Analysis shows that the cell cycle trajectory is sharply confined by the ambient energy barrier , and the landscape along this trajectory exhibits a generally flat shape.

Besides logarithmically equivalent to the invariant distribution S(x) ~ —6 ln P(x), the mean eXit time 1‘ that the system escapes from an attractive basin has the asymptotic form 1‘ oc exp(VAS), where AS is the energy barrier height between the boundary of the basin and the stable state.

Our results demonstrate that the cell cycle trajectory is sharply confined as a canal bounded by ambient energy barriers , with the landscape adaptively reshaping itself in response to external signals, such as the nutrients improving and the activation of DNA replication checkpoint in our work.

We can see that the G1 state is the global minimum on the energy landscape, and there exists an energy barrier between P1 and P2 to prevent small noise activation.

2D, the energy barrier between the canals of the S and early M phases greatly decreases the probability that the system passes the S/M transition without crossing P3, hence ensuring the robustness of the S/M transition.

2D), the energy barrier between the S canal and the early M canal disappears.

The red dashed boxes mark the energy barriers that contradict With the deter-S4 Fig.

Different free energy landscapes give different free energy barrier heights between the non-na-tive and native states.

As we can see the large intrinsic specificity characterized by high ISR gives smaller free energy barrier and lower ISR gives higher barrier.

This might be due to the increase of the free energy barrier for escaping the binding from the increase of the affinity.

We plot the free energy barrier height and the kinetic time for binding of these three cases as shown in Fig 10D.

Assuming two-state unfolding kinetics [39—42] we can estimate the characteristic time required to cross the unfolding free energy barrier (in fact it is the time spent in the native state waiting for sufficient thermal fluctuation to cross the barrier) as:

Where T137 is first-passage time from the folded to the unfolded state, AG# is the free energy barrier between the folded state and the transition state for unfolding (see Fig.

In order to see this we note that the mutational effect on protein stability AAG is related to the change in the unfolding free energy barrier AAG#, the difference between the WT barrier height and the mutant barrier height, shown in Fig.

1) The reaction of sulfenic acid to form sulfenyl amide has been previously studied in model compounds suggesting that electronic effects are relevant but they report a high energy barrier .

The free energy barrier is 13.9 kcal/mol (Fig.

According to our results the reaction mechanism that converts the sulfenic acid to a cyclic sulfenyl amide occurs through a seemingly dissociative mechanism, with a relative small free energy barrier .