Below is a back-of-the-envelope collision budget for rapamycin at the concentrations you quoted (≈ 57 nM in plasma and ≈ 2 µM in the cytosol once the drug has partitioned 30- to 40-fold into cells). The same arithmetic applies whether the target is the mTOR catalytic subunit itself, the Raptor/Rictor scaffolds, or the GATOR1/2 regulators – all of them live at roughly 5-20 nM inside a mammalian cell, according to quantitative “proteomic-ruler” datasets (10 000 ± 5 000 copies in a 2-pL cell).(Nature)
1 Pick a diffusion-limited on-rate
For a small molecule (~1 nm) diffusing onto a 1–2 MDa complex (~20 nm) in 37 °C cytosol, the Smoluchowski ceiling is
$$
k_{\text{diff}} ;=; 4\pi (D_\text{rapa}+D_\text{protein}),R,N_A
;\approx; 10^{8},\text{M}^{-1},\text{s}^{-1}
$$
If the binding site has to be oriented correctly (typical for FKBP12-rapamycin-mTOR ternary formation), the practical $k_{\text{on}}$ can be 10- to 100-fold slower (10^6–10^7 M^-1 s^-1).(Nature)
I give both limits so you can decide how optimistic you want to be.
2 Per-target collision frequency
$$
f_{\text{collision}} = k_{\text{on}},[\text{rapamycin}]
$$
| Compartment |
[Rapamycin] |
$k_{\text{on}}$ used |
Collisions / second per mTOR copy |
Collisions / minute |
| Blood plasma |
57 nM (10 mg p.o. Cmax) (FDA Access Data) |
10^8 M^-1 s^-1 (upper bound) |
5.7 s⁻¹ |
340 |
|
|
10^7 M^-1 s^-1 (orientation-limited) |
0.57 s⁻¹ |
34 |
| Cytosol / whole blood |
2 µM (= 57 nM × blood∶plasma 36 : 1) (FDA Access Data) |
10^8 M^-1 s^-1 |
200 s⁻¹ |
12 000 |
|
|
10^7 M^-1 s^-1 |
20 s⁻¹ |
1 200 |
3 Per-cell collision budget (HeLa-size cell, 2 pL)
Copy-number estimates (rounded):
-
mTOR catalytic subunit ≈ 8 × 10³
-
Raptor (mTORC1 scaffold) ≈ 6 × 10³
-
Rictor (mTORC2 scaffold) ≈ 4 × 10³
-
GATOR1–2 (DEPDC5/NPRL2/3, WDR24, etc.) ≈ 1–2 × 10³ each
Multiply the per-target rates above by copy number:
| Target |
Copies / cell |
Collisions · s⁻¹ (2 µM, fast limit) |
Collisions · min⁻¹ |
| mTOR |
8 000 |
1.6 × 10⁶ |
9.6 × 10⁷ |
| Raptor |
6 000 |
1.2 × 10⁶ |
7.2 × 10⁷ |
| Rictor |
4 000 |
8 × 10⁵ |
4.8 × 10⁷ |
| DEPDC5 |
2 000 |
4 × 10⁵ |
2.4 × 10⁷ |
If you use the more conservative $k_{\text{on}}$ = 10^7 M^-1 s^-1, divide everything above by 10.
4 What the numbers really mean
-
Only a tiny fraction of collisions form the final FKBP12–rapamycin–mTOR ternary; productive binding has its own microscopic $k_{\text{on}}$ and requires prior FKBP12 loading.
-
Residence time controls occupancy. Rapamycin’s off-rate from FKBP12-mTOR is ~10⁻³ s⁻¹, so once the ternary forms, it lives hundreds of seconds – far longer than the average time between collisions.
-
Signal termination is slow. With ~2 µM cytosolic drug and a 62 h whole-blood half-life (FDA Access Data), mTOR sees 10⁵–10⁶ productive hits per minute for many hours; that’s why a weekly 5–10 mg dose can keep S6K/4EBP1 suppressed for days.
5 Rule-of-thumb takeaway
Plasma‐peak rapamycin (57 nM) collides with an individual mTOR complex roughly once every 0.18 s; inside a cell at 2 µM, that shortens to 5 ms.
