Einstein Model of a Graph to Characterize Protein Folded/Unfolded States.

The folded structures of proteins can be accurately predicted by deep learning algorithms from their amino-acid sequences. By contrast, in spite of decades of research studies, the prediction of folding pathways and the unfolded and misfolded states of proteins, which are intimately related to diseases, remains challenging. A two-state (folded/unfolded) description of protein folding dynamics hides the complexity of the unfolded and misfolded microstates. Here, we focus on the development of simplified order parameters to decipher the complexity of disordered protein structures. First, we show that any connected, undirected, and simple graph can be associated with a linear chain of atoms in thermal equilibrium. This analogy provides an interpretation of the usual topological descriptors of a graph, namely the Kirchhoff index and Randic resistance, in terms of effective force constants of a linear chain. We derive an exact relation between the Kirchhoff index and the average shortest path length for a linear graph and define the free energies of a graph using an Einstein model. Second, we represent the three-dimensional protein structures by connected, undirected, and simple graphs. As a proof of concept, we compute the topological descriptors and the graph free energies for an all-atom molecular dynamics trajectory of folding/unfolding events of the proteins Trp-cage and HP-36 and for the ensemble of experimental NMR models of Trp-cage. The present work shows that the local, nonlocal, and global force constants and free energies of a graph are promising tools to quantify unfolded/disordered protein states and folding/unfolding dynamics. In particular, they allow the detection of transient misfolded rigid states.

Angstrom-Size Defect Creation and Ionic Transport through Pores in Single-Layer MoS2.

Atomic-defect engineering in thin membranes provides opportunities for ionic and molecular filtration and analysis. While molecular-dynamics (MD) calculations have been used to model conductance through atomic vacancies, corresponding experiments are lacking. We create sub-nanometer vacancies in suspended single-layer molybdenum disulfide (MoS2) via Ga+ ion irradiation, producing membranes containing ∼300 to 1200 pores with average and maximum diameters of ∼0.5 and ∼1 nm, respectively. Vacancies exhibit missing Mo and S atoms, as shown by aberration-corrected scanning transmission electron microscopy (AC-STEM). The longitudinal acoustic band and defect-related photoluminescence were observed in Raman and photoluminescence spectroscopy, respectively. As the irradiation dose is increased, the median vacancy area remains roughly constant, while the number of vacancies (pores) increases. Ionic current versus voltage is nonlinear and conductance is comparable to that of ∼1 nm diameter single MoS2 pores, proving that the smaller pores in the distribution display negligible conductance. Consistently, MD simulations show that pores with diameters <0.6 nm are almost impermeable to ionic flow. Atomic pore structure and geometry, studied by AC-STEM, are critical in the sub-nanometer regime in which the pores are not circular and the diameter is not well-defined. This study lays the foundation for future experiments to probe transport in large distributions of angstrom-size pores.

Patients with colorectal tumors with microsatellite instability and large deletions in HSP110 T17 have improved response to 5-fluorouracil­based chemotherapy.

BACKGROUND & AIMS: Patients with colorectal tumors with microsatellite instability (MSI) have better prognoses than patients with tumors without MSI, but have a poor response to 5-fluorouracil­based chemotherapy. A dominant-negative form of heat shock protein (HSP)110 (HSP110DE9) expressed by cancer cells with MSI, via exon skipping caused by somatic deletions in the T(17) intron repeat, sensitizes the cells to 5-fluorouracil and oxaliplatin.We investigated whether HSP110 T(17) could be used to identify patients with colorectal cancer who would benefit from adjuvant chemotherapy with 5-fluorouracil and oxaliplatin. METHODS: We characterized the interaction between HSP110 and HSP110DE9 using surface plasmon resonance. By using polymerase chain reaction and fragment analysis, we examined how the size of somatic allelic deletions in HSP110 T(17) affected the HSP110 protein expressed by tumor cells. We screened 329 consecutive patients with stage II­III colorectal tumors with MSI who underwent surgical resection at tertiary medical centers for HSP110 T(17). RESULTS: HSP110 and HSP110DE9 interacted in a1:1 ratio. Tumor cells with large deletions in T(17) had increased ratios of HSP110DE9:HSP110, owing to the loss of expression of full-length HSP110. Deletions in HSP110 T(17) were mostly biallelic in primary tumor samples with MSI. Patients with stage II­III cancer who received chemotherapy and had large HSP110 T(17) deletions (≥5 bp; 18 of 77 patients, 23.4%) had longer times of relapse-free survival than patients with small or no deletions (≤4 bp; 59 of 77 patients, 76.6%) in multivariate analysis (hazard ratio, 0.16; 95% confidence interval, 0.012­0.8; P = .03). We found a significant interaction between chemotherapy and T17 deletion (P =.009). CONCLUSIONS: About 25% of patients with stages II­III colorectal tumors with MSI have an excellent response to chemotherapy, due to large, biallelic deletions in the T(17) intron repeat of HSP110 in tumor DNA.

