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^α···C^α virtual-bond axis and two consecutive C^α···C^α 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_<i>i</i>–1^α···C_<i>i</i>^α (λ⁽¹⁾) and C_<i>i</i>^α···C_<i>i</i>+1^α (λ⁽²⁾) 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_<i>i</i>–1^α···C_<i>i</i>^α···C_<i>i</i>+1^α 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^α···C^α virtual-bond axis and two consecutive C^α···C^α 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_<i>i</i>–1^α···C_<i>i</i>^α (λ⁽¹⁾) and C_<i>i</i>^α···C_<i>i</i>+1^α (λ⁽²⁾) 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_<i>i</i>–1^α···C_<i>i</i>^α···C_<i>i</i>+1^α 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^α···C^α virtual-bond axis and two consecutive C^α···C^α 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_<i>i</i>–1^α···C_<i>i</i>^α (λ⁽¹⁾) and C_<i>i</i>^α···C_<i>i</i>+1^α (λ⁽²⁾) 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_<i>i</i>–1^α···C_<i>i</i>^α···C_<i>i</i>+1^α 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^α···C^α virtual-bond axis and two consecutive C^α···C^α 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_<i>i</i>–1^α···C_<i>i</i>^α (λ⁽¹⁾) and C_<i>i</i>^α···C_<i>i</i>+1^α (λ⁽²⁾) 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_<i>i</i>–1^α···C_<i>i</i>^α···C_<i>i</i>+1^α 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^α···C^α virtual-bond axis and two consecutive C^α···C^α 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_<i>i</i>–1^α···C_<i>i</i>^α (λ⁽¹⁾) and C_<i>i</i>^α···C_<i>i</i>+1^α (λ⁽²⁾) 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_<i>i</i>–1^α···C_<i>i</i>^α···C_<i>i</i>+1^α 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^α···C^α virtual-bond axis and two consecutive C^α···C^α 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_<i>i</i>–1^α···C_<i>i</i>^α (λ⁽¹⁾) and C_<i>i</i>^α···C_<i>i</i>+1^α (λ⁽²⁾) 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_<i>i</i>–1^α···C_<i>i</i>^α···C_<i>i</i>+1^α 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^αs), which serve only as geometrical points, and a united side chain (SC) attached to the respective C^α. 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^α···C^α···C^α···SC (τ⁽¹⁾), SC···C^α···C^α···C^α (τ⁽²⁾), and SC···C^α···C^α···SC (τ⁽³⁾) 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⁽¹⁾ and λ⁽²⁾ for rotation about the C^α···C^α 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