Review

.2024 Oct 25;14(5):20240010.

doi: 10.1098/rsfs.2024.0010. eCollection 2024 Oct 11.

Fundamental constraints to the logic of living systems

Ricard Solé^{1 2 3 4}, Christopher P Kempes⁴, Bernat Corominas-Murtra⁵, Manlio De Domenico^{6 7}, Artemy Kolchinsky^{1 8}, Michael Lachmann⁴, Eric Libby^{4 9}, Serguei Saavedra^{4 10}, Eric Smith^{4 11 12}, David Wolpert⁴

Affiliations

¹ ICREA-Complex Systems Lab, Universitat Pompeu Fabra, Dr Aiguader 88, Barcelona 08003, Spain.
² Institut de Biologia Evolutiva, CSIC-UPF, Pg Maritim de la Barceloneta 37, Barcelona 08003, Spain.
³ European Centre for Living Technology, Sestiere Dorsoduro, 3911, Venezia VE 30123, Italy.
⁴ Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA.
⁵ Institute of Biology, University of Graz, Graz 8010, Austria.
⁶ Complex Multilayer Networks Lab, Department of Physics and Astronomy 'Galileo Galilei', University of Padua, Via Marzolo 8, Padova 35131, Italy.
⁷ Padua Center for Network Medicine, University of Padua, Via Marzolo 8, Padova 35131, Italy.
⁸ Universal Biology Institute, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan.
⁹ Department of Mathematics and Mathematical Statistics, Umeå University, Umeå 90187, Sweden.
¹⁰ Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA.
¹¹ Department of Biology, Georgia Institute of Technology, Atlanta, GA 30332, USA.
¹² Earth-Life Science Institute, Tokyo Institute of Technology, Tokyo 152-8550, Japan.

PMID:39464646
PMCID: PMC11503024
DOI: 10.1098/rsfs.2024.0010

Review

Fundamental constraints to the logic of living systems

Ricard Solé et al. Interface Focus.2024.

.2024 Oct 25;14(5):20240010.

doi: 10.1098/rsfs.2024.0010. eCollection 2024 Oct 11.

Authors

Affiliations

¹ ICREA-Complex Systems Lab, Universitat Pompeu Fabra, Dr Aiguader 88, Barcelona 08003, Spain.
² Institut de Biologia Evolutiva, CSIC-UPF, Pg Maritim de la Barceloneta 37, Barcelona 08003, Spain.
³ European Centre for Living Technology, Sestiere Dorsoduro, 3911, Venezia VE 30123, Italy.
⁴ Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA.
⁵ Institute of Biology, University of Graz, Graz 8010, Austria.
⁶ Complex Multilayer Networks Lab, Department of Physics and Astronomy 'Galileo Galilei', University of Padua, Via Marzolo 8, Padova 35131, Italy.
⁷ Padua Center for Network Medicine, University of Padua, Via Marzolo 8, Padova 35131, Italy.
⁸ Universal Biology Institute, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan.
⁹ Department of Mathematics and Mathematical Statistics, Umeå University, Umeå 90187, Sweden.
¹⁰ Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA.
¹¹ Department of Biology, Georgia Institute of Technology, Atlanta, GA 30332, USA.
¹² Earth-Life Science Institute, Tokyo Institute of Technology, Tokyo 152-8550, Japan.

PMID:39464646
PMCID: PMC11503024
DOI: 10.1098/rsfs.2024.0010

Abstract

It has been argued that the historical nature of evolution makes it a highly path-dependent process. Under this view, the outcome of evolutionary dynamics could have resulted in organisms with different forms and functions. At the same time, there is ample evidence that convergence and constraints strongly limit the domain of the potential design principles that evolution can achieve. Are these limitations relevant in shaping the fabric of the possible? Here, we argue that fundamental constraints are associated with the logic of living matter. We illustrate this idea by considering the thermodynamic properties of living systems, the linear nature of molecular information, the cellular nature of the building blocks of life, multicellularity and development, the threshold nature of computations in cognitive systems and the discrete nature of the architecture of ecosystems. In all these examples, we present available evidence and suggest potential avenues towards a well-defined theoretical formulation.

Keywords: constraints; contingency; convergence; evolution; information; thermodynamics.

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Conflict of interest statement

We declare we have no competing interests.

Figures

**Figure 1.**
Cyclic structures characterize dissipative systems that reach non-equilibrium steady states due to external driving. In an abiotic system like a Bénard cell (a), a temperature gradient leads to the formation of cells that transport heat by cyclic convection (image adapted from Koschmieder & Pallas [97]). In living systems, chemical energy drives metabolic cycles such as the citric acid cycle (b), which plays a crucial role in energy production and biosynthesis. Such metabolic cycles consume resource molecules and synthesize energetic intermediates and building blocks while releasing heat. In the figure, both the intermediate metabolites of the cycle and the enzymes are indicated (image from David Goodsell).

