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1.
Inorg Chem ; 2024 Apr 24.
Artigo em Inglês | MEDLINE | ID: mdl-38656154

RESUMO

A series of ligands based upon a 1,3-diimino-isoindoline framework have been synthesized and investigated as pincer-type (N∧N∧N) chelates for Pt(II). The synthetic route allows different combinations of heterocyclic moieties (including pyridyl, thiazole, and isoquinoline) to yield new unsymmetrical ligands. Pt(L1-6)Cl complexes were obtained and characterized using a range of spectroscopic and analytical techniques: 1H and 13C NMR, IR, UV-vis and luminescence spectroscopies, elemental analyses, high-resolution mass spectrometry, electrochemistry, and one example via X-ray crystallography which showed a distorted square planar environment at Pt(II). Cyclic voltammetry on the complexes showed one irreversible oxidation between +0.75 and +1 V (attributed to Pt2+/3+ couple) and a number of ligand-based reductions; in four complexes, two fully reversible reductions were noted between -1.4 and -1.9 V. Photophysical studies showed that Pt(L1-6)Cl absorbs efficiently in the visible region through a combination of ligand-based bands and metal-to-ligand charge-transfer features at 400-550 nm, with assignments supported by DFT calculations. Excitation at 500 nm led to luminescence (studied in both solutions and solid state) in all cases with different combinations of the heterocyclic donors providing tuning of the emission wavelength around 550-678 nm.

2.
Molecules ; 29(5)2024 Mar 05.
Artigo em Inglês | MEDLINE | ID: mdl-38474663

RESUMO

The controlled formation of mixed-metal bimetallics was realised through use of a fac-[Re(CO)3(N,N'-bpy-P)Cl] complex bearing an exogenous 2,4,6-trioxa-1,3,5,7-tetramethyl-8-phosphaadamantane donor at the 5-position of the bpy. The introduction of gold, silver, and rhodium with appropriate secondary ligands was readily achieved from established starting materials. Restricted rotation about the C(bpy)-P bond was observed in several of the bimetallic complexes and correlated with the relative steric bulk of the second metal moiety. Related chemistry with the 6-substituted derivative proved more limited in scope with only the bimetallic Re/Au complex being isolated.

3.
Phys Chem Chem Phys ; 26(4): 2926-2935, 2024 Jan 24.
Artigo em Inglês | MEDLINE | ID: mdl-38193190

RESUMO

We report molecular dynamics simulation of dimers of α-synuclein, the peptide closely associated with onset of Parkinson's disease, both as metal-free dimer and with inter-chain bridging provided by Cu(II) ions. Our investigation reveals that the presence of copper-induced inter-chain bridging not only stabilizes α-synuclein dimers, but also leads to enhanced ß-sheet formation at critical regions within the N-terminal and NAC regions of the protein. These contacts are larger and longer-lived in the presence of copper, and as a result each peptide chain is more extended and less flexible than in the metal-free dimer. The persistence of these inter-peptide contacts underscores their significance in stabilising the dimers, potentially influencing the aggregation pathway. Moreover, the increased flexibility in the two termini, as well as the absence of persistent contacts in the metal-free dimer, correlates with the presence of amorphous aggregates. This phenomenon is known to mitigate fibrillation, while their absence in the metal-bound dimer suggests an increased propensity to form fibrils in the presence of copper ions.


Assuntos
Doença de Parkinson , alfa-Sinucleína , Humanos , alfa-Sinucleína/química , Cobre/química , Doença de Parkinson/metabolismo , Metais , Peptídeos , Íons
4.
J Inorg Biochem ; 249: 112395, 2023 12.
Artigo em Inglês | MEDLINE | ID: mdl-37820444

RESUMO

We report molecular dynamics simulations of two modifications to α-Synuclein, namely A53T mutation and phosphorylation at Ser129, which have been observed in Parkinson's disease patients. Both modifications are close to known metal binding sites, so as well as each modified peptide we also study Cu(II) bound to N-terminal and C-terminal residues. We show that A53T is predicted to cause increased ß-sheet content of the peptide, with a persistent ß-hairpin between residues 35-55 particularly notable. Phosphorylation has less effect on secondary structure but is predicted to significantly increase the size of the peptide, especially when bound to Cu(II), which is ascribed to reduced interaction of C-terminal sequence with central non-amyloid component. In addition, estimate of binding free energy to Cu(II) indicates A53T has little effect on metal-ion affinity, whereas phosphorylation markedly enhances the strength of binding. We suggest that the predicted changes in spatial extent and secondary structure of α-Synuclein may have implications for aggregation into Lewy bodies.


