Three subsets of sequence complexity and their relevance to biopolymeric information

Abstract

Genetic algorithms instruct sophisticated biological organization. Three qualitative kinds of sequence complexity exist: random (RSC), ordered (OSC), and functional (FSC). FSC alone provides algorithmic instruction. Random and Ordered Sequence Complexities lie at opposite ends of the same bi-directional sequence complexity vector. Randomness in sequence space is defined by a lack of Kolmogorov algorithmic compressibility. A sequence is compressible because it contains redundant order and patterns. Law-like cause-and-effect determinism produces highly compressible order. Such forced ordering precludes both information retention and freedom of selection so critical to algorithmic programming and control. Functional Sequence Complexity requires this added programming dimension of uncoerced selection at successive decision nodes in the string. Shannon information theory measures the relative degrees of RSC and OSC. Shannon information theory cannot measure FSC. FSC is invariably associated with all forms of complex biofunction, including biochemical pathways, cycles, positive and negative feedback regulation, and homeostatic metabolism. The algorithmic programming of FSC, not merely its aperiodicity, accounts for biological organization. No empirical evidence exists of either RSC of OSC ever having produced a single instance of sophisticated biological organization. Organization invariably manifests FSC rather than successive random events (RSC) or low-informational self-ordering phenomena (OSC).

Figure 1

The inverse relationship between order and complexity as demonstrated on a linear vector progression from high order toward greater complexity (modified from [93]).

Figure 2

The adding of a second dimension to Figure 2 allows visualization of the relationship of Kolmogorov algorithmic compressibility to complexity. The more highly ordered (patterned) a sequence, the more highly compressible that sequence becomes. The less compressible a sequence, the more complex is that sequence. A random sequence manifests no Kolmogorov compressibility. This reality serves as the very definition of a random, highly complex string.

Figure 3

Shannon's original 1948 communication diagram is here modified with an oval superimposed over the limits of Shannon's actual research. Shannon never left the confines of this oval to address the essence of meaningful communication. Any theory of Instruction would need to extend outside of the oval to quantify the ideal function and indirect "meaning" of any message.

Figure 4

Superimposition of Functional Sequence Complexity onto Figure 2. The Y₁ axis plane plots the decreasing degree of algorithmic compressibility as complexity increases from order towards randomness. The Y₂ (Z) axis plane shows where along the same complexity gradient (X-axis) that highly instructional sequences are generally found. The Functional Sequence Complexity (FSC) curve includes all algorithmic sequences that work at all (W). The peak of this curve (w*) represents "what works best." The FSC curve is usually quite narrow and is located closer to the random end than to the ordered end of the complexity scale. Compression of an instructive sequence slides the FSC curve towards the right (away from order, towards maximum complexity, maximum Shannon uncertainty, and seeming randomness) with no loss of function.