A derivation of a microscopic entropy and time irreversibility from the discreteness of time

All of the basic microsopic physical laws are time reversible. In contrast, the second law of thermodynamics, which is a macroscopic physical representation of the world, is able to describe irreversible processes in an isolated system through the change of entropy S larger than 0. It is the attempt of the present manuscript to bridge the microscopic physical world with its macrosocpic one with an alternative approach than the statistical mechanics theory of Gibbs and Boltzmann. It is proposed that time is discrete with constant step size. Its consequence is the presence of time irreversibility at the microscopic level if the present force is of complex nature (i.e. not const). In order to compare this discrete time irreversible mechamics (for simplicity a classical, single particle in a one dimensional space is selected) with its classical Newton analog, time reversibility is reintroduced by scaling the time steps for any given time step n by the variable sn leading to the Nose-Hoover Lagrangian. The corresponding Nose-Hoover Hamiltonian comprises a term Ndf *kB*T*ln(sn) (with kB the Boltzmann constant, T the temperature, and Ndf the number of degrees of freedom) which is defined as the microscopic entropy Sn at time point n multiplied by T. Upon ensemble averaging this microscopic entropy Sn in equilibrium for a system which does not have fast changing forces approximates its macroscopic counterpart known from thermodynamics. The presented derivation with the resulting analogy between the ensemble averaged microscopic entropy and its thermodynamic analog suggests that the original description of the entropy by Boltzmann and Gibbs is just an ensemble averaging of the time scaling variable sn which is in equilibrium close to 1, but that the entropy term itself has its root not in statistical mechanics but rather in the discreteness of time

Side chain: backbone projections in aromatic and ASX residues from NMR cross-correlated relaxation

The measurements of cross-correlated relaxation rates between HN-N and Cβ-Cγ intraresidual and sequential dipolar interactions is demonstrated in ASN, ASP and aromatic residues. The experiment can be used for deuterated samples and no additional knowledge such as Karplus parametrizations is required for the analysis. The data constitutes a new type of information since no other method relates the Cβ-Cγ bond to HN-N. Using this method the dominant populations of rotamer states of χ1 can be readily cross checked provided that φ or ψ are known. In addition, dynamics on all timescales can be probed. As opposed to standard dynamics analysis of isolated bonds, the presented observables depend on relative dynamics with an interesting prospect to analyze correlated fluctuations of the two torsion angles φ or ψ with χ1. Experimental rates are compared to single conformer and ensemble representations of GB3 and ubiquitin. In particular, it is found that the recently published ubiquitin ensemble 2k39 improves the agreement obtained for 1UBQ. In general, however, input data restricting ASX and aromatic side chains in structure calculation is sparse highlighting the need for new NMR observable

Rapid protein assignments and structures from raw NMR spectra with the deep learning technique ARTINA

Nuclear Magnetic Resonance (NMR) spectroscopy is one of the major techniques in structural biology with over 11,800 protein structures deposited in the Protein Data Bank. NMR can elucidate structures and dynamics of small and medium size proteins in solution, living cells, and solids, but has been limited by the tedious data analysis process. It typically requires weeks or months of manual work of a trained expert to turn NMR measurements into a protein structure. Automation of this process is an open problem, formulated in the field over 30 years ago. Here, we present a solution to this challenge that enables the completely automated analysis of protein NMR data within hours after completing the measurements. Using only NMR spectra and the protein sequence as input, our machine learning-based method, ARTINA, delivers signal positions, resonance assignments, and structures strictly without any human intervention. Tested on a 100-protein benchmark comprising 1329 multidimensional NMR spectra, ARTINA demonstrated its ability to solve structures with 1.44 {\AA} median RMSD to the PDB reference and to identify 91.36% correct NMR resonance assignments. ARTINA can be used by non-experts, reducing the effort for a protein assignment or structure determination by NMR essentially to the preparation of the sample and the spectra measurements

More than a Rumor Spreads in Parkinson's Disease

As Parkinson's disease progresses, a massive loss of dopaminergic neurons is accompanied by accumulation of alpha-Synuclein (αSyn) neuronal inclusions called Lewy bodies and Lewy neurites. Inclusions first appear in olfactory bulb and enteric neurons then in ascendant neuroanatomical interconnected areas, and finally, in late stages of the disease, Lewy bodies are observed in a substantia nigra pars compacta with clear signs of neuronal loss. It is believed that the spreading of Lewy bodies through the nervous system is a consequence of the cell-to-cell propagation of αSyn, that can occur via sequential steps of secretion and uptake. Certain pathological forms of transmitted αSyn are able to seed endogenous counterparts in healthy recipient cells, thus promoting the self-sustained cycle of inclusion formation, amplification and spreading, that ultimately underlies disease progression. Here we review the cell-to-cell propagation of αSyn focusing on its role in the progression of Parkinson’s disease

