Drugs are discovered by screening compounds for their influence on targets that are thought to underlie disease. Screen assays are typically bulk measurements - measurements that are averaged over the population of single cells that are exposed to the drug. This approach accepts the simplifying assumption that individual cells respond to a given compound in more or less the same way. Reality, however, does not conform to this simplification.


We are developing mathematical methods that exploit single cell variability to make inference onto the signaling that controls reporter targets. 


Over the past decade, significant pharmaceutical efforts have been directed towards screening for compounds, such as Imatinib (Gleevec), that specifically inhibit the “one” target or oncogene responsible for a pathology. While the approach has not been fruitless, its success is dimmer than its’ anticipated promise. One difficulty is that certain proteins, including oncogenic Ras, were found difficult to effectively inhibit. However, even when potent inhibitors are identified therapeutic success is often limited. In part, this is because current strategies target an oncogene in isolation from the network of signals within which it is embedded. Inhibiting oncogenic BRAF, for example, with the recently developed vemurafenib relives BRAF’s feedback inhibition of HER2, which affectively offsets therapy by giving rise to drug resistance. As a result, there is a growing urgency to identify compounds that target the “channels of communication” with which a pathogenic process communicates with, rather than the “one” specific target. 

Ergodic Rate Analysis (ERA) recovers growth rates from fixed time point measurements.

In 2013 we published a letter in Nature describing ergodic rate analysis (ERA), a method that retrieves a precise account of the intracellular dynamics of a labeled protein or phospho protein from a single snapshot image of fixed cells.  The novelty of ERA is that the temporal profile (dynamics) of a labeled target is obtained without the expensive need for temporal measurements (e.g. time course or time lapse measurements). While the mathematical details of ERA escape the scope of this overview, the intuition underlying it is simple: faster (more transient) molecular events will be observed in fewer cells in an imaged population. The logic underlying ERA can also be utilized to uncover additional details of the regulation of a labeled reporter target. A feedback inhibition on phospho-Akt, for example, would be revealed by “fewer than expected” cells with increased pAkt levels in an imaged population. Again, the latter statement is an intuitive over-simplification of a rigorously developed mathematical method.


In recent years we have been developing mathematical methods of inference to predict a compounds influence on the regulation of a reporter target from high throughput measurements with single cell microscopy. We anticipate that these statistical methods would not only reduce costs of drug discovery but also provide the ability to screen features that were previously "unscreanable".




Single cell measurements of cell size, DNA levels and a reporter of G1-exit (Geminin degron) are used to estimate a joint probability density finction that describes the dependency of cell size on cell cycle progression. The structure of this function is mathematically analysed to make inference on how cell size is regulated in cell cycle.