Modeling tumors as species-rich ecological communities.

Many advanced cancers resist therapeutic intervention. This process is fundamentally related to intra-tumor heterogeneity: multiple cell populations, each with different mutational and phenotypic signatures, coexist within a tumor and its metastatic nodes. Like species in an ecosystem, many cancer cell populations are intertwined in a complex network of ecological interactions. Most mathematical models of tumor ecology, however, cannot account for such phenotypic diversity nor are able to predict its consequences. Here we propose that the Generalized Lotka-Volterra model (GLV), a standard tool to describe complex, species-rich ecological communities, provides a suitable framework to describe the ecology of heterogeneous tumors. We develop a GLV model of tumor growth and discuss how its emerging properties, such as outgrowth and multistability, provide a new understanding of the disease. Additionally, we discuss potential extensions of the model and their application to three active areas of cancer research, namely phenotypic plasticity, the cancer-immune interplay and the resistance of metastatic tumors to treatment. Our work outlines a set of questions and a tentative road map for further research in cancer ecology.

Self-organization as a mechanism of resilience in dryland ecosystems.

Self-organized spatial patterns are a common feature of complex systems, ranging from microbial communities to mussel beds and drylands. While the theoretical implications of these patterns for ecosystem-level processes, such as functioning and resilience, have been extensively studied, empirical evidence remains scarce. To address this gap, we analyzed global drylands along an aridity gradient using remote sensing, field data, and modeling. We found that the spatial structure of the vegetation strengthens as aridity increases, which is associated with the maintenance of a high level of soil multifunctionality, even as aridity levels rise up to a certain threshold. The combination of these results with those of two individual-based models indicate that self-organized vegetation patterns not only form in response to stressful environmental conditions but also provide drylands with the ability to adapt to changing conditions while maintaining their functioning, an adaptive capacity which is lost in degraded ecosystems. Self-organization thereby plays a vital role in enhancing the resilience of drylands. Overall, our findings contribute to a deeper understanding of the relationship between spatial vegetation patterns and dryland resilience. They also represent a significant step forward in the development of indicators for ecosystem resilience, which are critical tools for managing and preserving these valuable ecosystems in a warmer and more arid world.

A synthetic microbial Daisyworld: planetary regulation in the test tube.

The idea that the Earth system self-regulates in a habitable state was proposed in the 1970s by James Lovelock, who conjectured that life plays a self-regulatory role on a planetary-level scale. A formal approach to such hypothesis was presented afterwards under a toy model known as the Daisyworld. The model showed how such life-geosphere homeostasis was an emergent property of the system, where two species with different properties adjusted their populations to the changing external environment. So far, this ideal world exists only as a mathematical or computational construct, but it would be desirable to have a real, biological implementation of Lovelock's picture beyond our one biosphere. Inspired by the exploration of synthetic ecosystems using genetic engineering and recent cell factory designs, here we propose a possible implementation for a microbial Daisyworld. This includes: (i) an explicit proposal for an engineered design of a two-strain consortia, using pH as the external, abiotic control parameter and (ii) several theoretical and computational case studies including two, three and multiple species assemblies. The special alternative implementations and their implications in other synthetic biology scenarios, including ecosystem engineering, are outlined.

Structured community transitions explain the switching capacity of microbial systems.

Microbial systems appear to exhibit a relatively high switching capacity of moving back and forth among few dominant communities (taxon memberships). While this switching behavior has been mainly attributed to random environmental factors, it remains unclear the extent to which internal community dynamics affect the switching capacity of microbial systems. Here, we integrate ecological theory and empirical data to demonstrate that structured community transitions increase the dependency of future communities on the current taxon membership, enhancing the switching capacity of microbial systems. Following a structuralist approach, we propose that each community is feasible within a unique domain in environmental parameter space. Then, structured transitions between any two communities can happen with probability proportional to the size of their feasibility domains and inversely proportional to their distance in environmental parameter space-which can be treated as a special case of the gravity model. We detect two broad classes of systems with structured transitions: one class where switching capacity is high across a wide range of community sizes and another class where switching capacity is high only inside a narrow size range. We corroborate our theory using temporal data of gut and oral microbiota (belonging to class 1) as well as vaginal and ocean microbiota (belonging to class 2). These results reveal that the topology of feasibility domains in environmental parameter space is a relevant property to understand the changing behavior of microbial systems. This knowledge can be potentially used to understand the relevant community size at which internal dynamics can be operating in microbial systems.

