Complex networks are noisy, whether they constitute food webs, power grids, or cells. And when networks buzz and crackle beyond normal bounds, bad things can happen: ecosystems can collapse, power grids can leave us in the dark, and cells can tumble into cancerous states.
All these networks are amenable to similar mathematical treatments says a scientific team at Northwestern University. The team, led by physicist Adilson E. Motter, Ph.D., substantiated this claim by focusing on a particularly difficult biophysical problem: the rational control of cellular behavior. To date, attempts to exert such control have been frustrated by the high dimensionality and noise that are inherent properties of large intracellular networks.
Dr. Motter and his colleagues noted that the response of biological systems to noise has been studied extensively. Yet they also realized that little had been done to exploit noise, or to at least channel it. They hoped to find a way to do so and thereby demonstrate the possibility of preserving or inducing desirable cell states.
Using a newly developed computational algorithm, Dr. Motter and colleagues showed that molecular-level noise can be manipulated to control the networks that govern the workings of living cells—promoting cellular health and potentially alleviating diseases such as cancer. They presented their results September 16 in the journal Physical Review X, in an article entitled, “Control of Stochastic and Induced Switching in Biophysical Networks.”
“Here we present a scalable, quantitative method based on the Freidlin-Wentzell action to predict and control noise-induced switching between different states in genetic networks that, conveniently, can also control transitions between stable states in the absence of noise,” wrote the authors. “We apply this methodology to models of cell differentiation and show how predicted manipulations of tunable factors can induce lineage changes, and further utilize it to identify new candidate strategies for cancer therapy in a cell death pathway model.”
Essentially, by leveraging noise, the team found that the high-dimensional gene regulatory dynamics could be controlled instead by controlling a much smaller and simpler network, termed a “network of state transitions.” In this network, cells randomly transition from one phenotypic state to another—sometimes from states representing healthy cell phenotypes to unhealthy states where the conditions are potentially cancerous. The transition paths between these states can be predicted, as cells making the same transition will typically travel along similar paths in their gene expression.
The team compared this phenomenon to the formation of pathways at a university campus. If there is no paved path between a pair of buildings, people will usually take the path that is the easiest to traverse, tromping down the grass to reveal the dirt beneath, creating a so-called desire path. Eventually, campus planners may see this predefined path and pave it.
“Even in systems as complex and high-dimensional as a gene regulatory network, there's typically only one best path that a noisy transition will follow from one state to the next,” said William L. Kath, a professor of engineering sciences and applied mathematics at Northwestern and one of the coauthors of the paper. “You would think that many different paths are possible, but that's not true: one path is much better than all of the others.”
The team began by using noise to define the most-likely transition pathway between different system states, and connecting these paths into the network of state transitions. By doing so, the researchers could then focus on just one path between any two states, distilling a multidimensional system to a series of one-dimensional interconnecting paths.
Then, using their computational approach, the team identified optimal modifications of experimentally adjustable parameters, such as protein activation rates, to encourage desired transitions between different states. The method lends itself to experimental implementations because it changes the system's response to noise rather than changing the noise itself, which is nearly impossible to control.
“Noise is extremely important for systems,” commented Daniel K. Wells, a graduate student in applied math and the paper’s first author. “Instead of directly controlling a cell to move from a bad state to a good state, which is hard, we just make it easier for noise to do this on its own. This is analogous to paving just one path departing a building and leaving all the others unpaved—people leaving the building are more likely to walk on the paved path, and will thus preferentially end up where that path goes.”