Temporal Precision of Gene Expression and Cell Migration
Important cellular processes such as migration, differentiation, and development often rely on precise timing. Yet, the molecular machinery that regulates timing is inherently noisy. How do cells achieve precise timing with noisy components? We investigate this question using a first-passage-time approach, for an event triggered by a molecule that crosses an abundance threshold. We investigate regulatory strategies that decrease the timing noise of molecular events. We look at several strategies which decrease the noise: i) Regulation performed by an accumulating activator, ii) Regulation dues to a degrading repressor, iii) Auto-regulation and the presence of feedback. We find that either activation or repression outperforms an unregulated strategy. The optimal regulation corresponds to a nonlinear increase in the amount of the target molecule over time, arises from a tradeoff between minimizing the timing noise of the regulator and that of the target molecule itself, and is robust to additional effects such as bursts and cell division. Our results are in quantitative agreement with the nonlinear increase and low noise of mig-1 gene expression in migrating neuroblast cells during Caenorhabditis elegans development. These findings suggest that dynamic regulation may be a simple and powerful strategy for precise cellular timing.
Autoregulatory feedback increases noise. Yet, we find that in the presence of regulation by a second species, autoregulatory feedback decreases noise. To explain this finding, we develop a method to calculate the optimal regulation function that minimizes the timing noise. Our method reveals that the combination of feedback and regulation minimizes noise by maximizing the number of molecular events that must happen in sequence before a threshold is crossed. We compute the optimal timing precision for all two-node networks with regulation and feedback, derive a generic lower bound on timing noise, and compare our results with the neuroblast migration during C. elegans development, as well as two mutants. We finds that indeed our model is aligned with the experimental findings.
Furthermore, we apply our framework of temporal regulation to explain how the stopping point of the migrating cells in C. elegans depends on the body size. Considering temporal regulation, we find the termination point of the cell for various larval sizes. We discuss three possible mechanisms: i) No compensation; here the migration velocity is constant across the mutants of C. elegans, and this results in the migration distance to be constant but the relative position to be different across various sizes; ii) Total compensation; here the velocity is compensated with body size, hence resulting in the same relative position of cells across mutants; and iii) Partial compensation; here the velocity of migration is correlated with body size to some degree, resulting in a non-linear relationship between termination point and body size. We find that our partial compensation model is consistent with experimental observations of cell termination.
Finally, we look at the detection of traveling waves by single-celled organisms. Cells must use temporal and spatial information to sense the direction of traveling waves, as seen in cAMP detection by the amoeba Dictyostelium. If a cell only uses spatial information to sense the direction of the wave then the cell will move forward when the wave hits the front of the cell, and move backward when the wave hits the back of the cell, resulting in neutral movement. Cells must use temporal information along with spatial information to effectively move towards the source. Here we develop a mechanism by which cells are able to integrate the spatial and temporal information through a system of inhibitors. We find the optimal time to release the inhibitors for maximizing the precision of directional sensing.