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Biological randomness is an even more complex issue. Both in phylogenesis and ontogenesis, randomness enhances variability and diversity; hence, it is core to biological dynamics. Each cell reproduction yields a (slightly) random distribution of proteomes⁸, DNA and membrane changes, both largely due to random effects. In Longo and Montévil (2014a), this is described as a fundamental “critical transition”, whose sensitivity to minor fluctuations, at transition, contributes to the formation of new coherence structures, within the cell and in its ecosystem. Typically, in a multicellular organism, the reconstruction of the cellular micro-environment, at cell doubling, from collagen to cell-to-cell connection and to the general tensegrity structure of the tissular matrix, all yield a changing coherence which contributes to variability and adaptation, from embryogenesis to aging. A similar phenomenon may be observed in an animal or plant ecosystem, a system yet to be described by a lesser coherence of the structure of correlations, in comparison to the global coherence of an organism⁹.

Similarly, the irregularity in the morphogenesis of organs may be ascribed to randomness at the various levels concerned (cell reproduction and frictions/interactions in a tissue). Still, this is functional, as the irregularities of lung alveolus or of branching in vascular systems enhance ontogenetic adaptation (Fleury and Gordon 2012). Thus, we do not call these intrinsically random aspects of onto-phylogenesis “noise”, but consider them as essential components of biological stability, a permanent production of diversity (Bravi Longo 2015). A population is stable because it is diverse “by low numbers”: 1,000 individuals of an animal species in a valley are more stable if they are diverse. From low numbers in proteome splitting to populations, this contribution of randomness to stability is very different from stability derived from stochasticity in physics, typically in statistical physics, where it depends on huge numbers.

We next discuss a few different manifestations of randomness in biology and stress their positive role. Note that, as for the “nature” of randomness in biology, one must refer, at least, to both quantum and classical phenomena.

First, there exists massive evidence of the role of quantum random phenomena at the molecular level, with phenotypic effects (see Buiatti and Longo 2013 for an introduction). A brand new discipline, quantum biology, studies applications of “non-trivial” quantum features such as superposition, non-locality, entanglement and tunneling to biological objects and problems (Ball 2011). “Tentative” examples include: (1) the absorbance of frequency-specific radiation, i.e. photosynthesis and vision; (2) the conversion of chemical energy into motion; and, (3) DNA mutation and activation of DNA transposons.

In principle, quantum coherence – a mathematical invariant for the wave function of each part of a system – would be destroyed almost instantly in the realm of a cell. Still, evidence of quantum coherence was found in the initial stage of photosynthesis (O’Reilly and Olaya-Castro 2014). Then, the problem remains: how can quantum coherence last long enough in a poorly controlled environment at ambient temperatures to be useful in photosynthesis? The issue is open, but it is possible that the organismal context (the cell) amplifies quantum phenomena by intracellular forms of “bio-resonance”, a notion defined below.

Moreover, it has been shown that double proton transfer affects spontaneous mutation in RNA duplexes (Kwon and Zewail 2007). This suggests that the “indeterminism” in a mutation may also be given by quantum randomness amplified by classical dynamics (classical randomness, see section 1.6).

Thus, quantum events coexist with classical dynamics, including classical randomness, a hardly treated combination in physics – they should be understood in conjunction, for lack of a unified understanding of the respective fields. Finally, both forms of randomness contribute to the interference between levels of organization, due to regulation and integration, called bio-resonance in Buiatti and Longo (2013). Bio-resonance is part of the stabilization of organismal and ecosystemic structures, but may also be viewed as a form of proper biological randomness, when enhancing unpredictability. It corresponds to the interaction of different levels of organization, each possessing its own form of determination. Cell networks in tissues, organs as the result of morphogenetic processes, including intracellular organelles, are each given different forms of statistical or equational descriptions, mostly totally unrelated. However, an organ is made of tissues, and both levels interact during their genesis, as well as along their continual regeneration.

Second, for classical randomness, besides the cell-to-cell interactions within an organism (or among multicellular organisms in an ecosystem) or the various forms of bio-resonance (Buiatti and Longo 2013), let us focus on macromolecules’ Brownian motion. As a key aspect of this approach, we observe that Brownian motion and related forms of random molecular paths and interactions must be given a fundamental and positive role in biology. This random activity corresponds to the thermic level in a cell, thus to a relevant component of the available energy: it turns out to be crucial for gene expression.

The functional role of stochastic effects has long since been known in enzyme induction (Novick and Weiner 1957), and even theorized for gene expression (Kupiec 1983). In the last decade (Elowitz et al. 2002), stochastic gene expression finally came into the limelight. The existing analyses are largely based on the classical Brownian motion (Arjun and van Oudenaarden 2008), while local quantum effects cannot be excluded.

