What do we mean by biological complexity?

Bird clades with less complex appendicular skeletons tend to have higher species richness

Species richness is strikingly uneven across taxonomic groups at all hierarchical levels, but the reasons for this heterogeneity are poorly understood. It is well established that morphological diversity (disparity) is decoupled from taxonomic diversity, both between clades and across geological time. Morphological complexity has been much less studied, but there is theory linking complexity with differential diversity across groups. Here we devise an index of complexity from the differentiation of the fore and hind limb pairs for a sample of 983 species of extant birds. We test the null hypothesis that this index of morphological complexity is uncorrelated with clade diversity, revealing a significant and negative correlation between the species richness of clades and the mean morphological complexity of those clades. Further, we find that more complex clades tend to occupy a smaller number of dietary and habitat niches, and that this proxy for greater ecological specialisation correlates with lower species richness. Greater morphological complexity in the appendicular skeleton therefore appears to hinder the generation and maintenance of species diversity. This may result from entrenchment into morphologies and ecologies that are less capable of yielding further diversity.

The capabilities of chaos and complexity

To what degree could chaos and complexity have organized a Peptide or RNA World of crude yet necessarily integrated protometabolism? How far could such protolife evolve in the absence of a heritable linear digital symbol system that could mutate, instruct, regulate, optimize and maintain metabolic homeostasis? To address these questions, chaos, complexity, self-ordered states, and organization must all be carefully defined and distinguished. In addition their cause-and-effect relationships and mechanisms of action must be delineated. Are there any formal (non physical, abstract, conceptual, algorithmic) components to chaos, complexity, self-ordering and organization, or are they entirely physicodynamic (physical, mass/energy interaction alone)? Chaos and complexity can produce some fascinating self-ordered phenomena. But can spontaneous chaos and complexity steer events and processes toward pragmatic benefit, select function over non function, optimize algorithms, integrate circuits, produce computational halting, organize processes into formal systems, control and regulate existing systems toward greater efficiency? The question is pursued of whether there might be some yet-to-be discovered new law of biology that will elucidate the derivation of prescriptive information and control. “System” will be rigorously defined. Can a low-informational rapid succession of Prigogine’s dissipative structures self-order into bona fide organization?

Protein kinases: starting a molecular systems view of endocytosis

The field of endocytosis is in strong need of formal biophysical modeling and mathematical analysis. At the same time, endocytosis must be much better integrated into cellular physiology to understand the former's complex behavior in such a wide range of phenotypic variations. Furthermore, the concept that endocytosis provides the space-time for signal transduction can now be experimentally addressed. In this review, we discuss these principles and argue for a systematic and top-down approach to study the endocytic membrane system. We provide a summary of published observations on protein kinases regulating endocytic machinery components and discuss global unbiased approaches to further map out kinase regulatory networks. In particular, protein phosphorylation is at the heart of controlling the physical properties of endocytosis and of integrating these physical properties into the signal transduction networks of the cell to allow a fine-tuned response to the continuously varying physiological conditions of a cell.

Functional information and the emergence of biocomplexity

Complex emergent systems of many interacting components, including complex biological systems, have the potential to perform quantifiable functions. Accordingly, we define "functional information," I(E(x)), as a measure of system complexity. For a given system and function, x (e.g., a folded RNA sequence that binds to GTP), and degree of function, E(x) (e.g., the RNA-GTP binding energy), I(E(x)) = -log(2)[F(E(x))], where F(E(x)) is the fraction of all possible configurations of the system that possess a degree of function > or = E(x). Functional information, which we illustrate with letter sequences, artificial life, and biopolymers, thus represents the probability that an arbitrary configuration of a system will achieve a specific function to a specified degree. In each case we observe evidence for several distinct solutions with different maximum degrees of function, features that lead to steps in plots of information versus degree of function.

Stochastic approaches in phyllotaxis

Theoretical models of phyllotaxis are based on geometric regularities appearing at the level of the shoot apical meristem (SAM). However, one cannot forget the presence of perturbed patterns in many plants. Disorganized patterns found in mutants of Arabidopsis and Antirrhinum bring new theoretical problems that cannot be solved by using models developed to analyse regular phyllotactic patterns. One way to take into account the perturbed patterns is to use a probabilistic approach to phyllotaxis. This review will focus mainly on recent probabilistic approaches that can be used to analyse perturbed patterns found in the plant kingdom in general and in phyllotactic mutants in particular. More precisely, it will be shown how probabilistic approaches can be used to determine the degree of order of phyllotactic patterns. By using particular tests, it is possible to statistically differentiate between whorled and distichous patterns (aggregated dispersion), spiral patterns (uniform dispersion), and random patterns (random dispersion). The elaboration of a general probabilistic model of phyllotaxis represents a new challenge for both theoretical and experimental research.

Emergence of complex patterns induced by dynamic systems implemented in dynamic structures (DS)2

We present the evolution of the simple system of Meinhardt implemented in both static or dynamic two-dimensional structures of almost-squared cells. In a static structure of 8 x 4=32 to 128 x 128=16384 cells, the pattern observed is periodic. An algorithm allows us to divide the cells following the greater size, and to define a dynamic structure. The implementation of the same Meinhardt system in this dynamic structure varying from 32 to 16 384 cells and a context of the same genotypic complexity for the model provides aperiodic patterns, with a higher phenotypic complexity than those observed in static structures, while the number of computations is comparable. We define that emergence occurs each time the ratio of phenotypic/genotypic complexities increases.

Three subsets of sequence complexity and their relevance to biopolymeric information

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).