Anomalous diffusion and dynamical correlation between the side chains and the main chain of proteins in their native state.

Structural fluctuations of a protein are essential for a protein to function and fold. By using molecular dynamics (MD) simulations of the model α/ß protein VA3 in its native state, the coupling between the main-chain (MC) motions [represented by coarse-grained dihedral angles (CGDAs) γ(n) based on four successive C(α) atoms (n - 1, n, n + 1, n + 2) along the amino acid sequence] and its side-chain (SC) motions [represented by CGDAs δ(n) formed by the virtual bond joining two consecutive C(α) atoms (n, n + 1) and the bonds joining these C(α) atoms to their respective C(ß) atoms] was analyzed. The motions of SCs (δ(n)) and MC (γ(n)) over time occur on similar free-energy profiles and were found to be subdiffusive. The fluctuations of the SCs (δ(n)) and those of the MC (γ(n)) are generally poorly correlated on a ps time-scale with a correlation increasing with time to reach a maximum value at about 10 ns. This maximum value is close to the correlation between the δ(n)(t) and γ(n)(t) time-series extracted from the entire duration of the MD runs (400 ns) and varies significantly along the amino acid sequence. High correlations between the SC and MC motions [δ(t) and γ(t) time-series] were found only in flexible regions of the protein for a few residues which contribute the most to the slowest collective modes of the molecule. These results are a possible indication of the role of the flexible regions of proteins for the biological function and folding.

Decipher the mechanisms of protein conformational changes induced by nucleotide binding through free-energy landscape analysis: ATP binding to Hsp70.

ATP regulates the function of many proteins in the cell by transducing its binding and hydrolysis energies into protein conformational changes by mechanisms which are challenging to identify at the atomic scale. Based on molecular dynamics (MD) simulations, a method is proposed to analyze the structural changes induced by ATP binding to a protein by computing the effective free-energy landscape (FEL) of a subset of its coordinates along its amino-acid sequence. The method is applied to characterize the mechanism by which the binding of ATP to the nucleotide-binding domain (NBD) of Hsp70 propagates a signal to its substrate-binding domain (SBD). Unbiased MD simulations were performed for Hsp70-DnaK chaperone in nucleotide-free, ADP-bound and ATP-bound states. The simulations revealed that the SBD does not interact with the NBD for DnaK in its nucleotide-free and ADP-bound states whereas the docking of the SBD was found in the ATP-bound state. The docked state induced by ATP binding found in MD is an intermediate state between the initial nucleotide-free and final ATP-bound states of Hsp70. The analysis of the FEL projected along the amino-acid sequence permitted to identify a subset of 27 protein internal coordinates corresponding to a network of 91 key residues involved in the conformational change induced by ATP binding. Among the 91 residues, 26 are identified for the first time, whereas the others were shown relevant for the allosteric communication of Hsp70 s in several experiments and bioinformatics analysis. The FEL analysis revealed also the origin of the ATP-induced structural modifications of the SBD recently measured by Electron Paramagnetic Resonance. The pathway between the nucleotide-free and the intermediate state of DnaK was extracted by applying principal component analysis to the subset of internal coordinates describing the transition. The methodology proposed is general and could be applied to analyze allosteric communication in other proteins.

