Molecular Dynamics Predicts The Solution Conformations of Poly-L-lysine in Salt Solutions

Ultraviolet resonance Raman (UVRR) studies recently discovered that increasing concentrations of NaClO$_4$ increase the fraction of $\alpha$-helical conformations of poly-L-lysine (PLL) in water solutions. In contrast, this $\alpha$-helical content increase does not occur for NaCl solutions. We used enhanced sampling molecular dynamics to explore the conformational space of PLL and to examine the effect of ions on PLL conformation. The free-energy landscapes of PLL in solutions were determined using the simulation data. The simulation results were also used to develop a molecular picture of ion-PLL interactions as well as the impact of ions on peptide hydration. The examination of pair interaction energies reveals the mechanisms whereby ions stabilize PLL conformations. ClO$_4$$^-$ increases the $\alpha$-helix conformation by decreasing the hydration of the peptide backbone which stabilizes the $\alpha$-helical intramolecular hydrogen bonds (H-bonds). This occurs because of the relatively large ClO$_4$$^-$ size and its tetrahedral structure. In contrast, the smaller Cl$^-$ negligibly impacts the peptide backbone hydration and does not stabilize intramolecular H-bonds. In summary the results reported here support the experimental observations and provide a molecular picture of the role ions play in PLL conformations in aqueous salt solutions

Single machine scheduling with release dates and job delivery to minimize the makespan

AbstractIn single machine scheduling with release dates and job delivery, jobs are processed on a single machine and then delivered by a capacitated vehicle to a single customer. Only one vehicle is employed to deliver these jobs. The vehicle can deliver at most c jobs at a shipment. The delivery completion time of a job is defined as the time at which the delivery batch containing the job is delivered to the customer and the vehicle returns to the machine. The objective is to minimize the makespan, i.e., the maximum delivery completion time of the jobs. When preemption is allowed to all jobs, we give a polynomial-time algorithm for this problem. When preemption is not allowed, we show that this problem is strongly NP-hard for each fixed c≥1. We also provide a 53-approximation algorithm for this problem, and the bound is tight