Assuntos
Cobre , alfa-Sinucleína , Humanos , alfa-Sinucleína/metabolismo , Cobre/química , Simulação de Dinâmica Molecular , Mutação , Processamento de Proteína Pós-Traducional , Peptídeos/metabolismo
5.
Dalton Trans ; 52(36): 12677-12685, 2023 Sep 19.
Artigo em Inglês | MEDLINE | ID: mdl-37655459

RESUMO

Platinum (Pt)(II) square planar complexes are well-known anticancer drugs whose Mechanism of Action (MOA) are finely tuned by the polar, hydrophobic and aromatic features of the ligands. In the attempt to translate this tunability to the identification of potential neurodrugs, herein, four Pt(II) complexes were investigated in their ability to modulate the self-aggregation processes of two amyloidogenic models: Sup35p7-13 and NPM1264-277 peptides. In particular, phenanthriplatin revealed the most efficient agent in the modulation of amyloid aggregation: through several biophysical assays, as Thioflavin T (ThT), electrospray ionization mass spectrometry (ESI-MS) and ultraviolet-visible (UV-vis) absorption spectroscopy, this complex revealed able to markedly suppress aggregation and to disassemble small soluble aggregates. This effect was due to a direct coordination of phenanthriplatin to the amyloid, with the loss of several ligands and different stoichiometries, by the formation of π-π and π-cation interactions as indicated from molecular dynamic simulations. Presented data support a growing and recent approach concerning the repurposing of metallodrugs as potential novel neurotherapeutics.


Assuntos
Proteínas Amiloidogênicas , Platina , Platina/farmacologia , Ligantes , Compostos Organoplatínicos/farmacologia
6.
J Biomol Struct Dyn ; 41(11): 5230-5245, 2023 07.
Artigo em Inglês | MEDLINE | ID: mdl-35670576

RESUMO

We report conventional and accelerated molecular dynamics simulations of α-Synuclein, designed to assess performance of using different starting conformation, solvation environment and force field combination. Backbone and sidechain chemical shifts, radius of gyration, presence of ß-hairpin structures in KTK(E/Q)GV repeats and secondary structure percentages were used to evaluate how variations in forcefield, solvation model and simulation protocol provide results that correlate with experimental findings. We show that with suitable choice of forcefield and solvent, ff03ws and OBC implicit model, respectively, acceptable reproduction of experimental data on size and secondary structure is obtained by both conventional and accelerated MD. In contrast to the implicit solvent model, simulations in explicit TIP4P/2005 solvent do not properly represent size or secondary structure of α-Synuclein.Communicated by Ramaswamy H. Sarma.


Assuntos
Simulação de Dinâmica Molecular , alfa-Sinucleína , Solventes/química , alfa-Sinucleína/química , Simulação por Computador , Estrutura Secundária de Proteína
7.
Inorg Chem ; 62(1): 192-200, 2023 Jan 09.
Artigo em Inglês | MEDLINE | ID: mdl-36547395

RESUMO

We present a combined experimental and theoretical study of the nature of the proposed metal-metal bonding in the tetranuclear cluster Ni4(NPtBu3)4, which features four nickel(I) centers engaged in strong ferromagnetic coupling. High-resolution single-crystal synchrotron X-ray diffraction data collected at 25 K provide an accurate geometrical structure and a multipole model electron density description. Topological analysis of the electron density in the Ni4N4 core using the quantum theory of atoms in molecules clearly identifies the bonding as an eight-membered ring of type [Ni-N-]4 without direct Ni-Ni bonding, and this result is generally corroborated by an analysis of the energy density distribution. In contrast, the calculated bond delocalization index of ∼0.6 between neighboring Ni atoms is larger than what has been found for other bridged metal-metal bonds and implies direct Ni-Ni bonding. Similar support for the presence of direct Ni-Ni bonding is found in the interacting quantum atom approach, an energy decomposition scheme, which suggests the presence of stabilizing Ni-Ni bonding interactions with an exchange-correlation energy contribution approximately 50% of that of the Ni-N interactions. Altogether, while the direct interactions between neighboring Ni centers are too weak and sterically constrained to bear the signature of a topological bond critical point, other continuous measures clearly indicate significant Ni-Ni bonding. These metal-metal bonding interactions likely mediate direct ferromagnetic exchange, giving rise to the high-spin ground state of the molecule.