Reconstructing the free-energy landscape of Met-enkephalin using dihedral principal component analysis and well-tempered metadynamics.

Well-Tempered Metadynamics (WTmetaD) is an efficient method to enhance the reconstruction of the free-energy surface of proteins. WTmetaD guarantees a faster convergence in the long time limit in comparison with the standard metadynamics. It still suffers, however, from the same limitation, i.e., the non-trivial choice of pertinent collective variables (CVs). To circumvent this problem, we couple WTmetaD with a set of CVs generated from a dihedral Principal Component Analysis (dPCA) on the Ramachandran dihedral angles describing the backbone structure of the protein. The dPCA provides a generic method to extract relevant CVs built from internal coordinates, and does not depend on the alignment to an arbitrarily chosen reference structure as usual in Cartesian PCA. We illustrate the robustness of this method in the case of a reference model protein, the small and very diffusive Met-enkephalin pentapeptide. We propose a justification a posteriori of the considered number of CVs necessary to bias the metadynamics simulation in terms of the one-dimensional free-energy profiles associated with Ramachandran dihedral angles along the amino-acid sequence.

Nonexponential decay of internal rotational correlation functions of native proteins and self-similar structural fluctuations.

Structural fluctuations of a protein are essential for the function of native proteins and for protein folding. To understand how the main chain in the native state of a protein fluctuates on different time scales, we examined the rotational correlation functions (RCFs), C(t), of the backbone N-H bonds and of the dihedral angles γ built on four consecutive C(α) atoms. Using molecular dynamics simulations of a model α/ß protein (VA3) in its native state, we demonstrate that these RCFs decay as stretched exponentials, ln[C(t)] ≈ D(α)t(α) with a constant D(α) and an exponent α (0 < α < 0.35) varying with the free-energy profiles (FEPs) along the amino acid sequence. The probability distributions of the fluctuations of the main chain computed at short time scale (1 ps) were identical to those computed at large time scale (1 ns) if the time is rescaled by a factor depending on α < 1. This self-similar property and the nonexponential decays (α ≠ 1) of the RCFs are described by a rotational diffusion equation with a time-dependent diffusion coefficient D(t) = αD(α)t(α-1). The present findings agree with observations of subdiffusion (α < 1) of fluorescent probes within a protein molecule. The subdiffusion of (15)N-H bonds did not affect the value of the order parameter S(2) extracted from the NMR relaxation data by assuming normal diffusion (α = 1) of (15)N-H bonds on a nanosecond time scale. However, we found that the RCF does not converge to S(2) on the nanosecond time scale for residues with multiple-minima FEPs.

Role of Insect and Mammal Glutathione Transferases in Chemoperception.

Glutathione transferases (GSTs) are ubiquitous key enzymes with different activities as transferases or isomerases. As key detoxifying enzymes, GSTs are expressed in the chemosensory organs. They fulfill an essential protective role because the chemosensory organs are located in the main entry paths of exogenous compounds within the body. In addition to this protective function, they modulate the perception process by metabolizing exogenous molecules, including tastants and odorants. Chemosensory detection involves the interaction of chemosensory molecules with receptors. GST contributes to signal termination by metabolizing these molecules. By reducing the concentration of chemosensory molecules before receptor binding, GST modulates receptor activation and, therefore, the perception of these molecules. The balance of chemoperception by GSTs has been shown in insects as well as in mammals, although their chemosensory systems are not evolutionarily connected. This review will provide knowledge supporting the involvement of GSTs in chemoperception, describing their localization in these systems as well as their enzymatic capacity toward odorants, sapid molecules, and pheromones in insects and mammals. Their different roles in chemosensory organs will be discussed in light of the evolutionary advantage of the coupling of the detoxification system and chemosensory system through GSTs.

