The fundamental theorem of natural selection with mutations

Protocell Effects on RNA Folding, Function, and Evolution

ConspectusCreating a living system from nonliving matter is a great challenge in chemistry and biophysics. The early history of life can provide inspiration from the idea of the prebiotic "RNA World" established by ribozymes, in which all genetic and catalytic activities were executed by RNA. Such a system could be much simpler than the interdependent central dogma characterizing life today. At the same time, cooperative systems require a mechanism such as cellular compartmentalization in order to survive and evolve. Minimal cells might therefore consist of simple vesicles enclosing a prebiotic RNA metabolism.The internal volume of a vesicle is a distinctive environment due to its closed boundary, which alters diffusion and available volume for macromolecules and changes effective molecular concentrations, among other considerations. These physical effects are mechanistically distinct from chemical interactions, such as electrostatic repulsion, that might also occur between the membrane boundary and encapsulated contents. Both indirect and direct interactions between the membrane and RNA can give rise to nonintuitive, "emergent" behaviors in the model protocell system. We have been examining how encapsulation inside membrane vesicles would affect the folding and activity of entrapped RNA.Using biophysical techniques such as FRET, we characterized ribozyme folding and activity inside vesicles. Encapsulation inside model protocells generally promoted RNA folding, consistent with an excluded volume effect, independently of chemical interactions. This energetic stabilization translated into increased ribozyme activity in two different systems that were studied (hairpin ribozyme and self-aminoacylating RNAs). A particularly intriguing finding was that encapsulation could rescue the activity of mutant ribozymes, suggesting that encapsulation could affect not only folding and activity but also evolution. To study this further, we developed a high-throughput sequencing assay to measure the aminoacylation kinetics of many thousands of ribozyme variants in parallel. The results revealed an unexpected tendency for encapsulation to improve the better ribozyme variants more than worse variants. During evolution, this effect would create a tilted playing field, so to speak, that would give additional fitness gains to already-high-activity variants. According to Fisher's Fundamental Theorem of Natural Selection, the increased variance in fitness should manifest as faster evolutionary adaptation. This prediction was borne out experimentally during in vitro evolution, where we observed that the initially diverse ribozyme population converged more quickly to the most active sequences when they were encapsulated inside vesicles.The studies in this Account have expanded our understanding of emergent protocell behavior, by showing how simply entrapping an RNA inside a vesicle, which could occur spontaneously during vesicle formation, might profoundly affect the evolutionary landscape of the RNA. Because of the exponential dynamics of replication and selection, even small changes to activity and function could lead to major evolutionary consequences. By closely studying the details of minimal yet surprisingly complex protocells, we might one day trace a pathway from encapsulated RNA to a living system.

Limits on the evolutionary rates of biological traits

This paper focuses on the maximum speed at which biological evolution can occur. I derive inequalities that limit the rate of evolutionary processes driven by natural selection, mutations, or genetic drift. These rate limits link the variability in a population to evolutionary rates. In particular, high variances in the fitness of a population and of a quantitative trait allow for fast changes in the trait's average. In contrast, low variability makes a trait less susceptible to random changes due to genetic drift. The results in this article generalize Fisher's fundamental theorem of natural selection to dynamics that allow for mutations and genetic drift, via trade-off relations that constrain the evolutionary rates of arbitrary traits. The rate limits can be used to probe questions in various evolutionary biology and ecology settings. They apply, for instance, to trait dynamics within or across species or to the evolution of bacteria strains. They apply to any quantitative trait, e.g., from species' weights to the lengths of DNA strands.