How Turing parasites expand the computational landscape of digital life.

Why are living systems complex? Why does the biosphere contain living beings with complexity features beyond those of the simplest replicators? What kind of evolutionary pressures result in more complex life forms? These are key questions that pervade the problem of how complexity arises in evolution. One particular way of tackling this is grounded in an algorithmic description of life: living organisms can be seen as systems that extract and process information from their surroundings to reduce uncertainty. Here we take this computational approach using a simple bit string model of coevolving agents and their parasites. While agents try to predict their worlds, parasites do the same with their hosts. The result of this process is that, to escape their parasites, the host agents expand their computational complexity despite the cost of maintaining it. This, in turn, is followed by increasingly complex parasitic counterparts. Such arms races display several qualitative phases, from monotonous to punctuated evolution or even ecological collapse. Our minimal model illustrates the relevance of parasites in providing an active mechanism for expanding living complexity beyond simple replicators, suggesting that parasitic agents are likely to be a major evolutionary driver for biological complexity.

An oncospace for human cancers.

Human cancers comprise an heterogeneous array of diseases with different progression patterns and responses to therapy. However, they all develop within a host context that constrains their natural history. Since it occurs across the diversity of organisms, one can conjecture that there is order in the cancer multiverse. Is there a way to capture the broad range of tumor types within a space of the possible? Here we define the oncospace, a coordinate system that integrates the ecological, evolutionary and developmental components of cancer complexity. The spatial position of a tumor results from its departure from the healthy tissue along these three axes, and progression trajectories inform about the components driving malignancy across cancer subtypes. We postulate that the oncospace topology encodes new information regarding tumorigenic pathways, subtype prognosis, and therapeutic opportunities: treatment design could benefit from considering how to nudge tumors toward empty evolutionary dead ends in the oncospace.

Ecological firewalls for synthetic biology.

It has been recently suggested that engineered microbial strains could be used to protect ecosystems from undesirable tipping points and biodiversity loss. A major concern in this context is the potential unintended consequences, which are usually addressed in terms of designed genetic constructs aimed at controlling overproliferation. Here we present and discuss an alternative view grounded in the nonlinear attractor dynamics of some ecological network motifs. These ecological firewalls are designed to perform novel functionalities (such as plastic removal) while containment is achieved within the resident community. That could help provide a self-regulating biocontainment. In this way, engineered organisms have a limited spread while-when required-preventing their extinction. The basic synthetic designs and their dynamical behavior are presented, each one inspired in a given ecological class of interaction. Their possible applications are discussed and the broader connection with invasion ecology outlined.

Unicellular-multicellular evolutionary branching driven by resource limitations.

Multicellular life forms have evolved many times on our planet, suggesting that this is a common evolutionary innovation. Multiple advantages have been proposed for the emergence of multicellularity (MC). In this paper, we address the problem of how the first precondition for MC, namely 'stay together', might have occurred under spatially limited resources exploited by a population of unicellular agents. Using a minimal model of evolved cell-cell adhesion among growing and dividing cells that exploit a localized resource with a given size, we show that a transition occurs at a critical resource size separating a phase of evolved multicellular aggregates from a phase where unicellularity (UC) is favoured. The two phases are separated by an intermediate domain where both UC and MC can be selected by evolution. This model provides a minimal approach to the early stages that were required to transition from individuality to cohesive groups of cells associated with a physical cooperative effect: when resources are present only in a localized portion of the habitat, MC is a desirable property as it helps cells to keep close to the available local nutrients.

Network-level containment of single-species bioengineering.

