12 research outputs found
What Makes Telomeres Unique?
Telomeres
are repetitive nucleotide sequences, which are essential
for protecting the termini of chromosomes. Thousands of such repetitions
are necessary to maintain the stability of the whole chromosome. Several
similar repeated telomeric sequences have been found in different
species, but why has nature chosen them? What features do telomeres
have in common? In this article, we study the physical properties
of human-like (TTAGGG), plant (TTTAGG), insect (TTAGG), and Candida guilermondi (GGTGTAC) telomeres in comparison
with seven control, nontelomeric sequences. We used steered molecular
dynamics with the nucleic acid united residue (NARES) coarse-grained
force field, which we compared with the all-atom AMBER14 force field
and experimental data. Our results reveal important features in all
of the telomeric sequences, including their exceptionally high mechanical
resistance and stability to untangling and stretching, compared to
those of nontelomeric sequences. We find that the additional stability
of the telomeres comes from their ability to form triplex structures
and wrap around loose chains of linear DNA by regrabbing the chain.
We find that, with slower pulling speed, regrabbing and triplex formation
is more frequent. We also found that some of the sequences can form
triplexes experimentally, such as TTTTTCCCC, and can mimic telomeric
properties
What Makes Telomeres Unique?
Telomeres
are repetitive nucleotide sequences, which are essential
for protecting the termini of chromosomes. Thousands of such repetitions
are necessary to maintain the stability of the whole chromosome. Several
similar repeated telomeric sequences have been found in different
species, but why has nature chosen them? What features do telomeres
have in common? In this article, we study the physical properties
of human-like (TTAGGG), plant (TTTAGG), insect (TTAGG), and Candida guilermondi (GGTGTAC) telomeres in comparison
with seven control, nontelomeric sequences. We used steered molecular
dynamics with the nucleic acid united residue (NARES) coarse-grained
force field, which we compared with the all-atom AMBER14 force field
and experimental data. Our results reveal important features in all
of the telomeric sequences, including their exceptionally high mechanical
resistance and stability to untangling and stretching, compared to
those of nontelomeric sequences. We find that the additional stability
of the telomeres comes from their ability to form triplex structures
and wrap around loose chains of linear DNA by regrabbing the chain.
We find that, with slower pulling speed, regrabbing and triplex formation
is more frequent. We also found that some of the sequences can form
triplexes experimentally, such as TTTTTCCCC, and can mimic telomeric
properties
Extension of UNRES Force Field to Treat Polypeptide Chains with d‑Amino Acid Residues
Coarse-grained force fields for protein simulations are
usually
designed and parametrized to treat proteins composed of natural l-amino acid residues. However, d-amino acid residues
occur in bacterial, fungal (e.g., gramicidins), as well as human-designed
proteins. For this reason, we have extended the UNRES coarse-grained
force field developed in our laboratory to treat systems with d-amino acid residues. We developed the respective virtual-bond-torsional
and double-torsional potentials for rotation about the C<sup>α</sup>···C<sup>α</sup> virtual-bond axis and two consecutive
C<sup>α</sup>···C<sup>α</sup> virtual-bond
axes, respectively, as functions of virtual-bond-dihedral angles γ.