Significant influence of four highly conserved amino-acids in lipochaperon-active sHsps on the structure and functions of the Lo18 protein.

To cope with environmental stresses, bacteria have developed different strategies, including the production of small heat shock proteins (sHSP). All sHSPs are described for their role as molecular chaperones. Some of them, like the Lo18 protein synthesized by Oenococcus oeni, also have the particularity of acting as a lipochaperon to maintain membrane fluidity in its optimal state following cellular stresses. Lipochaperon activity is poorly characterized and very little information is available on the domains or amino-acids key to this activity. The aim in this paper is to investigate the importance at the protein structure and function level of four highly conserved residues in sHSP exhibiting lipochaperon activity. Thus, by combining in silico, in vitro and in vivo approaches the importance of three amino-acids present in the core of the protein was shown to maintain both the structure of Lo18 and its functions.

Structure-activity analysis suggests an olfactory function for the unique antennal delta glutathione transferase of Apis mellifera.

Glutathione transferases (GST) are detoxification enzymes that conjugate glutathione to a wide array of molecules. In the honey bee Apis mellifera, AmGSTD1 is the sole member of the delta class of GSTs, with expression in antennae. Here, we structurally and biochemically characterized AmGSTD1 to elucidate its function. We showed that AmGSTD1 can efficiently catalyse the glutathione conjugation of classical GST substrates. Additionally, AmGSTD1 exhibits binding properties with a range of odorant compounds. AmGSTD1 has a peculiar interface with a structural motif we propose to call 'sulfur sandwich'. This motif consists of a cysteine disulfide bridge sandwiched between the sulfur atoms of two methionine residues and is stabilized by CH…S hydrogen bonds and S…S sigma-hole interactions. Thermal stability studies confirmed that this motif is important for AmGSTD1 stability and, thus, could facilitate its functions in olfaction.

Wild-Type α-Synuclein and Variants Occur in Different Disordered Dimers and Pre-Fibrillar Conformations in Early Stage of Aggregation.

α-Synuclein is a 140 amino-acid intrinsically disordered protein mainly found in the brain. Toxic α-synuclein aggregates are the molecular hallmarks of Parkinson's disease. In vitro studies showed that α-synuclein aggregates in oligomeric structures of several 10th of monomers and into cylindrical structures (fibrils), comprising hundred to thousands of proteins, with polymorphic cross-ß-sheet conformations. Oligomeric species, formed at the early stage of aggregation remain, however, poorly understood and are hypothezised to be the most toxic aggregates. Here, we studied the formation of wild-type (WT) and mutant (A30P, A53T, and E46K) dimers of α-synuclein using coarse-grained molecular dynamics. We identified two principal segments of the sequence with a higher propensity to aggregate in the early stage of dimerization: residues 36-55 and residues 66-95. The transient α-helices (residues 53-65 and 73-82) of α-synuclein monomers are destabilized by A53T and E46K mutations, which favors the formation of fibril native contacts in the N-terminal region, whereas the helix 53-65 prevents the propagation of fibril native contacts along the sequence for the WT in the early stages of dimerization. The present results indicate that dimers do not adopt the Greek key motif of the monomer fold in fibrils but form a majority of disordered aggregates and a minority (9-15%) of pre-fibrillar dimers both with intra-molecular and intermolecular ß-sheets. The percentage of residues in parallel ß-sheets is by increasing order monomer < disordered dimers < pre-fibrillar dimers. Native fibril contacts between the two monomers are present in the NAC domain for WT, A30P, and A53T and in the N-domain for A53T and E46K. Structural properties of pre-fibrillar dimers agree with rupture-force atomic force microscopy and single-molecule Förster resonance energy transfer available data. This suggests that the pre-fibrillar dimers might correspond to the smallest type B toxic oligomers. The probability density of the dimer gyration radius is multi-peaks with an average radius that is 10 Å larger than the one of the monomers for all proteins. The present results indicate that even the elementary α-synuclein aggregation step, the dimerization, is a complicated phenomenon that does not only involve the NAC region.