**Figure 2.**
Linear polymers, information and computation. Several molecular events involve information storage and processing, such as DNA replication (a) or transcription (b) or the RNA $\to$ DNA reverse transcription in viruses (c). All these examples involve linear polymers that are ‘read’ by special nanomachines (DNA and RNA polymerases or the reverse transcriptase). Here, RNApol is RNA polymerase, DNApol is DNA polymerase, ssDNA is single-stranded DNA, dsDNA is double-stranded DNA and vRNA is viral RNA. The classical model of computation defined by Turing (d) involves a machine with internal states that scans a linear string of symbols (here made of zeros and ones) and changes its internal states as computation proceeds. Images (a) and (b) are adapted from David Goodsell. Image (c) adapted from Hopcroft [117].

Required metabolic rate for information copying alone. — **Figure 3.**
Required metabolic rate for information copying alone, as calculated by equation (3.2). The key parameters are the number of letters in the informational alphabet ( $n$ ), the length of the genome ( $L$ ) and the time to copy the information ( $t_{d}$ ). We show the minimal metabolic rate for $n = 4$ at various division times $t_{d}$ , from 1 s to $10^{5}$ s. Dashed lines indicate a TBM rate of $W \approx 10^{- 12}$ J s⁻¹ [134], TGL of $L \approx 5 \times 10^{6}$ bases, with typical division time $t_{d} \approx 10^{3}$ s.

**Figure 4.**
The logic of self-replicating living ‘machines’. Cells reproduce through a complex process that uses DNA as a set of instructions but requires also DNA to be replicated. In von Neumann’s theory (a), a formal machine capable of copying itself would require a set of instructions to guide the construction of a new machine under some controlled states such that instructions also get replicated. In biology, one crucial component of the cellular translation machinery is the ribosome (b), made of two subunits (RibLU and RibSU) that ‘read’ RNA strings to synthesize proteins, playing the role of the Constructor. In a molecular, embodied implementation of cell reproduction, self-organized interactions between a compartment, metabolism and information must interact. An example of a simple implementation is shown in (c) for a synthetic cell involving a compartment coupled to double-stranded polymers and a minimal metabolism (adapted from Munteanuet al. [146]). Here, a precursor $p L$ is transformed into lipids ( $L$ ) that allow membrane growth until some instability triggers division.

**Figure 5.**
Information-free protocell division. In these two examples, a possible reproduction cycle involving growth G and division D occurs on micelles composed of lipid molecules constantly fed from the environment. In (a), these are hydrophobic precursors (indicated as T–T) that react to become a polar amphiphile (H–T), thanks to some reaction (figure adapted from Solé [164]). In (b), a similar scenario involves a diverse feeding of lipid molecules forming a heterogeneous aggregate where the recruitment of a particular lipid into the aggregate depends on the compositional information of the aggregate, which lipids already make up the aggregate. In thislipid world scenario, the two resulting daughter cells are different (adapted from Kahana & Lancet [171]).

**Figure 6.**
The logic of MC and development. (a) At the simplest description level, MC organisms can be assigned to two groups: clonal (upper plot) versus aggregative MC. In the former, a transition $C_{0} \to 𝐂$ occurs after repeated cell divisions with the final population forming a cluster. In the second, the transition is from a set of cells $𝐂_{0}$ towards another set (which might contain the same cells and where their states might or might not remain the same) where some interaction matrix $ω_{i j}$ between cell pairs can be defined. (b) MC life cycles can be classified within a well-defined taxonomy where transitions to individuality can be described as graphs connecting (grey arrows) single units (s) and aggregates that can be generated by coming together (CT) or staying together (ST) mechanisms, or even the coexistence of both. Shown, from top to bottom, are the life cycles ofDictyostelium discoideum (image by David Scharf),*Capsaspora owczarzaki* (from the Multigenome Lab) andBacillus subtilis (image by Arnaud Bridier). (c) Within MC organisms, cell differentiation increases organismal complexity and can be described by a succession of symmetry-breaking events on a Waddington landscape. Here, marbles indicate cell types (either transient or final). In (d) we show an example of the predictable tissue sorting emerging from a completely disordered cell assembly (adapted from Mombachet al. [195]). This can be explained through a simple differential adhesion model (*e,f*) based on cell sorting dynamics [196]. Here the two cell types are indicated by open and filled circles. Adhesion forces are present, and cells can switch their locations in space if the adhesion energy decreases. Panels (a) and (c) adapted from Márquez-Zacaríaset al. [197].