Responses to commentaries on "The gene: An appraisal"

The central conclusions of "The Gene: An Appraisal" are that genetic variance does not underpin biological evolution, and, therefore, that genes are not Mendel's units of inheritance. In this response, I will address the criticisms I have received via commentaries on that paper by defending the following statements: 1. Epistasis does not explain the power-law fitness profile of the Long-Term Evolution Experiment (LTEE). The data from the evolution of natural systems displays the power-law form ubiquitously. Epistasis plays no role in evolution. 2. The common characteristics of living things (natural systems) are described by the principle of least action in de Maupertuis's original form, which is synonymous with the 2nd law of thermodynamics and Newton's 2nd law of motion in its complete form, i.e., F = dp/dt. Organisms strive to achieve free energy balance with their environments. 3. Based on an appraisal of the scientific environment between 1880 and 1911, I conclude that Johannsen's genotype conception was perhaps, the only option available to him. 4. The power-law fitness profile of the LTEE falsifies Fisher's Genetical Theory of Natural Selection, Johannsen's genotype conception, and the idea that 'Darwinian evolution' is an exception to the generic thermodynamic process of evolution in natural systems. 5. The use of the technique of genome-wide association to identify the causes and the likelihoods of inherited common diseases and behavioural traits is a 'wild goose chase' because genes are not the units of inheritance.

Back to the fundamentals: a reply to Basener and Sanford 2018

Fisher's fundamental theorem of natural selection has haunted theoretical population genetic literature since it was proposed in 1930, leading to numerous interpretations. Most of the confusion stemmed from Fisher's own obscure presentation. By the 1970s, a clearer view of Fisher's theorem had been achieved and it was found that, regardless of its utility or significance, it represents a general theorem of evolutionary biology. Basener and Sanford (J Math Biol 76:1589-1622, 2018) writing in JOMB, however, paint a different picture of the fundamental theorem as one hindered by its assumptions and incomplete due to its failure to explicitly incorporate mutational effects. They argue that Fisher saw his theorem as a "mathematical proof of Darwinian evolution". In this reply, we show that, contrary to Basener and Sanford, Fisher's theorem is a general theorem that applies to any evolving population, and that, far from their assertion that it needed to be expanded, the theorem already implicitly incorporates ancestor-descendant variation. We also show that their numerical simulations produce unrealistic results. Lastly, we argue that Basener and Sanford's motivations were in undermining not merely Fisher's theorem, but the concept of universal common descent itself.

Modeling stress-induced responses: plasticity in continuous state space and gradual clonal evolution

Mathematical models of cancer and bacterial evolution have generally stemmed from a gene-centric framework, assuming clonal evolution via acquisition of resistance-conferring mutations and selection of their corresponding subpopulations. More recently, the role of phenotypic plasticity has been recognized and models accounting for phenotypic switching between discrete cell states (e.g., epithelial and mesenchymal) have been developed. However, seldom do models incorporate both plasticity and mutationally driven resistance, particularly when the state space is continuous and resistance evolves in a continuous fashion. In this paper, we develop a framework to model plastic and mutational mechanisms of acquiring resistance in a continuous gradual fashion. We use this framework to examine ways in which cancer and bacterial populations can respond to stress and consider implications for therapeutic strategies. Although we primarily discuss our framework in the context of cancer and bacteria, it applies broadly to any system capable of evolving via plasticity and genetic evolution.

The Gene: An appraisal

The gene can be described as the foundational concept of modern biology. As such, it has spilled over into daily discourse, yet it is acknowledged among biologists to be ill-defined. Here, following a short history of the gene, I analyse critically its role in inheritance, evolution, development, and morphogenesis. Wilhelm Johannsen's genotype-conception, formulated in 1910, has been adopted as the foundation stone of genetics, giving the gene a higher degree of prominence than is justified by the evidence. An analysis of the results of the Long-Term Evolution Experiment (LTEE) with E. coli bacteria, grown over 60,000 generations, does not support spontaneous gene mutation as the source of variance for natural selection. From this it follows that the gene is not Mendel's unit of inheritance: that must be Johannsen's transmission-conception at the gamete phenotype level, a form of inheritance that Johannsen did not consider. Alternatively, I contend that biology viewed on the bases of thermodynamics, complex system dynamics, and self-organisation, provides a new framework for the foundations of biology. In this framework, the gene plays a passive role as a vital information store: it is the phenotype that plays the active role in inheritance, evolution, development, and morphogenesis.

