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The second law of thermodynamics, with its positive change of entropy for a system not in equilibrium, defines an arrow of time. Interestingly, also, causality, which is the connection between a cause and an effect, requests a direction of time by definition. It is noted that no other standard physical theories show this property. It is the attempt of this work to connect causality with entropy, which is possible by defining time as the metric of causality. Under this consideration that time appears only through a cause–effect relationship (“measured”, typically, in an apparatus called clock), it is demonstrated that time must be discrete in nature and cannot be continuous as assumed in all standard theories of physics including general and special relativity, and classical physics. The following lines of reasoning include: (i) (mechanical) causality requests that the cause must precede its effect (i.e., antecedence) requesting a discrete time interval >0. (ii) An infinitely small time step d t > 0 is thereby not sufficient to distinguish between cause and effect as a mathematical relationship between the two (i.e., Poisson bracket) will commute at a time interval d t , while not evidently within discrete time steps Δ t . As a consequence of a discrete time, entropy emerges (Riek, 2014) connecting causality and entropy to each other.

The aggregation of proteins into structures known as amyloids is observed in many neurodegenerative diseases, including Alzheimer's disease. Amyloids are composed of pairs of tightly interacting, many stranded and repetitive intermolecular β-sheets, which form the cross-β-sheet structure. This structure enables amyloids to grow by recruitment of the same protein and its repetition can transform a weak biological activity into a potent one through cooperativity and avidity. Amyloids therefore have the potential to self-replicate and can adapt to the environment, yielding cell-to-cell transmissibility, prion infectivity and toxicity.

Nuclear Magnetic Resonance (NMR) spectroscopy is a major technique 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. 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 human intervention. Tested on a 100-protein benchmark comprising 1329 multidimensional NMR spectra, ARTINA demonstrated its ability to solve structures with 1.44 Å 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. The analysis of protein NMR spectra is time-consuming and can occupy a human expert for weeks or months. The researchers in this work present a deep learning-based method that delivers signal positions, chemical shift assignments, and structures of proteins within hours after completion of the NMR measurements.

The spacetime vectors with the Minkowski metric are cornerstones of special relativity, with the Minkowski metric and physical causality invariant under the Lorentz transformation. It is here demonstrated that the Minkowski metric can be reformulated into a metric of (mechanistic) causality through a division of the spacetime vector by the speed of light c , yielding the proper time as the Lorentz‐invariant line element. The proper time is, as such, the metric of physical causality. Consequently, the four‐dimensional manifold is reformulated by exchanging time with the proper time along with the use of the Pythagoras metric, generating a physical causality‐driven special relativity theory with a physical causality—information manifold.

In diseases called tauopathies, misfolded tau proteins form aggregates called fibrils. Fibrils from nine different tauopathies show that tau misfolds in many ways, enabling the diseases to be classified according to fibril structure. Tauopathies classified according to the conformation of tau fibrils.

Parkinson’s disease is a progressive neuropathological disorder that belongs to the class of synucleinopathies, in which the protein alpha-synuclein is found at abnormally high concentrations in affected neurons. Its hallmark are intracellular inclusions called Lewy bodies and Lewy neurites. We here report the structure of cytotoxic alpha-synuclein fibrils (residues 1–121), determined by cryo-electron microscopy at a resolution of 3.4 Å. Two protofilaments form a polar fibril composed of staggered β-strands. The backbone of residues 38 to 95, including the fibril core and the non-amyloid component region, are well resolved in the EM map. Residues 50–57, containing three of the mutation sites associated with familial synucleinopathies, form the interface between the two protofilaments and contribute to fibril stability. A hydrophobic cleft at one end of the fibril may have implications for fibril elongation, and invites for the design of molecules for diagnosis and treatment of synucleinopathies. People with Parkinson’s disease have damaged cells in a part of the brain involved in movement, learning and reward-seeking behaviors. These cells contain blob-like aggregates that contain abnormally high amounts of a protein called alpha-synuclein. It is generally believed that, within these blobs, this protein clusters together into small needles called fibrils. Discerning the structure of a fibril could help researchers to understand both how alpha-synuclein damages brain cells and how diseases like Parkinson’s spread. Biophysicists have attempted to reveal the fibril structure previously. But many of these efforts only looked at short segments of the alpha-synuclein protein. Researchers still need more detailed imagery of the fibrils to confirm previous findings regarding their architecture and ultimately to identify ways to counteract the damage they cause. Guerrero-Ferreira et al. used a technique called cryo-electron microscopy to capture images of frozen fibrils made from a version of human alpha-synuclein that readily aggregates and that is only slightly shorter than the full-length protein. Processing these high-resolution images with computer software then revealed a three-dimensional model of the fibril structure, in which fine details are clearly visible. In the fibril, the proteins cluster to form a helix, similar to a flight of stairs. Each turn of the helix is formed by two alpha-synuclein molecules, facing each other but rotated by almost 180 degrees from one another. The three-dimensional model displays which parts of the protein lie at the core of the helix and thereby stabilize the fibril structure. Guerrero-Ferreira et al. speculate that fibrils may also take alternative forms because common alpha-synuclein mutations, which correlate with disease, would destabilize the observed helical structure. In the future, researchers may be able to use the features of this three-dimensional model to help design molecules that would make the fibrils detectable via medical imaging. This could help doctors to diagnose people with Parkinson’s disease at an earlier stage. Further research is also needed to understand where and how fibrils form, if differences in fibril structures exist within or between patients, possibly leading to different sub-classes of the disease, and how such fibrils interact with and possibly damage human brain cells.

