Biomedical subjects

Mikael Peräkylä

Publications and source records attributed to Mikael Peräkylä.

At least 19 recordsLinked to original sources

PubMed2006

Vitamin D receptor agonists specifically modulate the volume of the ligand-binding pocket.

Existing crystal structure data has indicated that 1alpha,25-dihydroxyvitamin D(3) (1alpha,25(OH)(2) D(3)) and its analogues bind the ligand-binding pocket (LBP) of the human vitamin D receptor in a very similar fashion. Because docking of a ligand into the LBP is a more flexible process than crystallography can monitor, we analyzed 1alpha,25(OH)(2)D(3), its 20-epi derivative MC1288, the two side-chain analogues Gemini and Ro43-83582 (a hexafluoro-derivative) by molecular dynamics simulations in a complex with the vitamin D receptor ligand-binding domain and a co-activator peptide. Superimposition of the structures showed that the side chain of MC1288, the first side chain of the conformation II of Gemini, the second side chain of Ro43-83582 in conformation I and the first side chain of Ro43-83582 in conformation II take the same agonistic position as the side chain of 1alpha,25(OH)(2)D(3). Compared with the LBP of the natural hormone MC1288 reduced the volume by 17%, and Gemini expanded it by 19%. The shrinking of the LBP of MC1288 and its expansion to accommodate the second side chain of Gemini or Ro43-83582 is the combined result of minor movements of more than 30 residues and major movements of a few critical amino acids. The agonist-selective recognition of anchoring OH groups by the conformational flexible residues Ala-303, Leu-309, and His-397 was confirmed by in vitro assays. In summary, variations in the volume of agonists lead to adaptations in the volume of the LBP and alternative contacts of anchoring OH-groups.

Amino Acids↗

PubMed2005

Birch PR-10c interacts with several biologically important ligands.

PR-10c is a unique member of PR-10 proteins in birch, since it is the only one known to be post-translationally modified by glutathione and is not constitutively expressed in pollen. Both reduced and S-glutathiolated forms of PR-10c show low ribonuclease activity. However, the major function of the protein is apparently not yet resolved. Our protein-ligand interaction studies with saturation transfer difference (STD) NMR revealed that PR-10c interacts with several biologically important molecules, including cytokinin, flavonoid glycosides, sterols and emodin. Competition study with deoxycholate and kinetin revealed no statistically significant binding interference, indicating that these ligands have different binding sites in PR-10c. Ligand docking studies with a molecular model of PR-10c support the STD NMR results of ligand binding and binding epitopes, suggesting that there are three potential binding sites in PR-10c: two in the hydrophobic cavity and one in the glycine-rich loop. Our docking calculations suggested that only kinetin interacts with the glycine-rich loop, the binding occurring through its adenine moiety. Clear ligand specificity could be observed in the binding of nucleotide derivatives. S-glutathiolation of PR-10c did not affect kinetin binding. The present results suggest that birch PR-10c is a multifunctional protein, which has diverse roles in plant stress responses.

Betula↗

PubMed2005

Antagonist- and inverse agonist-driven interactions of the vitamin D receptor and the constitutive androstane receptor with corepressor protein.

Ligand-dependent signal transduction by nuclear receptors (NRs) includes dynamic exchanges of coactivator (CoA) and corepressor (CoR) proteins. Here we focused on the structural determinants of the antagonist- and inverse agonist-enhanced interaction of the endocrine NR vitamin D receptor (VDR) and the adopted orphan NR constitutive androstane receptor (CAR) from two species with the CoR NR corepressor. We found that the pure VDR antagonist ZK168281 and the human CAR inverse agonist clotrimazole are both effective inhibitors of the CoA interaction of their respective receptors, whereas ZK168281 resembled more the mouse CAR inverse agonist androstanol in its ability to recruit CoR proteins. Molecular dynamics simulations resulted in comparable models for the CoR receptor interaction domain peptide bound to VDR/antagonist or CAR/inverse agonist complexes. A salt bridge between the CoR and a conserved lysine in helix 4 of the NR is central to this interaction, but also helix 12 was stabilized by direct contacts with residues of the CoR. Fixation of helix 12 in the antagonistic/inverse agonistic conformation prevents an energetically unfavorable free floatation of the C terminus. The comparable molecular mechanisms that explain the similar functional profile of antagonist and inverse agonists are likely to be extended from VDR and CAR to other members of the NR superfamily and may lead to the design of even more effective ligands.

