Feedbacks, nonlinearities and nonequilibria: A thermodynamic perspective.

The feedback circuit approach to nonlinear dynamical systems pioneered by Thomas and coworkers is revisited in a thermodynamical perspective. The role of nonequilibrium conditions and of other types of constraints such as mass action kinetics or microscopic reversibility around thermodynamic equilibrium in the way positive feedback circuits are operating is analyzed. It is shown that the appearance of non-trivial steady-state and time-dependent behaviors necessitates that the strengths of the feedback loops present exceed some well-defined critical values. Illustrations are provided on prototypical systems giving rise to multiple steady states.

Sox2 is not required for melanomagenesis, melanoma growth and melanoma metastasis in vivo.

Melanoma is a dangerous form of skin cancer derived from the malignant transformation of melanocytes. The transcription factor SOX2 is not expressed in melanocytes, however, it has been shown to be differentially expressed between benign nevi and malignant melanomas and to be essential for melanoma stem cell maintenance and expansion in vitro and in xenograft models. By using a mouse model in which BRafV600E mutation cooperates with Pten loss to induce the development of metastatic melanoma, we investigated if Sox2 is required during the process of melanomagenesis, melanoma growth and metastasis and in the acquisition of resistance to BRAF inhibitors (BRAFi) treatments. We found that deletion of Sox2 specifically in Pten null and BRafV600E-expressing melanocytes did not prevent tumor formation and did not modify the temporal kinetics of melanoma occurrence compared to Sox2 wt mice. In addition, tumor growth was similar between Sox2 wt and Sox2 deleted (del) melanomas. By querying publicly available databases, we did not find statistically significant differences in SOX2 expression levels between benign nevi and melanomas, and analysis on two melanoma patient cohorts confirmed that Sox2 levels did not significantly change between primary and metastatic melanomas. Melanoma cell lines derived from both Sox2 genotypes showed a similar sensitivity to vemurafenib treatment and the same ability to develop vemurafenib resistance in long-term cultures. Development of vemurafenib resistance was not dependent on SOX2 expression also in human melanoma cell lines in vitro. Our findings exclude an oncogenic function for Sox2 during melanoma development and do not support a role for this transcription factor in the acquisition of resistance to BRAFi treatments.

Sox2 is dispensable for primary melanoma and metastasis formation.

Tumor initiation and metastasis formation in many cancers have been associated with emergence of a gene expression program normally active in embryonic or organ-specific stem cells. In particular, the stem cell transcription factor Sox2 is not only expressed in a variety of tumors, but is also required for their formation. Melanoma, the most aggressive skin tumor, derives from melanocytes that during development originate from neural crest stem cells. While neural crest stem cells do not express Sox2, expression of this transcription factor has been reported in melanoma. However, the role of Sox2 in melanoma is controversial. To study the requirement of Sox2 for melanoma formation, we therefore performed CRISPR-Cas9-mediated gene inactivation in human melanoma cells. In addition, we conditionally inactivated Sox2 in a genetically engineered mouse model, in which melanoma spontaneously develops in the context of an intact stroma and immune system. Surprisingly, in both models, loss of Sox2 did neither affect melanoma initiation, nor growth, nor metastasis formation. The lack of a tumorigenic role of Sox2 in melanoma might reflect a distinct stem cell program active in neural crest stem cells and during melanoma formation.

Collective choice in ants: the role of protein and carbohydrates ratios.

In a foraging context, social insects make collective decisions from individuals responding to local information. When faced with foods varying in quality, ants are known to be able to select the best food source using pheromone trails. Until now, studies investigating collective decisions have focused on single nutrients, mostly carbohydrates. In the environment, the foods available are a complex mixture and are composed of various nutrients, available in different forms. In this paper, we explore the effect of protein to carbohydrate ratio on ants' ability to detect and choose between foods with different protein characteristics (free amino acids or whole proteins). In a two-choice set up, Argentine ants Linepithema humile were presented with two artificial foods containing either whole protein or amino acids in two different dietary conditions: high protein food or high carbohydrate food. At the collective level, when ants were faced with high carbohydrate foods, they did not show a preference between free amino acids or whole proteins, while a preference for free amino acids emerged when choosing between high protein foods. At the individual level, the probability of feeding was higher for high carbohydrates food and for foods containing free amino acids. Two mathematical models were developed to evaluate the importance of feeding probability in collective food selection. A first model in which a forager deposits pheromone only after feeding, and a second model in which a forager always deposits pheromone, but with greater intensity after feeding. Both models were able to predict free amino acid selection, however the second one was better able to reproduce the experimental results suggesting that modulating trail strength according to feeding probability is likely the mechanism explaining amino acid preference at a collective level in Argentine ants.