Engineering and Expression Strategies for Optimization of L-Asparaginase Development and Production

Genetic engineering for heterologous expression has advanced in recent years. Model systems such as Escherichia coli, Bacillus subtilis and Pichia pastoris are often used as host microorganisms for the enzymatic production of L-asparaginase, an enzyme widely used in the clinic for the treatment of leukemia and in bakeries for the reduction of acrylamide. Newly developed recombinant L-asparaginase (L-ASNase) may have a low affinity for asparagine, reduced catalytic activity, low stability, and increased glutaminase activity or immunogenicity. Some successful commercial preparations of L-ASNase are now available. Therefore, obtaining novel L-ASNases with improved properties suitable for food or clinical applications remains a challenge. The combination of rational design and/or directed evolution and heterologous expression has been used to create enzymes with desired characteristics. Computer design, combined with other methods, could make it possible to generate mutant libraries of novel L-ASNases without costly and time-consuming efforts. In this review, we summarize the strategies and approaches for obtaining and developing L-ASNase with improved properties.

The contribution of evolvability to the eco-evolutionary dynamics of competing species

Evolvability is the capacity of a population to generate heritable variation that can be acted upon by natural selection. This ability influences the adaptations and fitness of individual organisms. By viewing this capacity as a trait, evolvability is subject to natural selection and thus plays a critical role in eco-evolutionary dynamics. Understanding this role provides insight into how species respond to changes in their environment and how species coexistence can arise and be maintained. Here, we create a G-function model of competing species, each with a different evolvability. We analyze population and strategy (= heritable phenotype) dynamics of the two populations under clade initiation (when species are introduced into a population), evolutionary tracking (constant, small changes in the environment), adaptive radiation (availability of multiple ecological niches), and evolutionary rescue (extreme environmental disturbances). We find that when species are far from an eco-evolutionary equilibrium, faster-evolving species reach higher population sizes, and when species are close to an equilibrium, slower-evolving species are more successful. Frequent, minor environmental changes promote the extinction of species with small population sizes, regardless of their evolvability. When several niches are available for a species to occupy, coexistence is possible, though slower-evolving species perform slightly better than faster-evolving ones due to the well-recognized inherent cost of evolvability. Finally, disrupting the environment at intermediate frequencies can result in coexistence with cyclical population dynamics of species with different rates of evolution.

Extinction scenarios in evolutionary processes: a multinomial Wright-Fisher approach

We study a discrete-time multi-type Wright-Fisher population process. The mean-field dynamics of the stochastic process is induced by a general replicator difference equation. We prove several results regarding the asymptotic behavior of the model, focusing on the impact of the mean-field dynamics on it. One of the results is a limit theorem that describes sufficient conditions for an almost certain path to extinction, first eliminating the type which is the least fit at the mean-field equilibrium. The effect is explained by the metastability of the stochastic system, which under the conditions of the theorem spends almost all time before the extinction event in a neighborhood of the equilibrium. In addition to the limit theorems, we propose a maximization principle for a general deterministic replicator dynamics and study its implications for the stochastic model.

The fundamental theorem of natural selection in optimization and games

The Fisher's fundamental theorem of natural selection (FTNS) is a matter of longstanding debate in the community of mathematical biologists. Many researchers proposed different clarifications and mathematical reconstructions of the Fisher's original statement. The present study is motivated by our opinion that the controversy can be resolved by examining the Fisher's statement within the framework of two mathematical theories that are inspired by the Darwinian formalism: evolutionary game theory (EGT) and evolutionary optimization (EO). We present four rigorous formulations (some of them previously reported) of FTNS in four different setups that come from EGT and EO. Our study demonstrates that FTNS in its original form is correct only in certain setups. In order to be recognized as a universal law, the Fisher's statement should be: (a) clarified and completed and (b) relaxed by replacing the words "is equal to" with "does not exceed". Moreover, the real meaning of FTNS can be best understood from the information-geometric point of view. Such an approach shows that FTNS imposes an upper geometric bound on information flows in evolutionary systems. In this light, FTNS appears to be a statement about the intrinsic time scale of an evolutionary system. This leads to a novel insight: FTNS is an analogue of the time-energy uncertainty relation in physics. This further emphasizes a close relation with results on speed limits in stochastic thermodynamics.