Amino Acid Sequence↗

PubMed2005

Gene regulatory potential of nonsteroidal vitamin D receptor ligands.

The seco-steroid 1alpha,25-dihydroxyvitamin D3 [1alpha,25(OH)2D3] is a promising drug candidate due to its pleiotropic function including the regulation of calcium homeostasis, bone mineralization and cellular proliferation, differentiation, and apoptosis. We report here a novel class of nonsteroidal compounds, represented by the bis-aromatic molecules CD4409, CD4420, and CD4528, as ligands of the 1alpha,25(OH)2D3 receptor (VDR). Taking the known diphenylmethane derivative LG190178 as a reference, this study provides molecular evaluation of the interaction of nonsteroidal ligands with the VDR. All four nonsteroidal compounds were shown to induce VDR-retinoid X receptor heterodimer complex formation on a 1alpha,25(OH)2D3 response element, stabilize the agonistic conformation of the VDR ligand-binding domain, enable the interaction of VDR with coactivator proteins and contact with their three hydroxyl groups the same residues within the ligand-binding pocket of the VDR as 1alpha,25(OH)2D3. Molecular dynamics simulations demonstrated that all four nonsteroidal ligands take a shape within the ligand-binding pocket of the VDR that is very similar to that of the natural ligand. CD4528 is mimicking the natural hormone best and was found to be in vitro at least five times more potent than LG190178. In living cells, CD4528 was only two times less potent than 1alpha,25(OH)2D3 and induced mRNA expression of the VDR target gene CYP24 in a comparable fashion. At a noncalcemic dose of 150 microg/kg, CD4528 showed in vivo a clear induction of CYP24 expression and therefore may be used as a lead compound for the development of therapeutics against psoriasis, osteoporosis, and cancer.

Animals↗

PubMed2004

Amino acids important for ligand specificity of the human constitutive androstane receptor.

The human constitutive androstane receptor (CAR, NR1I3) is an important ligand-activated regulator of oxidative and conjugative enzymes and transport proteins. Because of the lack of a crystal structure of the ligand-binding domain (LBD), wide species differences in ligand specificity and the scarcity of well characterized ligands, the factors that determine CAR ligand specificity are not clear. To address this issue, we developed highly defined homology models of human CAR LBD to identify residues lining the ligand-binding pocket and to perform molecular dynamics simulations with known human CAR modulators. The roles of 22 LBD residues for basal activity, ligand selectivity, and interactions with co-regulators were studied using site-directed mutagenesis, mammalian co-transfection, and yeast two-hybrid assays. These studies identified several amino acids within helices 3 (Asn(165)), 5 (Val(199)), 11 (Tyr(326), Ile(330), and Gln(331)), and 12 (Leu(343) and Ile(346)) that contribute to the high basal activity of human CAR. Unique residues within helices 3 (Ile(164) and Asn(165)), 5 (Cys(202) and His(203)), and 7 (Phe(234) and Phe(238)) were found control the selectivity for CAR activators and inhibitors. A single residue in helix 7 (Phe(243)) appears to explain the human/mouse species difference in response of CAR to 17alpha-ethynyl-3,17beta-estradiol.

Amino Acid Sequence↗

PubMed2004

Muscarinic toxin 7 selectivity is dictated by extracellular receptor loops.

Muscarinic toxin 7 (MT7) is a mamba venom protein antagonist with extremely high selectivity for the M1 muscarinic acetylcholine receptor. To map the sites for the interaction of MT7 with muscarinic receptors we have used chimeric M1:M3 receptors and site-directed mutagenesis of the M3 and M4 receptor subtypes. Two Glu residues in M1, one in extracellular loop 2 and one in extracellular loop 3, were found to be important for the high affinity binding of MT7. Substitution of the corresponding Lys residues in the M3 receptor with Glu converted the M3 mutant to an MT7 binding receptor, albeit with lower affinity compared with M1. A Phe --> Tyr substitution in extracellular loop 2 of M3 together with the 2 Glu mutations generated a receptor with an increased MT7 affinity (apparent Ki = 0.26 nM in a functional assay) compared with the M1 receptor (apparent Ki = 1.31 nM). The importance of the identified amino acid residues was confirmed with a mutated M4 receptor constructs. The results indicate that the high selectivity of MT7 for the M1 receptor depends on very few residues, thus providing good prospects for future design and synthesis of muscarinic receptor-selective ligands.

