  Interest in equilibrium-based sampling methods has grown with recent advances
in computational hardware and Markov state modeling (MSM) methods, yet
outstanding questions remain that hinder widespread adoption. Namely, how do
sampling strategies explore conformational space and how might this influence
predictions? Here, we seek to answer these questions for four commonly used
sampling methods: 1) a long simulation, 2) many short simulations, 3) adaptive
sampling, and 4) FAST. We first develop a theoretical framework for
analytically calculating the probability of discovering states and uncover the
drastic effects of varying the number and length of simulations. We then use
kinetic Monte Carlo simulations on a variety of physically inspired landscapes
to characterize state discovery and transition pathways. Consistently, we find
that FAST simulations discover target states with the highest probability and
traverse realistic pathways. Furthermore, we uncover the pathology that short
parallel simulations sometimes predict an incorrect transition pathway by
crossing large energy barriers that long simulations would typically
circumnavigate, which we refer to as pathway tunneling. To protect against
tunneling, we introduce FAST-string, which samples along the highest-flux
transition paths to refine an MSMs transition probabilities and discriminate
between competing pathways. Additionally, we compare MSM estimators in
describing thermodynamics and kinetics. For adaptive sampling, we recommend
normalizing the transition counts out of each state after adding pseudo-counts
to avoid creating sources or sinks. Lastly, we evaluate our insights from
simple landscapes with all-atom molecular dynamics simulations of the folding
of the {\lambda}-repressor protein. We find that FAST-contacts predicts the
same folding pathway as long simulations but with orders of magnitude less
simulation time.
