This answer will discuss all by the Nature inspired algorithms, past and the future ones. Behind each such algorithm, there is an observation of biologists, biochemists, physicists, mathematicians, and researchers working in other disciplines about the means of computation, information processing, and problem-solving present and observed within natural phenomena.

This means that the observations and understanding of inner workings of bio-computations goes first. Therefore, it is a great idea to study work of such researchers prior to starting development of a novel algorithm.

Just one starting review that will definitely help to initiate such search is provided in the end (Adamatzky), projects.

Theory of computation in biology is an extremely exciting field. What I do recommend is to focus on emergent computations that are robust with a high level of error resilience (see my paper of robust generalization of the 'Game of Life' for introduction).

When you have a wide and deep understanding of biocomputing, it becomes much easier to develop your own algorithms. The secret is that we still know very little about biocomputing and the future is hiding a lot of surprises for us.

You had chosen an exciting area of research, which is linking and laying at the frontiers of biology, medicine, mathematics, complex systems, computation & algorithms, and beyond.

References:

[1] " A brief history of liquid computers" by Andrew Adamatzky

https://www.researchgate.net/project/Complex-Systems-in-Physics-Biology-and-Medicine-Backgrounds-Understanding-Modeling-and-Software/update/6186589fb3729f0f619156ed

[2] There are more papers shared, which are dealing with the same and similar topics in my projects, that links biology, medicine, and computational approaches.

[3] Jiri Kroc: "Why Do Biology and Medicine Need to Study Robust Massive Parallel Information Processing Environments: Explained on the Game of Life and Its Generalization?", preprint, ResearchGate (Feb 2022)