8.
J Inorg Biochem ; 239: 112068, 2023 02.
Artigo em Inglês | MEDLINE | ID: mdl-36403437

RESUMO

We report accelerated molecular dynamics simulations of α-Synuclein and its complex with two Cu(II) ions bound to experimentally determined binding sites. Adding two Cu(II) ions, one bound to the N-terminal region and one to the C-terminus, decreases size and flexibility of the peptide while introducing significant new contacts within and between N-terminus and non-Aß component (NAC). Cu(II) ions also alter the pattern of secondary structure within the peptide, inducing more and longer-lasting elements of secondary structure such as ß-strands and hairpins. Free energy surfaces, obtained from reweighting the accelerated molecular dynamics boost potential, further demonstrate the restriction on size and flexibility that results from binding of copper ions.


Assuntos
Simulação de Dinâmica Molecular , alfa-Sinucleína , alfa-Sinucleína/metabolismo , Cobre/química , Sítios de Ligação , Estrutura Secundária de Proteína
10.
RSC Adv ; 12(25): 15670-15684, 2022 May 23.
Artigo em Inglês | MEDLINE | ID: mdl-35685708

RESUMO

The pharmaceutical agent theophylline (THEO) is primarily used as a bronchodilator and is commercially available in both tablet and liquid dosage forms. THEO is highly hygroscopic, reducing its stability, overall shelf-life, and therefore usage as a drug. THEO and dicarboxylic acid cocrystals were designed by Trask et al. in an attempt to decrease the hygroscopic behaviour of THEO; cocrystallisation of THEO with malonic acid (MA) did not improve the hygroscopic stability of THEO in simulated atmospheric humidity testing. The current study employed high-resolution X-ray crystallography, and Density Functional Theory (DFT) calculations to examine the electron density distribution (EDD) changes between the cocrystal and its individual components. The EED changes identified the reasons why the THEO:MA cocrystal did not alter the hygroscopic profile of THEO. The cocrystal was equally porous, with atomic packing factors (APF) similar to those of THEO 0.73 vs. 0.71, respectively. The THEO:MA (1) cocrystal structure is held together by an array of interactions; a heterogeneous synthon between the imidazole and a carboxylic fragment stabilising the asymmetric unit, a pyrimidine-imidazole homosynthon, and an aromatic cycle stack between two THEO moieties have been identified, providing 9.7-12.9 kJ mol-1 of stability. These factors did not change the overall relative stability of the cocrystal relative to its individual THEO and MA components, as shown by cocrystal (1) and THEO being equally stable, with calculated lattice energies within 2.5 kJ mol-1 of one other. The hydrogen bond analysis and fragmented atomic charge analysis highlighted that the formation of (1) combined both the EDD of THEO and MA with no net chemical change, suggesting that the reverse reaction - (1) back to THEO and MA - is of equal potential, ultimately producing THEO hydrate formation, in agreement with the work of Trask et al. These results highlight that a review of the EDD change associated with a chemical reaction can aid in understanding cocrystal design. In addition, they indicate that cocrystal design requires further investigation before becoming a reliable process, with particular emphasis on identifying the appropriate balance of synthon engineering, weak interactions, and packing dynamics.

