AttractorScaffolding | Baldwin effect explored by means of a Boolean network model | Genomics library

AttractorScaffolding is a C++ library typically used in Artificial Intelligence, Genomics applications. AttractorScaffolding has no bugs, it has no vulnerabilities and it has low support. You can download it from GitHub.

Note: The figures here (and their captions) are reproduced from the paper under the terms of the Creative Commons 4.0 license and are attributable to the authors of the paper. The paper associated with this code repository considers a system of Boolean gene networks. Consider a system of 5 genes, labelled a to e, which interact with each other in a region of biological tissue. Each gene can be expressed (1) or not expressed (0). The instantaneous state of all 5 genes can be represented as a 5 bit number with 32 possible values. Because the genes interact, the state of the system a small time into the future is dependent on the current state. The figure below illustrates; each gene receives inputs i to v from the current time step. A table can be created, and randomly populated so that each of the genes has its state a short time in the future (i.e. the next timestep of a simulation) specified. The randomly populated number, which is created by arranging all the coloured columns in Fig. 1 into a line to give a 160 bit number, is what we refer to as the 'genome' in the paper. Figure 1 Gene interaction network. A network of n=5 interacting genes, shown labelled a-e, each with inputs labelled i-v. The truth table determines the expression level of each gene in response to each of the 2^n=32 possible patterns of gene expression. The coloured elements thus constitute a 'genome' of N=n2^n=160 bits, which in this case specifies a maximally fit network (f=1). Referring to the example in Fig. 1, if all the genes are in the 'not expressed' (0) state (look at the first row of the 'input' table), then at the next time step, gene a (red) will be 'not expressing' or 0, gene b (yellow) will be 'expressing' or 1, and so on. If we have some pre-specified starting state (For example, [00001]) and some required target state (say [10101]), then we can compute the states that the system will progress through and see if the intial state maps to the target state. We regard as fully fit (fitness=1) a genome which progresses from the initial state [00001] to the target state (in any number of steps) and which then cycles back on itself - that is, the state [10101] leads directly to [10101] as a 'stable point attractor'. :warning: In Fig. 1, you'll see that the input row [10101] does not map directly to the output row [10101]. This looks like an error, but it's not. Refer to the connectivity pattern in the left side of the figure (the pentagon). Each gene 'sees' an input pattern which starts with its own expression as input i. It then receives the inputs clockwise around the pentagon; For example, b sees the state of b as input i, the state of c as its input ii, d is input iii, e maps to iv and finally, the state of a is b's input v. When the expression pattern is [10101], then the input pattern seen by a is [10101], but b sees [01011], c sees [10110], d sees [01101] and e sees [11010]. To determine the system's expression at the next time step, you have to consult five rows of the input/output table to determine the output: [10101] for a (red) is 1, [01011] for b (yellow) is 0, [10110] for c (green) is 1, [01101] for d (blue) is 0, [11010] for e (purple) is 1: [10101]! Thus, the state [10101] does indeed map directly back to itself. Although it is possible to 'wire' the pentagon diagram so that a single row in the table can conveniently be used to read the next state of the system, this convenience disappears as soon as we study a system for which the number of inputs to each gene is less than n. Figure 2 The attractor landscape. The developmental dynamics of the network that is specified by the genome in Fig. 1 reveals five attractors (four point attractors and one with a limit cycle of length two). Every possible gene expression pattern is represented by one dot, and the transitions between states are represented by arrows. Initial states [10000] and [00000] map to target states [10101] and [01010] as point attractors. The blue path corresponds to the development of the network in the anterior context and the red path corresponds to the development of the network in the posterior context. The attractor landscape specified by the genome in the table in Fig. 1 is shown in Fig. 2. Each dot in the figure represents a single gene expression state and indicates how the system develops over time. Here, the initial state [10000] follows a path through 5 intermediate states to finally end up on the stable point attractor [10101], which cycles back on itself. The same genome also takes a starting state of [00000] to the state [01010]. Up to this point, I've referred to 5 genes interacting within a 'single context'; meaning that the genes are in the same spatial location. This work relates the genes a-e to a specific set of genes which are known to be important in the arealization of the mammalian neocortex. These genes (Fgf8, Pax6, Emx2, Sp8 and Coup-tf1) produce specific patterns of expression; Fgf8 is initially expressed at the anterior part of the cortical plate, and initiates a cascade of interactions which result in anterior to posterior or posterior to anterior gradients of expression for each of the 5 genes. We divided space up into only two compartments, anterior and posterior and asked how easy is it to find the genome which takes the anterior state [10000] to the anterior target [10101] and the posterior initial state [00000] to the target [01010]. The anterior and posterior target states represent a spatial gradient in expression for all 5 genes. By random search, this is difficult. Approximately 1 in every 60000 genomes achieves this, where we define the desired, stable target states as having fitness 1, and anything else fitness 0.