Amino Acid Sequence↗

PubMed2004

Free energy simulations and MM-PBSA analyses on the affinity and specificity of steroid binding to antiestradiol antibody.

Antiestradiol antibody 57-2 binds 17beta-estradiol (E2) with moderately high affinity (K(a) = 5 x 10(8) M(-1)). The structurally related natural estrogens estrone and estriol as well synthetic 17-deoxy-estradiol and 17alpha-estradiol are bound to the antibody with 3.7-4.9 kcal mol(-1) lower binding free energies than E2. Free energy perturbation (FEP) simulations and the molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) method were applied to investigate the factors responsible for the relatively low cross-reactivity of the antibody with these four steroids, differing from E2 by the substituents of the steroid D-ring. In addition, computational alanine scanning of the binding site residues was carried out with the MM-PBSA method. Both the FEP and MM-PBSA methods reproduced the experimental relative affinities of the five steroids in good agreement with experiment. On the basis of FEP simulations, the number of hydrogen bonds formed between the antibody and steroids, which varied from 0 to 3 in the steroids studied, determined directly the magnitude of the steroid-antibody interaction free energies. One hydrogen bond was calculated to contribute about 3 kcal mol(-1) to the interaction energy. Because the relative binding free energies of estrone (two antibody-steroid hydrogen bonds), estriol (three hydrogen bonds), 17-deoxy-estradiol (no hydrogen bonds), and 17alpha-estradiol (two hydrogen bonds) are close to each other and clearly lower than that of E2 (three hydrogen bonds), the water-steroid interactions lost upon binding to the antibody make an important contribution to the binding free energies. The MM-PBSA calculations showed that the binding of steroids to the antiestradiol antibody is driven by van der Waals interactions, whereas specificity is solely due to electrostatic interactions. In addition, binding of steroids to the antiestradiol antibody 57-2 was compared to the binding to the antiprogesterone antibody DB3 and antitestosterone antibody 3-C4F5, studied earlier with the MM-PBSA method.

Antibodies, Monoclonal↗

PubMed2004

Conformational and biochemical analysis of the cyclic peptides which modulate serine protease activity.

Prostate-specific antigen (PSA), a member of the kallikrein sub-group of the trypsin serine protease family, is a widely used marker for prostate cancer. Several sequences with specific binding to PSA have been identified by using phage display peptide libraries. The GST-fusion proteins of the characterized sequences have been shown to increase the enzyme activity of PSA to a synthetic substrate. The corresponding three cyclic synthetic analogues CVFTSNYAFC (A-1), CVFAHNYNYLVC (B-2) and CVAYCIEHHCWTC (C-4) have similar PSA promoting activity. Despite differences in the amino acid sequences, all three peptides bind to the same region of PSA. The conformation of the peptides was investigated by proton NMR spectroscopy. In addition, alanine replacement was used to characterize the prerequisites for binding. It is proposed that interactions with PSA are based on the aromatic and hydrophobic features of the amino acid side chains. Furthermore, it is suggested that peptides form beta-turn structures forced by cysteine bridges directing important aromatic side chains to the same side of the turn-structure.

Amino Acid Sequence↗

PubMed2004

A structural basis for the species-specific antagonism of 26,23-lactones on vitamin D signaling.

The 26,23-lactone derivative of 1alpha,25-dihydroxyvitamin D3, TEI-9647, is a partial antagonist of the of human vitamin D receptor (VDR). However, we found that TEI-9647 in rat cells behaves as a weak VDR agonist. This behavior could be mimicked in human cells by the double mutagenesis of human VDR (specifically C403S and C410N). The increased agonistic action of TEI-9647 correlates to a gain in the interaction of the VDR with coactivator protein and a decreased stabilization of the antagonistic conformation of the receptor. Molecular dynamics simulations indicated that TEI-9647 acts as antagonist of human VDR by reducing the stability of helix 12 of the ligand binding domain. In contrast, N410 of the rat VDR stabilized, via backbone contacts, the interaction between helices 11 and 12. This results in TEI-9647 becoming a weak agonist in this organism.

