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 Randić 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.

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 β-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 β-sheet from C^α-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 β-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, β-sheets) and a heterogeneous phase (state HB, mixture of α-helices and β-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 β-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.

Description of Participants in the "Atout Age Mobility" Prevention Workshops at the University Hospital Center of La Réunion: A Prospective Study

INTRODUCTION

As the population ages, loss of autonomy is becoming a priority public health issue. "Atout Age Mobility" prevention interventions for seniors aim to limit frailty, which is a predictive and reversible factor in the loss of autonomy and disability.

OBJECTIVES

The objective of this study is to describe the impact of these interventions on the physical performance and quality of life of a pilot sample of participants.

DESIGN

We conducted a prospective study named 5P PILOT with 3 months of follow up.

SETTINGS

Subjects were recruited by convenience sampling from participants in the "Atout Age Mobility" workshops at Saint Joseph from 04/09/2017 to 29/01/2019.

PARTICIPANTS

Retired people over 55 years old with no contraindications to physical activity recruited from participants in the "Atout Age Mobility" workshops in Saint Joseph. Intervention(s) (for clinical trials) or Exposure(s) (for observational studies): All participants completed 12 weeks of physical exercise called the "Atout Age Mobility" workshop, which lasted 60 minutes each week and was supervised by physical activity coaches. Main Outcome(s) and Measure(s): Physical performance was assessed by Short physical performance battery (SPPB), 10-m gait speed and grip strength measurement. Quality of life through the SF-36 test.

RESULTS

Ninety-six patients were included and 55 (57.3%) completed the study. There was a significant improvement in gait speed (1.35±0.26m/s vs. 1.27±0.24m/s; p=0.008). There was no significant change in SF-36, grip strength dominant arm and SPPB at the 0.01 significance level.

CONCLUSION

The "Atout Ages Mobility" workshops seem to significantly improve gait speed but not other aspects of physical performance or quality of life.

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.

Curvature and Torsion of Protein Main Chain as Local Order Parameters of Protein Unfolding

Thermal protein unfolding resembles a global (two-state) phase transition. At the local scale, protein unfolding is, however, heterogeneous and probe dependent. Here, we consider local order parameters defined by the local curvature and torsion of the protein main chain. Because chemical shifts (CS's) measured by NMR spectroscopy are extremely sensitive to the local atomic environment, CS has served as a local probe of thermal unfolding of proteins by varying the position of the atomic isotope along the amino acid sequence. The variation of the CS of each C^α atom along the sequence as a function of the temperature defines a local heat-induced denaturation curve. We demonstrate that these local heat-induced denaturation curves mirror the local protein nativeness defined by the free energy landscape of the local curvature and torsion of the protein main chain described by the C^α-C^α virtual bonds. Comparison between molecular dynamics simulations and CS data of the gpW protein demonstrates that some local native states defined by the local curvature and torsion of the main chain, mainly located in secondary structures, are coupled to each other whereas others, mainly located in flexible protein segments, are not. Consequently, CS's of some residues are faithful reporters of global protein unfolding, with heat-induced denaturation curves similar to the average global one, whereas other residues remain silent about the protein unfolded state. For the latter, the local deformation of the protein main chain, characterized by its local curvature and torsion, is not cooperatively coupled to global unfolding.

Data on the expression of GSTE1 and GSTE7 in Drosophila chemosensory organs after isothiocyanate exposure

The data presented in this article are related to the research article entitled "Characterization of a Drosophila glutathione transferase involved in isothiocyanate detoxification." (Gonzalez et al., 2018) [1]. This article includes the expression level of Drosophila melanogaster GSTE1 and GSTE7 in chemosensory male tissues and the expression level of the mRNAs coding for the same enzymes after a PEITC exposure in food.