11.
Phys Chem Chem Phys ; 24(21): 13015-13025, 2022 Jun 01.
Artigo em Inglês | MEDLINE | ID: mdl-35583143

RESUMO

This study investigated the effect of 2-methylimidazole (2-MIM) addition on the fluorescence of ethyl-7-hydroxy-2-oxo-2H-chromene-3-carboxylate using low-cost density functional theory (DFT) and Time-Dependent DFT calculations on single crystal X-ray geometries of ethyl-7-hydroxy-2-oxo-2H-chromene-3-carboxylate hydrate (1), 2-MIM (2), and the 1 : 1 co-crystal of (1) and (2), (3). At low concentrations (1 : 1-1 : 10) of 2-MIM, the fluorophore shows a decrease in the fluorescence intensity, but at higher concentrations (above 1 : 10) the fluorescence excitation maximum shifted from 354 nm to 405 nm, with a significant emission intensity increase. The changed excitation and emission profile at high concentrations is due to the deprotonation of the coumarin's phenolic group, which was confirmed by the increased shielding of the aromatic protons in the titration 1H NMR spectra. The experimental fluorescence data between the 1 : 1 and 1 : 10 ratios agreed with the theoretical fluorescence data, with a redshift and decreased intensity when comparing (1) and (3). The data indicated that combining the fluorophore with 2-MIM increased levels of vibronic coupling between 2-MIM and the fluorophore decreasing de-excitation efficiency. These increased vibronic changes were due to charge transfer between the fluorophore and 2-MIM in (3). The subtle movement of the proton, H(5) toward N(2') (0.07 Å) caused a significant decrease in fluorescence due to electron density distribution (EDD) changes. This was identified by comparison of the EDD in the excited (S1) and ground (S0) states plotted as an isosurface of EDD difference. For the higher concentrations, an alternative excitation pathway was explored by modifying the crystal geometry of (3) based on 1H NMR spectroscopy data to resemble excitoplexes. Theses excitoplex geometries reflected the fluorescence profile of the fluorophore with high concentrations of 2-MIM; there were dramatic changes in the theoretical fluorescence pathway, which was 100% vibronic coupling compared to 15.31% in the free fluorophore. At this concentration, the de-excitation pathway causes remodelling of the lactone ring via stretching/breaking the CO bond in the S1 causing increased fluorescence by movement of the transition dipole moment. These results reflect previous studies, but the methods used are less experimentally and computationally expensive. This study is among the first to explain charge transfer fluorescence using crystalline geometries. This study will be of interest to the fields of crystal engineering and fluorescence spectroscopy.


Assuntos
Prótons , Teoria Quântica , Corantes Fluorescentes , Imidazóis , Umbeliferonas , Difração de Raios X
12.
J Phys Chem A ; 125(45): 9736-9756, 2021 Nov 18.
Artigo em Inglês | MEDLINE | ID: mdl-34731566

RESUMO

The charge density distribution in a novel cocrystal (1) complex of 1,3-dimethylxanthine (theophylline) and propanedioic acid (malonic acid) has been determined. The molecules crystallize in the triclinic, centrosymmetric space group P1̅, with four independent molecules (Z = 4) in the asymmetric unit (two molecules each of theophylline and malonic acid). Theophylline has a notably high hygroscopic nature, and numerous cocrystals have shown a significant improvement in stability to humidity. A charge density study of the novel polymorph has identified interesting theoretical results correlating the stability enhancement of theophylline via cocrystallization. Topological analysis of the electron density highlighted key differences (up to 17.8) in Laplacian (∇2ρ) between the experimental (EXP) and single-point (SP) models, mainly around intermolecular-bonded carbonyls. Further investigation via molecular electrostatic potential maps reaffirmed that the charge redistribution enhanced intramolecular hydrogen bonding, predominantly for N(2') and N(2) (61.2 and 61.8 kJ mol-1, respectively). An overall weaker lattice energy of the triclinic form (-126.1 kJ mol-1) compared to that of the monoclinic form (-133.8 kJ mol-1) suggests a lower energy threshold to overcome to initiate dissociation. Future work via physical testing of the novel cocrystal in both dissolution and solubility will further solidify the correlation between theoretical and experimental results.


Assuntos
Teofilina , Cristalização , Ligação de Hidrogênio , Solubilidade , Molhabilidade
13.
ACS Chem Neurosci ; 12(21): 4065-4075, 2021 11 03.
Artigo em Inglês | MEDLINE | ID: mdl-34669379

RESUMO

We report the accelerated molecular dynamics (aMD) simulation of amyloid-ß (Aß) peptides of four different lengths (16, 28, 40, and 42 residues) and their complexes when bound to Cu(II), Fe(II), or Zn(II). 600 ns equilibrated trajectory data were analyzed for each structure from three independent 200 ns aMD simulations, generating 16 aMD trajectories. We show that the presence of a metal ion leads to reduced size and decreased mobility relative to the free peptide due to the anchoring effect of the ions. The reduced mobility was shown largely to be due to the restricted movement in N-terminal residues, most notably Asp1 and His6 that are involved in the metal-ion coordination in all cases. Significant disruption of the secondary structure and patterns of salt bridge interactions arise on the coordination of metal ions. In this regard, similarities were noted between results for Zn(II) and Fe(II), whereas results for Cu(II) are more comparable to that of the free peptides. Reweighting of free energy surfaces was carried out from aMD data to identify the properties and descriptions of local minima structures.


