This work poses and partially explores an astrobiological hypothesis: might polymeric sulfur and phosphorus-based oxides form heteropolymers in the acidic cloud decks of Venus’ atmosphere? Following an introduction to the emerging field of computational astrobiology, we demonstrate the use of quantum chemical methods to evaluate basic properties of a hypothetical carbon-free heteropolymer that might be sourced from feedstock in the Venusian atmosphere. Our modeling indicates that R-substituted polyphosphoric sulfonic ester polymers may form via multiple thermodynamically favorable pathways and exhibit sufficient kinetic stability to persist in the Venusian clouds. Their thermodynamic stability compares favorably to polypeptides, whose formation is slightly thermodynamically unfavored relative to amino acids in most known abiotic conditions. We propose a combined approach of vibrational spectroscopy and mass spectrometry to search for related materials in Venus’s atmosphere but note that none of the currently planned missions are well suited for their detection. While predicted Ultraviolet–Visible spectra suggest that the studied polymers are unlikely candidates for Venus’s unidentified UV absorbers, the broader possibility of sulfuric acid–based chemistry supporting alternative biochemistries challenges the traditional carbon-centric models of life. We argue that such unconventional lines of inquiry are warranted in the search for life beyond Earth.

Single-molecule methods offer powerful insights into DNA-protein interactions at the individual DNA molecule level. We developed an automated, high-throughput nanofluidic imaging platform to characterize DNA-protein complexes in solution. The platform uses a nanofluidic chip with 10 sets of nanochannels where thousands of DNA molecules can be simultaneously analyzed in different conditions. Using this approach, we investigate Rok, a multifunctional Bacillus subtilis protein involved in genome organization and transcription regulation. Our findings confirm the DNA-condensing activity of Rok, likely attributed to its ability to bridge distant DNA segments. Additionally, Rok promotes the hybridization of 12 base complementary single-stranded DNA overhangs, suggesting a potential role in homology search during recombination. Rok also displays sequence-selective binding, preferentially associating with adenine and thymine-rich (AT-rich) DNA regions. To explore the structural features of Rok underlying these activities and test our nanofluidic system further, we compare wild-type Rok with two variants: ∆Rok, lacking the neutral part of the internal linker, and sRok, a naturally occurring variant without the linker. This comparison highlights the role of the linker in hybridization, i.e., interaction with single-stranded DNA. Together, these findings enhance our understanding of Rok-mediated DNA dynamics and establish single-molecule nanofluidics as a powerful tool for high-throughput studies of DNA–protein interactions.

Given a self-morphism $\phi$ on a projective variety defined over a number field k, we prove two results which bound the largest iterate of $\phi$ whose evaluation at P is quasi-integral with respect to a divisor D, uniformly across P defined over a field of bounded degree over k. The first result applies when the pullback of D by some iterate of $\phi$ breaks up into enough irreducible components which are numerical multiples of each other. The proof uses Le’s algebraic-point version of a result of Ji–Yan–Yu, which is based on Schmidt subspace theorem. The second result applies more generally but relies on a deep conjecture by Vojta for algebraic points. The second result is an extension of a recent result of Matsuzawa, based on the theory of asymptotic multiplicity. Both results are generalisations of Hsia–Silverman, which treated the case of morphisms on ${\mathbb{P}}^1$.

A classical result of Erdős, Lovász and Spencer from the late 1970s asserts that the dimension of the feasible region of densities of graphs with at most k vertices in large graphs is equal to the number of non-trivial connected graphs with at most k vertices. Indecomposable permutations play the role of connected graphs in the realm of permutations, and Glebov et al. showed that pattern densities of indecomposable permutations are independent, i.e., the dimension of the feasible region of densities of permutation patterns of size at most k is at least the number of non-trivial indecomposable permutations of size at most k. However, this lower bound is not tight already for $k=3$. We prove that the dimension of the feasible region of densities of permutation patterns of size at most k is equal to the number of non-trivial Lyndon permutations of size at most k. The proof exploits an interplay between algebra and combinatorics inherent to the study of Lyndon words.

Protein circular dichroism (CD) and infrared absorbance (IR) spectra are widely used to estimate the secondary structure content of proteins in solution. A range of algorithms have been used for CD analysis (SELCON, CONTIN, CDsstr, SOMSpec) and some of these have been applied to IR data, though IR is more commonly analysed by bandfitting or statistical approaches. In this work we provide a Python version of SELCON3 and explore how to combine CD and IR data to best effect. We used CD data in Δε/amino acid residue and scaled the IR spectra to similar magnitudes. Normalising the IR amide I spectra scaled to a maximum absorbance of 15 gives best general performance. Combining CD and IR improves predictions for both helix and sheet by ~2% and helps identify anomalously large errors for high helix proteins such as haemoglobin when using IR data alone and high sheet proteins when using CD data alone.

