Molecular dynamics (MD) simulations have emerged as a transformative approach to analyse molecular systems at the atomic level, offering valuable insights into complex biological processes. Many biological phenomena can only accurately be described by incorporating a quantum-mechanical (QM) description of atomic interactions, known as first-principles MD (FPMD). However, their computational cost precludes the simulation of large systems without compromising simulation time or accuracy. In MD simulations, the time step is limited by the fastest motions of the system. Multiple time step (MTS) algorithms mitigate this limitation by integrating the fast and slow force components with different time steps. In FPMD, two distinct QM methods can be used to capture these force contributions. A low-level method defines the fast force components and its difference with forces computed with a high-level method serves as the slow components. Throughout this thesis project, we have used and developed diverse MD techniques, with a specific emphasis on MTS and biological applications. The first project covers a preclinical investigation of drug candidates against the infection schistosomiasis. In close collaboration with experimental chemists and biologists, we provided computational insights on the mode of action of these putative drugs. Our simulations revealed their diverse binding poses in the target proteins resulting in different frequency of near-attack configurations of the reactive groups activating the drug. This finding could explain the different in vitro activities against schistosome species. However, all drugs proved unstable in acidic environments, precluding in vivo activity. Then, we switched to the further development of MD methods by pursuing an ongoing project where fewest-switches surface hopping was combined with MTS to accelerate non-adiabatic MD simulations. This method computes Tully's transition probabilities at the outer steps and the Landau-Zener formula is used to detect transitions during the inner steps, that are then confirmed with a high-level fewest switches calculation. The method was successfully tested on a small prototypical system, the photorelaxation of protonated formaldimine. Next, we focus on using machine learning (ML) to infer forces during MTS simulations. We investigate two schemes. In the first, ML provides an estimate of the slow force components to bypass the high-level calculations. This method yields large speedups of 163 at the cost of sampling phase space according to an approximation of the high-level method. In the second, ML infers a correction to the fast force components to reduce the gap between the two levels and thus allowing large increases of the outer time step for speedups of 7 while sampling phase space according to the high-level method is guaranteed. Both schemes accurately reproduced the structure of liquid water. Finally, we expand the ML-MTS approach by adding two significant improvements. First, we successfully incorporate the second ML-MTS scheme into a QM/MM framework. In addition, we develop an adaptive ML-MTS algorithm which enables on-the-fly retraining of the ML model based on the kernel-induced distance between new and current training configurations. The MTS ratio is then dynamically adjusted to optimize the use of high-level calculations. We successfully test this method on a molecule of acetone solvated in water and a small metalloprotein in aqueous solution.