Biomarkers or biotargets? Using competition to lure cancer cells into evolutionary traps

Background and Objectives

Cancer biomarkers provide information on the characteristics and extent of cancer progression and help inform clinical decision-making. However, they can also play functional roles in oncogenesis, from enabling metastases and inducing angiogenesis to promoting resistance to chemotherapy. The resulting evolution could bias estimates of cancer progression and lead to suboptimal treatment decisions.

Methodology

We create an evolutionary game theoretic model of cell-cell competition among cancer cells with different levels of biomarker production. We design and simulate therapies on top of this pre-existing game and examine population and biomarker dynamics.

Results

Using total biomarker as a proxy for population size generally underestimates chemotherapy efficacy and overestimates targeted therapy efficacy. If biomarker production promotes resistance and a targeted therapy against the biomarker exists, this dynamic can be used to set an evolutionary trap. After chemotherapy selects for a high biomarker-producing cancer cell population, targeted therapy could be highly effective for cancer extinction. Rather than using the most effective therapy given the cancer's current biomarker level and population size, it is more effective to 'overshoot' and utilize an evolutionary trap when the aim is extinction. Increasing cell-cell competition, as influenced by biomarker levels, can help prime and set these traps.

Conclusion and Implications

Evolution of functional biomarkers amplify the limitations of using total biomarker levels as a measure of tumor size when designing therapeutic protocols. Evolutionarily enlightened therapeutic strategies may be highly effective, assuming a targeted therapy against the biomarker is available.

A life history model of the ecological and evolutionary dynamics of polyaneuploid cancer cells

Therapeutic resistance is one of the main reasons for treatment failure in cancer patients. The polyaneuploid cancer cell (PACC) state has been shown to promote resistance by providing a refuge for cancer cells from the effects of therapy and by helping them adapt to a variety of environmental stressors. This state is the result of aneuploid cancer cells undergoing whole genome doubling and skipping mitosis, cytokinesis, or both. In this paper, we create a novel mathematical framework for modeling the eco-evolutionary dynamics of state-structured populations and use this framework to construct a model of cancer populations with an aneuploid and a PACC state. Using in silico simulations, we explore how the PACC state allows cancer cells to (1) survive extreme environmental conditions by exiting the cell cycle after S phase and protecting genomic material and (2) aid in adaptation to environmental stressors by increasing the cancer cell's ability to generate heritable variation (evolvability) through the increase in genomic content that accompanies polyploidization. In doing so, we demonstrate the ability of the PACC state to allow cancer cells to persist under therapy and evolve therapeutic resistance. By eliminating cells in the PACC state through appropriately-timed PACC-targeted therapies, we show how we can prevent the emergence of resistance and promote cancer eradication.

The gene: An appraisal

The gene can be described as the foundational concept of modern biology. As such, it has spilled over into daily discourse, yet it is acknowledged among biologists to be ill-defined. Here, following a short history of the gene, I analyse critically its role in inheritance, evolution, development, and morphogenesis. Wilhelm Johannsen's genotype-conception, formulated in 1910, has been adopted as the foundation stone of genetics, giving the gene a higher degree of prominence than is justified by the evidence. An analysis of the results of the Long-Term Evolution Experiment (LTEE) with E. coli bacteria, grown over 60,000 generations, does not support spontaneous gene mutation as the source of variance for natural selection. From this it follows that the gene is not Mendel's unit of inheritance: that must be Johannsen's transmission-conception at the gamete phenotype level, a form of inheritance that Johannsen did not consider. Alternatively, I contend that biology viewed on the bases of thermodynamics, complex system dynamics and self-organisation, provides a new framework for the foundations of biology. In this framework, the gene plays a passive role as a vital information store: it is the phenotype that plays the active role in inheritance, evolution, development, and morphogenesis.