How main-chains of proteins explore the free-energy landscape in native states.

Understanding how a single native protein diffuses on its free-energy landscape is essential to understand protein kinetics and function. The dynamics of a protein is complex, with multiple relaxation times reflecting a hierarchical free-energy landscape. Using all-atom molecular dynamics simulations of an alpha/beta protein (crambin) and a beta-sheet polypeptide (BS2) in their "native" states, we demonstrate that the mean-square displacement of dihedral angles, defined by 4 successive C(alpha) atoms, increases as a power law of time, t(alpha), with an exponent alpha between 0.08 and 0.39 (alpha = 1 corresponds to Brownian diffusion), at 300 K. Residues with low exponents are located mainly in well-defined secondary elements and adopt 1 conformational substate. Residues with high exponents are found in loops/turns and chain ends and exist in multiple conformational substates, i.e., they move on multiple-minima free-energy profiles.

Missense Mutations Modify the Conformational Ensemble of the α-Synuclein Monomer Which Exhibits a Two-Phase Characteristic.

α-Synuclein is an intrinsically disordered protein occurring in different conformations and prone to aggregate in ß-sheet structures, which are the hallmark of the Parkinson disease. Missense mutations are associated with familial forms of this neuropathy. How these single amino-acid substitutions modify the conformations of wild-type α-synuclein is unclear. Here, using coarse-grained molecular dynamics simulations, we sampled the conformational space of the wild type and mutants (A30P, A53P, and E46K) of α-synuclein monomers for an effective time scale of 29.7 ms. To characterize the structures, we developed an algorithm, CUTABI (CUrvature and Torsion based of Alpha-helix and Beta-sheet Identification), to identify residues in the α-helix and ß-sheet from Cα -coordinates. CUTABI was built from the results of the analysis of 14,652 selected protein structures using the Dictionary of Secondary Structure of Proteins (DSSP) algorithm. DSSP results are reproduced with 93% of success for 10 times lower computational cost. A two-dimensional probability density map of α-synuclein as a function of the number of residues in the α-helix and ß-sheet is computed for wild-type and mutated proteins from molecular dynamics trajectories. The density of conformational states reveals a two-phase characteristic with a homogeneous phase (state B, ß-sheets) and a heterogeneous phase (state HB, mixture of α-helices and ß-sheets). The B state represents 40% of the conformations for the wild-type, A30P, and E46K and only 25% for A53T. The density of conformational states of the B state for A53T and A30P mutants differs from the wild-type one. In addition, the mutant A53T has a larger propensity to form helices than the others. These findings indicate that the equilibrium between the different conformations of the α-synuclein monomer is modified by the missense mutations in a subtle way. The α-helix and ß-sheet contents are promising order parameters for intrinsically disordered proteins, whereas other structural properties such as average gyration radius, R g , or probability distribution of R g cannot discriminate significantly the conformational ensembles of the wild type and mutants. When separated in states B and HB, the distributions of R g are more significantly different, indicating that global structural parameters alone are insufficient to characterize the conformational ensembles of the α-synuclein monomer.

Investigation of Phosphorylation-Induced Folding of an Intrinsically Disordered Protein by Coarse-Grained Molecular Dynamics.

Apart from being the most common mechanism of regulating protein function and transmitting signals throughout the cell, phosphorylation has an ability to induce disorder-to-order transition in an intrinsically disordered protein. In particular, it was shown that folding of the intrinsically disordered protein, eIF4E-binding protein isoform 2 (4E-BP2), can be induced by multisite phosphorylation. Here, the principles that govern the folding of phosphorylated 4E-BP2 (pT37pT46 4E-BP218-62) are investigated by analyzing canonical and replica exchange molecular dynamics trajectories, generated with the coarse-grained united-residue force field, in terms of local and global motions and the time dependence of formation of contacts between Cαs of selected pairs of residues. The key residues involved in the folding of the pT37pT46 4E-BP218-62 are elucidated by this analysis. The correlations between local and global motions are identified. Moreover, for a better understanding of the physics of the formation of the folded state, the experimental structure of the pT37pT46 4E-BP218-62 is analyzed in terms of a kink (heteroclinic standing wave solution) of a generalized discrete nonlinear Schrödinger equation. It is shown that without molecular dynamics simulations the kinks are able to identify not only the phosphorylated sites of protein, the key players in folding, but also the reasons for the weak stability of the pT37pT46 4E-BP218-62.