Ecological systems are facing major diversity losses in this century owing to Anthropogenic effects. Habitat loss, overexploitation of resources, invasion and pollution are rapidly jeopardizing the survival of whole communities. It has been recently suggested that a potential approach to flatten the curve of species extinction and prevent catastrophic shifts would involve the engineering of one selected species within one of these communities. Such possibility has started to become part of potential intervention scenarios to preserve biodiversity. Despite its potential, very little is known about the actual dynamic responses of complex ecological networks to the introduction of a synthetic strains derived from a resident species. In this paper, we address this problem by modelling the response of a community to the addition of a synthetic strain derived from a member of a stable ecosystem. We show that the community interaction matrix largely limits the spread of the engineered strain, thus suggesting that species diversity acts as an ecological firewall. The implications for future scenarios of ecosystem engineering are outlined. This article is part of the theme issue 'Ecological complexity and the biosphere: the next 30 years'.

Ecological complexity and the biosphere: the next 30 years.

Global warming, habitat loss and overexploitation of limited resources are leading to alarming biodiversity declines. Ecosystems are complex adaptive systems that display multiple alternative states and can shift from one to another in abrupt ways. Some of these tipping points have been identified and predicted by mathematical and computational models. Moreover, multiple scales are involved and potential mitigation or intervention scenarios are tied to particular levels of complexity, from cells to human-environment coupled systems. In dealing with a biosphere where humans are part of a complex, endangered ecological network, novel theoretical and engineering approaches need to be considered. At the centre of most research efforts is biodiversity, which is essential to maintain community resilience and ecosystem services. What can be done to mitigate, counterbalance or prevent tipping points? Using a 30-year window, we explore recent approaches to sense, preserve and restore ecosystem resilience as well as a number of proposed interventions (from afforestation to bioengineering) directed to mitigate or reverse ecosystem collapse. The year 2050 is taken as a representative future horizon that combines a time scale where deep ecological changes will occur and proposed solutions might be effective. This article is part of the theme issue 'Ecological complexity and the biosphere: the next 30 years'.

Evolution of Brains and Computers: The Roads Not Taken.

When computers started to become a dominant part of technology around the 1950s, fundamental questions about reliable designs and robustness were of great relevance. Their development gave rise to the exploration of new questions, such as what made brains reliable (since neurons can die) and how computers could get inspiration from neural systems. In parallel, the first artificial neural networks came to life. Since then, the comparative view between brains and computers has been developed in new, sometimes unexpected directions. With the rise of deep learning and the development of connectomics, an evolutionary look at how both hardware and neural complexity have evolved or designed is required. In this paper, we argue that important similarities have resulted both from convergent evolution (the inevitable outcome of architectural constraints) and inspiration of hardware and software principles guided by toy pictures of neurobiology. Moreover, dissimilarities and gaps originate from the lack of major innovations that have paved the way to biological computing (including brains) that are completely absent within the artificial domain. As it occurs within synthetic biocomputation, we can also ask whether alternative minds can emerge from A.I. designs. Here, we take an evolutionary view of the problem and discuss the remarkable convergences between living and artificial designs and what are the pre-conditions to achieve artificial intelligence.

Transition Therapy: Tackling the Ecology of Tumor Phenotypic Plasticity.

Phenotypic switching in cancer cells has been found to be present across tumor types. Recent studies on Glioblastoma report a remarkably common architecture of four well-defined phenotypes coexisting within high levels of intra-tumor genetic heterogeneity. Similar dynamics have been shown to occur in breast cancer and melanoma and are likely to be found across cancer types. Given the adaptive potential of phenotypic switching (PHS) strategies, understanding how it drives tumor evolution and therapy resistance is a major priority. Here we present a mathematical framework uncovering the ecological dynamics behind PHS. The model is able to reproduce experimental results, and mathematical conditions for cancer progression reveal PHS-specific features of tumors with direct consequences on therapy resistance. In particular, our model reveals a threshold for the resistant-to-sensitive phenotype transition rate, below which any cytotoxic or switch-inhibition therapy is likely to fail. The model is able to capture therapeutic success thresholds for cancers where nonlinear growth dynamics or larger PHS architectures are in place, such as glioblastoma or melanoma. By doing so, the model presents a novel set of conditions for the success of combination therapies able to target replication and phenotypic transitions at once. Following our results, we discuss transition therapy as a novel scheme to target not only combined cytotoxicity but also the rates of phenotypic switching.