Co-expression of LKB1, MO25α and STRADα in bacteria yield the functional and active heterotrimeric complex

The tumour suppressor LKB1 plays a critical role in cell proliferation, polarity and energy metabolism. LKB1 is a Ser/Thr protein kinase that is associated with STRAD and MO25 invivo. Here, we describe the individual expression of the three components of the LKB1 complex using monocistronic vectors and their co-expression using tricistronic vectors that were constructed from monocistronic vectors using a fully modular cloning approach. The data show that among the three individually expressed components of the LKB1 complex, only MO25α can be expressed in soluble form, whereas the other two, LKB1 and STRADα are found almost exclusively in inclusion bodies. However, using the tricistronic vector system, functional LKB1-MO25α-STRADα complex was expressed and purified from soluble extracts by sequential immobilized-metal affinity and heparin chromatography, as shown by Western blotting using specific antibodies. In size exclusion chromatography, MO25α and STRADα exactly co-elute with LKB1 with an apparent molecular weight of the heterotrimeric complex of 160kDa. The specific activity in the peak fraction of the size exclusion chromatography was 250U/mg at approximately 25% purity. As shown by autoradiography, LKB1 and STRADα, both strongly autophosphorylate in vitro. Moreover, recombinant LKB1 complex activates AMPK by phosphorylation of the α-subunit at the Thr-172 site as shown (i) by Western blotting using phospho-specific antibodies after LKB1-dependent phosphorylation, (ii) by LKB1-dependent incorporation of radioactive phosphate into the α-subunit of kinase dead AMPK heterotrimer, and (iii) by activity determination of AMPK. Functional mammalian LKB1 complex is constitutively active, and when enriched from bacteria should prove to be a valuable tool for studying its molecular function and regulatio

Discrete Three-dimensional Representation of Macromolecular Motion from eNOE-based Ensemble Calculation

Three-dimensional structural data and description of dynamics are fundamental to infer and understand protein function. Structure determination by NMR follows well-established protocols while NMR relaxation phenomena provide insights into local molecular dynamics. However, methods to detect concerted motion were not pursued until very recently. Here, we present an ensemble-based structure determination protocol using ensemble-averaged distance restraints obtained from exact NOE (eNOE) rate constants. An application of our protocol to the model protein GB3 established an ensemble of structures that reveals correlated motion across the ?-sheet and concerted motion between the backbone and side chains localized in the core. Furthermore, the data repudiate concerted conformational exchange between the ?-sheet and the ?-helix

13C, 15N Resonance Assignment of Parts of the HET-s Prion Protein in its Amyloid Form

The partial 15N and 13C solid-state NMR resonance assignment of the HET-s prion protein fragment 218-289 in its amyloid form is presented. It is based on experiments measured at MAS frequencies in the range of 20-40kHz using exclusively adiabatic polarization-transfer schemes. The resonance assignment within each residue is based on two-dimensional 13C--13C correlation spectra utilizing the DREAM mixing scheme. The sequential linking of the assigned residues used a set of two- and three-dimensional 15N--13C correlation experiments. Almost all cross peaks visible in the spectra are assigned, but only resonances from 43 of the 78 amino-acid residues could be detected. The missing residues are thought to be highly disordered and/or highly dynamic giving rise to broad resonance lines that escaped detection in the experiments applied. The line widths of the observed resonances are narrow and comparable to line widths observed in micro-crystalline samples. The 43 assigned residues are located in two fragments of about 20 residue

Uncovering the Mechanism of Aggregation of Human Transthyretin.

The tetrameric thyroxine transport protein transthyretin (TTR) forms amyloid fibrils upon dissociation and monomer unfolding. The aggregation of transthyretin has been reported as the cause of the life-threatening transthyretin amyloidosis. The standard treatment of familial cases of TTR amyloidosis has been liver transplantation. Although aggregation-preventing strategies involving ligands are known, understanding the mechanism of TTR aggregation can lead to additional inhibition approaches. Several models of TTR amyloid fibrils have been proposed, but the segments that drive aggregation of the protein have remained unknown. Here we identify β-strands F and H as necessary for TTR aggregation. Based on the crystal structures of these segments, we designed two non-natural peptide inhibitors that block aggregation. This work provides the first characterization of peptide inhibitors for TTR aggregation, establishing a novel therapeutic strategy