A straightforward method to compute average stochastic oscillations from data samples.
BACKGROUND
Many biological systems exhibit sustained stochastic oscillations in their steady state. Assessing these oscillations is usually a challenging task due to the potential variability of the amplitude and frequency of the oscillations over time. As a result of this variability, when several stochastic replications are averaged, the oscillations are flattened and can be overlooked. This can easily lead to the erroneous conclusion that the system reaches a constant steady state.


RESULTS
This paper proposes a straightforward method to detect and asses stochastic oscillations. The basis of the method is in the use of polar coordinates for systems with two species, and cylindrical coordinates for systems with more than two species. By slightly modifying these coordinate systems, it is possible to compute the total angular distance run by the system and the average Euclidean distance to a reference point. This allows us to compute confidence intervals, both for the average angular speed and for the distance to a reference point, from a set of replications.


CONCLUSIONS
The use of polar (or cylindrical) coordinates provides a new perspective of the system dynamics. The mean trajectory that can be obtained by averaging the usual cartesian coordinates of the samples informs about the trajectory of the center of mass of the replications. In contrast to such a mean cartesian trajectory, the mean polar trajectory can be used to compute the average circular motion of those replications, and therefore, can yield evidence about sustained steady state oscillations. Both, the coordinate transformation and the computation of confidence intervals, can be carried out efficiently. This results in an efficient method to evaluate stochastic oscillations.
Cambridge Systems Biology Centre, University of Cambridge, Tennis Court RoadCB2 1GA, Cambridge, United Kingdom. jj425@cam.ac.uk.|Department of Computer Science and Systems Engineering, University of Zaragoza, María de Luna 1, Zaragoza, 50018, Spain. jj425@cam.ac.uk.
Jorge
J
Júlvez
D000465:Algorithms; D019295:Computational Biology / Q000379:methods*; D008390:Markov Chains; D011157:Population Dynamics