Foraging at the edge of chaos: internal clock versus external forcing.

Activity rhythms in animal groups arise both from external changes in the environment, as well as from internal group dynamics. These cycles are reminiscent of physical and chemical systems with quasiperiodic and even chaotic behavior resulting from "autocatalytic" mechanisms. We use nonlinear differential equations to model how the coupling between the self-excitatory interactions of individuals and external forcing can produce four different types of activity rhythms: quasiperiodic, chaotic, phase locked, and displaying over or under shooting. At the transition between quasiperiodic and chaotic regimes, activity cycles are asymmetrical, with rapid activity increases and slower decreases and a phase shift between external forcing and activity. We find similar activity patterns in ant colonies in response to varying temperature during the day. Thus foraging ants operate in a region of quasiperiodicity close to a cascade of transitions leading to chaos. The model suggests that a wide range of temporal structures and irregularities seen in the activity of animal and human groups might be accounted for by the coupling between collectively generated internal clocks and external forcings.

Emx2 is a dose-dependent negative regulator of Sox2 telencephalic enhancers.

The transcription factor Sox2 is essential for neural stem cells (NSC) maintenance in the hippocampus and in vitro. The transcription factor Emx2 is also critical for hippocampal development and NSC self-renewal. Searching for 'modifier' genes affecting the Sox2 deficiency phenotype in mouse, we observed that loss of one Emx2 allele substantially increased the telencephalic ß-geo (LacZ) expression of a transgene driven by the 5' or 3' Sox2 enhancer. Reciprocally, Emx2 overexpression in NSC cultures inhibited the activity of the same transgene. In vivo, loss of one Emx2 allele increased Sox2 levels in the medial telencephalic wall, including the hippocampal primordium. In hypomorphic Sox2 mutants, retaining a single 'weak' Sox2 allele, Emx2 deficiency substantially rescued hippocampal radial glia stem cells and neurogenesis, indicating that Emx2 functionally interacts with Sox2 at the stem cell level. Electrophoresis mobility shift assays and transfection indicated that Emx2 represses the activities of both Sox2 enhancers. Emx2 bound to overlapping Emx2/POU-binding sites, preventing binding of the POU transcriptional activator Brn2. Additionally, Emx2 directly interacted with Brn2 without binding to DNA. These data imply that Emx2 may perform part of its functions by negatively modulating Sox2 in specific brain areas, thus controlling important aspects of NSC function in development.

Information flow and information production in a population system.

An approach aiming to quantify the dynamics of information within a population is developed based on the mapping of the processes underlying the system's evolution into a birth and death type stochastic process and the derivation of a balance equation for the information entropy. Information entropy flux and information entropy production are identified and their time-dependent properties, as well as their dependence on the parameters present in the problem, are analyzed. States of minimum information entropy production are shown to exist for appropriate parameter values. Furthermore, uncertainty and information production are transiently intensified when the population traverses the inflexion point stage of the logisticlike growth process.

Resource exploitation strategies in the presence of traffic between food sources.

A mathematical model of food recruitment and resource exploitation in group-living organisms accounting for direct traffic of individuals between the available sources is developed. It is shown that traffic between sources gives rise to the enhancement of the range of stability of the homogeneous mode of exploitation and of the range of coexistence of homogeneous and semi-inhomogeneous ones, as well as the appearance of symmetry breaking transitions leading to fully inhomogeneous exploitation modes.

The selfish to egalitarian transition in young children: developmental processes versus cooperative interactions.

There is evidence that a tendency to share resources equitably among members of a social group emerges in middle childhood. It is regarded by many investigators as a central and unique feature of human social life. In this work the relative roles of developmental processes and collective effects generated by interindividual interactions on the selfish to egalitarian transition observed in middle childhood are analyzed. Using mathematical modeling, conditions are identified under which the transition becomes sharp and gives rise to hysteretic behavior.

The transcription factor Sox2 is required for osteoblast self-renewal.