Effect of hydrogen bonds on polarizability of a water molecule in (H2O)(N) (N = 6, 10, 20) isomers.

Polarizabilities of the low-lying isomers of (H(2)O)(N) (N = 6, 10, 20) clusters were computed by using Density Functional Theory. The global polarizabilities of the water isomers were found to depend mainly on the total number of water molecules rather than their cluster structures. We show that this result hides in fact a strong heterogeneity of the molecular polarizability within the different isomers. The global polarizability of a cluster was divided into a sum of molecular contributions by using the Hirshfeld partitioning scheme. We reveal that the value of the local polarizability of a molecule in the cluster is correlated with the number and type of the hydrogen bonds (HB) the molecule forms. Consequently, the molecules located in the interior of the cluster, which usually form more HBs, have smaller molecular polarizabilities than the molecules at the surface, which form less HBs. The contribution of intermolecular interaction to the global polarizability was analyzed by decomposing the cluster polarizability into intra- and inter-molecular contributions. The former measures the polarization within the molecular basin against the external electric field, while the latter is described as the sum of polarizability caused by charge flow through the HBs. These two contributions vary with the cluster size: the intermolecular contribution decreases with the cluster size on the contrary of the intramolecular contribution which increases.

Investigation of protein folding by coarse-grained molecular dynamics with the UNRES force field.

Coarse-grained molecular dynamics simulations offer a dramatic extension of the time-scale of simulations compared to all-atom approaches. In this article, we describe the use of the physics-based united-residue (UNRES) force field, developed in our laboratory, in protein-structure simulations. We demonstrate that this force field offers about a 4000-times extension of the simulation time scale; this feature arises both from averaging out the fast-moving degrees of freedom and reduction of the cost of energy and force calculations compared to all-atom approaches with explicit solvent. With massively parallel computers, microsecond folding simulation times of proteins containing about 1000 residues can be obtained in days. A straightforward application of canonical UNRES/MD simulations, demonstrated with the example of the N-terminal part of the B-domain of staphylococcal protein A (PDB code: 1BDD, a three-alpha-helix bundle), discerns the folding mechanism and determines kinetic parameters by parallel simulations of several hundred or more trajectories. Use of generalized-ensemble techniques, of which the multiplexed replica exchange method proved to be the most effective, enables us to compute thermodynamics of folding and carry out fully physics-based prediction of protein structure, in which the predicted structure is determined as a mean over the most populated ensemble below the folding-transition temperature. By using principal component analysis of the UNRES folding trajectories of the formin-binding protein WW domain (PDB code: 1E0L; a three-stranded antiparallel beta-sheet) and 1BDD, we identified representative structures along the folding pathways and demonstrated that only a few (low-indexed) principal components can capture the main structural features of a protein-folding trajectory; the potentials of mean force calculated along these essential modes exhibit multiple minima, as opposed to those along the remaining modes that are unimodal. In addition, a comparison between the structures that are representative of the minima in the free-energy profile along the essential collective coordinates of protein folding (computed by principal component analysis) and the free-energy profile projected along the virtual-bond dihedral angles gamma of the backbone revealed the key residues involved in the transitions between the different basins of the folding free-energy profile, in agreement with existing experimental data for 1E0L .

Origin of the size-dependence of the polarizability per atom in heterogeneous clusters: The case of AlP clusters.

