IV. Ecosmomics: An Independent, UniVersal, Source Code-Script of Generative Complex Network Systems

5. Common Code: A Further Report of Reliable, Invariant Principles

Kelso, Scott and David Engstrom. The Complementary Nature. Cambridge: MIT Press, 2006. This unique work is mainly noted in Current Vistas and by an extensive review in Recent Writings. An important, overdue statement of this obvious universal quality which is a main theme of this website.

Khaluf, Yara, et al. Scale Invariance in Natural and Artificial Collective Systems. Journal of the Royal Society Interface. Online November, 2017. From General systems theory in the 1960s and before, the Santa Fe Institute in the 1980s, unto this site going online in 2004, the hope and goal has been a common, code-like, form and flow that recurs in kind everywhere. Here complex bioinformatics theorists Khaluf and Pieter Simoens, Ghent University, Eliseo Ferrante, KU Leuven Belgium and Cristian Huepe, Northwestern University provide a deep and wide affirmation. From physical nature to human cultures and in between, an iconic fractal-like, self-organizing, network dynamics is recurrent effect as an exemplary presence. An aspect is its tendency to reach a critical state between discrete individuals and a communal whole, e.g. biofilms, brains and flocks. The authors then begin to consider ways to apply these findings for a better, viable society and technology. And if to reflect at this late day, here is an epochal, salutary discovery coming together in our midst due to worldwise humankinder. In the long arc of uniVerse to humanVerse evolution, nature’s procreative code may pass to our sentient, palliative and creative, intention.

Self-organized collective coordinated behaviour is an impressive phenomenon, observed in a variety of natural and artificial systems, in which coherent global structures or dynamics emerge from local interactions between individual parts. If the degree of collective integration of a system does not depend on size, its level of robustness and adaptivity is typically increased and we refer to it as scale-invariant. In this review, we first identify three main types of self-organized scale-invariant systems: scale-invariant spatial structures, scale-invariant topologies and scale-invariant dynamics. We then provide examples of scale invariance from different domains in science, describe their origins and main features and discuss potential challenges and approaches for designing and engineering artificial systems with scale-invariant properties. (Abstract)

Khovanov, Igor, et al. Editorial. European Physical Journal Special Topics. 222/10, 2013. An introduction to an issue on Nonlinear Dynamics of Deterministic and Stochastic Systems: Unraveling Complexity. And again a standard format for articles of this kind is held to by first citing how every realm from stellar to snail are now known to exemplify this emergent phenomena. With this place, a revitalized systems physics can be sighted as quite morphing into a true cosmic biology.

From the dynamics of the solar system to the functioning of the nerve cell of a snail, nonlinear phenomena are related to some of the most intriguing features of the world around us. In the form of self-sustained oscillations, synchronization, bifurcations, pattern formation, and chaos, nonlinear dynamic phenomena are manifest in physical, chemical, ecological and biological systems. Life itself is characterized by the large number of mutually interacting rhythmic processes it sustains. Nonlinear dynamic phenomena are also important for many types of engineering systems, and the same type of phenomena may be involved in the generation of complex forms of economic and managerial dynamics. (1)

Investigation of the complex dynamic phenomena that can arise in all of these different circumstances help us to get a deeper understanding of the mechanisms underlying a broad range of important problems that, for lack of a proper theoretical framework, were inaccessible for many years and, hence, considered as irrelevant or poorly posed. At the same time the study of nonlinear dynamic phenomena has proved to challenge several classical concepts in physics and mathematics. (1)

Kim, Hyunju, et al. Universal Scaling Across Biochemical Networks of Earth. Science Advances. 5/eaau0149, 2019. This Arizona State University based team, herein HK, Harrison Smith, Cole Mathis, Jason Raymond and Sara Walker, contribute to a flow of papers which lately seem to be closing on, as the extended quotes say, an ability to discern and quantify a common, iterative recurrence from the physical cosmos to chemistry, biology, psychology, cultures and onto the Earth’s biosphere. A prime feature is the formation of generic network activities, along with scale-invariant phase transitions, autocatalytic processes and hierarchical self-organization. As a result, a specific affinity can be drawn between individuals and ecosystems.

