Optimal spatial allocation of enzymes as an investment problem

Given a limited number of molecular components, cells face various allocation problems demanding decisions on how to distribute their resources. For instance, cells decide which enzymes to produce at what quantity, but also where to position them. Here we focus on the spatial allocation problem of how to distribute enzymes such as to maximize the total reaction flux produced by them in a system with given geometry and boundary conditions. So far, such distributions have been studied by computational optimization, but a deeper theoretical understanding was lacking. We derive an optimal allocation principle, which demands that the available enzymes are distributed such that the marginal flux returns at each occupied position are equal. This ‘homogeneous marginal returns criterion’ (HMR criterion) corresponds to a portfolio optimization criterion in a scenario where each investment globally feeds back onto all payoffs. The HMR criterion allows us to analytically understand and characterize a localization-delocalization transition in the optimal enzyme distribution that was previously observed numerically. In particular, our analysis reveals the generality of the transition, and produces a practical test for the optimality of enzyme localization by comparing the reaction flux to the influx of substrate. Based on these results, we devise an additive construction algorithm, which builds up optimal enzyme arrangements systematically rather than by trial and error. Taken together, our results reveal a common principle in allocation problems from biology and economics, which can also serve as a design principle for synthetic biomolecular systems.

Optimizing Non-Pharmaceutical Intervention Strategies Against COVID-19 Using Artificial Intelligence

One key task in the early fight against the COVID-19 pandemic was to plan non-pharmaceutical interventions to reduce the spread of the infection while limiting the burden on the society and economy. With more data on the pandemic being generated, it became possible to model both the infection trends and intervention costs, transforming the creation of an intervention plan into a computational optimization problem. This paper proposes a framework developed to help policy-makers plan the best combination of non-pharmaceutical interventions and to change them over time. We developed a hybrid machine-learning epidemiological model to forecast the infection trends, aggregated the socio-economic costs from literature and expert knowledge, and used a multi-objective optimization algorithm to find and evaluate various intervention plans. The framework is modular and easily adjustable to a real-world situation, it is trained and tested with data collected from almost all countries of the world, and its proposed intervention plans generally outperform those used in real life in terms of both the number of infections and intervention costs.