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A novel method for solving ordinary and partial differential equations, based on grammatical evolution is presented. The method forms generations of trial solutions expressed in an analytical closed form. Several examples are worked out and in most cases the exact solution is recovered. When the solution cannot be expressed in a closed analytical form then our method produces an approximation with a controlled level of accuracy. We report results on several problems to illustrate the potential of this approach.

Arenicin-2 is a 21 residue antimicrobial cyclic peptide, possessing one disulphide bond between residues Cys(3) and Cys(20). NMR and CD studies suggested that the structure of arenicin-2 in water represented a well formed, but highly twisted beta-hairpin. To investigate the spatial arrangement of the peptide side chains and to get a clear view of its possible amphipathic properties we performed molecular dynamics in explicit water. Four independent trajectories, 50 ns in length, were produced, starting from various initial conformations or by applying different simulation conditions. Arenicin-2 retained its beta-hairpin structure during simulations, although the residues close to strand ends were found to escape from the ideal hairpin conformation. The type I' beta-turn connecting the two strands fluctuated between type IV and II' beta-turn. Conversely, the right-handed twist of the beta-hairpin was well conserved with average twist value 203 degrees +/- 19 degrees per eight residues. Several nonbonded interactions, like hydrophobic interactions between aliphatic side chains, cation/pi-aromatic interactions, CH...pi aromatic bond and water bridges, contributed to the hairpin stabilization.

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Background: The motor subscale of the Movement Disorder Society-Unified Parkinson’s Disease Rating Scale (MDS-UPDRS-III) has limited applicability for the assessment of motor fluctuations in the home setting. Methods: To assess whether a self-administered, tablet-based application can reliably quantify differences in motor performance using two-target finger tapping and forearm pronation-supination tasks in the ON (maximal dopaminergic medication efficacy) and OFF (reemergence of parkinsonian deficits) medication states, we recruited 11 Parkinson disease (PD) patients (age, 60.6 ± 9.0 years; disease duration, 12.8 ± 4.1 years) and 11 healthy age-matched controls (age, 62.5 ± 10.5 years). The total number of taps, tap interval, tap duration, and tap accuracy were algorithmically calculated by the application, using the more affected side in patients and the dominant hand in healthy controls. Results: Compared to the OFF state, PD patients showed a higher number of taps (84.2 ± 20.3 vs. 54.9 ± 26.9 taps; p = 0.0036) and a shorter tap interval (375.3 ± 97.2 vs. 708.2 ± 412.8 ms; p = 0.0146) but poorer tap accuracy (2,008.4 ± 995.7 vs. 1,111.8 ± 901.3 pixels; p = 0.0055) for the two-target task in the ON state, unaffected by the magnitude of coexistent dyskinesia. Overall, test-retest reliability was high (r >0.75) and the discriminatory ability between OFF and ON states was good (0.60 ≤ AUC ≤ 0.82). The correlations between tapping data and MDS-UPDRS-III scores were only moderate (–0.55 to 0.55). Conclusions: A self-administered, tablet-based application can reliably distinguish between OFF and ON states in fluctuating PD patients and may be sensitive to additional motor phenomena, such as accuracy, not captured by the MDS-UPDRS-III.