A formula for the calculation of the number of Wyckoff sequences of a given length is presented, based on the combinatorics of multisets with finite multiplicities and a generating function approach, assuming a certain space-group type and taking into account the number of non-fixed and fixed Wyckoff positions, respectively. The formula is applied to the 44 distinguishable combinatorial types of the 230 space-group types. A comparison is made between the calculated frequencies of occurrence of Wyckoff sequences of given space-group type and length and the observed ones for actual crystal structures, as retrieved from the Pearson's Crystal Data Crystal Structure Database for Inorganic Compounds.

• Klíčová slova
• Wyckoff sequences, combinatorics,
• Publikační typ
• časopisecké články MeSH

Wyckoff sequences are a way of encoding combinatorial information about crystal structures of a given symmetry. In particular, they offer an easy access to the calculation of a crystal structure's combinatorial, coordinational and configurational complexity, taking into account the individual multiplicities (combinatorial degrees of freedom) and arities (coordinational degrees of freedom) associated with each Wyckoff position. However, distinct Wyckoff sequences can yield the same total numbers of combinatorial and coordinational degrees of freedom. In this case, they share the same value for their Shannon entropy based subdivision complexity. The enumeration of Wyckoff sequences with this property is a combinatorial problem solved in this work, first in the general case of fixed subdivision complexity but non-specified Wyckoff sequence length, and second for the restricted case of Wyckoff sequences of both fixed subdivision complexity and fixed Wyckoff sequence length. The combinatorial results are accompanied by calculations of the combinatorial, coordinational, configurational and subdivision complexities, performed on Wyckoff sequences representing actual crystal structures.

• Klíčová slova
• Shannon entropy, Wyckoff sequences, combinatorics, structural complexity,
• Publikační typ
• časopisecké články MeSH

In this Letter we propose a simple algebraic recursion for the complete one-loop integrands of N-graviton correlators. This formula automatically yields the correct symmetry factors of individual diagrams, taking into account both the graviton and the ghost loop, and seamlessly controlling the related combinatorics.

• Publikační typ
• časopisecké články MeSH

Cardiovascular diseases, such as myocardial infarction, ischemic stroke, and pulmonary embolism, are the most common causes of disability and death worldwide. Blood clot hydrolysis by thrombolytic enzymes and thrombectomy are key clinical interventions. The most widely used thrombolytic enzyme is alteplase, which has been used in clinical practice since 1986. Another clinically used thrombolytic protein is tenecteplase, which has modified epitopes and engineered glycosylation sites, suggesting that carbohydrate modification in thrombolytic enzymes is a viable strategy for their improvement. This comprehensive review summarizes current knowledge on computational and experimental identification of glycosylation sites and glycan identity, together with methods used for their reengineering. Practical examples from previous studies focus on modification of glycosylations in thrombolytics, e.g., alteplase, tenecteplase, reteplase, urokinase, saruplase, and desmoteplase. Collected clinical data on these glycoproteins demonstrate the great potential of this engineering strategy. Outstanding combinatorics originating from multiple glycosylation sites and the vast variety of covalently attached glycan species can be addressed by directed evolution or rational design. Directed evolution pipelines would benefit from more efficient cell-free expression and high-throughput screening assays, while rational design must employ structure prediction by machine learning and in silico characterization by supercomputing. Perspectives on challenges and opportunities for improvement of thrombolytic enzymes by engineering and evolution of protein glycosylation are provided.

• Klíčová slova
• Alteplase, Biopharmaceutical, Cell-free glycoprotein synthesis, Computational design, Desmoteplase, Glycosylation, Protein engineering, Tenecteplase, Thrombolytic, Urokinase,
• MeSH
• fibrinolytika terapeutické užití   MeSH
• glykosylace MeSH
• infarkt myokardu * farmakoterapie   MeSH
• lidé MeSH
• tenektepláza MeSH
• tkáňový aktivátor plazminogenu * MeSH
• Check Tag
• lidé MeSH
• Publikační typ
• časopisecké články MeSH
• práce podpořená grantem MeSH
• přehledy MeSH
• Názvy látek
• fibrinolytika MeSH
• tenektepláza MeSH
• tkáňový aktivátor plazminogenu * MeSH

Two-dimensional transition metal carbides and nitrides (MXenes) are a promising group of materials with a broad palette of applications. Surface terminations are a result of MXene preparation, and post-processing can also lead to partial coverage. Despite applicability and fundamental properties being driven by termination patterns, it is not fully clear how they behave on MXene surfaces with various degrees of surface coverage. Here, as the first step, we used density functional theory to predict possible patterns in prototypic Ti2C MXene, demonstrating the different behavior of the two most frequent terminal atoms, oxygen, and fluorine. Oxygen (with formal charge -2e) prefers a zigzag line both-side adsorption pattern on bare Ti2C, attracting the next adsorbent at a minimal distance. Oxygen defects in fully O-terminated MXene tend to form similar zigzag line vacancy patterns. On the other hand, fluorine (with a formal charge of -1e) prefers one-side flake (island) adsorption on bare Ti2C and a similar desorption style from fully fluorinated Ti2C. The magnetic behavior of the MXene is subsequently driven by the patterns, either compensating locally and holding the global magnetic state of the MXene until some limit (oxygen case) or gradually increasing the total magnetism through summation of local effects (fluorine case). The systematic combinatoric study of Ti2CTx with various coverages (0 ≤ x ≤ 2) of distinct terminal atoms T = O or F brings encouraging possibilities of tunable behavior of MXenes and provides useful guidance for its modeling towards electronic nanodevices.

• Publikační typ
• časopisecké články MeSH

ATLAS has measured two-particle correlations as a function of the relative azimuthal angle, Δϕ, and pseudorapidity, Δη, in sqrt[s]=13 and 2.76 TeV pp collisions at the LHC using charged particles measured in the pseudorapidity interval |η|<2.5. The correlation functions evaluated in different intervals of measured charged-particle multiplicity show a multiplicity-dependent enhancement at Δϕ∼0 that extends over a wide range of Δη, which has been referred to as the "ridge." Per-trigger-particle yields, Y(Δϕ), are measured over 2<|Δη|<5. For both collision energies, the Y(Δϕ) distribution in all multiplicity intervals is found to be consistent with a linear combination of the per-trigger-particle yields measured in collisions with less than 20 reconstructed tracks, and a constant combinatoric contribution modulated by cos(2Δϕ). The fitted Fourier coefficient, v_{2,2}, exhibits factorization, suggesting that the ridge results from per-event cos(2ϕ) modulation of the single-particle distribution with Fourier coefficients v_{2}. The v_{2} values are presented as a function of multiplicity and transverse momentum. They are found to be approximately constant as a function of multiplicity and to have a p_{T} dependence similar to that measured in p+Pb and Pb+Pb collisions. The v_{2} values in the 13 and 2.76 TeV data are consistent within uncertainties. These results suggest that the ridge in pp collisions arises from the same or similar underlying physics as observed in p+Pb collisions, and that the dynamics responsible for the ridge has no strong sqrt[s] dependence.

• Publikační typ
• časopisecké články MeSH