In turn, these were calculated as potentials of mean force (PMFs)
from the diabatic energy surfaces of terminally blocked model compounds
for glycine, alanine, and proline. The potential-energy surfaces were
calculated by using the <i>ab initio</i> method of molecular
quantum mechanics at the Møller–Plesset (MP2) level of
theory and the 6-31G(d,p) basis set, with the rotation angles of the
peptide groups about C<sub><i>i</i>–1</sub><sup>α</sup>···C<sub><i>i</i></sub><sup>α</sup> (λ<sup>(1)</sup>) and C<sub><i>i</i></sub><sup>α</sup>···C<sub><i>i</i>+1</sub><sup>α</sup> (λ<sup>(2)</sup>) used as variables, and the energy was minimized
with respect to the remaining degrees of freedom. The PMFs were calculated
by numerical integration for all pairs and triplets with all possible
combinations of types (glycine, alanine, and proline) and chirality
(d or l); however, symmetry relations reduce the
number of nonequivalent torsional potentials to 13 and the number
of double-torsional potentials to 63 for a given C-terminal blocking
group. Subsequently, one- (for torsional) and two-dimensional (for
double-torsional potentials) Fourier series were fitted to the PMFs
to obtain analytical expressions. It was found that the torsional
potentials of the x–Y and X–y types, where X and Y are
Ala or Pro, respectively, and a lowercase letter denotes d-chirality, have global minima for small absolute values of γ,
accounting for the double-helical structure of gramicidin A, which
is a dimer of two chains, each possessing an alternating d-Tyr–l-Tyr sequence, and similar peptides. The side-chain
and correlation potentials for d-amino acid residues were
obtained by applying the reflection about the C<sub><i>i</i>–1</sub><sup>α</sup>···C<sub><i>i</i></sub><sup>α</sup>···C<sub><i>i</i>+1</sub><sup>α</sup> plane
to the respective potentials for the l-amino acid residues
Extension of UNRES Force Field to Treat Polypeptide Chains with d‑Amino Acid Residues
Coarse-grained force fields for protein simulations are
usually
designed and parametrized to treat proteins composed of natural l-amino acid residues. However, d-amino acid residues
occur in bacterial, fungal (e.g., gramicidins), as well as human-designed
proteins. For this reason, we have extended the UNRES coarse-grained
force field developed in our laboratory to treat systems with d-amino acid residues. We developed the respective virtual-bond-torsional
and double-torsional potentials for rotation about the C<sup>α</sup>···C<sup>α</sup> virtual-bond axis and two consecutive
C<sup>α</sup>···C<sup>α</sup> virtual-bond
axes, respectively, as functions of virtual-bond-dihedral angles γ.
In turn, these were calculated as potentials of mean force (PMFs)
from the diabatic energy surfaces of terminally blocked model compounds
for glycine, alanine, and proline. The potential-energy surfaces were
calculated by using the <i>ab initio</i> method of molecular
quantum mechanics at the Møller–Plesset (MP2) level of
theory and the 6-31G(d,p) basis set, with the rotation angles of the
peptide groups about C<sub><i>i</i>–1</sub><sup>α</sup>···C<sub><i>i</i></sub><sup>α</sup> (λ<sup>(1)</sup>) and C<sub><i>i</i></sub><sup>α</sup>···C<sub><i>i</i>+1</sub><sup>α</sup> (λ<sup>(2)</sup>) used as variables, and the energy was minimized
with respect to the remaining degrees of freedom. The PMFs were calculated
by numerical integration for all pairs and triplets with all possible
combinations of types (glycine, alanine, and proline) and chirality
(d or l); however, symmetry relations reduce the
number of nonequivalent torsional potentials to 13 and the number
of double-torsional potentials to 63 for a given C-terminal blocking
group. Subsequently, one- (for torsional) and two-dimensional (for
double-torsional potentials) Fourier series were fitted to the PMFs
to obtain analytical expressions. It was found that the torsional
potentials of the x–Y and X–y types, where X and Y are
Ala or Pro, respectively, and a lowercase letter denotes d-chirality, have global minima for small absolute values of γ,
accounting for the double-helical structure of gramicidin A, which
is a dimer of two chains, each possessing an alternating d-Tyr–l-Tyr sequence, and similar peptides. The side-chain
and correlation potentials for d-amino acid residues were
obtained by applying the reflection about the C<sub><i>i</i>–1</sub><sup>α</sup>···C<sub><i>i</i></sub><sup>α</sup>···C<sub><i>i</i>+1</sub><sup>α</sup> plane
to the respective potentials for the l-amino acid residues
Extension of UNRES Force Field to Treat Polypeptide Chains with d‑Amino Acid Residues
Coarse-grained force fields for protein simulations are
usually
designed and parametrized to treat proteins composed of natural l-amino acid residues. However, d-amino acid residues
occur in bacterial, fungal (e.g., gramicidins), as well as human-designed
proteins. For this reason, we have extended the UNRES coarse-grained
force field developed in our laboratory to treat systems with d-amino acid residues. We developed the respective virtual-bond-torsional
and double-torsional potentials for rotation about the C<sup>α</sup>···C<sup>α</sup> virtual-bond axis and two consecutive
C<sup>α</sup>···C<sup>α</sup> virtual-bond
axes, respectively, as functions of virtual-bond-dihedral angles γ.