Increasingly, researchers have found that even genetically identical individuals can be very different, and that some of the most striking sources of this variability are random fluctuations in the expression of individual genes. Fundamentally, this is because the expression of a gene involves the discrete and inherently random biochemical reactions involved in the production of mRNA and proteins. The fact that DNA (and hence the genes encoded therein) is present in very low numbers means that these fluctuations do not just average away but can instead lead to easily detectable differences between otherwise identical cells; in other words, gene expression must be thought of as a stochastic process. (Arjun and van Oudenaarden 2008)

Different degrees of stochasticity in gene expression have been observed – with major differences in ranges of expression – in the same population (in the same organ or even tissue) (Chang et al. 2008).

A major consequence that we can derive from this view is the key role that we can attribute to this relevant component of the available energy, heath. The cell also uses it for gene expression instead of opposing to it. As a matter of fact, the view that DNA is a set of “instructions” (a program) proposes an understanding of the cascades from DNA to RNA to proteins in terms of a deterministic and predictable, thus programmable, sequence of stereospecific interactions (physico-chemical and geometric exact correspondences). That is, gene expression or genetic “information” is physically transmitted by these exact correspondences: stereospecificity is actually “necessary” for this (Monod 1970). The random movement of macromolecules is an obstacle that the “program” constantly fights. Indeed, both Shannon’s transmission and Turing’s elaboration of information, in spite of their theoretical differences, are both designed to oppose noise (see Longo et al. 2012b). Instead, in stochastic gene expression, Brownian motion, thus heath, is viewed as a positive contribution to the role of DNA.

Clearly, randomness, in a cell, an organism and an ecosystem, is highly constrained. The compartmentalization in a cell, the membrane, the tissue tensegrity structure, the integration and regulation by and within an organism, all contribute to restricting and canalizing randomness. Consider that an organism like ours has about 10¹³ cells, divided into many smaller parts, including nuclei: few physical structures are so compartmentalized. So, the very “sticky” oscillating and randomly moving macromolecules are forced within viable channels. Sometimes, though, it may not work, or it may work differently. This belongs to the exploration proper to biological dynamics: a “hopeful monster” (Dietrich 2003), if viable in a changing ecosystem, may yield a new possibility in ontogenesis, or even a new branch in evolution.

Activation of gene transcription, in these quasi-chaotic environments, with quasi-turbulent enthalpic oscillations of macro-molecules, is thus canalized by the cell structure, in particular in eukaryotic cells, and by the more or less restricted assembly of the protein complexes that initiate it (Kupiec 2010). In short, proteins can interact with multiple partners (they are “sticky”) causing a great number of combinatorial possibilities. Yet, protein networks have a central hub where the connection density is the strongest and this peculiar canalization further forces statistical regularities (Bork et al. 2004). The various forms of canalization mentioned in the literature include some resulting from environmental constraints, which are increasingly acknowledged to produce “downwards” or Lamarckian inheritance or adaptation, mostly by a regulation of gene expression (Richards 2006). Even mutations may be both random and not random, highly constrained or even induced by the environment. For example, organismal activities, from tissular stresses to proteomic changes, can alter genomic sequences in response to environmental perturbations (Shapiro 2011).

By this role of constrained stochasticity in gene expression, molecular randomness in cells becomes a key source of the cell’s activity. As we hinted above, Brownian motion, in particular, must be viewed as a positive component of the cell’s dynamics (Munsky et al. 2009), instead of being considered as “noise” that opposes the elaboration of the genetic “program” or the transmission of genetic “information” by exact stereospecific macro-molecular interactions. Thus, this view radically departs from the understanding of the cell as a “Cartesian Mechanism” occasionally disturbed by noise (Monod 1970), as we give heath a constitutive, not a “disturbing” role (also for gene expression and not only for some molecular/enzymatic reactions).

The role of stochasticity in gene expression is increasingly accepted in genetics and may be generally summarized by saying that “macromolecular interactions, in a cell, are largely stochastic, they must be given in probabilities and the values of these probabilities depend on the context” (Longo and Montévil 2015). The DNA then becomes an immensely important physico-chemical trace of history, continually used by the cell and the organism. Its organization is stochastically used, but in a very canalized way, depending on the epigenetic context, to produce proteins and, at the organismal level, biological organization from a given cell. Random phenomena, Brownian random paths first, crucially contribute to this.

There is a third issue that is worth being mentioned. Following Gould (1997), we recall how the increasing phenotypic complexity along evolution (organisms become more “complex”, if this notion is soundly defined) may be justified as a random complexification of the early bacteria along an asymmetric diffusion. The key point is to invent the right phase space for this analysis, as we hint: the tridimensional space of “biomass × complexity × time” (Longo and Montévil 2014b).