Characterization of a Drosophila glutathione transferase involved in isothiocyanate detoxification

Glutathione transferases (GSTs) are ubiquitous key enzymes that catalyse the conjugation of glutathione to xenobiotic compounds in the detoxification process. GSTs have been proposed to play a dual role in the signal termination of insect chemodetection by modifying odorant and tasting molecules and by protecting the chemosensory system. Among the 40 GSTs identified in Drosophila melanogaster, the Delta and Epsilon groups are insect-specific. GSTs Delta and Epsilon may have evolved to serve in detoxification, and have been associated with insecticide resistance. Here, we report the heterologous expression and purification of the D. melanogaster GST Delta 2 (GSTD2). We investigated the capacity of GSTD2 to bind tasting molecules. Among them, we found that isothiocyanates (ITC), insecticidal compounds naturally present in cruciferous plant and perceived as bitter, are good substrates for GSTD2. The X-ray structure of GSTD2 was solved, showing the absence of the classical Ser catalytic residue, conserved in the Delta and Epsilon GSTs. Using molecular dynamics, the interaction of ITC with the GSTD2 three-dimensional structure is analysed and discussed. These findings allow us to consider a biological role for GSTD2 in chemoperception, considering GSTD2 expression in the chemosensory organs and the potential consequences of insect exposure to ITC.

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.

Fingerprints of Conformational States of Human Hsp70 at Sub-THz Frequencies

Large multidomain proteins occur in different conformational states to function. Detection and monitoring of these different structural states are of crucial interest for understanding the mechanics of proteins. Using computational methods, we show that different protein conformational states of the two-domain 70 kDa human Heat-shock protein (hHsp70), with similar vibrational density of states, lead to remarkably different far-IR spectra at acoustical frequencies (ν < 300 GHz). We found that the slow damped motions of the positively charged residues of hHsp70 contribute the most to collective IR active modes at low frequencies (ν < 300 GHz). We predicted that different structural states and functional modes of large proteins, such as hHsp70, might be detected in the sub-THz frequency range by single-molecule spectroscopy similar to the recent extraordinary acoustic Raman spectroscopy (Wheaton S.; Nat. Photonics2015, 9, 68-72).

Theoretical Insights into Sub-Terahertz Acoustic Vibrations of Proteins Measured in Single-Molecule Experiments

Proteins are an important class of nanobioparticles with acoustical modes in the sub-THz frequency range. There is considerable interest to measure and establish the role of these acoustical vibrations for biological function. So far, the technique providing the most detailed information about the acoustical modes of proteins is the very recent Extraordinary Acoustic Raman (EAR) spectroscopy. In this technique, proteins are trapped in nanoholes and excited by two optical lasers of slightly different wavelengths producing an electric field at low frequency (<100 GHz). We demonstrate that the acoustical modes of proteins studied by EAR spectroscopy are both infrared- and Raman-active modes, and we provided interpretation of the spectroscopic fingerprints measured at the single-molecule level. A combination of the present calculations with techniques based on the excitation of a single nanobioparticle by an electric field, such as EAR spectroscopy, should provide a wealth of information on the role of molecular dynamics for biological function.

Beyond static structures: Putting forth REMD as a tool to solve problems in computational organic chemistry

Computational studies of organic systems are frequently limited to static pictures that closely align with textbook style presentations of reaction mechanisms and isomerization processes. Of course, in reality chemical systems are dynamic entities where a multitude of molecular conformations exists on incredibly complex potential energy surfaces (PES). Here, we borrow a computational technique originally conceived to be used in the context of biological simulations, together with empirical force fields, and apply it to organic chemical problems. Replica-exchange molecular dynamics (REMD) permits thorough exploration of the PES. We combined REMD with density functional tight binding (DFTB), thereby establishing the level of accuracy necessary to analyze small molecular systems. Through the study of four prototypical problems: isomer identification, reaction mechanisms, temperature-dependent rotational processes, and catalysis, we reveal new insights and chemistry that likely would be missed using static electronic structure computations. The REMD-DFTB methodology at the heart of this study is powered by i-PI, which efficiently handles the interface between the DFTB and REMD codes.