In turn, these were calculated as potentials of mean force (PMFs)
from the diabatic energy surfaces of terminally blocked model compounds
for glycine, alanine, and proline. The potential-energy surfaces were
calculated by using the <i>ab initio</i> method of molecular
quantum mechanics at the Møller–Plesset (MP2) level of
theory and the 6-31G(d,p) basis set, with the rotation angles of the
peptide groups about C<sub><i>i</i>–1</sub><sup>α</sup>···C<sub><i>i</i></sub><sup>α</sup> (λ<sup>(1)</sup>) and C<sub><i>i</i></sub><sup>α</sup>···C<sub><i>i</i>+1</sub><sup>α</sup> (λ<sup>(2)</sup>) used as variables, and the energy was minimized
with respect to the remaining degrees of freedom. The PMFs were calculated
by numerical integration for all pairs and triplets with all possible
combinations of types (glycine, alanine, and proline) and chirality
(d or l); however, symmetry relations reduce the
number of nonequivalent torsional potentials to 13 and the number
of double-torsional potentials to 63 for a given C-terminal blocking
group. Subsequently, one- (for torsional) and two-dimensional (for
double-torsional potentials) Fourier series were fitted to the PMFs
to obtain analytical expressions. It was found that the torsional
potentials of the x–Y and X–y types, where X and Y are
Ala or Pro, respectively, and a lowercase letter denotes d-chirality, have global minima for small absolute values of γ,
accounting for the double-helical structure of gramicidin A, which
is a dimer of two chains, each possessing an alternating d-Tyr–l-Tyr sequence, and similar peptides. The side-chain
and correlation potentials for d-amino acid residues were
obtained by applying the reflection about the C<sub><i>i</i>–1</sub><sup>α</sup>···C<sub><i>i</i></sub><sup>α</sup>···C<sub><i>i</i>+1</sub><sup>α</sup> plane
to the respective potentials for the l-amino acid residues
Extension of UNRES Force Field to Treat Polypeptide Chains with d‑Amino Acid Residues
Coarse-grained force fields for protein simulations are
usually
designed and parametrized to treat proteins composed of natural l-amino acid residues. However, d-amino acid residues
occur in bacterial, fungal (e.g., gramicidins), as well as human-designed
proteins. For this reason, we have extended the UNRES coarse-grained
force field developed in our laboratory to treat systems with d-amino acid residues. We developed the respective virtual-bond-torsional
and double-torsional potentials for rotation about the C<sup>α</sup>···C<sup>α</sup> virtual-bond axis and two consecutive
C<sup>α</sup>···C<sup>α</sup> virtual-bond
axes, respectively, as functions of virtual-bond-dihedral angles γ.
In turn, these were calculated as potentials of mean force (PMFs)
from the diabatic energy surfaces of terminally blocked model compounds
for glycine, alanine, and proline. The potential-energy surfaces were
calculated by using the <i>ab initio</i> method of molecular
quantum mechanics at the Møller–Plesset (MP2) level of
theory and the 6-31G(d,p) basis set, with the rotation angles of the
peptide groups about C<sub><i>i</i>–1</sub><sup>α</sup>···C<sub><i>i</i></sub><sup>α</sup> (λ<sup>(1)</sup>) and C<sub><i>i</i></sub><sup>α</sup>···C<sub><i>i</i>+1</sub><sup>α</sup> (λ<sup>(2)</sup>) used as variables, and the energy was minimized
with respect to the remaining degrees of freedom. The PMFs were calculated
by numerical integration for all pairs and triplets with all possible
combinations of types (glycine, alanine, and proline) and chirality
(d or l); however, symmetry relations reduce the
number of nonequivalent torsional potentials to 13 and the number
of double-torsional potentials to 63 for a given C-terminal blocking
group. Subsequently, one- (for torsional) and two-dimensional (for
double-torsional potentials) Fourier series were fitted to the PMFs
to obtain analytical expressions. It was found that the torsional
potentials of the x–Y and X–y types, where X and Y are
Ala or Pro, respectively, and a lowercase letter denotes d-chirality, have global minima for small absolute values of γ,
accounting for the double-helical structure of gramicidin A, which
is a dimer of two chains, each possessing an alternating d-Tyr–l-Tyr sequence, and similar peptides. The side-chain
and correlation potentials for d-amino acid residues were
obtained by applying the reflection about the C<sub><i>i</i>–1</sub><sup>α</sup>···C<sub><i>i</i></sub><sup>α</sup>···C<sub><i>i</i>+1</sub><sup>α</sup> plane
to the respective potentials for the l-amino acid residues
Extension of UNRES Force Field to Treat Polypeptide Chains with d‑Amino Acid Residues
Coarse-grained force fields for protein simulations are
usually
designed and parametrized to treat proteins composed of natural l-amino acid residues. However, d-amino acid residues
occur in bacterial, fungal (e.g., gramicidins), as well as human-designed
proteins. For this reason, we have extended the UNRES coarse-grained
force field developed in our laboratory to treat systems with d-amino acid residues. We developed the respective virtual-bond-torsional
and double-torsional potentials for rotation about the C<sup>α</sup>···C<sup>α</sup> virtual-bond axis and two consecutive
C<sup>α</sup>···C<sup>α</sup> virtual-bond
axes, respectively, as functions of virtual-bond-dihedral angles γ.
