麻豆淫院

The seemingly unpredictable, and thereby uncontrollable, dynamics of living organisms have perplexed and fascinated scientists for a long time. While these dynamics can be represented by reaction networks, which can model a variety of biological systems, taming and therefore controlling these dynamics can be challenging.

Now, researchers from Japan have taken a major step toward solving the control problem by integrating concepts from information theory.

In an article in PRX Life, researchers from the Institute of Industrial Science, The University of Tokyo have developed a mathematical theory that can be used to design optimization strategies for dynamical networks, such as those comprising living organisms.

The researchers used optimal control theory, a branch of mathematics that studies strategies capable of guiding a system toward the best possible reward. Everyday applications of this theory include self-driving cars, robots, and financial plans. However, this theory is difficult to apply to biological systems with discrete population sizes, nonlinear many-to-many interactions and non-Gaussian randomness, which differ enormously from conventional continuous, linear and Gaussian systems.

"Most control theory applications involve things that change smoothly, but biological systems often exhibit distinct jumps," says Shuhei Horiguchi, lead author of the paper. "Furthermore, a biological population can become extinct, which presents a major complication when modeling these systems."

The population dynamics were highly nonlinear鈥攖he relationships between variables were many-to-many鈥攚hich made the optimization problem extremely difficult to solve. However, the team found that tools from another branch of mathematics, information theory, provided exactly what they needed to simplify them.

In particular, the f-divergence, which measures how similar two probability distributions are, had several desirable mathematical properties that gave the researchers a way to find a simpler solution.

"It is often challenging to solve nonlinear optimization problems efficiently," explains Tetsuya J. Kobayashi, senior author.

"However, in our case, we were able to use a little-known trick called the Cole鈥揌opf transformation, together with the Kullback鈥揕eibler divergence, to convert our nonlinear equation into a linear one, rendering the problem solvable."

The power of the new mathematical framework lies in how widely it can be applied. It can be used to investigate topics as diverse as molecular motor transport, biological diversity, and epidemic control, among others. The developed model has been shown to elucidate certain behaviors that are common to these seemingly contrasting and varied scenarios.

"We found that in systems that can grow or decline rapidly over time, the optimal strategy may be to alternate between a waiting period and an active period," says Horiguchi.

"For example, in the conservation of species diversity, active interventions turn out to be efficient only when one of the species is suffering a severe decline and is being threatened with extinction. Optimal strategies for other biological systems may share this mode-switching strategy."

Given that these findings can apply to a range of subjects, this work holds promise in explaining and improving phenomena from a variety of fields including medicine, environmental management, and synthetic biology.

The team is optimistic that this new framework can be extended to handle even larger and more complicated biological systems.