Human Inducible Hsp70: Structures, Dynamics, and Interdomain Communication from All-Atom Molecular Dynamics Simulations

The 70 kDa human heat shock protein is a major molecular chaperone involved in de novo folding of proteins in vivo and refolding of proteins under stress conditions. Hsp70 is related to several "misfolding diseases" and other major pathologies, such as cancer, and is a target for new therapies. Hsp70 is comprised of two main domains: an N-terminal nucleotide binding domain (NBD) and a C-terminal substrate protein binding domain (SBD). The chaperone function of Hsp70 is based on an allosteric mechanism. Binding of ATP in NBD decreases the affinity of the substrate for SBD, and hydrolysis of ATP is promoted by binding of polypeptide segments in the SBD. No complete structure of human Hsp70 is known. Here, we report two models of human Hsp70, constructed by homology with Saccharomyces cerevisiae cochaperone protein Hsp110 (open model) and with Escherichia coli 70 kDa DnaK (closed model) and relaxed for several tens to hundreds of nanoseconds by using all-atom molecular dynamics simulations in explicit solvent. We obtain two stable states, Hsp70 with SBD open and SBD closed, which agree with experimental and structural information for ATP-Hsp70 and ADP-Hsp70, respectively. The dynamics of the transition from the open to closed states is investigated with a coarse-grained model and normal-mode analysis. The results show that the conformational change between the two states can be represented by a relatively small number of collective modes which involved major conformational changes in the two domains. These modes provide a mechanistic representation of the communication between NBD and SBD and allow us to identify subdomains and residues that appear to have a critical role in the conformational change mechanism that guides the chaperoning cycle of Hsp70.

Exploiting Dispersion-Driven Aggregators as a Route to New One-Dimensional Organic Nanowires

The efficiency of charge carrier mobility in organic semiconductors is heavily dependent upon the long-range organization (i.e., morphology) and the local relative arrangement of the transporting molecules. Here, we exploit London dispersion forces as a design principle to construct compact one-dimensional (1-D) assemblies of quaterthiophene cores. We demonstrate that the substitution of quaterthiophene with dispersion-driven aggregators (e.g., [7]ladderanes, hydrogenated pyrenes, etc.) leads to the formation of highly stable and tightly packed 1-D supramolecular assemblies with electronic compactness superior to that of quaterthiophene crystals. Tunability and even tighter stacking arrangements can be achieved by inserting molecular linkers between the quaterthiophene fragments and the dispersion-driven components. The proposed 1-D nanowires represent an original route toward the rational design of efficient organic semiconductors.

On-Surface Synthesis of BN-Substituted Heteroaromatic Networks

We report on the bottom-up fabrication of BN-substituted heteroaromatic networks achieved by surface-assisted polymerization and subsequent cyclodehydrogenation of specifically designed BN-substituted precursor monomers based on a borazine core structural element. To get insight into the cyclodehydrogenation pathway and the influence of molecular flexibility on network quality, two closely related precursor monomers with different degrees of internal cyclodehydrogenation have been employed. Scanning tunneling microscopy shows that, for both monomers, surface-assisted cyclodehydrogenation allows for complete monomer cyclization and the formation of covalently interlinked BN-substituted polyaromatic hydrocarbon networks on the Ag(111) surface. In agreement with experimental observations, density functional theory calculations reveal a significantly lower energy barrier for the cyclodehydrogenation of the conformationally more rigid precursor monomer, which is also reflected in a higher degree of long-range order of the obtained heteroaromatic network. Our proof-of-concept study will allow for the fabrication of atomically precise substitution patterns within BNC heterostructures.

