Complex Systems Made Simple

Just as the name implies, com­plex sys­tems are dif­fi­cult to tease apart. An organism’s genome, a bio­chem­ical reac­tion, or even a social net­work all con­tain many inter­de­pen­dent components—and changing any one of them can have per­va­sive effects on all the others. In the case of a very large system, like the human genome, which con­tains 20,000 inter­con­nected genes, it’s impos­sible to mon­itor the whole system at once.

But that may not matter any­more. In a paper pub­lished in the pres­ti­gious mul­ti­dis­ci­pli­nary journal Pro­ceed­ings of the National Academy of Sci­ence, North­eastern net­work sci­en­tists have devel­oped an algo­rithm capable of iden­ti­fying the subset of components—or nodes—that are nec­es­sary to reveal a com­plex system’s overall nature.

The approach takes advan­tage of the inter­de­pen­dent nature of com­plexity to devise a method for observing sys­tems that are oth­er­wise beyond quan­ti­ta­tive scrutiny.

“Con­nect­ed­ness is the essence of com­plex sys­tems,” said Albert-​​László Barabási, one of the paper’s authors and a Dis­tin­guished Pro­fessor of Physics with joint appoint­ments in biology and the Col­lege of Com­puter and Infor­ma­tion Sci­ence. “Thanks to the links between com­po­nents, infor­ma­tion is dis­trib­uted throughout a net­work. Hence I do not need to mon­itor everyone to have a full sense of what the system does.”

Barabási’s col­lab­o­ra­tors com­prise Jean-​​Jacques Slo­tine of M.I.T. and Yang-​​Yu Liu, lead author and research asso­ciate pro­fessor in Northeastern’s Center for Com­plex Net­work Research, for which Barabási is the founding director.

Using their novel approach, the researchers first iden­tify all the math­e­mat­ical equa­tions that describe the system’s dynamics. For example, in a bio­chem­ical reac­tion system, sev­eral smaller reac­tions between periph­er­ally related mol­e­cules may col­lec­tively account for the final product. By looking at how the vari­ables are affected by each of the reac­tions, the researchers can then draw a graph­ical map of the system. The nodes that form the foun­da­tion of the map reveal them­selves as indis­pen­sible to under­standing any other part of the whole.

“What sur­prised me,” said Liu, “was that the nec­es­sary nodes are also suf­fi­cient in most cases.” That is, the indis­pen­sible nodes can tell the whole story without drawing on any of the other components.

The meta­bolic system of any organism is a col­lec­tion of hun­dreds of mol­e­cules involved in thou­sands of bio­chem­ical reac­tions. The new method, which com­bines exper­tise from con­trol theory, graph theory, and net­work sci­ence, reduces large com­plex sys­tems like this to a set of essen­tial “sensor nodes.”

In the case of metab­o­lism, the researchers’ algo­rithm could sim­plify the process of iden­ti­fying bio­markers, which are mol­e­cules in the blood that tell clin­i­cians whether an indi­vidual is healthy or sick. “Most of the cur­rent bio­markers were selected almost by chance,” said Barabási. “Chemists and doc­tors found that they happen to work. Observ­ability offers a rational way to choose bio­markers, if we know the system we need to monitor.”