The amylome is the universe of proteins that are capable of forming amyloid-like fibrils. Here we investigate the factors that enable a protein to belong to the amylome. A major factor is the presence in the protein of a segment that can form a tightly complementary interface with an identical segment, which permits the formation of a steric zipper--two self-complementary beta sheets that form the spine of an amyloid fibril. Another factor is sufficient conformational freedom of the self-complementary segment to interact with other molecules. Using RNase A as a model system, we validate our fibrillogenic predictions by the 3D profile method based on the crystal structure of NNQQNY and demonstrate that a specific residue order is required for fiber formation. Our genome-wide analysis revealed that self-complementary segments are found in almost all proteins, yet not all proteins form amyloids. The implication is that chaperoning effects have evolved to constrain self-complementary segments from interaction with each other.

Careful measurements of light scattering can provide information on individual macromolecules and complexes. Young et al. used a light-scattering approach for accurate mass determination of proteins as small as 20 kDa (see the Perspective by Lee and Klenerman). Movies of protein complex association and dissociation were analyzed to extract biophysical parameters from single molecules and assemblies without labeling. Using this approach, the authors determined in vitro kinetics of fibril and aggregate growth and association constants for a complex protein-glycoprotein assembly. Science , this issue p. 423 ; see also p. 378 Light scattering allows dynamic observation of biomolecule mass, interactions, and assembly. The cellular processes underpinning life are orchestrated by proteins and their interactions. The associated structural and dynamic heterogeneity, despite being key to function, poses a fundamental challenge to existing analytical and structural methodologies. We used interferometric scattering microscopy to quantify the mass of single biomolecules in solution with 2% sequence mass accuracy, up to 19-kilodalton resolution, and 1-kilodalton precision. We resolved oligomeric distributions at high dynamic range, detected small-molecule binding, and mass-imaged proteins with associated lipids and sugars. These capabilities enabled us to characterize the molecular dynamics of processes as diverse as glycoprotein cross-linking, amyloidogenic protein aggregation, and actin polymerization. Interferometric scattering mass spectrometry allows spatiotemporally resolved measurement of a broad range of biomolecular interactions, one molecule at a time.

The prebiotic replication of information-coding molecules is a central problem concerning life’s origins. Here, we report that amyloids composed of short peptides can direct the sequence-selective, regioselective and stereoselective condensation of amino acids. The addition of activated DL-arginine and DL-phenylalanine to the peptide RFRFR-NH 2 in the presence of the complementary template peptide Ac-FEFEFEFE-NH 2 yields the isotactic product FRFRFRFR-NH 2 , 1 of 64 possible triple addition products, under conditions in which the absence of template yields only single and double additions of mixed stereochemistry. The templating mechanism appears to be general in that a different amyloid formed by (Orn)V(Orn)V(Orn)V(Orn)V-NH 2 and Ac-VDVDVDVDV-NH 2 is regioselective and stereoselective for N-terminal, L-amino-acid addition while the ornithine-valine peptide alone yields predominantly sidechain condensation products with little stereoselectivity. Furthermore, the templating reaction is stable over a wide range of pH (5.6–8.6), salt concentration (0–4 M NaCl), and temperature (25–90 °C), making the amyloid an attractive model for a prebiotic peptide replicating system. Amyloids may have played an important role in prebiotic molecular evolution but understanding replication of such information-coding molecules is still a problem. Here the authors design a model amyloid substrate and demonstrate sequence regio- and stereoselectivity during template-based replication.

Alzheimer's disease is the most fatal neurodegenerative disorder wherein the process of amyloid-β (Aβ) amyloidogenesis appears causative. Here, we present the 3D structure of the fibrils comprising Aβ(1-42), which was obtained by using hydrogen-bonding constraints from quenched hydrogen/deuterium-exchange NMR, side-chain packing constraints from pairwise mutagenesis studies, and parallel, in-register β-sheet arrangement from previous solid-state NMR studies. Although residues 1-17 are disordered, residues 18-42 form a β-strand-turn-β-strand motif that contains two intermolecular, parallel, in-register β-sheets that are formed by residues 18-26 (β1) and 31-42 (β2). At least two molecules of Aβ(1-42) are required to achieve the repeating structure of a protofilament. Intermolecular side-chain contacts are formed between the odd-numbered residues of strand β1 of the nth molecule and the even-numbered residues of strand β2 of the (n - 1)th molecule. This interaction pattern leads to partially unpaired β-strands at the f ibrillar ends, which explains the sequence selectivity, the cooperativity, and the apparent unidirectionality of Aβ fibril growth. It also provides a structural basis for fibrillization inhibitors.