Retinylidene proteins are retinal-binding light-sensitive proteins found in organisms ranging from microbes to human. Microbial opsins have been utilized in optogenetics, while animal opsins are essential for vision and light-dependent metabolic functions. However, retinylidene proteins have hydrophobic transmembrane (TM) domains, which makes them challenging to study. In this structural and functional bioinformatics study, I use the QTY (glutamine, threonine, tyrosine) code to design water-soluble QTY analogues of retinylidene proteins, including nine human and three microbial opsins. I provide superpositions of the AlphaFold3-predicted hydrophobic native proteins and their water-soluble QTY analogues, and experimentally determined structures when available. I also provide a comparison of surface hydrophobicity of the variants. Despite significant changes to the protein sequence (35.53–50.24% in the TM domain), protein characteristics and structures are well preserved. Furthermore, I run molecular dynamics (MD) simulations of native and QTY-designed OPN2 (rhodopsin) and analyze their response to the isomerization of 11-cis-retinal to all-trans-retinal. The results show that the QTY analogue has similar functional behavior to the native protein. The findings of this study indicate that the QTY code can be used as a robust tool to design water-soluble retinylidene proteins. These have potential applications in protein studies, therapeutic treatments, and bioengineering.

DNA unzipping by nanopore translocation has implications in diverse contexts, from polymer physics to single-molecule manipulation to DNA–enzyme interactions in biological systems. Here we use molecular dynamics simulations and a coarse-grained model of DNA to address the nanopore unzipping of DNA filaments that are knotted. This previously unaddressed problem is motivated by the fact that DNA knots inevitably occur in isolated equilibrated filaments and in vivo. We study how different types of tight knots in the DNA segment just outside the pore impact unzipping at different driving forces. We establish three main results. First, knots do not significantly affect the unzipping process at low forces. However, knotted DNAs unzip more slowly and heterogeneously than unknotted ones at high forces. Finally, we observe that the microscopic origin of the hindrance typically involves two concurrent causes: the topological friction of the DNA chain sliding along its knotted contour and the additional friction originating from the entanglement with the newly unzipped DNA. The results reveal a previously unsuspected complexity of the interplay of DNA topology and unzipping, which should be relevant for interpreting nanopore-based single-molecule unzipping experiments and improving the modeling of DNA transactions in vivo.

Human mitochondrial Complex I is one of the largest multi-subunit membrane protein megacomplexes, which plays a critical role in oxidative phosphorylation and ATP production. It is also involved in many neurodegenerative diseases. However, studying its structure and the mechanisms underlying proton translocation remains challenging due to the hydrophobic nature of its transmembrane parts. In this structural bioinformatic study, we used the QTY code to reduce the hydrophobicity of megacomplex I, while preserving its structure and function. We carried out the structural bioinformatics analysis of 20 key enzymes in the integral membrane parts. We compare their native structure, experimentally determined using Cryo-electron microscopy (CryoEM), with their water-soluble QTY analogs predicted using AlphaFold 3. Leveraging AlphaFold 3’s advanced capabilities in predicting protein–protein complex interactions, we further explore whether the QTY-code integral membrane proteins maintain their protein–protein interactions necessary to form the functional megacomplex. Our structural bioinformatics analysis not only demonstrates the feasibility of engineering water-soluble integral membrane proteins using the QTY code, but also highlights the potential to use the water-soluble membrane protein QTY analogs as soluble antigens for discovery of therapeutic monoclonal antibodies, thus offering promising implications for the treatment of various neurodegenerative diseases.

Let $b \geqslant 3$ be an integer and C(b, D) be the set of real numbers in [0,1] whose base b expansion only consists of digits in a set $D {\subseteq} \{0,...,b-1\}$. We study how close can numbers in C(b, D) be approximated by rational numbers with denominators being powers of some integer t and obtain a zero-full law for its Hausdorff measure in several circumstances. When b and t are multiplicatively dependent, our results correct an error of Levesley, Salp and Velani (Math. Ann. 338 (2007), 97–118) and generalise their theorem. When b and t are multiplicatively independent but have the same prime divisors, we obtain a partial result on the Hausdorff measure and bounds for the Hausdorff dimension, which are close to the multiplicatively dependent case. Based on these results, several conjectures are proposed.

This research employs an enhanced Polar Operation Limit Assessment Risk Indexing System (POLARIS) and multi-scale empirical analysis methods to quantitatively evaluate the risks in icy region navigation. It emphasises the significant influence of spatial effects and external environmental factors on maritime accidents. Findings reveal that geographical location, environmental and ice conditions are crucial contributors to accidents. The models indicate that an increase in ports, traffic volume and sea ice density directly correlates with higher accident rates. Additionally, a novel risk estimation model is introduced, offering a more accurate and conservative assessment than current standards. This research enriches the understanding of maritime accidents in icy regions, and provides a robust framework for different navigation stages and conditions. The proposed strategies and model can effectively assist shipping companies in route planning and risk management to enhance maritime safety in icy regions.

