Scientists at Washington University in St. Louis and collaborating institutions say they have developed a unified, data-driven computational approach to infer and reveal the connections in biological and chemical oscillatory networks that impact circadian rhythms, based on their time-series data. Once they establish the topology of these complex networks, they can infer how cells in the network work together in synchrony, an important state for the brain.

Abnormal synchrony has been linked to a variety of brain disorders, such as epilepsy, Alzheimer's disease and Parkinson's disease. The team published its study (“Inferring dynamic topology for decoding spatiotemporal structures in complex heterogeneous networks”) in PNAS.

“Extracting complex interactions (i.e., dynamic topologies) has been an essential, but difficult, step toward understanding large, complex, and diverse systems including biological, financial, and electrical networks. However, reliable and efficient methods for the recovery or estimation of network topology remain a challenge due to the tremendous scale of emerging systems (e.g., brain and social networks) and the inherent nonlinearity within and between individual units,” write the investigators.

“We develop a unified, data-driven approach to efficiently infer connections of networks (ICON). We apply ICON to determine topology of networks of oscillators with different periodicities, degree nodes, coupling functions, and time scales, arising in silico, and in electrochemistry, neuronal networks, and groups of mice. This method enables the formulation of these large-scale, nonlinear estimation problems as a linear inverse problem that can be solved using parallel computing. Working with data from networks, ICON is robust and versatile enough to reliably reveal full and partial resonance among fast chemical oscillators, coherent circadian rhythms among hundreds of cells, and functional connectivity mediating social synchronization of circadian rhythmicity among mice over weeks.”

Jr-Shin Li, Ph.D., professor of systems science and mathematics and an applied mathematician in the School of Engineering and Applied Science, Washington University, developed an algorithm, called the ICON (infer connections of networks) method, that shows the strength of these connections over time. Previously, researchers could only determine whether a connection existed between networks.

Dr. Li and collaborators first tested their method on a simulated network of different sizes they created. Next, they tested the method on a network of oscillators  (populations of dynamic units that repeatedly fire together, go silent, then fire together again ) created in the lab by Istvan Kiss, Ph.D., professor of chemistry at Saint Louis University.

When they applied Dr. Li's algorithm to the network of interactions among the synthetic oscillators, the results matched what Dr. Kiss had determined through his experiments, finding the same connections in a network of 15 chemical oscillators. Such prediction of this dynamic topology was not previously possible, the researchers said.

Dr. Li points out that this method has a variety of applications beyond cell networks.

“This lays the foundation to analyze real-world complex networks of tremendous size, such as transportation, internet, power grids, and social networks,” he says.

Dr. Li also collaborated with Erik Herzog, Ph.D., professor of biology in arts and sciences at Washington University who studies the cellular and molecular basis of circadian rhythms in mammals to determine the connections between cells in a mouse brain. Dr. Herzog measured the circadian rhythm from 541 cells from the right and left sides of the mouse brain, then asked Dr. Li to estimate how these connections changed over time, something that hadn't been done in the biology field.

“The connection at one time may be strong, but at another time it may be stronger or weaker, so we can use this data to recover the functional connectivity,” Dr. Li says. “If we know this, then we know the network, then we can do more study and investigate over time whether this network will be synchronized or whether specific dynamic patterns will emerge.”

Dr. Herzog says ICON would help him and other scientists to understand principles that allow systems to efficiently synchronize.

For example, we want to define the essential features of networks of cells that keep daily time under different conditions,” notes Dr. Herzog. “We hope that ICON can map out connections and describe the interactions, such as attraction versus repulsion, of cells at different developmental stages so we can understand more about how circadian systems assemble after birth, adapt to challenges such as winter or summer, and fail to coordinate during stressors such as shift work or flying across multiple time zones.”

In another experiment, collaborator William Schwartz, Ph.D., a former visiting professor of biology at Washington University now at the University of Texas at Austin, tested the method on seven groups of five mice who were housed together for a period of time as social networks. Dr. Schwartz measured the oscillations of the mice at the end of the experiment and provided the data to Dr. Li, who applied his algorithm to infer results from the data. In the end, both Drs. Schwartz and Li found that four of the groups of mice had social synchronization because they had the same body temperatures at the end of their time together. Three groups did not have the same body temperatures and were not socially synchronized.








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