Variability of Human rDNA

In human cells, ribosomal DNA (rDNA) is arranged in ten clusters of multiple tandem repeats. Each repeat is usually described as consisting of two parts: the 13 kb long ribosomal part, containing three genes coding for 18S, 5.8S and 28S RNAs of the ribosomal particles, and the 30 kb long intergenic spacer (IGS). However, this standard scheme is, amazingly, often altered as a result of the peculiar instability of the locus, so that the sequence of each repeat and the number of the repeats in each cluster are highly variable. In the present review, we discuss the causes and types of human rDNA instability, the methods of its detection, its distribution within the locus, the ways in which it is prevented or reversed, and its biological significance. The data of the literature suggest that the variability of the rDNA is not only a potential cause of pathology, but also an important, though still poorly understood, aspect of the normal cell physiology.

Origin of Life: The Point of No Return

Origin of life research is one of the greatest scientific frontiers of mankind. Many hypotheses have been proposed to explain how life began. Although different hypotheses emphasize different initial phenomena, all of them agree around one important concept: at some point, along with the chain of events toward life, Darwinian evolution emerged. There is no consensus, however, how this occurred. Frequently, the mechanism leading to Darwinian evolution is not addressed and it is assumed that this problem could be solved later, with experimental proof of the hypothesis. Here, the author first defines the minimum components required for Darwinian evolution and then from this standpoint, analyzes some of the hypotheses for the origin of life. Distinctive features of Darwinian evolution and life rooted in the interaction between information and its corresponding structure/function are then reviewed. Due to the obligatory dependency of the information and structure subject to Darwinian evolution, these components must be locked in their origin. One of the most distinctive characteristics of Darwinian evolution in comparison with all other processes is the establishment of a fundamentally new level of matter capable of evolving and adapting. Therefore, the initiation of Darwinian evolution is the "point of no return" after which life begins. In summary: a definition and a mechanism for Darwinian evolution are provided together with a critical analysis of some of the hypotheses for the origin of life.

Using statistical methods to model the fine-tuning of molecular machines and systems

Fine-tuning has received much attention in physics, and it states that the fundamental constants of physics are finely tuned to precise values for a rich chemistry and life permittance. It has not yet been applied in a broad manner to molecular biology. However, in this paper we argue that biological systems present fine-tuning at different levels, e.g. functional proteins, complex biochemical machines in living cells, and cellular networks. This paper describes molecular fine-tuning, how it can be used in biology, and how it challenges conventional Darwinian thinking. We also discuss the statistical methods underpinning fine-tuning and present a framework for such analysis.

Molecular footprints of selection effects and whole genome duplication (WGD) events in three blueberry species: detected by transcriptome dataset

BACKGROUND

Both selection effects and whole genome duplication played very important roles in plant speciation and evolution, and to decipher the corresponding molecular footprint has always been a central task of geneticists. Vaccinium is species rich genus that comprised of about 450 species, and blueberry is one of the most important species of Vaccinium genus, which is gaining popularity because of high healthful value. In this article, we aimed to decipher the molecular footprints of natural selection on the single copy genes and WGD events occur in the evolutionary history of blueberry species.