Assuntos
Doença de Alzheimer , Simulação de Dinâmica Molecular , Peptídeos beta-Amiloides , Cobre , Humanos , Íons , Metais , Fragmentos de Peptídeos , Estrutura Secundária de Proteína
14.
Comput Biol Chem ; 93: 107540, 2021 Aug.
Artigo em Inglês | MEDLINE | ID: mdl-34271422

RESUMO

We report conventional and accelerated molecular dynamics simulation of Zn(II) bound to the N-terminus of amyloid-ß. By comparison against NMR data for the experimentally determined binding mode, we find that certain combinations of forcefield and solvent model perform acceptably in describing the size, shape and secondary structure, and that there is no appreciable difference between implicit and explicit solvent models. We therefore used the combination of ff14SB forcefield and GBSA solvent model to compare the result of different binding modes of Zn(II) to the same peptide, using accelerated MD to enhance sampling and comparing the free peptide simulated in the same way. We show that Zn(II) imparts significant rigidity to the peptide, disrupts the secondary structure and pattern of salt bridges seen in the free peptide, and induces closer contact between residues. Free energy surfaces in 1 or 2 dimensions further highlight the effect of metal coordination on peptide's spatial extent. We also provide evidence that accelerated MD provides improved sampling over conventional MD by visiting as many or more configurations in much shorter simulation times.


Assuntos
Peptídeos beta-Amiloides/química , Simulação de Dinâmica Molecular , Zinco/química , Sítios de Ligação , Estrutura Molecular
15.
Inorg Chem ; 60(10): 7031-7043, 2021 May 17.
Artigo em Inglês | MEDLINE | ID: mdl-33900771

RESUMO

We report the formation of dinuclear complexes from, and photochemical oxidation of, (CH3)3-Pt(IV)(N^N) (N^N = 1,2-diimine derivatives) complexes of thiophenolate ligands to the analogous sulfinates (CH3)3Pt(N^N)(SO2Ph) and structural, spectroscopic, and theoretical studies of the latter revealing tunable photophysics depending upon the 1,2-diimine ligands. Electron-rich thiolate and conjugated 1,2-diimines encourage formation of thiolate-bridged dinuclear complexes; smaller 1,2-diimines or electron-poor thiolates favor mononuclear complexes. Photooxidation of the thiolate ligand yields hitherto unreported Pt(IV)-SO2R complexes, promoted by electron-deficient thiolates such as 4-nitrothiophenol, which exclusively forms the sulfinate complex. Such complexes exhibit expected absorptions due to π-π* ligand transitions of the 1,2-diimines mixed with spin-allowed singlet MLCT (d-π*) at relatively high energy (270-290 nm), as well as unexpected broad, lower energy absorptions between 360 and 490 nm. DFT data indicate that these low energy absorption bands result from excitation of Pt-S and Pt-C σ-bonding electrons to π* orbitals on sulfinate and 1,2-diimine, the latter of which gives rise to emission in the visible range.

16.
J Mol Graph Model ; 105: 107846, 2021 06.
Artigo em Inglês | MEDLINE | ID: mdl-33588351

RESUMO

This review endeavours to explore the power of quantum chemistry, especially density functional theory (DFT) to unravel mechanisms underlying the fascinating field of FLP chemistry. Apart from the fundamental mechanism of hydrogen activation by FLPs, borylation, silylation, polymerization, formation of heterocycles, reaction with small gaseous molecules, alkenes, terminal alkynes have also been reviewed. The role of DFT in understanding regio-selectivity, steric effects, London dispersion and covalent Interactions in FLPs are also discussed.


