On a computer-aided approach to the computation of Abelian integrals

An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is applied to the study of bifurcations of limit cycles arising from a cubic perturbation of an elliptic Hamiltonian of degree four

Para-infectious brain injury in COVID-19 persists at follow-up despite attenuated cytokine and autoantibody responses

To understand neurological complications of COVID-19 better both acutely and for recovery, we measured markers of brain injury, inflammatory mediators, and autoantibodies in 203 hospitalised participants; 111 with acute sera (1–11 days post-admission) and 92 convalescent sera (56 with COVID-19-associated neurological diagnoses). Here we show that compared to 60 uninfected controls, tTau, GFAP, NfL, and UCH-L1 are increased with COVID-19 infection at acute timepoints and NfL and GFAP are significantly higher in participants with neurological complications. Inflammatory mediators (IL-6, IL-12p40, HGF, M-CSF, CCL2, and IL-1RA) are associated with both altered consciousness and markers of brain injury. Autoantibodies are more common in COVID-19 than controls and some (including against MYL7, UCH-L1, and GRIN3B) are more frequent with altered consciousness. Additionally, convalescent participants with neurological complications show elevated GFAP and NfL, unrelated to attenuated systemic inflammatory mediators and to autoantibody responses. Overall, neurological complications of COVID-19 are associated with evidence of neuroglial injury in both acute and late disease and these correlate with dysregulated innate and adaptive immune responses acutely

Equilibrium hydrogen exchange reveals extensive hydrogen bonded secondary structure in the on-pathway intermediate of Im7

The four-helical immunity protein Im7 folds through an on-pathway intermediate that has a specific, but partially misfolded, hydrophobic core. In order to gain further insight into the structure of this species, we have identified the backbone hydrogen bonds formed in the ensemble by measuring the amide exchange rates (under EX2 conditions) of the wild-type protein and a variant, I72V. In this mutant the intermediate is significantly destabilised relative to the unfolded state (ΔΔG(ui)=4.4kJ/mol) but the native state is only slightly destabilised (ΔΔG(ui)=1.8kJ/mol) at 10 °C in (2(H(2)O, pH(∗) 7.0 containing 0.4 M Na(2)SO(4), consistent with the view that this residue forms significant non-native stabilising interactions in the intermediate state. Comparison of the hydrogen exchange rates of the two proteins, therefore, enables the state from which hydrogen exchange occurs to be identified. The data show that amides in helices I, II and IV in both proteins exchange slowly with a free energy similar to that associated with global unfolding, suggesting that these helices form highly protected hydrogen-bonded helical structure in the intermediate. By contrast, amides in helix III exchange rapidly in both proteins. Importantly, the rate of exchange of amides in helix III are slowed substantially in the Im7(∗) variant, I72V, compared with the wild-type protein, whilst other amides exchange more rapidly in the mutant protein, in accord with the kinetics of folding/unfolding measured using chevron analysis. These data demonstrate, therefore, that local fluctuations do not dominate the exchange mechanism and confirm that helix III does not form stable secondary structure in the intermediate. By combining these results with previously obtained Φ-values, we show that the on-pathway folding intermediate of Im7 contains extensive, stable hydrogen-bonded structure in helices I, II and IV, and that this structure is stabilised by both native and non-native interactions involving amino acid side-chains in these helices