With increased global navigation satellite system (GNSS) signals and degraded observation environments, the correctness of ambiguity resolution is disturbed, causing unexpected real-time kinematic (RTK) positioning solutions. This paper presents an improved fault detection and exclusion (FDE) method based on the generalized least squares (GLS) model. The correlated GLS model is constructed by regarding double-differencing (DD) integer ambiguities as the known parameters. Meanwhile, the validity of residuals as crucial components of fault detection could be enhanced by the iterative re-weighted least squares (IRLS) method rather than the least squares (LS) without robustness. A static test with artificial faults and a dynamic test with natural faults were carried out, respectively. By analyzing test statistics of the enhanced FDE algorithm and comparing its positioning errors with those from the classical LS, it is shown that our method can provide high-precision and high-reliability RTK solutions facing wrong DD fixed ambiguities due to observation faults.

The q-colour Ramsey number of a k-uniform hypergraph H is the minimum integer N such that any q-colouring of the complete k-uniform hypergraph on N vertices contains a monochromatic copy of H. The study of these numbers is one of the central topics in Combinatorics. In 1973, Erdős and Graham asked to maximise the Ramsey number of a graph as a function of the number of its edges. Motivated by this problem, we study the analogous question for hypergaphs. For fixed $k \ge 3$ and $q \ge 2$ we prove that the largest possible q-colour Ramsey number of a k-uniform hypergraph with m edges is at most $\mathrm{tw}_k(O(\sqrt{m})),$ where tw denotes the tower function. We also present a construction showing that this bound is tight for $q \ge 4$. This resolves a problem by Conlon, Fox and Sudakov. They previously proved the upper bound for $k \geq 4$ and the lower bound for $k=3$. Although in the graph case the tightness follows simply by considering a clique of appropriate size, for higher uniformities the construction is rather involved and is obtained by using paths in expander graphs.

Manipulating matter by strong coupling to the vacuum field has attracted intensive interests over the last decade. In particular, vibrational strong coupling (VSC) has shown great potential for modifying ground state properties in solution chemistry and biochemical processes. In this work, the effect of VSC of water on the melting behaviour of ds-DNA, an important biophysical process, is explored. Several experimental conditions, including the concentration of ds-DNA, cavity profile, solution environment, as well as thermal annealing treatment, were tested. No significant effect of VSC was observed for the melting behaviour of the ds-DNA sequence used. This demonstrates yet again the robustness of ds-DNA to outside perturbations. Our work also provides a general protocol to probe the effects of VSC on biological systems inside microfluid Fabry–Perot cavities and should be beneficial to better understand and harness this phenomenon.

DNA helicases are molecular motors that use the energy from nucleotide hydrolysis to move along DNA, promoting the unwinding or rewinding of the double helix. Here, we use magnetic and optical tweezers to track the motion of three helicases, gp41, RecQ, and RecG, while they unwind or rewind a DNA hairpin. Their activity is characterized by measuring the helicase velocity and diffusivity under different force and ATP conditions. We use a continuous-time random walk framework that allows us to compute the mean helicase displacement and its fluctuations analytically. Fitting the model to the measured helicase velocity and diffusivity allows us to determine the main states and transitions in the helicase mechanochemical cycle. A general feature for all helicases is the need to incorporate an off-pathway pausing state to reproduce the data, raising the question of whether pauses play a regulatory role. Diffusivity measurements also lead to estimations of the thermodynamic uncertainty factor related to the motor efficiency. Assuming a tight mechano-chemical coupling, we find that the RecG helicase reaches a high efficiency when operating uphill, whereas the unwinding gp41 and RecQ helicases display much lower efficiencies. Incorporating the analysis of fluctuations allows for better characterization of the activity of molecular machines, which represents an advance in the field.

Given a surface $\Sigma$ equipped with a set P of marked points, we consider the triangulations of $\Sigma$ with vertex set P. The flip-graph of $\Sigma$ is the graph whose vertices are these triangulations, and whose edges correspond to flipping arcs in these triangulations. The flip-graph of a surface appears in the study of moduli spaces and mapping class groups. We consider the number of geodesics in the flip-graph of $\Sigma$ between two triangulations as a function of their distance. We show that this number grows exponentially provided the surface has enough topology, and that in the remaining cases the growth is polynomial.

Vessel collision risk estimation is crucial in navigation manoeuvres, route planning, risk control, safety management and forewarning issues. The interaction possibility is a good method to quantify the near-miss collision risks of multi-ships. Current models, however, are mostly concerned about the movements in an unrestricted isotropic travel environment or network environment. This article simultaneously addresses these issues by developing a novel environment–kinetic compound space–time prism to capture potential spatial–temporal interactions of multi-ships in constrained dynamic environments. The approach could significantly reduce the overestimation of the individual vessel’s potential travel area and the interaction possibility of encountering vessels in restricted water. The proposed environmental–kinetical compound space–time prism (EKC-STP)-based method enables identifying where and when multi-ships possibly interacted in the constraint water area, as well as how the interaction possibility pattern changed from day to day. The collision risk evaluation results were validated through comparison with other methods. The full picture of hierarchical collision risk distribution in port areas is determined and could be employed to provide quantifiable references for efficient and practical anti-collision measures establishment.