Intelligent data analysis to model and understand live cell time-lapse sequences

Abstract

Background: One important aspect of cellular function, which is at the basis of tissue homeostasis, is the delivery of proteins to their correct destinations. Significant advances in live cell microscopy have allowed tracking of these pathways by following the dynamics of fluorescently labelled proteins in living cells.

Objectives: This paper explores intelligent data analysis techniques to model the dynamic behavior of proteins in living cells as well as to classify different experimental conditions.

Methods: We use a combination of decision tree classification and hidden Markov models. In particular, we introduce a novel approach to "align" hidden Markov models so that hidden states from different models can be cross-compared.

Results: Our models capture the dynamics of two experimental conditions accurately with a stable hidden state for control data and multiple (less stable) states for the experimental data recapitulating the behaviour of particle trajectories within live cell time-lapse data.

Conclusions: In addition to having successfully developed an automated framework for the classification of protein transport dynamics from live cell time-lapse data our model allows us to understand the dynamics of a complex trafficking pathway in living cells in culture.

Fig. 1

Image of living cell transfected with a green fluorescent protein chimera that is transported in vesicles towards the plasma membrane (A). Movement of vesicles was observed for 30 seconds with total internal reflection microscopy and individual vesicle tracks were detected by computer software (B).

Fig. 2

The typical Hidden Markov Model architecture where H_i represents the hidden state in position i and x_i represents the observed variable x in position i.

Fig. 3

The Auto Regressive Hidden Markov Model architecture where observed variables are conditioned upon previous observations.

Fig. 4

Top: 10 sampled trajectories of the particles within the cell generated from AR-HMMs learnt from basal data. Bottom: a zoomed-in plot showing some differing characteristics of the trajectories. The different symbols used represent different discovered hidden states.

Fig. 5

10 sampled trajectories of the particles within the cell generated from AR-HMMs learnt from TGFβ data. The different symbols used represent different discovered hidden states. The scale is the same as the top plot in Fig 4 for comparison.

Fig. 6

Decision Tree learnt from the 5-state HMM parameters using experimental set up 1 with processed parameters. N represents the Basal experiments and Y represents TGFβ-induced experiments. probchange represents the probability of changing state, probstable represents the probability of staying in the same state, mostprobdisp represents the mean value for displacement when in the state with the highest probability, and mostprobdist represents the mean value for distance for the most probable state. Finally, mostprobcovx represents the covariance of the x coordinate for the most probable state.

Fig. 7

The “realigned” state transition diagrams (links represent transitions that appear with p>0.5 for the majority of experiments for basal and TGFβ. The dashed line only appears in the TGFβ transitions.

Fig. 8

Decision Tree learnt from the 5-state HMMs having been realigned (allowing more exploration of the states). pC represents probability of being in state C, AC represents the probability of switching from state A to state C. Similarly, DC and EB represents the probability of switching from state A and E to state C and B respectively. covdist_A represents the covariance of the distance for state A. N represents the Basal experiments and Y represents TGFβ-induced experiments.

Fig. 9

Summaries of the parameter values for the different discovered states for TGFβ-induced and Basal Hidden Markov Models.

Fig 10

(Top) Samples of different manually labelled trajectories: Directed, Simple and Restricted. (Bottom) Mean Square Displacement (MSD) calculations for these trajectories.