Note that the available energy consumption and transformation, thus entropy production, are the unavoidable physical processes underlying all biological activities, including reproduction with variation and motility, organisms’ “default state” (Longo et al. 2015). Now, entropy production goes with energy dispersal, which is realized by random paths, as with any diffusion in physics.

At the origin of life, bacterial exponential proliferation was (relatively) unconstrained, as other forms of life did not contrast it. Increasing diversity, even in bacteria, by random differentiation started the early divergence of life, a process that would never stop – and a principle for Darwin. However, it also produced competition within a limited ecosystem and a slower exponential growth.

Gould (1989, 1997) uses the idea of random diversification to understand a blatant but often denied fact: life becomes increasingly “complex”, if one accords a reasonable meaning to this notion. The increasing complexity of biological structures, whatever this may mean, has often been denied in order to oppose finalist and anthropocentric perspectives, where life is described as aiming at Homo sapiens, particularly at the reader of this chapter, the highest result of the (possibly intelligent) evolutionary path (or Design).

It is a fact that, under many reasonable measures, an eukaryotic cell is more complex than a bacterium; a metazoan, with its differentiated cells, tissues and organs, is more complex than a cell and that, by counting neurons and their connections, cell networks in mammals are more complex than in early triploblast (which have three tissues layers), and these have more complex networks of all sorts than diplobasts (like jellyfish, a very ancient life form). This nonlinear increase can be quantified by counting tissue differentiations, networks and more, as very informally suggested by Gould and more precisely quantified in (Bailly and Longo 2009) (see Longo and Montévil 2014b for a survey). The point is: how are we to understand this change toward complexity without invoking global aims?

Gould provides a remarkable, but very informal answer to this question. He bases it on the analysis of the asymmetric random diffusion of life, as constrained proliferation and diversification. Asymmetric because, by a common assumption, life cannot be less complex than bacterial life¹⁰. We may understand Gould’s analysis by the general principle: any asymmetric random diffusion propagates, by local interactions, the original symmetry breaking along the diffusion.

The point is to propose a pertinent (phase) space for this diffusive phenomenon. For example, in a liquid, a drop of dye against a (left) wall diffuses in space (toward the right) when the particles bump against each other locally. That is, particles transitively inherit the original (left) wall asymmetry and propagate it globally by local random interactions. By considering the diffusion of biomass, after the early formation (and explosion) of life, over complexity, one can then apply the principle above to this fundamental evolutionary dynamic: biomass asymmetrically diffuses over complexity in time. Then, there is no need for a global design or aim: the random paths that compose any diffusion, also in this case, help to understand a random growth of complexity, on average. On average, as there may be local inversion in complexity, the asymmetry is randomly forced to “higher complexity”, a notion to be defined formally, of course.

In Bailly and Longo (2009), and more informally in Longo and Montévil (2014b), a close definition of phenotypic complexity was given, by counting fractal dimensions, networks, tissue differentiations, etc., hence, a mathematical analysis of this phenomenon was developed. In short, in the suitable phase space, that is “biomass × complexity × time”, we can give a diffusion equation with real coefficients, inspired by Schrödinger’s equation (which is a diffusion equation, but in a Hilbert space). In a sense, while Schrödinger’s equation is a diffusion of a law (an amplitude) of probability, the potential of variability of biomass over complexity in time was analyzed when the biological or phenotypic complexity was quantified, in a tentative but precise way, as hinted above (and better specified in the references).

Note that the idea that the complexity (however defined) of living organisms increases with time has been more recently adopted in Shanahan (2012) as a principle. It is thus assumed that there is a trend toward complexification and that this is intrinsic to evolution, while Darwin only assumed the divergence of characters. The very strong “principle” in Shanahan (2012), instead, may be derived, if one gives a due role to randomness, along an asymmetric diffusion, also in evolution.

A further but indirect fall-out of this approach to phenotypic complexity results from some recent collaborations with biologists of cancer (see Longo et al. 2015). We must first distinguish the notion of complexity, based on “counting” some key anatomical features, from biological organization. The first is given by the “anatomy” of a dead animal, and the second usually refers to the functional activities of a living organism. It seems that cancer is the only disease that diminishes functional organization by increasing complexity. When tissue is infected by cancer, ducts in glands, villi in epithelia, etc., increase in topological numbers (e.g. ducts have more lumina) and fractal dimensions (as for villi). This very growth of mathematical complexity reduces functionality, by reduced flow rates, thus the biological organization. This is probably a minor remark, but in the very obscure etiology of cancer, it may provide a hallmark for this devastating disease.