**Figure 7.**
Cognitive networks may exhibit a unique logic of nonlinear response functions. Neurons (a) are specialized cells that gather and propagate information in a threshold-like manner. They have a well-defined polarity connected with the input–output signal transmission. The standard McCulloch–Pitts model of a formal neuron (b) captures the essence of this transmission in terms of a weighted threshold function, which in its simplest form can be represented as a binary on-or-off response (c). Other information transmission systems, like genetic networks, are usually modelled similarly (*d,e*). For example, TFs ( $T_{i}$ ) are proteins expressed by some genes that bind to DNA (d; image by David Goodsell) and regulate the expression of other genes. The input–output diagram in (e) is analogous to the neural counterpart, and the corresponding response functions are also highly nonlinear threshold functions. The outcome of these interactions can modify the expression of a given protein (f) or set of proteins.

**Figure 8.**
Universal patterns in ecosystems and digital ecologies. Despite their huge diversity, ecosystem architectures are identified in current and fossil communities (a) and the ecological network (so-called ‘paleo food webs’) reconstructed, as shown in (b) for a fossil ecosystem before the K–T extinction. One approach to the evolution of these ecological networks relies on digital versions of species and their interactions. An example is shown in (c), where the virtual CPU of the Tierra system is summarized (adapted from Adami [300]). Here, S and R stand for the Slicer and Reaper queues, which introduce rewards and ageing. It is possible to evolve food webs (d) with a discrete number of layers using evolutionary dynamics on bit strings encoding game-theoretic models (adapted from Kristian & Nordahl [301]). Algorithmic reactors allow evolving interaction networks and see sequences of increase in complexity, as illustrated in (e), where different ‘species’ are indicated as filled nodes, where interactions can happen directly (continuous arrows) or through an intermediate operator rule (adapted from Banzhaf [302]). The evolved networks always include parasitic interactions.

**Figure 9.**
Parasites and functional evolutionary trees. Digital ecologies generate well-defined, qualitative classes of agents that we can identify as parasites, predators or natural counterparts associated with a discrete set of constraints in the repertoire of potential functional roles. In (a,b), we display the evolutionary trees of an artificial life implementation usingAvida, where parasites are present (a) or suppressed (b). The resulting phylogenies indicate that parasites promote diversity (adapted from Zamanet al. [333]). The convergent patterns exhibited by ecosystems are illustrated using a diagrammatic representation of two ‘runs’ (*c,d*) of an abstract world, starting from an initial set of species $Σ_{0}$ and looking at a final set of species $Σ_{t}$ . Branches appear each time a new functional class emerges. Although the branching patterns might differ, we conjecture thatfunctional trees will branch into the same qualitative, discrete classes $Σ_{t} = ⋃_{k = 1} Γ_{k}$ . A thick branch associated with parasites will always be present in both cases, with diverse (but common) solutions indicated on the right (*e,f*) using examples from extant viruses (images generated using BioRender). Each time viruses emerge, they will influence the dynamics and even the emergence of new branches, as sketched by the wiggled lines.

**Figure 10.**
Phase transition in physics versus evolutionary transitions. In (a), the phase transition associated with the two-dimensional Ising model is shown, displaying the average magnetization (the order parameter) $M (T) = \sum_{i} S_{i}$ (i.e. a sum over all spins $S_{i} \in {- 1, + 1}$ ) against the temperature (the control parameter). The snapshots are obtained by indicating ‘up’ (+1) and ‘down’ (−1) spins as black and white squares, respectively. Two possible ordered configurations are obtained for temperatures lower than the critical $T_{c}$ , associated with a symmetry-breaking phenomenon. For $T > T_{c}$ , a disordered phase is present, with an essentially random arrangement of spins, lacking spatial correlations. A critical point $T_{c}$ separates these two phases. The inset curves represent the macroscopic potential function derived from a mean-field approximation. Open and filled circles stand for unstable and stable states, respectively. In (*b,c*), we display three examples of models of evolutionary innovations that exhibit some phase transition, along with some of their underlying mathematical descriptions. These are (b) the emergence of homochirality (figure from Wikipedia [364]), (c) the emergence of autocatalytic cycles out of random chemistry of reacting species (figure redrawn from Farmeret al. [365]) and (d) the collective evolution of genomes as described by the transition from horizontal to vertical genetic transition (figure from Goldenfeldet al. [59]).

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Fundamental constraints to the logic of living systems

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Fundamental constraints to the logic of living systems

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Affiliations

Abstract

Conflict of interest statement

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