Short-range component of the molecular interaction energy

Kuprievich, V. A.; Kudritskaya, Z. G.

doi:10.1007/bf00526016

Cited by 4 publications

(5 citation statements)

References 4 publications

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“…6 and 7, the value of 8 cm −1 ≈ 1.55 ⋅ 10 −22 J that has been mostly used for longitudinal interactions along a single chain will be adopted. The elasticity constant of the hydrogen bond has been calculated theoretically to be 19.5 N/m, 27 similar to that estimated experimentally from the vibrational spectra of crystalline formamide, namely, 13 N/m, 28 which is applied in most studies. Also as in many other studies, all the sites have the same mass and the value is the average mass of the amino acids that constitute myosin, as calculated by Scott, 15 i.e., 1.9 ⋅ 10 −25 kg.…”

Section: The Davydov Modelsupporting

confidence: 63%

“…Indeed, quantum calculations give rather different values, and sometimes positive and other times negative, according to the level of theory used and according to the basis set chosen. 20,27,[29][30][31] In Secs. 6 and 7 two values will be considered, one of which is 62 pN, the value estimated from experimental data by Careri and Scott 32 and the second one of which is 35 pN, recently used in Ref.…”

Section: The Davydov Modelmentioning

confidence: 99%

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Knowns and unknowns in the Davydov model for energy transfer in proteins

Cruzeiro

2022

Low Temperature Physics

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The Davydov model for amide I propagation in hydrogen-bonded chains of proteins is revisited. The many similarities between the mixed quantum-classical dynamical equations and those that are derived from the full quantum Davydov model while applying the so-called D2 ansatz are highlighted. The transition from a minimum energy localized amide I state to a fully delocalized state is shown to operate in four phases, one of which is abrupt and the last of which is a fast but smooth change from a very broad yet localized state to a completely delocalized one. Exploration of the dynamical phase space at zero temperature includes the well-known soliton propagation as well as double and triple discrete breathers, and dispersion of initially localized states. The uncertainties related to the question of the thermal stability of the Davydov soliton are illustrated. A solution to the seemingly endless problem of the short radiative lifetime of the amide I excitations is proposed.

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Section: The Davydov Modelsupporting

confidence: 63%

Section: The Davydov Modelmentioning

confidence: 99%

Knowns and unknowns in the Davydov model for energy transfer in proteins

Cruzeiro

2022

Low Temperature Physics

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“…The primary mathematical model used here is the above Anharmonic Davydov-Scott system of ODEs (1,2), which modifies Davydov's original ODE model of α-helix protein by adopting a one-sided form for the exciton-phonon coupling (proposed by A. Scott [Sco84] based on the observations of V. Kuprievich and V. Kudritskaya [KK82]) and using a nonlinear force for the hydrogen bonds (as introduced by A. Davydov and A. Zolotariuk in [DZ84], and resembling the familiar FPU model). The helical structure of this protein has roughly three residues per twist, with hydrogen bonds connecting third-nearest neighbors into nearly straight spines: spatial proximity leads to attractive exciton coupling along spines in addition to repulsive coupling between neighbors along the molecular backbone as the two dominant exciton interactions.…”

Section: A the Anharmonic Davydov-scott Ode Systemmentioning

confidence: 99%

Energetic pulses in exciton-phonon molecular chains and conservative numerical methods for quasilinear Hamiltonian systems

LeMesurier

2013

Phys. Rev. E

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The phenomenon of coherent energetic pulse propagation in exciton-phonon molecular chains such as α-helix protein is studied using an ODE system model of Davydov-Scott type, both with numerical studies using a new unconditionally stable fourth order accurate energy-momentum conserving time discretization, and with analytical explanation of the main numerical observations.Physically natural impulsive initial data associated with the energy released by ATP hydrolysis are used, and the best current estimates of physical parameter values. In contrast to previous studies based on a proposed long wave approximation by the nonlinear Schrödinger (NLS) equation and focusing on initial data resembling the soliton solutions of that equation, the results here instead lead to approximation by the third derivative nonlinear Schrödinger equation, giving a far better fit to observed behavior. A good part of the behavior is indeed explained well by the linear part of that equation, the Airy PDE, while other significant features do not fit any PDE approximation, but are instead explained well by a linearized analysis of the ODE system. A convenient method is described for construction the highly stable, accurate conservative time discretizations used, with proof of its desirable properties for a large class of Hamiltonian systems, including a variety of molecular models.

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“…In reality, a sequence of amide units (-CONH-) forms a helical structure, which is stabilized by three quasilinear strands of hydrogen bonds [27]. The properties of such soliton states were studied analytically and numerically in [28][29][30][31][32][33][34][35]. A detailed analytical study on the dynamics of a slightly modified Davydov's model of alpha helical proteins was also conducted by Daniel and Latha [36] both at the discrete and continuum levels giving consideration to the interspine coupling and the dynamics were found to be governed by a set of integrable three-coupled discrete NLS equations for specific choices of parameters and very recently the interaction properties of the one, two and three-soliton solutions were studied by Latha and Veni [37].…”

Section: Introductionmentioning

confidence: 99%

A generalized Davydov model with interspine coupling and its integrable discretization

Veni¹,

Latha²

2012

Phys. Scr.

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We propose a generalized model for the dynamics of alpha helical proteins by including excitations of dipole and quadrupole types, nearest and next nearest-neighbour interactions and interspine coupling at higher order. We investigate the dynamics in the continuum limit by identifying the underlying completely integrable model for specific parameters and study the solitonic aspects including Lax pair, soliton solutions, etc. We analyse the energy sharing properties between the spines during the propagation of solitons through them by constructing multi-soliton solutions to the resulting completely integrable three-coupled fourth-order nonlinear Schrödinger equation. We identify the equivalent integrable higher-order discrete three-coupled equations through an appropriate generalization of the Lax pair of the original Ablowitz–Ladik lattice. By means of systematic simulations, we study the nature of energy transfer in discrete alpha helical protein lattice.

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Short-range component of the molecular interaction energy

Cited by 4 publications

References 4 publications

Knowns and unknowns in the Davydov model for energy transfer in proteins

Knowns and unknowns in the Davydov model for energy transfer in proteins

Energetic pulses in exciton-phonon molecular chains and conservative numerical methods for quasilinear Hamiltonian systems

A generalized Davydov model with interspine coupling and its integrable discretization

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