An analysis of the atomic polarizabilities α in stoichiometric aluminum phosphide clusters, computed at the MP2 and density functional theory (DFT) levels, the latter using the B3LYP functional, and partitioned using the classic and iterative versions of the Hirshfeld method, is presented. Two sets of clusters are examined: the ground-state Al(n)P(n) clusters (n=2-9) and the prolate clusters (Al(2)P(2))(N) and (Al(3)P(3))(N) (N≤6). In the ground-state clusters, the mean polarizability per atom, i.e., α/2n, decreases with the cluster size but shows peaks at n=5 and at n=7. We demonstrate that these peaks can be explained by a large polarizability of the Al atoms and by a low polarizability of the P atoms in Al(5)P(5) and Al(7)P(7) due to the presence of homopolar bonds in these clusters. We show indeed that the polarizability of an atom within an Al(n)P(n) cluster depends on the cluster size and the heteropolarity of the bonds it forms within the cluster, i.e., on the charges of the atoms. The polarizabilities of the fragments Al(2)P(2) and Al(3)P(3) in the prolate clusters were found to depend mainly on their location within the cluster. Finally, we show that the iterative Hirshfeld method is more suitable than the classic Hirshfeld method for describing the atomic polarizabilities and the atomic charges in clusters with heteropolar bonds, although both versions of the Hirshfeld method lead to similar conclusions.

Variational Principle for Eigenmodes of Reactivity in Conceptual Density Functional Theory.

In conceptual density functional theory, reactivity indexes as the Fukui function, the global hardness/softness, and hardness/softness kernels are fundamental linear responses extensively studied to predict the nucleophilic and electrophilic propensities of atoms in molecules. We demonstrate that the hardness/softness kernels of an isolated system can be expanded in eigenmodes, solutions of a variational principle. These modes are divided into two groups: the polarization modes and the charging modes. The eigenvectors of the polarization modes are orthogonal to the Fukui function and can be interpreted as densities induced at a constant chemical potential. The charging modes of an isolated system are associated with virtual charge transfers weighted by the Fukui function and obey an exact nontrivial sum rule. The exact relation between these charging eigenmodes and those of the polarizability kernel is established. The physical interpretation of the modes is discussed. Applications of the present findings to the Thomas-Fermi and von Weizacker kinetic energy functionals are presented. For a confined free quantum gas, described by the von Weizacker kinetic energy functional, we succeed to derive an approximate analytical solution for the Fukui function and for hardness/softness and polarizability kernels. Finally, we indicate how numerical calculations of the hardness kernel of a molecule could be performed from the Kohn-Sham orbitals.

Nanopore sensing of single-biomolecules: a new procedure to identify protein sequence motifs from molecular dynamics.

Solid-state nanopores have emerged as one of the most versatile tools for single-biomolecule detection and characterization. Nanopore sensing is based on the measurement of variations in ionic current as charged biomolecules immersed in an electrolyte translocate through nanometer-sized channels, in response to an external voltage applied across the membrane. The passage of a biomolecule through a pore yields information about its structure and chemical properties, as demonstrated experimentally with sub-microsecond temporal resolution. However, extracting the sequence of a biomolecule without the information about its position remains challenging due to the fact there is a large variability of sensing events recorded. In this paper, we performed microsecond time scale all-atom non-equilibrium Molecular Dynamics (MD) simulations of peptide translocation (motifs of alpha-synuclein, associated with Parkinson's disease) through single-layer MoS2 nanopores. First, we present an analysis based on the current threshold to extract and characterize meaningful sensing events from ionic current time series computed from MD. Second, a mechanism of translocation is established, for which side chains of each amino acid are oriented parallel to the electric field when they are translocating through the pore and perpendicular otherwise. Third, a new procedure based on the permutation entropy (PE) algorithm is detailed to identify protein sequence motifs related to ionic current drop speed. PE is a technique used to quantify the complexity of a given time series and it allows the detection of regular patterns. Here, PE patterns were associated with protein sequence motifs composed of 1, 2 or 3 amino acids. Finally, we demonstrate that this very promising procedure allows the detection of biological mutations and could be tested experimentally, despite the fact that reconstructing the sequence information remains unachievable at this time.