Elastic energy and phase structure in a continuous spin Ising chain with applications to chiral homopolymers

Chernodub, M. N.; Lundgren, Martin; Niemi, Antti J.

doi:10.1103/physreve.83.011126

Cited by 14 publications

(33 citation statements)

References 19 publications

(72 reference statements)

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“…All additional parameters in the energy function determine the regular secondary structures such as (13) and (14). The profiles of all loops are completely fixed by the unique dark solution solution to (28).…”

Section: G: Parametersmentioning

confidence: 99%

“…We propose that by learning how to compute the parameter values directly from the sequence, the geometric shape of most folded proteins can be constructed simply by solving the Master equation (28).…”

Section: G: Parametersmentioning

confidence: 99%

“…We select = 0.01. A fixed point of (40) clearly satisfies the DNLS equation (28). Following [11] we utilize step-functions to construct an initial configuration for κ i .…”

Section: C: Soliton Solution and 1lmbmentioning

confidence: 99%

“…But this time we have not extended the values of κ i outside of the range κ i ∈ [−π, π]. In Figure 10 we display the distance between the 1LMB and the soliton solution to (28), (23) for the individual C α atoms. For the most part the distance between our multi-soliton solution and 1LMB is below the Debye-Waller fluctuation distance.…”

Section: C: Soliton Solution and 1lmbmentioning

confidence: 99%

“…We select the numerical value of the temperature factor kT so that the model describes the appropriate phase. In [28] it has been shown that (36), (37) is capable of describing the three phases of polymers. At low values of kT we are in the phase of collapsed proteins.…”

Section: Iv: Collapse Studies Of 1lmbmentioning

confidence: 99%

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Solitons and collapse in theλ−repressor protein

2012

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The enterobacteria lambda phage is a paradigm temperate bacteriophage. Its lysogenic and lytic life cycles echo competition between the DNA binding λ-repressor (CI) and CRO proteins. Here we scrutinize the structure, stability and folding pathways of the λ-repressor protein, that controls the transition from the lysogenic to the lytic state. We first investigate the super-secondary helix-loophelix composition of its backbone. We use a discrete Frenet framing to resolve the backbone spectrum in terms of bond and torsion angles. Instead of four, there appears to be seven individual loops. We model the putative loops using an explicit soliton Ansatz. It is based on the standard soliton profile of the continuum nonlinear Schrödinger equation. The accuracy of the Ansatz far exceeds the B-factor fluctuation distance accuracy of the experimentally determined protein configuration. We then investigate the folding pathways and dynamics of the λ-repressor protein. We introduce a coarse-grained energy function to model the backbone in terms of the Cα atoms and the side-chains in terms of the relative orientation of the C β atoms. We describe the folding dynamics in terms of relaxation dynamics, and find that the folded configuration can be reached from a very generic initial configuration. We conclude that folding is dominated by the temporal ordering of soliton formation. In particular, the third soliton should appear before the first and second. Otherwise, the DNA binding turn does not acquire its correct structure. We confirm the stability of the folded configuration by repeated heating and cooling simulations. I: INTRODUCTIONThe transition between the lysogenic and the lytic state in bacteriophage λ infected E. coli cell is the paradigm genetic switch mechanism. It is described in numerous molecular biology textbooks and review articles [1]- [7]. The interplay between the lysogeny maintaining λ-repressor (CI) protein and the CRO regulator protein that controls the transition to the lytic state is a simple model for more complex regulatory networks, including those that can lead to cancer in humans.In the present article we describe the physical properties of the λ-repressor protein, that controls the lysogenic-to-lytic transition. We investigate in detail the stability of its native conformation, the dynamics of the folding process, and the landscape of folding pathways. We find that the folded configuration displays a structure which is unique among all known protein structures. We also conclude that the folding pathways are entirely dominated by the loop regions. In particular, the temporal ordering of loop formation appears to be the decisive factor for the protein's ability to reach its native fold. If solitons form in a wrong order the protein may misfold.Full crystallographic information of the experimental λ-repressor structure that we use in our investigation is available in Protein Data Bank (PDB) [8] under the code 1LMB. This structure is a homo-dimer with 92 residues in each of the two monomers. It maintain...

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Section: G: Parametersmentioning

confidence: 99%

Section: G: Parametersmentioning

confidence: 99%

“…We select = 0.01. A fixed point of (40) clearly satisfies the DNLS equation (28). Following [11] we utilize step-functions to construct an initial configuration for κ i .…”

Section: C: Soliton Solution and 1lmbmentioning

confidence: 99%

Section: C: Soliton Solution and 1lmbmentioning

confidence: 99%

Section: Iv: Collapse Studies Of 1lmbmentioning

confidence: 99%

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Solitons and collapse in theλ−repressor protein

2012

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Thermodynamic properties of the one-dimensional Ising model with magnetoelastic interaction

Balcerzak

Szałowski

Jaščur

2020

Journal of Magnetism and Magnetic Materials

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The Ising one-dimensional (1D) chain with spin S = 1/2 is studied with the lattice contribution included in the form of elastic interaction and thermal vibrations simultaneously taken into account.The magnetic energy term and the elastic (static) energy term based on the Morse potential are calculated exactly. The vibrational energy is calculated in the Debye approximation, in which the anharmonicity is introduced by the Grüneisen parameter. The total Gibbs potential, including both the magnetic field, as well as the external force term, is constructed and from its minimum the equation of state is derived.From the Gibbs energy all the thermodynamic properties are calculated in a self-consistent manner. The comprehensive numerical calculations are performed in a full temperature range, i.e., from zero temperature up to the vicinity of melting. In particular, a role of magneto-elastic coupling is emphasized and examined. The numerical results are illustrated in figures and discussed.

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Coexistence of Phases in a Protein Heterodimer

Krokhotin

Liwo

Niemi

et al. 2012

The Journal of Chemical Physics

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A heterodimer consisting of two or more different kinds of proteins can display an enormous number of distinct molecular architectures. The conformational entropy is an essential ingredient in the Helmholtz free energy and, consequently, these heterodimers can have a very complex phase structure. Here, it is proposed that there is a state of proteins, in which the different components of a heterodimer exist in different phases. For this purpose, the structures in the protein data bank (PDB) have been analyzed, with radius of gyration as the order parameter. Two major classes of heterodimers with their protein components coexisting in different phases have been identified. An example is the PDB structure 3DXC. This is a transcriptionally active dimer. One of the components is an isoform of the intra-cellular domain of the Alzheimer-disease related amyloid precursor protein (AICD), and the other is a nuclear multidomain adaptor protein in the Fe65 family. It is concluded from the radius of gyration that neither of the two components in this dimer is in its own collapsed phase, corresponding to a biologically active protein. The UNRES energy function has been utilized to confirm that, if the two components are separated from each other, each of them collapses. The results presented in this work show that heterodimers whose protein components coexist in different phases, can have intriguing physical properties with potentially important biological consequences.

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Elastic energy and phase structure in a continuous spin Ising chain with applications to chiral homopolymers

Cited by 14 publications

References 19 publications

Solitons and collapse in theλ−repressor protein

Solitons and collapse in theλ−repressor protein

Thermodynamic properties of the one-dimensional Ising model with magnetoelastic interaction

Coexistence of Phases in a Protein Heterodimer

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