= CDK1 activity and protein abundance
{c}
<CDK1 activity and protein abundance> are different observables. A total-<CDK1> <Western blot> estimates <protein> amount under its calibration and loading assumptions. A phosphosite-specific <Western blot> asks about a particular <CDK1 phosphorylation state>. A <histone H1 kinase assay> asks how much <substrate> modification occurs under specified assay conditions. Any conversion between them needs a model and suitable controls.
An original counting example stipulates $100$ <CDK1> <molecules>, with $60$ bound to <cyclin B> in each of two hypothetical samples. In sample A, $10$ bound <molecules> are activity-permissive and $50$ are inhibited; in sample B, $40$ are activity-permissive and $20$ are inhibited. The other $40$ are unbound in both samples. Total <CDK1> and bound <CDK1> agree, but activity-permissive counts differ fourfold. These are invented counts for bookkeeping, not measured biological populations.
If each activity-permissive <molecule> contributes the same <reaction rate>, <substrate> and <ATP> remain available, and the assay stays linear in time, a simple illustrative readout is
$$
R-R_0=\alpha N_{\mathrm{active}}t.
$$
Here $R$ is the recorded signal, $R_0$ is a matched blank signal, $N_{\mathrm{active}}$ is the activity-permissive count, $t$ the reaction interval, and $\alpha$ a common signal contribution per active <molecule> per unit time. The corrected signals in the stipulated samples have <ratio> $40/10=4$, although their total <protein> amounts agree. This is an assay accounting assumption, not an <ordinary differential equation> for the <cell cycle>. The no-added-<cyclin B> baseline in the inspected experiment can itself contain catalytic activity; it need not equal an enzyme-free blank $R_0$.
<Substrate> depletion, differing inhibitory conditions or a saturated detector can break the simple proportionality. Comparing samples therefore requires matched reaction intervals, <substrate> supply, loading and detector response, rather than assuming that brighter <histone H1> labeling automatically means more total <CDK1>.
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