Illustrative model example
Three states become two. The slow transition survives.
Consider a model in which states B and C exchange rapidly while A exchanges more slowly with both. Merging B and C gives a simpler question: how does the system move between A and the combined state? This illustrative model makes the acceptance test visible: preserve the slow relaxation time, then use the smaller representation for questions that depend on that mode.
- A · B · CThree-state model
B and C exchange with probability 0.40 in each direction per lag.
- A · BCMerge the fast pair
A → BC: 0.10 per lag. BC → A: 0.05 per lag.
- 6.15 → 6.15Slow relaxation, in lag units
The analytical slow-mode survival ratio is 1.00.
- What goes in · Each lag, A stays A with probability 0.90 and moves to B or C with probability 0.05 each. B and C each stay put with probability 0.55, exchange with each other at 0.40, and return to A at 0.05. Their stationary populations are equal.
- What comes out · The reduced model retains A and BC, with populations 1/3 and 2/3. Both models have the same slow eigenvalue, 0.85, giving a relaxation time of −1 / ln(0.85) = 6.15 lags. The faster B–C mode is removed.
- The decision it supports · Use the two-state representation for this slow-relaxation question. Keep B and C separate when their individual behavior matters. Established MSM tools also support coarse-graining; BioTwin’s useful connection is to carry the preservation check alongside subsequent landscape questions.
Check what the reduction changes
The declared operation merges rapidly exchanging macrostates, then compares a remaining slow relaxation timescale with the original model. It takes transition and stationary models as inputs. A smaller state count is useful only when the dynamics relevant to the question survive.
Work alongside established kinetic modeling
Markov-state-model tools such as deeptime already estimate, analyze and coarse-grain dynamics. BioTwin’s proposed use connects its slow-mode check to ensemble representations and downstream landscape questions. A binding-state comparison could then retain both a reduced model and the evidence for accepting that reduction. A competent conventional MSM workflow is the appropriate comparison for any claim of saved work.
Conformations alone do not supply a clock
This reduction method is under development. Related kinetic calculations are implemented, while the reduction’s scientific performance still needs evaluation. Arbitrary or uniform transitions between structural conformers do not establish molecular rates. Start from a defensible trajectory or kinetic model, and compare retained timescales and transitions on held-out data.