The application of network science to biology has advanced our understanding of the metabolism of individual organisms and the organization of ecosystems but has scarcely been applied to life at a planetary scale. To characterize planetary-scale biochemistry, we constructed biochemical networks using a global database of 28,146 annotated genomes and metagenomes, and 8,658 cataloged biochemical reactions. We uncover scaling laws governing biochemical diversity and network structure shared across levels of organization from individuals to ecosystems, and the biosphere as a whole. Taken together our results point to a deeper level of organization in biochemical networks than what has been understood so far. (Abstract excerpt)

There is increasing interest in whether biology is governed by general principles, rather than chemical instantiation or evolutionary contingency. Such principles would be strong candidates for being universal to all life. Universal biology, if it exists, would have important implications for our search for life beyond Earth, for engineering synthetic life in the lab, and for solving the origin of life. So far, systems biology has primarily focused on specific levels of organization within biological hierarchies, such as individual organisms or ecological communities, and is rarely applied to the biosphere as a whole. But, biology exhibits some of its most striking regularities moving up in levels from individuals to ecosystems, and these regularities may ultimately manifest at the level of the biosphere. (1-2)

In order to explore regularities within and between levels of organization, we adopt a network view of biochemistry by constructing reaction networks from genomic and metagenomic data. We show that biochemical networks share universal properties characterized by scaling laws for topology and biochemical diversity. These scaling relations exist independent of evolutionary domain of organization, applying across the nested hierarchy of individuals, ecosystems, and the biosphere. Our results provide a first quantitative application of network theory at a planetary scale that can uncover properties and be predictive of major divisions within a given level. (2)

Koonin, Eugene. Are There Laws of Genome Evolution? PLoS Computational Biology. 7/8, 2011. As now broadly evident, as documented herein, life from cosmos to cities seems to be graced by repetitive, similar nonlinear patterns and processes in manifest effect everywhere. A NIH bioinformatician, geneticist, and author, ponders whether this ubiquitous presence, as apparent in cellular protoplasm, would in fact imply and arise from a realm of independent natural principles. In lieu of more review, the gist of these insights is well conveyed by extended excerpts. See also Koonin’s new book The Logic of Chance: The Nature and Origin of Biological Evolution (Financial Times Press, 2011).

Research in quantitative evolutionary genomics and systems biology led to the discovery of several universal regularities connecting genomic and molecular phenomic variables. These universals include the log-normal distribution of the evolutionary rates of orthologous genes; the power law–like distributions of paralogous family size and node degree in various biological networks; the negative correlation between a gene's sequence evolution rate and expression level; and differential scaling of functional classes of genes with genome size. The universals of genome evolution can be accounted for by simple mathematical models similar to those used in statistical physics…. These models do not explicitly incorporate selection; therefore, the observed universal regularities do not appear to be shaped by selection but rather are emergent properties of gene ensembles. (Abstract, 1)

The most conspicuous universals include: log-normal distribution of the evolutionary rates between orthologous genes; power law–like distributions of membership in paralogous gene families and node degree in biological ‘‘scale-free’’ networks; negative correlation between a gene’s sequence evolution rate and expression level (or protein abundance); distinct scaling of functional classes of genes with genome size. (1)

The universality of these dependencies appears genuinely surprising. For example, the distributions of sequence evolution rate of orthologous genes are virtually indistinguishable in all evolutionary lineages for which genomic data are available, including diverse groups of bacteria, archaea, and eukaryotes. The shape of the distribution did not perceptibly change through about 3.5 billion years of the evolution of life even though the number of genes in the compared organisms differs by more than an order of magnitude, and the repertoires of gene functions are dramatically different as well. The same conundrum pertains to the other universals: despite major biological differences between organisms, these quantitative regularities hold, often to a high precision. What is the nature of the genomic universals? Do they reflect fundamental ‘‘laws’’ of genome evolution or are they ‘‘just’’ pervasive statistical patterns that do not really help us understand biology? (1)

Networks have become ubiquitous images and tools of systems biology. Indeed, any class of interacting objects can be naturally represented by nodes, and the interactions between these objects, regardless of their specific nature, can be represented by edges. (3) These networks are said to be scale-free because the shape of their node degree distribution remains the same regardless of the chosen scale, that is, any subnetwork is topologically similar to the complete network (in other words, scale-free networks display fractal properties). (3) Collectively, the ability of simple models to generate the universals of genome evolution and additional results indicating that the global architecture of biological networks is not a selected feature suggest that all evolutionary universals are not results of adaptive evolution. (3)

