Testing the transition state theory in stochastic dynamics of a genetic switch

Stochastic dynamics of chemical reactions in a mutually repressing two-gene circuit is numerically simulated. The circuit has a rich variety of different states when the kinetic change of DNA status is slow. The stochastic switching transition between those states are compared with the theoretical estimation of the switching rate derived from the idea similar to the transition state theory. Even though the circuit is kept far from equilibrium, the method gives a consistent explanation of the switching kinetics for a wide range of parameters. The transition state theory-like estimation, however, fails to describe transitions involving the state which has the extremely small numbers of protein molecules

Effect of Laterally Wedged Insoles on the External Knee Adduction Moment across Different Reference Frames.

Biomechanical effects of laterally wedged insoles are assessed by reduction in the knee adduction moment. However, the degree of reduction may vary depending on the reference frame with which it is calculated. The purpose of this study was to clarify the effect of reference frame on the reduction in the knee adduction moment by laterally wedged insoles.Twenty-nine healthy participants performed gait trials with a laterally wedged insole and with a flat insole as a control. The knee adduction moment, including the first and second peaks and the angular impulse, were calculated using four different reference frames: the femoral frame, tibial frame, laboratory frame and the Joint Coordinate System.There were significant effects of reference frame on the knee adduction moment first and second peaks (P < 0.001 for both variables), while the effect was not significant for the angular impulse (P = 0.84). No significant interaction between the gait condition and reference frame was found in either of the knee adduction moment variables (P = 0.99 for all variables), indicating that the effects of laterally wedged insole on the knee adduction moments were similar across the four reference frames. On the other hand, the average percent changes ranged from 9% to 16% for the first peak, from 16% to 18% for the second peak and from 17% to 21% for the angular impulse when using the different reference frames.The effects of laterally wedged insole on the reduction in the knee adduction moment were similar across the reference frames. On the other hand, Researchers need to recognize that when the percent change was used as the parameter of the efficacy of laterally wedged insole, the choice of reference frame may influence the interpretation of how laterally wedged insoles affect the knee adduction moment

Knee adduction moment parameters expressed using the different reference frames during gait with flat insole and laterally wedged insole.

<p>Values are shown as mean ± standard deviation (95% confident interval).</p><p>TF, tibial frame</p><p>FF, femoral frame</p><p>LF, laboratory frame</p><p>JCS, Joint Coordinate System.</p><p>*Repeated measure ANOVA.</p><p>Knee adduction moment parameters expressed using the different reference frames during gait with flat insole and laterally wedged insole.</p

Knee adduction moment curves expressed using the different reference frames.

<p>TF, tibial frame; FF, femoral frame; LF, laboratory frame; JCS, Joint Coordinate System.</p

Percent changes in the knee adduction moment in response to laterally wedged insoles expressed using the different reference frames.

<p>Values are shown as mean ± standard deviation (95% confident interval).</p><p>TF, tibial frame</p><p>FF, femoral frame</p><p>LF, laboratory frame</p><p>JCS, Joint Coordinate System.</p><p>Horizontal bars indicate statistical differences in post-hoc pair-wise comparisons.</p><p>*Friedman test.</p><p>**Significant differences between TF and FF, TF and JCS, and LF and JCS in post-hoc pair-wise comparisons.</p><p>Percent changes in the knee adduction moment in response to laterally wedged insoles expressed using the different reference frames.</p

Reduction in the knee adduction moment in response to laterally wedged insoles expressed using the different reference frames.

<p>Extreme cases. Participant 7 (a), 13 (b) and 29 (c). TF, tibial frame; FF, femoral frame; LF, laboratory frame; JCS, Joint Coordinate System; KAM, knee adduction moment.</p

Illustration of reference frames and ground reaction forces in the axial plane.

<p>White arrows indicate ground reaction force in the flat insole condition, and black arrows indicate ground reaction force in the laterally wedged insole condition. TF, tibial frame; FF, femoral frame. When the reference frames are aligned parallel in the axial plane (a), the lever arm of the ground reaction force is smaller in the laterally wedged insole condition than in the flat insole condition for both TF and FF. When the reference frames are rotated with each other (e.g. external rotation of the knee)(b), the lever arm in the laterally wedged insole condition is the smaller than in the flat insole condition for TF, while the lever arm in the laterally wedged insole condition is larger than in the flat insole condition for FF.</p