Assuntos
Alcenos , Alcinos , Hidrogênio , Polimerização
17.
RSC Adv ; 11(54): 34170-34173, 2021 Oct 18.
Artigo em Inglês | MEDLINE | ID: mdl-35497314

RESUMO

An asymmetric bipy/NHC ligand L has been used to construct Au/Au, Au/Ag and Au/Cu bimetallic complexes through prior coordination of the NHC to Au(i) and subsequent introduction of the second group 11 metal ion at the bipy donor of the hybrid ligand. The complex [Au(κC-L)2]BF4,1, has been used as the precursor for the formation of [AuAg(κ-C Au,κ2-N,N'Ag-1)2](BF4)2, 2a, [AuCu(κ-C Au,κ2-N,N'Cu-1)2](BF4)2, 2b and [AuAu'(κ-CAu/Au',κ1-NAu/Au'-1)2](BF4)2, 3.

18.
J Biomol Struct Dyn ; 39(6): 2003-2013, 2021 Apr.
Artigo em Inglês | MEDLINE | ID: mdl-32189584

RESUMO

We report results of molecular dynamic (MD) simulations on N-terminus mutants of the copper-bound, amyloid-ß (Aß) peptide. Eight structures of Aß were modelled, including seven mutant peptides in addition to the unaltered wild-type (WT). Trajectories analysed for each individual system were all approximately 1.4 µs in length, yielding a total of over 11 µs in total. The impact of these mutations are marked and varied compared to the wild-type peptide, including effects on secondary structure, stability and conformational changes. Each system showed differing levels of stability with some showing consistent, compact conformations whereas others displayed more flexible structures. Contrasts between comparable mutations at similar sites, such as A2T/A2V and D7H/D7N, show the location as well as the type of mutation have effects on protein structure observed in Ramachandran plots. We also report notable changes in peptide structure at residues remote to the site of substitution showing these mutations influence the entirety of Aß. Salt-bridge profiles show this most clearly: addition or removal of charged residues affecting all salt-bridge interactions present in WT, even those remote from the site of mutation. Effects on secondary structure differ between mutations, most notably a change in incidence of ß-strand, which has been linked to enhanced aggregational properties for the peptide. GFN2-xTB semi-empirical calculations show clear differences in binding energies of the copper-centre for each system.Communicated by Ramaswamy H. Sarma.


Assuntos
Doença de Alzheimer , Simulação de Dinâmica Molecular , Peptídeos beta-Amiloides/genética , Cobre , Humanos , Interações Hidrofóbicas e Hidrofílicas , Fragmentos de Peptídeos/genética
19.
Comput Biol Chem ; 86: 107265, 2020 Jun.
Artigo em Inglês | MEDLINE | ID: mdl-32371360

RESUMO

We report ligand field molecular mechanics, density functional theory and semi-empirical studies on the binding of Cu(II) to GlyHisLys (GHK) peptide. Following exhaustive conformational searching using molecular mechanics, we show that relative energy and geometry of conformations are in good agreement between GFN2-xTB semi-empirical and B3LYP-D DFT levels. Conventional molecular dynamics simulation of Cu-GHK shows the stability of the copper-peptide binding over 100 ps trajectory. Four equatorial bonds in 3N1O coordination remain stable throughout simulation, while a fifth in apical position from C-terminal carboxylate is more fluxional. We also show that the automated conformer and rotamer search algorithm CREST is able to correctly predict the metal binding position from a starting point consisting of separated peptide, copper and water.


Assuntos
Cobre/química , Oligopeptídeos/química , Simulação de Dinâmica Molecular
20.
R Soc Open Sci ; 7(2): 191562, 2020 Feb.
Artigo em Inglês | MEDLINE | ID: mdl-32257321

RESUMO

We report semi-empirical tight-binding simulations of the interaction between Al(III) and biologically relevant peptides. The GFN2-XTB method is shown to accurately reproduce previously reported and density functional theory (DFT)-calculated geometries of model systems. Molecular dynamics simulations based on this method are able to sample peptide flexibility over timescales of up to nanoseconds, but these timescales are insufficient to explore potential changes in metal-peptide binding modes. To achieve this, metadynamics simulations using root mean square deviation as a collective variable were employed. With suitably chosen biasing potentials, these are able to efficiently explore diverse coordination modes, for instance, through Glu and/or Asp residues in a model peptide. Using these methods, we find that Al(III) binding to the N-terminal sequence of amyloid-ß is highly fluxional, with all acidic sidechains and several backbone oxygens participating in coordination. We also show that such simulations could provide a means to predict a priori possible binding modes as a precursor to longer, atomistic simulations.

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