Kovacs, Istvan, et al. Community Landscapes: An Integrative Approach to Determine Overlapping Network Module Hierarchy, Identify Key Nodes and Predict Network Dynamics. PLoS One. 5/9, 2010. In this 100 page entry with bioinformatic programs and references, Semmelweis University, Budapest, living system scientists, including Peter Csermely, parse modular networks to uncover a ubiquitous topological feature. Indeed, nature seems intent on forming communal groupings of an appropriate size and populace at each and every strata and instance. Might one even broach an “ubuntu Universe.”

Background: Network communities help the functional organization and evolution of complex networks. However, the development of a method, which is both fast and accurate, provides modular overlaps and partitions of a heterogeneous network, has proven to be rather difficult. Methodology/Principal Findings: Here we introduce the novel concept of ModuLand, an integrative method family determining overlapping network modules as hills of an influence function-based, centrality-type community landscape, and including several widely used modularization methods as special cases. As various adaptations of the method family, we developed several algorithms, which provide an efficient analysis of weighted and directed networks, and (1) determine pervasively overlapping modules with high resolution; (2) uncover a detailed hierarchical network structure allowing an efficient, zoom-in analysis of large networks; (3) allow the determination of key network nodes and (4) help to predict network dynamics.

Labra, Fabio, et al. Scaling Metabolic Rate Fluctuations. Proceedings of the National Academy of Sciences. 104/10900, 2007. Another example of an international collaboration from Chile and the United States, which again reports general principles and topologies, in this case for metabolism dynamics, that hold across 71 individual types from 25 vertebrate species including reptiles, birds, and mammals. Once more deep in the primary literature, a cerebral humankind goes on to describe and discover an organic natural genesis graced by the same recurrent phenomena at each stage and instance.

Complex ecological and economic systems show fluctuations in macroscopic quantities such as exchange rates, size of companies or populations that follow non-Gaussian tent-shaped probability distributions of growth rates with power-law decay, which suggests that fluctuations in complex systems may be governed by universal mechanisms, independent of particular details and idiosyncrasies. We propose here that metabolic rate with individual organisms may be considered as an example of an emergent property of a complex system and test the hypothesis that the probability distribution of fluctuations in the metabolic rate of individuals has a “universal” form regardless of body size or taxonomic affiliation. (10900)

Laurienti, Paul, et al. Universal Fractal Scaling of Self-Organized Networks. Physica A. 390/20, 2011. After some two decades of complex systems studies from every angle, in disparate fields and terms, on every continent, a maturity is lately being reached so it is possible, for example, for this team of Wake Forest University biomedical researchers to propose a natural “universality” of “node and interaction” dynamic network phenomena. To wit, the same fractal pattern and process faithfully recurs across broad Biological, Information, Social, and Technological domains. These extended quotes might portend, circa 2011, a new animate nature suffused with intrinsic creativities that repeat and reiterate across every regnant realm. At what point, and by what insight, might this realization become a revolution, and its spontaneity be appreciated as genetic in kind?

There is an abundance of literature on complex networks describing a variety of relationships among units in social, biological, and technological systems. Such networks, consisting of interconnected nodes, are often self-organized, naturally emerging without any overarching designs on topological structure yet enabling efficient interactions among nodes. Here we show that the number of nodes and the density of connections in such self-organized networks exhibit a power law relationship. We examined the size and connection density of 47 self-organizing networks of various biological, social, and technological origins, and found that the size-density relationship follows a fractal relationship spanning over 6 orders of magnitude. This finding indicates that there is an optimal connection density in self-organized networks following fractal scaling regardless of their sizes. (Abstract, 1)

The findings reported here demonstrate a universal relationship in self-organized networks such that the network size dictates the density. The fractal behavior observed is of particular interest because it indicates that self-organized networks are critically organized. The number of connections within each network is scaled to the size of the network, and this universal behavior likely represents an optimal organization that ensures maximal capacity as a minimal cost. (4-5) We show an important, apparently universal feature of self-organized networks: fractal of size and density connections. This fractal scaling is independent of network types, as the analysis spanned a wide gamut of networks, including biological, information, social, and technological. Thus, it appears that there is an underlying principle to organizing these self-emergent networks, a principle that probably ensures optimal network functioning. (Conclusion, 5)

Letsou, William and Long Cai. Noncommutative Biology: Sequential Regulation of Complex Networks. PLoS Computational Biology. Online August, 2016. CalTech biochemists first describe an apparently constant recurrence in genomes of a common network dynamics and geometry. With this iconic system in place, its similar presence can be noted in many other, far removed natural and social realms.

