The tasks of designing messenger RNAs and non-coding RNAs are discrete
optimization problems, and several versions of these problems are NP-hard. As
an alternative to commonly used local search methods, we formulate these
problems as continuous optimization and develop a general framework for this
optimization based on a new concept of “expected partition function”. The basic
idea is to start with a distribution over all possible candidate sequences, and
extend the objective function from a sequence to a distribution. We then use
gradient descent-based optimization methods to improve the extended objective
function, and the distribution will gradually shrink towards a one-hot sequence
(i.e., a single sequence). We consider two important case studies within this
framework, the mRNA design problem optimizing for partition function (i.e.,
ensemble free energy) and the non-coding RNA design problem optimizing for
conditional (i.e., Boltzmann) probability. In both cases, our approach
demonstrate promising preliminary results. We make our code available at

The Complexity of Designing Messenger RNAs and Non-Coding RNAs

In recent years, the field of RNA design has gained significant attention due to its potential applications in various areas of biology and medicine. The ability to design messenger RNAs (mRNAs) and non-coding RNAs with specific properties holds great promise for advancing our understanding of gene expression and facilitating the development of novel therapeutic interventions.

However, designing these RNA molecules is far from a straightforward task. In fact, the design process can be seen as a discrete optimization problem, with multiple versions of these problems being classified as NP-hard. This complexity arises from the vast search space of possible RNA sequences and the need to optimize specific objective functions.

Traditionally, local search methods have been employed to tackle these optimization problems. These methods involve iteratively improving an initial solution by exploring neighboring solutions. While effective, they often suffer from limitations such as getting stuck in suboptimal solutions or not exploring the entire solution space.

As an alternative approach, a team of researchers has formulated the mRNA and non-coding RNA design problems as continuous optimization problems. Their approach involves using a new concept called the “expected partition function” as the basis for optimization.

The fundamental idea of this framework is to start with a distribution over all possible candidate sequences and extend the objective function from a sequence to a distribution. By using gradient descent-based optimization methods, the researchers aim to improve the extended objective function, gradually narrowing down the distribution towards a one-hot sequence, which represents a single optimal solution.

Within this general framework, the researchers applied their approach to two important case studies: mRNA design optimization for partition function (ensemble free energy) and non-coding RNA design optimization for conditional probability (Boltzmann probability).

The preliminary results obtained from these case studies show great promise. The approach demonstrates the potential to design mRNAs and non-coding RNAs with desired properties more effectively compared to traditional local search methods. By formulating the design problems as continuous optimization, the researchers have overcome some of the limitations associated with discrete optimization approaches.

One notable aspect of this research is the multi-disciplinary nature of the concepts involved. The approach combines concepts from optimization theory, statistical physics, and molecular biology to create a unified framework for RNA design. This interdisciplinary approach highlights the importance of collaboration between different fields in tackling complex biological problems.

To facilitate further exploration and development in this area, the researchers have made their code available on GitHub, allowing other scientists and researchers to build upon their work and contribute to the advancement of RNA design.

Overall, this study represents a significant step forward in the field of RNA design. By leveraging continuous optimization methods and adopting a multi-disciplinary approach, the researchers have provided valuable insights into the complexity of designing messenger RNAs and non-coding RNAs. This work has the potential to drive further innovation in RNA design and contribute to advancements in various biological and medical applications.

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