In turn, these were calculated as potentials of mean force (PMFs)
from the diabatic energy surfaces of terminally blocked model compounds
for glycine, alanine, and proline. The potential-energy surfaces were
calculated by using the <i>ab initio</i> method of molecular
quantum mechanics at the Møller–Plesset (MP2) level of
theory and the 6-31G(d,p) basis set, with the rotation angles of the
peptide groups about C<sub><i>i</i>–1</sub><sup>α</sup>···C<sub><i>i</i></sub><sup>α</sup> (λ<sup>(1)</sup>) and C<sub><i>i</i></sub><sup>α</sup>···C<sub><i>i</i>+1</sub><sup>α</sup> (λ<sup>(2)</sup>) used as variables, and the energy was minimized
with respect to the remaining degrees of freedom. The PMFs were calculated
by numerical integration for all pairs and triplets with all possible
combinations of types (glycine, alanine, and proline) and chirality
(d or l); however, symmetry relations reduce the
number of nonequivalent torsional potentials to 13 and the number
of double-torsional potentials to 63 for a given C-terminal blocking
group. Subsequently, one- (for torsional) and two-dimensional (for
double-torsional potentials) Fourier series were fitted to the PMFs
to obtain analytical expressions. It was found that the torsional
potentials of the x–Y and X–y types, where X and Y are
Ala or Pro, respectively, and a lowercase letter denotes d-chirality, have global minima for small absolute values of γ,
accounting for the double-helical structure of gramicidin A, which
is a dimer of two chains, each possessing an alternating d-Tyr–l-Tyr sequence, and similar peptides. The side-chain
and correlation potentials for d-amino acid residues were
obtained by applying the reflection about the C<sub><i>i</i>–1</sub><sup>α</sup>···C<sub><i>i</i></sub><sup>α</sup>···C<sub><i>i</i>+1</sub><sup>α</sup> plane
to the respective potentials for the l-amino acid residues
Extension of UNRES Force Field to Treat Polypeptide Chains with d‑Amino Acid Residues
Coarse-grained force fields for protein simulations are
usually
designed and parametrized to treat proteins composed of natural l-amino acid residues. However, d-amino acid residues
occur in bacterial, fungal (e.g., gramicidins), as well as human-designed
proteins. For this reason, we have extended the UNRES coarse-grained
force field developed in our laboratory to treat systems with d-amino acid residues. We developed the respective virtual-bond-torsional
and double-torsional potentials for rotation about the C<sup>α</sup>···C<sup>α</sup> virtual-bond axis and two consecutive
C<sup>α</sup>···C<sup>α</sup> virtual-bond
axes, respectively, as functions of virtual-bond-dihedral angles γ.