DNA Translocation in Nanometer Thick Silicon Nanopores

Solid-state nanopores are single-molecule sensors that detect changes in ionic conductance (ΔG) when individual molecules pass through them. Producing high signal-to-noise ratio for the measurement of molecular structure in applications such as DNA sequencing requires low noise and large ΔG. The latter is achieved by reducing the nanopore diameter and membrane thickness. While the minimum diameter is limited by the molecule size, the membrane thickness is constrained by material properties. We use molecular dynamics simulations to determine the theoretical thickness limit of amorphous Si membranes to be ∼1 nm, and we designed an electron-irradiation-based thinning method to reach that limit and drill nanopores in the thinned regions. Double-stranded DNA translocations through these nanopores (down to 1.4 nm in thickness and 2.5 nm in diameter) provide the intrinsic ionic conductance detection limit in Si-based nanopores. In this regime, where the access resistance is comparable to the nanopore resistance, we observe the appearance of two conductance levels during molecule translocation. Considering the overall performance of Si-based nanopores, our work highlights their potential as a leading material for sequencing applications.

Temperature-dependent and bistable current-voltage measurements in zinc porphyrin molecular junctions

We report bistability in current-voltage curves from di(PEP)PorZn in an electromigrated molecular junction. Bistability was observed at ±0.3 V at 300 K but did not occur at 4 K. No bistability was identified at 300 K for another porphyrin molecule (di(Xyl)PorZn), where the phenyl-ethnyl-phenyl (PEP) side groups were replaced with a flexible p-xylene. Molecular dynamics simulations show that bistability may be due to conformation changes related to the fluctuation of the dihedral angle surrounding the zinc and/or the rotation of the porphyrin central plane of the molecule. Results suggest that other mechanisms may play a role in the current-voltage characteristics observed.

Tunable water desalination across graphene oxide framework membranes

The performance of graphene oxide framework (GOF) membranes for water desalination is assessed using classical molecular dynamics (MD) simulations. The coupling between water permeability and salt rejection of GOF membranes is studied as a function of linker concentration n, thickness h and applied pressure ΔP. The simulations reveal that water permeability in GOF-(n,h) membranes can be tuned from ∼5 (n = 32 and h = 6.5 nm) to 400 L cm(-2) day(-1) MPa(-1) (n = 64 and h = 2.5 nm) and follows a Cnh(-αn) law. For a given pore size (n = 16 or 32), water permeability of GOF membranes increases when the pore spacing decreases, whereas for a given pore spacing (n = 32 or 64), water permeability increases by up to two orders of magnitude when the pore size increases. Furthermore, for linker concentrations n ≤ 32, the high water permeability corresponds to a 100% salt rejection, elevating this type of GOF membrane as an ideal candidate for water desalination. Compared to experimental performance of reverse osmosis membranes, our calculations suggest that under the same conditions of applied pressure and characteristics of membranes (ΔP ∼ 10 MPa and h ∼ 100 nm), one can expect a perfect salt rejection coupled to a water permeability two orders of magnitude higher than existing technologies, i.e., from a few cL cm(-2) day(-1) MPa(-1) to a few L cm(-2) day(-1) MPa(-1).