RESULTS

We identified 30,143, 29,922 and 28,891 putative protein coding sequences from 45,535, 42,914 and 43,630 unigenes assembled from the leaves' transcriptome assembly of 19 rabbiteye (T1), 13 southern highbush (T2) and 22 northern highbush (T3) blueberry cultivars. A total of 17, 21 and 27 single copy orthologs were found to undergone positive selection in T1 versus T2, T1 versus T3, and T2 versus T3, respectively, and these orthologs were enriched in metabolic pathways including "Terpenoid backbone biosynthesis", "Valine, leucine and isoleucine biosynthesis", "Butanoate metabolism", "C5-Branched dibasic acid metabolism" "Pantothenate and CoA biosynthesis". We also detected significant molecular footprints of a recent (about 9.04 MYA), medium (about 43.44 MYA) and an ancient (about 116.39 MYA) WGD events that occurred in the evolutionary history of three blueberry species.

CONCLUSION

Some important functional genes revealed positive selection effect in blueberry. At least three rounds of WGD events were detected in the evolutionary history of blueberry species. Our work provides insights about the genetic mechanism of adaptive evolution in blueberry and species radiation of Vaccinium in short geological scale time.

Convergent Evolution, Evolving Evolvability, and the Origins of Lethal Cancer

Advances in curative treatment to remove the primary tumor have increased survival of localized cancers for most solid tumor types, yet cancers that have spread are typically incurable and account for >90% of cancer-related deaths. Metastatic disease remains incurable because, somehow, tumors evolve resistance to all known compounds, including therapies. In all of these incurable patients, de novo lethal cancer evolves capacities for both metastasis and resistance. Therefore, cancers in different patients appear to follow the same eco-evolutionary path that independently manifests in affected patients. This convergent outcome, that always includes the ability to metastasize and exhibit resistance, demands an explanation beyond the slow and steady accrual of stochastic mutations. The common denominator may be that cancer starts as a speciation event when a unicellular protist breaks away from its multicellular host and initiates a cancer clade within the patient. As the cancer cells speciate and diversify further, some evolve the capacity to evolve: evolvability. Evolvability becomes a heritable trait that influences the available variation of other phenotypes that can then be acted upon by natural selection. Evolving evolvability may be an adaptation for cancer cells. By generating and maintaining considerable heritable variation, the cancer clade can, with high certainty, serendipitously produce cells resistant to therapy and cells capable of metastasizing. Understanding that cancer cells can swiftly evolve responses to novel and varied stressors create opportunities for adaptive therapy, double-bind therapies, and extinction therapies; all involving strategic decision making that steers and anticipates the convergent coevolutionary responses of the cancers.

Genetic trajectory and immune microenvironment of lung-specific oligometastatic colorectal cancer

Genetics and immunologic dynamics pushing the evolution of colorectal cancer (CRC) from the primary tumor to the metastases are largely unknown; cancer heterogeneity makes challenging both therapy and mechanistic studies. We selected patients developing CRC with lung-limited metastatic disease as only illness during their life in order to find any relevant genotype–phenotype relationship. Analysis of 523 cancer-relevant genes and of immune cells infiltration in primary and metastatic tissues revealed atypical genomic trajectories (TMB decrease, KRAS and SMAD4 regressive mutations), specific genetic events (ERBB2 point mutations) and scarce T-cell infiltration. These insights provide novel information in oligometastatic CRC biology and new perspectives for cancer monitoring and anti-cancer therapeutic strategies.

A percolation model of natural selection

A new approach has been proposed and developed: the selection of optimal variants in the evolutionary mutation flow is considered as an analogue of a percolation filter. Interaction of mutations in a series of generations and random processes of drift determine the collective behavior of nodes (individuals - carriers and converters of mutations) and bonds (mutations) in the space of percolation lattice. It is shown that the choice of the development trajectory at the population level depends on the spectrum of supporting and prohibiting mutations under the influence of conjugate deterministic and random factors. From the point of view of the fluctuation-bifurcation process, new concepts of the lower and upper thresholds of the percolation selection grid are defined in the hierarchical structure of speciation. The upper threshold determines the state of self-organized criticality, which, when overcome, leads to irreversible self-organization processes in the population caused by the accumulation of mutations.