Session K04: Non-Equilibrium Thermodynamics: From Chemical Reaction Networks to Natural Selection I

Combinatorics in evolution: from rule-based systems to the thermodynamics of selectivities

Life on Earth uses quite specific and often universal chemical pathways, which have apparently been selected through evolution among many alternatives possible with the same or comparable mechanisms. Both network chemistry and Darwinian evolution are stochastic population processes, with natural associated entropy and information measures.  The free recombination possible for elementary mechanisms, either in prebiotic chemistry or within evolutionary potential, produces a third combinatorics of possibilities to be filtered by selection.  We would like to understand how statistical mechanics spans these three combinatorial levels, to learn for example whether there is a natural dimensional analysis of the costs of selection.  In this study we use a rule-based model to generate "all possible" solutions to a biological problem of sugar-phosphate conversion, deriving the natural dissipaton costs and information geometry that constitute fitness criteria and separability of solutions.  From these we show there is a minimum cost to select a subnetwork or single pathway from a network of prior possibilities, computed from the tilted generating function for the driven chemical ensemble.   

Thermally induced habitat for the emergence of life - enrichment of phosphorus, divalent salts and compact oligomer folds.

The early Earth 4 billion years ago was a scarce place for the emergence of life. After the formation of the oceans, it was most likely difficult to extract the essential ionic building blocks of life, such as phosphate or salts, from the existing geomaterial in sufficiently high concentrations and suitable mixing ratios. We show how ubiquitous heat fluxes through rock fractures implement a physical solution to this problem: Thermal convection and thermophoresis together are able to separate calcium from phosphorus and thus use ubiquitous but otherwise inert apatite as a phosphate source. Furthermore, the mixing ratio of different salts is modified according to their thermophoretic properties, providing a suitable non-equilibrium environment for the first prebiotic reactions.   

A robust transition to homochirality in complex chemical reaction networks

The selection of a single molecular handedness, or homochirality across all living matter, is a mystery in the origin of life. Frank’s seminal model showed in the fifties how chiral symmetry breaking can occur in non-equilibrium chemical networks. However, an important shortcoming in this classic model is that it considers a small number of species, while there is no reason for the prebiotic system, in which homochirality first appeared, to have had such a simple composition.

In this work, using random matrix theory, we show that large non-equilibrium reaction networks can undergo a generic and robust phase transition towards a homochiral state as a consequence of the fact that they contain a large number of chiral species. We also quantify how abundant are chiral species in the chemical universe of all possible molecules of a given length by data analysis, to determine the caracterstic molecule size beyond which this symmetry breaking could occur easily. Finally, we propose that Frank’s model should be extended to include a large number of species, in order to possess the transition towards homochirality as confirmed by numerical simulations.   

How the drive for Survival of the Fittest might have arisen from a physico-chemical ratcheting process

It is not known how life originated, but it must have roughly coincided with the origin of the Survival of the Fittest (SoF). SoF is the dynamics of growth, innovation, persistence, and variation that is at the heart of biology.  In SoF, cells that are better at converting food to ATP energy and biomass replicate faster and grow in population.  We seek the roots of SoF in prebiotic physical chemistry of simple molecules.  A physico-chemical mechanism that could have presaged SoF is that the better a catalyst is at producing an action, the more that action results in duplicating the catalyst itself.  Proteins are today's biological catalysts.  We develop dynamical modeling that describes how SoF dynamics might have arisen from the earliest simple random processes of peptide synthesis.   

Spatial Patterns in Winning Mediated Thermodynamic Strategy Evolution

The emergence of single strategy communities is often observed in spatial games played repeatedly. However, many social and biological systems exhibit a memory effect of successful strategy choices, represented by a caching of winnings which mediates future survival. We study a dynamical system defined by a repeated game on a lattice in one and two dimensions, where each agent stores their winnings as a measure of past success. Strategy updates are governed by a Boltzmann distribution, with the local energy given by the negative of the total local cache value for each strategy. Sites with higher cache values are effectively colder, and thus less likely to change strategy than sites with lower values. For a parameterized rock-paper-scissors game, we find a condition under which stationary local communities form, for which the domain sizes scale with the size of the system. We analyze a special case where community formation occurs but without fixed boundaries, leading to pattern migration. Using this analysis, we show which spatial structures are unstable in 1D. Comparison is made with numerical results for similar patterns in 2D.   

Dynamical mean-field theory: from ecosystems to reaction networks

Both natural ecosystems and biochemical reaction networks involve populations of heterogeneous agents whose cooperative and competitive interactions lead to a rich dynamics of species' abundances, albeit at vastly different scales. The maintenance of diversity in large ecosystems is a longstanding puzzle, towards which recent progress has been made by the derivation of dynamical mean-field theories of random models. In particular, it has recently been shown that these random models have a chaotic phase in which abundances display wild fluctuations. When modest spatial structure is included, these fluctuations are stabilized and diversity is maintained. If and how these phenomena have parallels in biochemical reaction networks is currently unknown, but is of obvious interest since life requires cooperation among a large number of molecular species, and the origin of life is hotly debated. To connect these phenomena, in this work we find a reaction network whose large-scale behavior precisely recovers the random Lotka-Volterra model considered recently. This clarifies the assumptions necessary to obtain a reduced large-scale description, and shows how the noise must be approximated to recover the previous mean-field theories. Then, we show how local detailed balance and the positivity of reaction rates, which are key physical requirements of chemical reaction networks, provide obstructions towards the construction of an associated dynamical mean-field theory of biochemical reaction networks. We outline prospects and challenges for the future, and argue for a synthetic approach to a physical theory of the origin of life.   

It Doesn't Always Pay to be Fit: Success Landscapes

Landscapes play an important role in many areas of biology, which biological lives are deeply entangled with.  Here we discuss a form of landscape in evolutionary biology which takes into account (1) initial growth rates, (2) mutation rates, (3) resource consumption by organisms, and (4) cyclic changes in the resources with time.  The long term equilibrium number of surviving organisms as a function of these four parameters forms what we call a success landscape, a landscape we would claim is qualitatively different from fitness landscapes which commonly do not include mutations or resource consumption/changes in mapping genomes to the final number of survivors. Although our analysis is purely theoretical, we believe the results have possibly strong connections to how we might treat diseases such as cancer in the future with a deeper understanding of the interplay between resource degradation, mutation, and uncontrolled cell growth.   

Dynamics of bacterial replisomes

Replisomes are large protein complexes that replicate genomes with remarkable speed and accuracy. In my talk, I will present a theoretical connection between the dynamics of replisomes and the distribution of DNA abundance in an exponentially growing bacterial population. Our approach permits inference of the replisome dynamics from deep sequencing measurements. As an application, we experimentally measured the DNA abundance distribution in growing Escherichia coli populations.  We find that the replisome speed increases with temperature and present regular and repeatable oscillations along the genome. I will discuss possible dynamical origins of these oscillations. Our approach has the potential to elucidate replication dynamics in other bacterial species.   

Modeling circadian clocks in real environments

A broad range of living systems exhibit oscillations on the timescale of a day, known as circadian rhythms. These often persist even in the absence of external daily signals. These system are commonly studied in laboratory settings, which have been very effective at helping understand the structure of these networks but don't necessarily replicate the complexity of the actual stimuli that these systems evolved to respond to. We use a dynamical systems model of circadian clocks and real-world weather data to study tradeoffs in parameters in these systems, and to understand potential relationships between geography and underlying parameters and structure in circadian clocks. We then interpret this in the light of potential for migrations and the generalization of one circadian estimate in another environment.