Kalman filters for biological signal analysis

In this project, work with both the Kalman Filter (KF) and the Extended Kalman Filter (EKF) was made to make sense of noisy spatiotemporal data from optical traps, using them in both lab-controlled and live biological settings. It started with control experiments, tracking polystyrene microspheres in water and in polyacrylamide gel. These setups gave me a stable baseline to test the filters. Both KF and EKF did a solid job cleaning up high-frequency noise, all while keeping the key oscillatory signals intact. This was especially clear when looking at the power spectral density (PSD). The EKF stood out by better handling the non-linear aspects of the data. With those results in hand, the next step was to focus to a more complex biological environment: live HeLa cells. These cells showed different nuclear morphologies; some normal, others more granular, or with ramified chromatin structures. Out representative optical traps were picked for each type and looked at the filtered force trajectories. Even with the noise and variability that come with live cells, both filters (and especially the EKF) were able to tease out meaningful patterns and highlight shifts in dynamic behaviour. It was also created correlation heatmaps to see how traps across the nucleus interacted with one another. Finally, a comparation was made between bead experiments with the messier but more interesting cellular data. Bead signals were stable and repeatable, piconewton(pN)-range forces that didn’t change much. In contrast, the signals from live cells were more unpredictable, smaller in magnitude, and clearly shaped by things like chromatin changes, molecular crowding, and active forces within the cell. This comparison really emphasized the importance of using the right filter settings, because being too aggressive, there is a risk wiping out the very signals you're trying to study.