Amino Acid Sequence↗

PubMed2004

Ligand intramolecular motions in ligand-protein interaction: ALPHA, a novel dynamic descriptor and a QSAR study with extended steroid benchmark dataset.

The role of intramolecular motions in ligand-macromolecule interactions has been explored by developing and validating ALPHA, a novel QSAR (quantitative structure-activity relationship) descriptor. It is based on the spectral exponents (alpha), which measure the degree of 1/f alpha noise of coordinate fluctuations in molecular dynamics (MD) simulations. ALPHA is the first truly 'dynamic' QSAR descriptor, i.e., it can be derived directly from an MD trajectory. The performance of ALPHA was tested in detail employing the CBG (corticosteroid binding globulin) affinity of 31 benchmark steroids, supplemented with 11 steroids as an external test set. The only fair (42-50%) correlations of ALPHA with static 3D and electronic descriptors mean that ALPHA forms an independent molecular property. Furthermore, inclusion of ALPHA in the SOMFA/ESP model improves the correlation coefficient from 0.86 to 0.91, and /delta/ave from 0.46 to 0.36 for the benchmark dataset. The predictive ability of ALPHA can be interpreted as indirect evidence of the dynamic contribution to ligand-macromolecule interactions. The physical background of ALPHA is discussed and the importance of molecular motions for biological activity is anticipated.

Ligands↗

PubMed2003

Stabilisation of the transition state of phosphodiester bond cleavage within linear single-stranded oligoribonucleotides.

The effect of base sequence on the stability of the transition state (TS) of phosphodiester bond cleavage within linear single-stranded oligoribonucleotides has been studied in order to better understand why the reactivity of some phosphodiester bonds is enhanced compared to an unconstrained linkage. Molecular dynamics simulations of 3.0 ns were carried out for 14 oligonucleotides that contain in the place of the scissile phosphodiester bond a phosphorane structure mimicking the TS of the bond cleavage. The hydrolytic stability of the same oligonucleotides had previously been reported. Both the non-bridging oxyanions and the leaving 5[prime or minute]-oxygen of the pentacoordinated phosphorane moiety were observed to form hydrogen bonds with solvent water molecules in a similar way with all the compounds studied. In addition, water mediated hydrogen bonds between the phosphorane non-bridging oxyanions and the bases of the 3[prime or minute]-flanking sequence were detected with some of the compounds, but not with the most labile ones. Hence, it seems that the enhanced cleavage of some internucleosidic linkages does not result from the TS stabilisation by hydrogen bonding. With heterooligomers, the stacking of bases next to the cleavage site was observed to be enhanced on going from the initial state to the TS, whereas within uracil homooligomer, having initially negligible stacking, no change in the magnitude of stacking was seen. Accordingly, while strong stacking in the initial state is known to retard the phosphodiester bond cleavage, it may in the TS accelerate the reaction. Therefore, enhanced stacking on going from the initial state to transition state appears to be a factor that markedly contributes to the hydrolytic stability of phosphodiester bonds within oligonucleotides and may, at least partly, explain accelerated cleavage compared to fully unconstrained bonds, such as those in polyuridylic acid.

Base Sequence↗

PubMed2003

MM-PBSA free energy analysis of endo-1,4-xylanase II (XynII)-substrate complexes: binding of the reactive sugar in a skew boat and chair conformation.

The binding of xylotetraose in different conformations to the active site of endo-1,4-beta-xylanase II (XynII) from Trichoderma reesei was studied using molecular dynamics (MD) simulations and free energy analyses employing the MM-PBSA (Molecular Mechanics-Poisson-Boltzmann Surface Area) method. MD simulations of 1 ns were done for the substrate xylotetraose having the reactive sugar, which is bound in the -1 subsite of XynII in the 4C1 (chair) and 2So (skew boat) ground state conformations, and for the transition state of the XynII catalysed hydrolysis of the beta-glycosidic linkage. According to the simulations and free energy analysis, XynII binds the substrate with the -1 sugar in the 2So conformation 59.8 kJ mol(-1) tighter than the substrate with the sugar in the 4C1 conformation. The reactive 2So conformation resembles closely the reaction transition state and has the breaking glycosidic bond in a pseudo-axial orientation ready for facile bond cleavage. The transition state was calculated to be bound 77.1 kJ mol(-1) tighter than the 4C1 ground state conformation. The molecular mechanical interaction energy between the enzyme and the reactive pyranoside unit at the -1 subsite was 75.7 kJ mol(-1) more favorable for the binding of the 2So conformation than the 2C1 conformation, explaining the clearly tighter binding of the reactive structure The results of this study indicate that in the Michaelis complex XynII, a member of the family 11 xylanase, the substrate is bound in a skew boat conformation and in the catalytic reaction, the -1 sugar proceeds from the 4C1 conformation through 2So to the transition state with the -1 sugar in the 2,5B conformation.

