest (R-to-A-to-R) (gel-sol-gel) double phase transition [14, 18, 19, 36, 39, 95] in agreement with Ling’s AIH, Pollack’s GSH and the Fröhlich wave concept [80-82]. These studies show that an action potential is much more than the outdated concept of temporary permeability changes, as MT proponents believe (see Ling [12, 18, 19, 36]).…”

Section: Introductionmentioning

confidence: 89%

“…In the case of Davydov-solitons , dispersion of mechanical pulses along an α-helix (in an apolar environment) is exactly counteracted electronically by enhanced inductive effects on the longitudinal amide-2 hydrogen bonds, so that coherence is reached. Similarly, Davydov also described ‘electro-solitons’ and ‘protonic solitons’ (loss-less displacement of an electron charge respectively a protonic charge along an α-helix) [89] (see [91] for an overview). One or more of these types of solitons are believed to travel along microfilaments and microtubules, providing them with the ability to transmit and process data [92, 93].…”

Section: Introductionmentioning

confidence: 99%

“…In the early 1970s a third independent approach was taken by Davydov [87-90, also 91 for review]. He applied quantum mechanics to protein α-helices and showed theoretically that the latter might be able to conduct non-dispersed one-dimensional elastic lattice pulses along their length, which became known as ‘Davydov-solitons’ .…”

Section: Introductionmentioning

confidence: 99%

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Coherent Behavior and the Bound State of Water and K+ Imply Another Model of Bioenergetics: Negative Entropy Instead of High-energy Bonds

Jaeken

Матвеев²

2012

TOBIOCJ

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Observations of coherent cellular behavior cannot be integrated into widely accepted membrane (pump) theory (MT) and its steady state energetics because of the thermal noise of assumed ordinary cell water and freely soluble cytoplasmic K+. However, Ling disproved MT and proposed an alternative based on coherence, showing that rest (R) and action (A) are two different phases of protoplasm with different energy levels. The R-state is a coherent metastable low-entropy state as water and K+ are bound to unfolded proteins. The A-state is the higher-entropy state because water and K+ are free. The R-to-A phase transition is regarded as a mechanism to release energy for biological work, replacing the classical concept of high-energy bonds. Subsequent inactivation during the endergonic A-to-R phase transition needs an input of metabolic energy to restore the low entropy R-state. Matveev’s native aggregation hypothesis allows to integrate the energetic details of globular proteins into this view.

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Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

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Coherent Behavior and the Bound State of Water and K+ Imply Another Model of Bioenergetics: Negative Entropy Instead of High-energy Bonds

Jaeken

Матвеев²

2012

TOBIOCJ

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“…Excellent reviews exist on nonlinear waves in biological systems [34,35]; I would also like to mention, as a source of a wealth of inspiring material on the relations between nonlinear structures and biology (or more specifically biological molecules) the volume collecting the proceedings of the Les Houches 1994 School [28].…”

Section: Introductionmentioning

confidence: 99%

Untitled

Gaeta¹

1999

Journal of Biological Physics

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It has been suggested by several authors that nonlinear excitations, in particular solitary waves, could play a fundamental functional role in the process of DNA transcription, effecting the opening of the double chain needed for RNA Polymerase to be able to copy the genetic code. Some models have been proposed to model the relevant DNA dynamics in terms of a reduced number of effective degrees of freedom. Here I discuss advantages and disadvantages of such an approach, and discuss in more detail one of the models, i.e. the one proposed by Yakushevich.

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“…Far from being a intellectual curiosity, the production of solitary waves in optical fibres has profound consequences for next-generation optical communications [186] . In addition, the study of solitary waves has found applications in such diverse fields as biology, electronics, polymer physics, oceanography and medicine to name but a few [187][188][189][190] .…”

Section: Truncated Wigner Approximationmentioning

confidence: 99%

Non-equilibrium dynamics of Bose Einstein condensates

Mills¹

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This thesis examines two aspects of the non-equilibrium dynamics of Bose-Einstein condensates (BECs). Our particular interests are the relaxation of near-integrable systems, and the inter-particle correlations present in BECs, both in equilibrium and following an abrupt change in the Hamiltonian.In the first part of this thesis we investigate the stability of solitary wave solutions to a system of two coupled one-dimensional non-linear Schrödinger equations (CNLSE). This system has an integrable point known as the Manakov [1] model which has analytic dark-bright soliton solutions [2] . We break the integrability of this model by varying the inter-species interaction strength, and employ variational and numerical methods in order to find dark-bright solitary wave solutions, away from the integrable point.The time evolution of these states is calculated via numerical integration of the CNLSE, which allows us to assess the stability of these solutions in isolation and to quantify their robustness against collisions with a dark soliton. We find that there is a broad region of the parameter space in which solutions for black-bright (stationary) solitary waves can be found. In this domain, the integrability breaking is revealed only during collisions. Prior to a collision, the numerical solutions are indistinguishable from true solitons, however, the collisional stability of these solitary waves is significantly affected by the extent to which integrability is broken. We find that there is a smooth transition between the non-dispersive particle-like nature of soliton interactions for integrable systems, and the destructive collisions which take place when the system is perturbed far from the integrable point.In the case of moving (grey-bright) solitary waves, we find a more restricted region of the parameter space which admits solitary wave solutions. In this domain we are able to find approximately stable solitary wave solutions using a variational ansatz. The collisional stability of these grey-bright solitary waves is also found to depend upon the extent to which integrability is broken.We conclude that the observation of stable, long-lived dark-bright solitary waves is not sufficient to indicate near-integrability of the two-component system. However, near-integrability may inferred if dark-bright solitary waves are observed to survive multiple collisions. These results are not only of theoretical interest, but may also inform future experiments which explore the behaviour of solitary waves in two-component Bose-Einstein condensates.Following this we investigate the properties of magnetic solitary wave solutions to the CNLSE. We find that the analytic 'magnetic soliton' solutions derived in reference [3] are dynamically unstable and relax to non-stationary magnetic solitary wave states over a short timescale. We investigate the collisional dynamics of these magnetic solitary waves and find that these excitations are remarkably robust.In the second part of this thesis we calculate the fluctuations in the nu...

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Solitary waves in biology

Cited by 7 publications

References 40 publications

Coherent Behavior and the Bound State of Water and K+ Imply Another Model of Bioenergetics: Negative Entropy Instead of High-energy Bonds

Coherent Behavior and the Bound State of Water and K+ Imply Another Model of Bioenergetics: Negative Entropy Instead of High-energy Bonds

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Non-equilibrium dynamics of Bose Einstein condensates

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