MSM & kinetic seeding

Trails-MD separates adaptive exploration from kinetic estimation. In exploration mode (the default, and the subject of this page) walkers are short and their velocities are redrawn from a Maxwell–Boltzmann (MB) distribution at each spawn point. Everything below — including the lag/segment-length trap — is a property of that exploration data.

Kinetics mode takes a different route to a rate

If you want a rate without building an MSM, use kinetics mode: walkers inherit their parent's velocities and a source→sink recycling box gives MFPT = 1/flux (the Hill relation). That steady-state estimator involves no lag time, so it is immune to the trap described below. This page is about the other route — an MSM built from exploration trajectories.

What velocity resampling does and does not do

MB resampling is not a bias — but it does cap your lag time

For a separable Hamiltonian $H(x,p)=K(p)+U(x)$ the Boltzmann density factorizes, so momenta are statistically independent of positions at equilibrium. Drawing $p \sim \mathrm{MB}(T)$ at any position $x$ therefore reproduces exactly the equilibrium conditional density $\rho(p\mid x)$. A segment launched from $(x,\,p\sim\mathrm{MB})$ is a legitimate realization of the equilibrium dynamics conditioned on $x$.

Likewise, adaptively choosing where to start walkers does not bias the MSM. Each row of the transition matrix is estimated from the counts leaving that state, which are unbiased estimates of $p(j \mid i, \tau)$ no matter how often you chose to start there. Adaptive selection changes where you collect statistics, not the transition probabilities. This is exactly why adaptive-sampling → MSM is a standard, rigorous workflow.

What resampling does cost is trajectory continuity. It severs phase-space continuity at every parent→child boundary, so each walker segment must be treated as an independent trajectory (Trails-MD does this correctly and never stitches walkers together). The consequence is a hard cap:

$$\tau \le L \qquad (L = \text{walker segment length})$$

You cannot count a transition at a lag longer than the trajectory carrying it.

The trap: convergence in iteration is not convergence in lag

Markovianity also needs $\tau \gg 1/\gamma$ (the momentum relaxation time, ~1 ps for friction = 1 ps⁻¹), so the usable window is $1/\gamma \ll \tau \le L$. If the implied timescales have not plateaued by $\tau = L$, the MSM systematically underestimates the slow timescales — and the failure is silent, because you cannot push $\tau$ past $L$ to test it. The convergence monitor watches the ITS across iterations: as data accumulate the estimate stops moving and looks "converged" while still being wrong.

Trails-MD therefore refuses to certify convergence when msm.lagtime exceeds 1/5 of the shortest walker segment, and warns. If you need a longer lag, increase spawning.step so that segments get longer.

For quantitative kinetics on slow processes you have three options: the two-stage strategy below; seeding longer unbiased runs and reweighting with TRAM/dTRAM; or bypassing the MSM entirely with weighted-ensemble kinetics mode, whose lag-free steady-state flux estimator is immune to the trap above.

The two-stage strategy

1. Adaptive exploration. Run a Trails-MD campaign (see Concepts) to discover conformational space and identify representative structures across the explored region.
2. Kinetic seeding. Use representative structures selected from the adaptive campaign to seed longer, unbiased production trajectories.
3. Post-hoc MSM construction. Build a Markov State Model from the production trajectories using standard external tools (e.g. deeptime) — clustering, transition-matrix estimation, implied-timescale analysis, and coarse-graining into metastable states.

This two-stage approach is useful because the adaptive stage identifies representative starting structures across the explored space, while the production stage generates trajectories that are directly suitable for MSM estimation — avoiding the bias that would come from building a kinetic model directly on short, velocity-randomized adaptive walkers.

What Trails-MD provides for this workflow

• Coverage diagnostics (trails-md-log) to identify well- and under-sampled regions of the CV space at the end of a campaign.
• Lineage tracking (trails-md-path) to reconstruct connected parent-child trajectories, useful for selecting seeding structures along a hypothesized transition path.
• Checkpointed campaign state, so representative-structure selection can be revisited without rerunning the adaptive stage.

Example: chignolin folding

The paper demonstrates this workflow on chignolin (CLN025) folding in explicit water: an adaptive Trails-MD campaign explores the CV space, representative spawn points are selected from the discretized explored space, and long production trajectories seeded from those points are used to build a two-state coarse-grained MSM with implied-timescale validation. See Results in the paper.