Phase transitions in virology.

Viruses have established relationships with almost every other living organism on Earth and at all levels of biological organization: from other viruses up to entire ecosystems. In most cases, they peacefully coexist with their hosts, but in most relevant cases, they parasitize them and induce diseases and pandemics, such as the AIDS and the most recent avian influenza and COVID-19 pandemic events, causing a huge impact on health, society, and economy. Viruses play an essential role in shaping the eco-evolutionary dynamics of their hosts, and have been also involved in some of the major evolutionary innovations either by working as vectors of genetic information or by being themselves coopted by the host into their genomes. Viruses can be studied at different levels of biological organization, from the molecular mechanisms of genome replication, gene expression and encapsidation, to global pandemics. All these levels are different and yet connected through the presence of threshold conditions allowing for the formation of a capsid, the loss of genetic information or epidemic spreading. These thresholds, as occurs with temperature separating phases in a liquid, define sharp qualitative types of behaviour. Thesephase transitionsare very well known in physics. They have been studied by means of simple, but powerful models able to capture their essential properties, allowing us to better understand them. Can the physics of phase transitions be an inspiration for our understanding of viral dynamics at different scales? Here we review well-known mathematical models of transition phenomena in virology. We suggest that the advantages of abstract, simplified pictures used in physics are also the key to properly understanding the origins and evolution of complexity in viruses. By means of several examples, we explore this multilevel landscape and how minimal models provide deep insights into a diverse array of problems. The relevance of these transitions in connecting dynamical patterns across scales and their evolutionary and clinical implications are outlined.

Engineering self-organized criticality in living cells.

Complex dynamical fluctuations, from intracellular noise, brain dynamics or computer traffic display bursting dynamics consistent with a critical state between order and disorder. Living close to the critical point has adaptive advantages and it has been conjectured that evolution could select these critical states. Is this the case of living cells? A system can poise itself close to the critical point by means of the so-called self-organized criticality (SOC). In this paper we present an engineered gene network displaying SOC behaviour. This is achieved by exploiting the saturation of the proteolytic degradation machinery in E. coli cells by means of a negative feedback loop that reduces congestion. Our critical motif is built from a two-gene circuit, where SOC can be successfully implemented. The potential implications for both cellular dynamics and behaviour are discussed.

Synthetic Lateral Inhibition in Periodic Pattern Forming Microbial Colonies.

Multicellular entities are characterized by intricate spatial patterns, intimately related to the functions they perform. These patterns are often created from isotropic embryonic structures, without external information cues guiding the symmetry breaking process. Mature biological structures also display characteristic scales with repeating distributions of signals or chemical species across space. Many candidate patterning modules have been used to explain processes during development and typically include a set of interacting and diffusing chemicals or agents known as morphogens. Great effort has been put forward to better understand the conditions in which pattern-forming processes can occur in the biological domain. However, evidence and practical knowledge allowing us to engineer symmetry-breaking is still lacking. Here we follow a different approach by designing a synthetic gene circuit in E. coli that implements a local activation long-range inhibition mechanism. The synthetic gene network implements an artificial differentiation process that changes the physicochemical properties of the agents. Using both experimental results and modeling, we show that the proposed system is capable of symmetry-breaking leading to regular spatial patterns during colony growth. Studying how these patterns emerge is fundamental to further our understanding of the evolution of biocomplexity and the role played by self-organization. The artificial system studied here and the engineering perspective on embryogenic processes can help validate developmental theories and identify universal properties underpinning biological pattern formation, with special interest for the area of synthetic developmental biology.

The ecology of cancer differentiation therapy.