Binding Sites↗

PubMed2003

First synthesis of etidronate partial amides starting from PCl3.

Methods for the preparation of mixed tetra-amide esters 1 and 2, the partial amide ester 3, and tri- and P,P-diamides 4 and 5 from monophosphorus spieces 12, 8 and 9, respectively, were developed. Compounds 8 and 9 were obtained from phosphorus trichloride via MeOPCl2, which was treated with 2 eq. and 4 eq. of piperidine, followed by water or acetyl chloride, respectively. Tetrasubstituted amide bisphosphonates 1 and 2 were selectively dealkylated with lithium or silyl halide to achieve target compounds 3-5. Piperidine was found to be a good desilylation reagent. Quantum mechanical calculations illustrate why derivative 2 was produced in low yield. The usefulness of compounds 1, 3 and 4 as prodrugs of etidronate was determined in aqueous buffer and human serum.

Alkylation↗

PubMed2003

The base sequence dependent flexibility of linear single-stranded oligoribonucleotides correlates with the reactivity of the phosphodiester bond.

The effect of base sequence on the structure and flexibility of linear single-stranded RNA molecules and the influence of the base sequence on phosphodiester bond reactivity have been studied. Molecular dynamics simulations of 2.1 ns were carried out for nine chimeric oligonucleotides containing only one unsubstituted ribo unit, all the rest of sugars being 2'-O-methylated. The base sequence has recently been reported to make a big contribution to the reactivity of these compounds. A detailed examination of the interaction energies between the base moieties shows that base stacking is strongly context-dependent and cooperative. The strength of stacking at the site susceptible to chain cleavage by intramolecular transesterification was observed to be dependent on both the flanking bases of the cleavage site and those further apart in the molecule. The interaction energies between the bases in the vicinity of the scissile linkage were found to correlate well with the experimental phosphodiester bond cleavage rates: the stronger the bases close to the cleavage site are stacked, the slower the cleavage rate is.

Base Sequence↗

PubMed2003

Corepressor excess shifts the two-side chain vitamin D analog Gemini from an agonist to an inverse agonist of the vitamin D receptor.

The vitamin D receptor (VDR) is an endocrine nuclear receptor that binds with high affinity its natural ligand 1alpha,25-dihydroxyvitamin D3. Gemini is a 1alpha,25-dihydroxyvitamin D3 analog with two identical side chains that, despite its significantly increased volume, binds to the VDR and can function as a potent agonist. This study demonstrates that, at excess corepressor (CoR) levels, Gemini shifts from an agonist to an inverse agonist that actively recruits CoR proteins to the VDR and mediates superrepression. Under these conditions Gemini stabilizes the VDR into a silent conformation, in which helix 12 of the ligand-binding domain is repositioned and thus unable to contribute to coactivator interaction. Amino acid F422 has been described as the lock of helix 12 and seems to be the most critical VDR residue in the inverse agonistic action of Gemini. Molecular dynamics simulations of the Gemini-VDR complex support these observation by indicating that the second side chain of Gemini induces tension to the receptor structure that can be released by a shift of helix 12. Taken together, Gemini is the first described (conditional) inverse agonist to an endocrine nuclear receptor and may function as a sensor for the cell-specific coactivator/CoR ratio.

Animals↗

PubMed2003

Analysis of the binding energies of testosterone, 5alpha-dihydrotestosterone, androstenedione and dehydroepiandrosterone sulfate with an antitestosterone antibody.