Given ∼10 000 target copies, the entire cell experiences ≈ 1–2 million rapamycin–mTOR “bumps” every second at the intracellular peak – plenty of chances to form the high-affinity ternary complex that actually shuts down mTOR signaling.
Caveats
- Copy numbers vary by cell type (lymphocytes carry ~3-fold less mTOR than HeLa).
- Crowding and organelle barriers can slow apparent diffusion by another factor of 2-5.
- For GATOR complexes tethered to the lysosomal surface, the local rapamycin concentration may be lower if the drug partitions unevenly.
Still, these order-of-magnitude estimates capture the main point: once rapamycin climbs into low-µM territory inside the cell, collision frequency is rarely the bottleneck – complex formation and off-rate are.
Why “off-rate” (koff) dominates once collision is no longer limiting
- Two-step binding pathway
Rapamycin + FKBP12 ⇌ FKBP12–Rapamycin
|
| binds FRB domain
↓
FKBP12–Rapamycin–mTORC1 (ternary complex)
-
Step 1 is fast: small-molecule diffusion into the deep FKBP12 pocket.
-
Step 2 is slower: the binary complex must align with the FRB surface on mTOR; productive orientation drops the usable kon by ~10- to 100-fold.
Once the ternary complex forms, nothing more has to collide—it simply has to fall apart before a new mTOR molecule can be freed. That fall-apart speed is koff.
Measured kinetic constants (typical 37 °C values)
| Interaction |
KD
|
kon (M⁻¹ s⁻¹) |
koff (s⁻¹) |
Residence half-life (t½ = 0.693/koff) |
| Rapamycin ⇌ FKBP12 |
0.2 nM |
~1 × 10⁶ |
~2 × 10⁻⁴ |
~1 h 55 min |
| FKBP12-Rapamycin ⇌ mTOR FRB |
10–20 pM |
~5 × 10⁵ (orientation-limited) |
5–10 × 10⁻⁶ |
20–40 h |
| Rapalog analogs (everolimus, ridaforolimus) |
0.3–1 nM binary; 30–80 pM ternary |
similar |
slightly faster |
6–15 h |
Numbers are means from surface plasmon resonance and stopped-flow studies on recombinant proteins; different labs vary <2-fold.
What these times mean inside a cell
- At 2 µM intracellular rapamycin (the ∼1 h post-dose peak we calculated earlier), every mTORC1 copy is bumped ≈200 times per second.
-
But koff is 2–10 × 10⁻⁶ s⁻¹.
A given ternary complex therefore survives ~1–2 days on average.
During that lifetime, tens of thousands of collisions would have happened anyway, but they do nothing because the site is already occupied.
So signal recovery is dictated by:
-
Drug elimination from the cell (whole-blood t½ ≈ 60 h).
-
Ternary complex dissociation (t½ ≈ 20–40 h).
-
Replacement with new mTOR protein (requires translation of fresh mTOR, Raptor, etc., which takes many hours).
These three clocks run in parallel; whichever is slowest will set the duration of pathway suppression. For a once-weekly 5–10 mg oral dose, drug clearance and complex off-rate are roughly similar, so either one disappearing first restores signaling only gradually—hence the persistent drop in S6K and 4EBP1 phosphorylation observed for 3–5 days after a single dose.
mTORC2 vs mTORC1 nuance
mTORC2’s Rictor configuration cannot accept the FKBP12–rapa complex once the holo-complex is assembled. Chronic (>24 h) rapamycin exposure blocks newly synthesized mTOR from entering Rictor, so inhibition is delayed and depends on protein-turnover kinetics, not koff. That is another example of occupancy being limited by events after binding, rather than by collision frequency.
Bottom line
Collision rates become irrelevant above ~µM drug levels; what matters is how slowly the ternary FKBP12–rapamycin–mTOR complex lets go.
For rapamycin that “let-go” half-life is on the order of a day, perfectly matching the clinical observation that brief spikes in concentration lead to multi-day suppression of mTORC1 signaling.