DNA is the blueprint of life. Yet the order in which a cell follows these instructions makes it capable of generating thousands of different fates. How this information is extracted from underlying gene regulatory networks is unclear, especially given that biological networks are highly interconnected, and that the number of signaling pathways is relatively small. The conventional approach for increasing the information capacity of a limited set of regulators is to use them in combination. Surprisingly, combinatorial logic does not increase the diversity of target configurations or cell fates, but instead causes information bottlenecks. A different approach, called sequential logic, uses noncommutative sequences of a small set of regulators to drive networks to a large number of novel configurations. In this paper we show how sequential logic outperforms combinatorial logic, and argue that noncommutative sequences underlie a number of cases of biological regulation, e.g. how a small number of signaling pathways generates a large diversity of cell types in development. (Summary)

A fundamental question in systems biology is how a small number of signaling inputs specifies a large number of cell fates through the coordinated expression of thousands of genes. This problem is especially challenging given that gene regulatory and other types of networks in biology tend to be highly interconnected and their regulators promiscuous, with regulators affecting multiple targets and targets being affected by multiple regulators. Examples of this architecture include: transcription factor binding networks in bacteria, yeast, plants, and animals; cellular signalling pathways involved in growth and differentiation; the interactome of protein kinases and phosphatases; and synaptic connections between different layers of the brain. (2)

Finally, our results connect outside of biology to strategic planning in social, political, and economic arenas. Anyone familiar with negotiating knows about the limitations inherent in trying to make interconnected groups of people move in specific directions, especially when the actions affect all participants at once. Multiparty negotiations and tournaments may benefit from time-ordered strategies in which enemies temporarily team up, or fringe interest groups are transiently pacified. Determining whether this prediction is borne out in congressional and international negotiations, for example, is an interesting question for political science. In conclusion, the direct path to an outcome in a networks with many interacting parts may have many unintended and prohibitively expensive consequences. A multi-step strategy may achieve the same outcome with minimal cost and side effects. (18-19)

Levin, Simon. Complex Adaptive Systems. Bulletin of the American Mathematical Society. 40/1, 2003. The article lays out guidelines by which to study the evolving biosphere in terms of its nonlinear properties of many autonomous agents, diversity, resiliency, localized interactions, cooperation, pattern emergence and so on.

The notion of complex adaptive systems has found expression in every from cells to societies, in general with reference to the self-organization of complex entities, across scales of space, time and organizational complexity. (3)

Levin, Simon. The Evolution of Ecology. The Chronicle Review. August 13, 2010. The Princeton ecologist notes how this environmental science, since a systems view was necessary from its inception, has grown to be an exemplary model for studies across the ranges of nature and society.

Ecology views biological systems as wholes, not as independent parts, while seeking to elucidate how the wholes emerge from and affect the parts. Increasingly, such a holistic perspective, rechristened at places like the Santa Fe Institute as "the theory of complex adaptive systems," has informed understanding and improved management of economic and financial systems, social systems, complex materials, and even physiology and medicine. Essentially, that means little more than taking an ecological approach to such systems. (13)

Locey, Ken and Jay Lennon. Scaling Laws Predict Global Microbial Diversity. Proceedings of the National Academy of Sciences. 113/5970, 2016. Indiana University biologists attest to the natural presence of a consistent mathematical organization across a widest range of bacterial entities and colonies.

Ecological scaling laws are intensively studied for their predictive power and universal nature but often fail to unify biodiversity across domains of life. Using a global-scale compilation of microbial and macrobial data, we uncover relationships of commonness and rarity that scale with abundance at similar rates for microorganisms and macroscopic plants and animals. We then show a unified scaling law that predicts the abundance of dominant species across 30 orders of magnitude to the scale of all microorganisms on Earth. Using this scaling law combined with the lognormal model of biodiversity, we predict that Earth is home to as many as 1 trillion (1012) microbial species. (Significance)

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