In turn, these were calculated as potentials of mean force (PMFs)
from the diabatic energy surfaces of terminally blocked model compounds
for glycine, alanine, and proline. The potential-energy surfaces were
calculated by using the <i>ab initio</i> method of molecular
quantum mechanics at the Møller–Plesset (MP2) level of
theory and the 6-31G(d,p) basis set, with the rotation angles of the
peptide groups about C<sub><i>i</i>–1</sub><sup>α</sup>···C<sub><i>i</i></sub><sup>α</sup> (λ<sup>(1)</sup>) and C<sub><i>i</i></sub><sup>α</sup>···C<sub><i>i</i>+1</sub><sup>α</sup> (λ<sup>(2)</sup>) used as variables, and the energy was minimized
with respect to the remaining degrees of freedom. The PMFs were calculated
by numerical integration for all pairs and triplets with all possible
combinations of types (glycine, alanine, and proline) and chirality
(d or l); however, symmetry relations reduce the
number of nonequivalent torsional potentials to 13 and the number
of double-torsional potentials to 63 for a given C-terminal blocking
group. Subsequently, one- (for torsional) and two-dimensional (for
double-torsional potentials) Fourier series were fitted to the PMFs
to obtain analytical expressions. It was found that the torsional
potentials of the x–Y and X–y types, where X and Y are
Ala or Pro, respectively, and a lowercase letter denotes d-chirality, have global minima for small absolute values of γ,
accounting for the double-helical structure of gramicidin A, which
is a dimer of two chains, each possessing an alternating d-Tyr–l-Tyr sequence, and similar peptides. The side-chain
and correlation potentials for d-amino acid residues were
obtained by applying the reflection about the C<sub><i>i</i>–1</sub><sup>α</sup>···C<sub><i>i</i></sub><sup>α</sup>···C<sub><i>i</i>+1</sub><sup>α</sup> plane
to the respective potentials for the l-amino acid residues
Physics-Based Potentials for the Coupling between Backbone- and Side-Chain-Local Conformational States in the United Residue (UNRES) Force Field for Protein Simulations
The
UNited RESidue (UNRES) model of polypeptide chains is a coarse-grained
model in which each amino-acid residue is reduced to two interaction
sites, namely, a united peptide group (p) located halfway between
the two neighboring α-carbon atoms (C<sup>α</sup>s), which
serve only as geometrical points, and a united side chain (SC) attached
to the respective C<sup>α</sup>. Owing to this simplification,
millisecond molecular dynamics simulations of large systems can be
performed. While UNRES predicts overall folds well, it reproduces
the details of local chain conformation with lower accuracy. Recently,
we implemented new knowledge-based torsional potentials (Krupa et
al. <i>J. Chem. Theory Comput.</i> <b>2013</b>, <i>9</i>, 4620–4632) that depend on the virtual-bond dihedral
angles involving side chains: C<sup>α</sup>···C<sup>α</sup>···C<sup>α</sup>···SC
(τ<sup>(1)</sup>), SC···C<sup>α</sup>···C<sup>α</sup>···C<sup>α</sup> (τ<sup>(2)</sup>), and SC···C<sup>α</sup>···C<sup>α</sup>···SC (τ<sup>(3)</sup>) in the
UNRES force field. These potentials resulted in significant improvement
of the simulated structures, especially in the loop regions. In this
work, we introduce the physics-based counterparts of these potentials,
which we derived from the all-atom energy surfaces of terminally blocked
amino-acid residues by Boltzmann integration over the angles λ<sup>(1)</sup> and λ<sup>(2)</sup> for rotation about the C<sup>α</sup>···C<sup>α</sup> virtual-bond angles
and over the side-chain angles χ. The energy surfaces were,
in turn, calculated by using the semiempirical AM1 method of molecular
quantum mechanics. Entropy contribution was evaluated with use of
the harmonic approximation from Hessian matrices. One-dimensional
Fourier series in the respective virtual-bond-dihedral angles were
fitted to the calculated potentials, and these expressions have been
implemented in the UNRES force field. Basic calibration of the UNRES
force field with the new potentials was carried out with eight training
proteins, by selecting the optimal weight of the new energy terms
and reducing the weight of the regular torsional terms. The force
field was subsequently benchmarked with a set of 22 proteins not used
in the calibration. The new potentials result in a decrease of the
root-mean-square deviation of the average conformation from the respective
experimental structure by 0.86 Å on average; however, improvement
of up to 5 Å was observed for some proteins
Physics-Based Potentials for Coarse-Grained Modeling of Protein–DNA Interactions
Physics-based
potentials have been developed for the interactions
between proteins and DNA for simulations with the UNRES + NARES-2P
force field. The mean-field interactions between a protein and a DNA
molecule can be divided into eight categories: (1) nonpolar side chain–DNA
base, (2) polar uncharged side chain–DNA base, (3) charged
side chain–DNA base, (4) peptide group–phosphate group,
(5) peptide group–DNA base, (6) nonpolar side chain–phosphate
group, (7) polar uncharged side chain–phosphate group, and
(8) charged side chain–phosphate group. Umbrella-sampling molecular
dynamics simulations in explicit TIP3P water using the AMBER force
field were carried out to determine the potentials of mean force (PMF)
for all 105 pairs of interacting components. Approximate analytical
expressions for the mean-field interaction energy of each pair of
the different kinds of interacting molecules were then fitted to the
PMFs to obtain the parameters of the analytical expressions. These
analytical expressions can reproduce satisfactorily the PMF curves
corresponding to different orientations of the interacting molecules.
The results suggest that the physics-based mean-field potentials of
amino acid–nucleotide interactions presented here can be used
in coarse-grained simulation of protein–DNA interactions