Characterizing the Complex Spatial Patterns in Biological Systems

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Spatial point patterns are ubiquitous in natural systems, from the patterns of raindrops on a sidewalk to the organization of stars in a galaxy. In cell biology, these patterns can represent the locations of fluorescently-labeled molecules inside or on the surface of cells, or even represent the centers of the cells themselves. These patterns arise due to the signaling activity of the cells which are mediated by a broad range of chemicals, and understanding this activity is vital to investigating these complex systems. Luckily, though each pattern is unique, the statistical properties of the patterns embed information about the underlying pattern formation process.

In this work, I demonstrate techniques to characterize the complex spatial patterns found in unicellular systems. Using topologically-derived measures, I demonstrated a technique to automatically classify sets of point patterns into groups to identify changes in higher order statistical moments due to experimental variation. This technique utilizes functional principal component analysis (FPCA) on the Minkowski functionals of a secondary pattern formed by imposing disks on each point center. I demonstrate that this better classifies a range of point pattern sets, and then applied this technique to pattern sets representing membrane-bound proteins in human immune cells, showing that this procedure correctly identifies non-interacting proteins.

Further, I demonstrate a simulation-based technique to diminish the statistical impact of large-scale pattern features. In protein patterns, these represent the effects of membrane ruffling during pattern formation. These features dominate correlation measures, obscuring any hint of nanoscale clustering. Using heterogeneous Poisson null models for each cell to re-normalize their pairwise correlation functions, I found that patterns of LAT proteins ("linker for the activation of T-cells") do indeed cluster, with a characteristic length-scale of approximately 500 nm. By performing clustering analysis at this length scale on both the LAT patterns and their respective null models, I found that clusters are most commonly dimers, but that this clustering is strongly diminished upon T-cell activation. This loss of clustering may be due to the presence of unlabeled molecules that have been recruited to the cell membrane to form complexes with LAT.

I also investigate both molecular and cell-center patterns in Dictyostellium discoideum cells, which are a model organism for amoeboid motion and G-protein receptor-mediated chemotaxis. These cells migrate using "autocrine" signal relay in that they both secrete and sense the same chemoattractant, cyclic adenosine monophosphate (cyclic AMP or cAMP). They also secrete phosphodiesterases that degrade the chemoattractant. This leads to streaming patterns of cells towards aggregation centers, which serve as sites of sporulation. To study these cells, I demonstrate an image analysis technique that statistically infers the local population of fluorescently-labeled mRNA units in fluorescent images of self-aggregating cells. The images were of experiments where two particular mRNAs were labeled along with their respective proteins, the first being adenylyl cyclase A (ACA), a molecule involved in the production of cAMP. ACA itself has already been seen to accumulate at the back of migrating cells. The location of these molecules were compared to that of the locations of cyclic AMP receptor 1 (cAR1), which is the cell's mechanism for gradient sensing. Using my analysis technique, I found that statistically significant proportions of ACA mRNA preferentially locate towards the rear of migrating cells, an assymetry that was also found to identically correlate with the asymmetry of ACA itself. This asymmetry was not seen in cAR1 mRNA, which tends to distribute uniformly. Further, the asymmetry in ACA was most exaggerated in cells migrating at the rear of streams, with the approach to the local aggregate center diminishing leading to more uniformly distributed molecules. This may suggest that ACA is locally translated at the back of migrating cells, a result requiring further investigation.

I then construct a computational migration model of D. discoideum chemotaxis and use it to investigate how the streaming phase is effected by cell-cell adhesion as well as by the global degradation of cAMP. To classify the dynamics of the model with respect to cell density and external chemical gradient, the two relevant phase variables, I develop an order parameter based on the fraction of broken cell-cell contacts over time. This parameter successfully classifies the dynamic steady states of the model (independent motion, streaming, and aggregation), outperforming the often used "chemotactic index". I found that the elimination of degradation strongly diminishes any presence of streaming, suggesting that chemical degradation is vital to stream formation. In contrast, the addition of cell-cell adhesion expanded the streaming phase, stabilizing streams that were formed initially through signal relay.