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Asymmetric interactions between different species of molecules have previously been demonstrated to result in self-organized patterns and functions. If one species A is attracted to B, but in turn, B is repelled by A, run-and-chase dynamic emerges.

This is a common phenomenon observed in minimal models of living matter. In contrast, if the attraction and repulsion are mutual, the system typically acquires a more static state with separated phases—such as oil droplets in water.

Suropriya Saha and Ramin Golestanian from the department of Living Matter Â鶹ÒùÔºics at MPI-DS have now extended the model of non-reciprocal interactions. They investigated what would happen to the system if the role of the two molecule species were not linear. Their findings are in Nature Communications.

"When we introduce nonlinearity into the system, the resulting behavior becomes dynamic and unpredictable," explains Saha, the first author of the study. "This means that the roles of molecule A and B can be reversed, spontaneously reversing the roles in the run-and-chase interaction—or also acquiring a reciprocal behavior. Nonlinearities arise generically in real systems in nature, yielding to a more comprehensive model describing living matter."

The result of such nonlinear non-reciprocal interactions is the coexistence of run-and-chase dynamics and phase separation. Moreover, since the role of the two species can reverse dynamically, the entire system becomes chaotic.

"In living systems, such non-reciprocal interactions are more the rule than the exception," says Golestanian. "Hence this model reflects the versatile dynamics of living systems and thus helps us understand the complexity of how matter can organize and contribute to the formation of life."