A promising, yet still under development approach to cancer treatment is based on the idea of differentiation therapy (DTH). Most tumours are characterized by poorly differentiated cell populations exhibiting a marked loss of traits associated to communication and tissue homeostasis. DTH has been suggested as an alternative (or complement) to cytotoxic-based approaches, and has proven successful in some specific types of cancer such as acute promyelocytic leukemia (APL). While novel drugs favouring the activation of differentiation therapies are being tested, several open problems emerge in relation to its effectiveness on solid tumors. Here we present a mathematical framework to DTH based on a well-known ecological model used to describe habitat loss. The models presented here account for some of the observed clinical and in vitro outcomes of DTH, providing relevant insight into potential therapy design. Furthermore, the same ecological approach is tested in a hierarchical model that accounts for cancer stem cells, highlighting the role of niche specificity in CSC therapy resistance. We show that the lessons learnt from metapopulation ecology can help guide future developments and potential difficulties of DTH.

Criticality in Pareto Optimal Grammars?

What are relevant levels of description when investigating human language? How are these levels connected to each other? Does one description yield smoothly into the next one such that different models lie naturally along a hierarchy containing each other? Or, instead, are there sharp transitions between one description and the next, such that to gain a little bit accuracy it is necessary to change our framework radically? Do different levels describe the same linguistic aspects with increasing (or decreasing) accuracy? Historically, answers to these questions were guided by intuition and resulted in subfields of study, from phonetics to syntax and semantics. Need for research at each level is acknowledged, but seldom are these different aspects brought together (with notable exceptions). Here, we propose a methodology to inspect empirical corpora systematically, and to extract from them, blindly, relevant phenomenological scales and interactions between them. Our methodology is rigorously grounded in information theory, multi-objective optimization, and statistical physics. Salient levels of linguistic description are readily interpretable in terms of energies, entropies, phase transitions, or criticality. Our results suggest a critical point in the description of human language, indicating that several complementary models are simultaneously necessary (and unavoidable) to describe it.

Tumour neoantigen heterogeneity thresholds provide a time window for combination immunotherapy.

Following the advent of cancer immunotherapy, increasing insight has been gained on the role of mutational load and neoantigens as key ingredients in T cell recognition of malignancies. However, not all highly mutational tumours react to immune therapies, and initial success is often followed by eventual relapse. Heterogeneity in the neoantigen landscape of a tumour might be key in the failure of immune surveillance. In this work, we present a mathematical framework to describe how neoantigen distributions shape the immune response. The model predicts the existence of an antigen diversity threshold level beyond which T cells fail at controlling heterogeneous tumours. Incorporating this diversity marker adds predictive value to antigen load for two cohorts of anti-CTLA-4 treated melanoma patients. Furthermore, our analytical approach indicates rapid increases in epitope heterogeneity in early malignancy growth following immune escape. We propose a combination therapy scheme that takes advantage of preexisting resistance to a targeted agent. The model indicates that the selective sweep for a resistant subclone reduces neoantigen heterogeneity, and we postulate the existence of a time window before tumour relapse where checkpoint blockade immunotherapy can become more effective.

Synthetic soil crusts against green-desert transitions: a spatial model.

Semiarid ecosystems are threatened by global warming due to longer dehydration times and increasing soil degradation. Mounting evidence indicates that, given the current trends, drylands are likely to expand and possibly experience catastrophic shifts from vegetated to desert states. Here, we explore a recent suggestion based on the concept of ecosystem terraformation, where a synthetic organism is used to counterbalance some of the nonlinear effects causing the presence of such tipping points. Using an explicit spatial model incorporating facilitation and considering a simplification of states found in semiarid ecosystems including vegetation, fertile and desert soil, we investigate how engineered microorganisms can shape the fate of these ecosystems. Specifically, two different, but complementary, terraformation strategies are proposed: Cooperation-based: C-terraformation; and Dispersion-based: D-terraformation. The first strategy involves the use of soil synthetic microorganisms to introduce cooperative loops (facilitation) with the vegetation. The second one involves the introduction of engineered microorganisms improving their dispersal capacity, thus facilitating the transition from desert to fertile soil. We show that small modifications enhancing cooperative loops can effectively modify the aridity level of the critical transition found at increasing soil degradation rates, also identifying a stronger protection against soil degradation by using the D-terraformation strategy. The same results are found in a mean-field model providing insights into the transitions and dynamics tied to these terraformation strategies. The potential consequences and extensions of these models are discussed.