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Encyclopedia of Complexity and Systems Science pp 489–511Cite as

Biological Complexity and Biochemical Information

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Definition of the Subject

Biological complexity refers to a measure of the intricateness, or complication, of a biological organism that is directly related to thatorganism's ability to successfully function in a complex environment. Because organismal complexity is difficult to define, several differentmeasures of complexity are often used as proxies for biological complexity, such as structural, functional, or sequence complexity. While the complexityof single proteins can be estimated using tools from information theory, a whole organism's biological complexity is reflected in its set ofexpressed proteins and its interactions, whereas the complexity of an ecosystem is summarized by the network of interacting species and their interactionwith the environment.

Introduction

Mankind's need to classify the world around him is perhaps nowhere more apparent than in our zeal to attach to each and every living organisma tag that reveals its relationship to ourselves. The idea that all forms...

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Abbreviations

C-value:

The haploid genome size of an organism, measured either in picograms (pg) or base pairs (bp).

Degree distribution:

The probability distribution P(d) to find a node with d edges in a network.

Entropic profile:

A graph of the per-site entropy along the sites of a biomolecular sequence, such as a DNA, RNA, or protein sequence.

Epistasis:

Generally, an interaction between genes, where the fitness effect of the modification of one gene influences the fitness effect of the modification of another gene. More specifically, an interaction between mutations that can be either positive (reinforcing or synergistic), or negative (mitigating or antagonistic).

Erdös–Rényi network:

A random graph with a binomial degree distribution.

Fitness:

A numerical measure predicting the long-term success of a lineage.

Jensen–Shannon divergence:

In probability and statistics, a measure for the similarity of probability distributions, given by the symmetrized relative entropy of the distributions.

Module:

In network theory, a group of nodes that is closely associated in connections or function, but only weakly associated to other such groups.

Motif:

In network theory, a subgraph of small size.

Network diameter:

For networks, the average geodesic distance between nodes, defined as \( D= 1 / m \sum_{i=1}^n\sum_{j=1}^n d(i,j) \), where m is the number of edes of the graph, n is the number of nodes, and \( { d(i } \), \( { j) } \) is the shortest path distance between nodes i and j.

Phylogenetic depth:

A measure of the genetic distance between a genome and its ancestor on the same line of descent, given by the number of genetically different genomes on the line between the genomes plus one.

Random variable:

In probability and statistics, a mathematical object with discrete or continuous states that the object takes on with probabilities drawn from a probability distribution associated to the random variable.

Source entropy:

The entropy of a sequence generated by a process that generates symbols with a given probability distribution.

Wright–Fisher process:

In population genetics, a stochastic process that describes how genes are transmitted from one generation to the next.

Turing machine:

In mathematics, an abstract automaton that manipulates symbols on a tape directed by a finite set of rules.

Watson-Crick pairing:

In biochemistry, the pairing between nucleotides adenine and thymine (A-T), and guanine and cytosine (G-C).

Zipf's law:

A relationship between the frequency f and the rank k of words in a text, of the form \( { f(k)\sim k^s } \), where s is the exponent of the distribution.

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Acknowledgments

I am grateful to Arend Hintze for the collaborative work in Sect. “ NetworkComplexity”, as well as numerous discussions. I am also indebted to Matthew Rupp for the analysis shown in Figs. 5 and 6. This work was supported in part by the National Science FoundationsFrontiers in Integrative Biological Research grant FIBR-0527023, a Templeton Foundation research grant, and DARPA's FunBio initiative.

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  1. Keck Graduate Institute of Applied Life Sciences, State University of New York, Claremont, USA

    Christoph Adami

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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Adami, C. (2009). Biological Complexity and Biochemical Information . In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_33

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