Interfacial properties and design of functional energy materials

CONSPECTUS: The vital importance of energy to society continues to demand a relentless pursuit of energy responsive materials that can bridge fundamental chemical structures at the molecular level and achieve improved functionality and performance. This demand can potentially be realized by harnessing the power of self-assembly, a spontaneous process where molecules or much larger entities form ordered aggregates as a consequence of predominately noncovalent (weak) interactions. Self-assembly is the key to bottom-up design of molecular devices, because the nearly atomic-level control is very difficult to realize in a top-down, for example, lithographic, approach. However, while function in simple systems such as single crystals can often be evaluated a priori, predicting the function of the great variety of self-assembled molecular architectures is complicated by the lack of understanding and control over nanoscale interactions, mesoscale architectures, and macroscale order. To establish a foundation toward delivering practical solutions, it is critical to develop an understanding of the chemical and physical mechanisms responsible for the self-assembly of molecular and hybrid materials on various support substrates. Typical molecular self-assembly involves noncovalent intermolecular and substrate-molecule interactions. These interactions remain poorly understood, due to the combination of many-body interactions compounded by local or collective influences from the substrate atomic lattice and electronic structure. Progress toward unraveling the underlying physicochemical processes that control the structure and macroscopic physical, chemical, mechanical, electrical, and transport properties of materials increasingly requires tight integration of theory, modeling, and simulation with precision synthesis, advanced experimental characterization, and device measurements. Theory, modeling, and simulation can accelerate the process of materials understanding and design by providing atomic level understanding of the underlying physicochemical phenomena (illuminating connections between experiments). It can also provide the ability to explore new materials and conditions before they are realized in the laboratory. With tight integration and feedback with experiment, it becomes feasible to identify promising materials or processes for targeted energy applications. In this Account, we highlight recent advances and success in using an integrated approach based on electronic structure simulations and scanning probe microscopy techniques to study and design functional materials formed from the self-assembly of molecules into supramolecular or polymeric architectures on substrates.

Circadian dosing time dependency in the forearm skin penetration of methyl and hexyl nicotinate

The forearm skin penetration of hydrophilic methyl nicotinate (MN) and lipophilic hexyl nicotinate (HN) was assessed around the clock. The sixteen healthy women (median age: 22 years, weight: 57 kg and height: 162 cm) who volunteered for the study were synchronized with a diurnal activity from 07.00h (+/- 1h) to 23.00h (+/- 1h.30min) and a nocturnal rest before and during the 48h sojourn in air-conditioned rooms (26 degrees C +/- 0.5 degrees C). Both HN (0.5% ethanol solution) and MN (5% ethanol solution) have a vasodilative effect on dermal vessels. The lag time (LT) between the delivery of a fixed volume (10 microliters) of the agent at the skin surface and the beginning of the vasodilatation, detected with a laser-Doppler method, was used to quantify the penetration kinetics. Tests were performed every 4h, at fixed clock hours, over a span of a 40h. Two types of tests were done with each of the agents: fixed site (one site only) and shifted sites (10 different places). Both cosinor and ANOVA have been used for statistical analyses. The shortest LT (fastest penetration) was located around 04.00h. The longest LT (slowest penetration) occurred during the day with a single peak around 13.00h in three of the situations, or two peaks (HN with fixed site). A rather large rhythm amplitude (peak-to-trough difference larger than 50% of the 24h mean LT) was validated.

Internal desynchronization of circadian rhythms and tolerance of shift work

Fifteen male subjects including 12 shift workers (oil refinery operators) volunteered to document circadian rhythms in sleep-wake, grip strength of both hands, peak expiratory flow, heart rate, self-rated drowsiness, fatigue and attention. Each of these variables was measured 4 to 6 times/day for 2 to 3 weeks. In addition, both axillary temperature (with a shielded probe) and wrist activity were almost continuously recorded at 15 min intervals during the same time span. Individual time series were analyzed according to several statistical methods (power spectrum, cosinor, chi 2, etc.), in order to estimate the prominent circadian period tau and to evaluate both individual and subgroup differences with regard to tolerance of shift work, age, duration of shift work. The present study confirms for continuously recorded temperature and wrist activity, grip strength of both hands, heart rate and peak expiratory flow that intolerance of shift work is frequently associated with an internal desynchronization. However, this conclusion cannot be extended to circadian rhythms in self-rated drowsiness, fatigue and attention. The internal desynchronization among several circadian rhythms supports the hypothesis that these latter are driven by several oscillators, with presumable differences between right and left hemispheres as suggested by unequal values of tau in rhythms of both hand grip strength. Since an internal desynchronization can be observed in tolerant shift workers having no complaint, it is likely that symptoms of intolerance are related to the subject's sensitivity to internal desynchronization rather than to the desynchronization itself.