Charles Darwin meets Rube Goldberg: a tale of biological convolutedness

Charles Darwin studying a Rube Goldberg Machine (Freepik Generative AI, text-to-image)

For this Darwin Day post (2024), I will discuss the paper Machinery of Biocomplexity [1]. This paper introduces the notion of Rube Goldberg machines as a way to explore biological complexity and non-optimal function. This concept was first highlighted on Synthetic Daises in 2009 [2], while an earlier version of the paper was discussed on Synthetic Daisies in 2013 [3]. The paper was revised in 2014 to include a number of more advanced computational concepts, after a talk to the Network Frontiers Workshop at Northwestern University in 2013 [4]. 

Figure 1. Block and arrow model of a biological RGM (bRGM) that captures the non-optimal changes resulting from greater complexity. Mutation/Co-option removes the connection between A and B, then establishes a new set of connection with D. Inversion (bottom) flips the direction of connections between C-B and C-A, while also removing the output. This results in the addition of E and D which reestablishes the output in a circuitous manner.

Biological Rube Goldberg Machines (bRGNs) are defined as a computational abstraction of convoluted, non-optimal mechanisms. Non-optimal biological systems are represented using flexible Markovian box and arrow models that can be mutated and expanded given functional imperatives [5]. Non-optimality is captured through the principle of "maximum intermediate steps": biological systems such as neural pathways, metabolic reactions, and serial interactions do not evolve to the shortest route but is constrained (and perhaps even converge to) the largest number of steps. This results in a set of biological traits that functionally emerge as a biological process. Figure 1B shows an example where maximal steps represents a balance between the path of least resistance and exploration given constraints on possible interconnections [6]. The paths from A-E, E-B, and C-D are the paths of least resistance given the constraints of structure and function. In the sense that optimality is a practical outcome of physiological function, a great degree of intermediacy can preserve unconventional pathways that are utilized only spontaneously.

This can be seen in a wide variety of biological systems and is a consequence of evolution. Evolutionary exaptation, the evolution of alternative functions, and serial innovation all result in systems with a large number of steps from input to output. But sometimes convolution is the evolutionary imperative in and of itself. As fitness criteria change over evolutionary time, traces of these historical trajectories can be observed in redundant pathways and other results of subsequent evolutionary neutrality. One example from the paper involves a multiscale model (genotype-to-phenotype) that exploits both tree depth and lateral connectivity to maximize innovation in the production of a phenotype (Figure 2). While our models are based on connections between discrete states, bRGMs can also provide insight into the evolution of looser collections of single traits and even networks, where the sequence of function is bidirectional and hard to follow in stepwise fashion.

Figure 2.  A hypothetical biological RGM representing a multi-scale relationship. Each set of elements (A-F) represents the number of elements at each scale (actual and potential connections are shown with bold and thin lines, respectively). Examples of convolutedness incorporate both loops (as with E5,1 and E5,5) and the depth of the entire network.

The paper also features extensions of the basic bRGM, including massively convoluted architectures and microfluidic implementations. In the former, interconnected networks represent systems that are not only maximal in terms of size or length, but also massively topologically complex [7]. One example of this is cortical folding and the resulting neuronal connectivity in Mammalian brains. The latter example is based on fluid dynamics and combinatorial architectures that are more in line with discrete bRGMs (Figure 3). 

Figure 3. A microfluidic-inspired bRGM model that mimics the complexity of biological fluid dynamics (e.g. blood vessel networks). G1, G2, and G3 represent iterations of the system.

References:

[1] Alicea, B. (2014). The "Machinery" of Biocomplexity: understanding non-optimal architectures in biological systems. arXiv, 1104.3559.

[2] Non-razors, unite! January 30, 2009. https://syntheticdaisies.blogspot.com/2009/01/non-razors-unite.html

[3] Maps, Models, and Concepts: July Edition. Synthetic Daises blog. July 13, 2013. https://syntheticdaisies.blogspot.com/2013/07/maps-models-and-concepts-july-edition.html

[4] Inspired by a visit to the Network's Frontier....  Synthetic Daises blog. December 16, 2013. https://syntheticdaisies.blogspot.com/2013/12/fireside-science-inspired-by-visit-to.html

[5] when dealing with a large number of steps or in a polygenic context, these types of models can also resemble renormalization groups. For more on renormalization group, please see: Wilson, K.G. (1975). Renormalization group methods. Advances in Mathematics, 16(2), 170-186.

[6] this balance is as predicted by Constructive Neutral Evolution (CNE). For a relevant paper, please see: Gray et.al (2010). Irremediable Complexity? Science, 330(6006), 920-921.

[7] in the paper, this is referred to as Spaghettification, a term borrowed from the physics of gravitation. See this reference for an interesting implementation of this in soft materials:  Bonamassa et.al (2024). Bundling by volume exclusion in non-equilibrium spaghetti. arXiv, 2401.02579.