Molecular dynamics simulations and molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) free energy calculations were used to study the binding of testosterone (TES), 5alpha-dihydrotestosterone (5ADHT), androstenedione (AND), and dehydroepiandrosterone sulfate (DHEAS) to the monoclonal antitestosterone antibody 3-C(4)F(5). The relative binding free energy of TES and AND was also calculated with free energy perturbation (FEP) simulations. The antibody 3-C(4)F(5) has a relatively high affinity (3 x 10(8) M(-1)) and on overall good binding profile for testosterone but its cross-reactivity with DHEAS has been the main reason for the failure to use this antibody in clinical immunoassays. The relative binding free energies obtained with the MM-PBSA method were 1.5 kcal/mol for 5ADHT, 3.8 kcal/mol for AND, and 4.3 kcal/mol for DHEAS, as compared to TES. When a water molecule of the ligand binding site, observed in the antibody-TES crystal structure, was explicitly included in MM-PBSA calculations, the relative binding energies were 3.4, 4.9, and 5.4 kcal/mol for 5ADHT, AND, and DHEAS, respectively. The calculated numbers are in correct order but larger than the corresponding experimental energies of 1.3, 1.5, and 2.6 kcal/mol, respectively. The fact that the MM-PBSA method reproduced the relative binding free energies of DHEAS, a steroid having a negatively charged sulfate group, and the neutrally charged TES, 5ADHT, and AND in satisfactory agreement with experiment shows the robustness of the method in predicting relative binding affinities. The 800-ps FEP simulations predicted that the antibody 3-C(4)F(5) binds TES 1.3 kcal/mol tighter than AND. Computational mutagenesis of selected amino acid residues of the ligand binding site revealed that the lower affinities of AND and DHEAS as compared to TES are due to a combined effect of several residues, each contributing a small fraction to the tighter binding of TES. An exception to this is Tyr99H, whose mutation to Ala lowered the binding of DHEAS 0.7 kcal/mol more than the binding of TES. This is probably due to the hydrogen bonding interaction formed between the OH group of Tyr99H and the sulfate group of DHEAS. Computational mutagensis data also showed that the affinity of the steroids to the antitestosterone antibody 3-C(4)F(5) would be enhanced if Trp47H were repositioned so that it would make more extensive contacts with the bound ligands. In addition, the binding of steroids to antitestosterone, antiprogesterone, and antiestradiol antibodies is discussed.

Androgens↗

PubMed2003

Structural evaluation of the agonistic action of a vitamin D analog with two side chains binding to the nuclear vitamin D receptor.

The vitamin D receptor (VDR) is one of the endocrine members of the nuclear receptor superfamily and has a characteristic high affinity for its natural ligand 1alpha,25-dihydroxyvitamin D3 [1alpha,25(OH)2D3]. From a mechanistic point of view, the most interesting analog of 1alpha,25(OH)2D3 is the one that carries two side chains, referred to as Gemini. In this study, molecular dynamics (MD) simulations of the Gemini-VDR complex were performed that demonstrated that the binding of a ligand with a 25% increased volume does not disturb the overall structure of the ligand-binding domain (LBD). It was found that one of the two side chains takes exactly the same position as the single side chain of the natural ligand, which suggests that the molecular mechanism of the agonism of Gemini is identical to that of 1alpha,25(OH)2D3. VDR single and double point mutants at L227, A303, I313, and L397 and in vitro and ex vivo assessment of their agonistic action confirmed the predictions of the MD simulations. Moreover, it was found that the second side chain of Gemini can choose between two binding positions within the ligand-binding pocket of the VDR. These two newly identified "corners" were characterized most specifically by the amino acids pairs L227/A303 and I313/L397. Therefore, Gemini is an important model compound that allows further insight into the molecular actions of the VDR but is, in parallel, also a promising precursor for the design of even more potent 1alpha,25(OH)2D3 analogs.

Animals↗

PubMed2002

Correlative motions and memory effects in molecular dynamics simulations of molecules: principal components and rescaled range analysis suggest that the motions of native BPTI are more correlated than those of its mutants.

In this work MD simulations of the native bovine pancreatic trypsin inhibitor (BPTI) and 16 mutants were done in vacuum in order to study memory effects in the mutants using principal component analysis (PCA) and the rescaled range analysis (Hurst exponents). Both PCA and the rescaled range analysis support our previous proposition, based on PCA of lysozyme, that the motions of a native protein are more correlated than those of mutants. The methods are compared, the nature and applications of the rule and the role of the long-range correlations in MD time series (i.e. memory) are discussed in the context of collective motions.

Algorithms↗