The development and maintenance of most tissues and organs require the presence of multipotent and unipotent stem cells that have the ability of self-renewal as well as of generating committed, further differentiated cell types. The transcription factor Sox2 is essential for embryonic development and maintains pluripotency and self-renewal in embryonic stem cells. It is expressed in immature osteoblasts/osteoprogenitors in vitro and in vivo and is induced by fibroblast growth factor signaling, which stimulates osteoblast proliferation and inhibits differentiation. Sox2 overexpression can by itself inhibit osteoblast differentiation. To elucidate its function in the osteoblastic lineage, we generated mice with an osteoblast-specific, Cre-mediated knockout of Sox2. These mice are small and osteopenic, and mosaic for Sox2 inactivation. However, culturing calvarial osteoblasts from the mutant mice for 2-3 passages failed to yield any Sox2-null cells. Inactivation of the Sox2 gene by Cre-mediated excision in cultured osteoblasts showed that Sox2-null cells could not survive repeated passage in culture, could not form colonies, and arrested their growth with a senescent phenotype. In addition, expression of Sox2-specific shRNAs in independent osteoblastic cell lines suppressed their proliferative ability. Osteoblasts capable of forming 'osteospheres' are greatly enriched in Sox2 expression. These data identify a novel function for Sox2 in the maintenance of self-renewal in the osteoblastic lineage.

Propagation of extremes in space.

The propagation of extreme events in space is analyzed for a class of dynamical systems giving rise to spatiotemporal chaos. It is shown that this process can be mapped into a generalized random walk, whereby the mean square displacement increases linearly in time and there is a nonvanishing probability for jumps beyond first neighbors. The relative roles of the local dynamics and of the spatial coupling are identified.

Noise improves collective decision-making by ants in dynamic environments.

Recruitment via pheromone trails by ants is arguably one of the best-studied examples of self-organization in animal societies. Yet it is still unclear if and how trail recruitment allows a colony to adapt to changes in its foraging environment. We study foraging decisions by colonies of the ant Pheidole megacephala under dynamic conditions. Our experiments show that P. megacephala, unlike many other mass recruiting species, can make a collective decision for the better of two food sources even when the environment changes dynamically. We developed a stochastic differential equation model that explains our data qualitatively and quantitatively. Analysing this model reveals that both deterministic and stochastic effects (noise) work together to allow colonies to efficiently track changes in the environment. Our study thus suggests that a certain level of noise is not a disturbance in self-organized decision-making but rather serves an important functional role.

The role of multiple pheromones in food recruitment by ants.

In this paper we investigate the foraging activity of an invasive ant species, the big headed ant Pheidole megacephala. We establish that the ants' behavior is consistent with the use of two different pheromone signals, both of which recruit nestmates. Our experiments suggest that during exploration the ants deposit a long-lasting pheromone that elicits a weak recruitment of nestmates, while when exploiting food the ants deposit a shorter lasting pheromone eliciting a much stronger recruitment. We further investigate experimentally the role of these pheromones under both static and dynamic conditions and develop a mathematical model based on the hypothesis that exploration locally enhances exploitation, while exploitation locally suppresses exploration. The model and the experiments indicate that exploratory pheromone allows the colony to more quickly mobilize foragers when food is discovered. Furthermore, the combination of two pheromones allows colonies to track changing foraging conditions more effectively than would a single pheromone. In addition to the already known causes for the ecological success of invasive ant species, our study suggests that their opportunistic strategy of rapid food discovery and ability to react to changes in the environment may have strongly contributed to their dominance over native species.

Extreme events in bimodal systems.

The extreme value statistics of systems possessing a two-hump probability density of the relevant variable, in which the left peak is more pronounced than the right one, is studied. It is shown that systems of this type display a nontrivial transient behavior in the form of anomalous fluctuations around the mean, for certain (finite) ranges of observational time windows. The results are illustrated on independent identically distributed random variables, systems possessing two locally stable states and subjected to additive white noise, and dynamical systems in the regime of deterministic chaos.

Collective decision-making and behavioral polymorphism in group living organisms.

Collective foraging in group living animal populations displaying behavioral polymorphism is considered. Using mathematical modeling it is shown that symmetric, spatially homogeneous (food sources are used equally) and asymmetric, spatially inhomogeneous (only one food source is used) regimes can coexist, as a result of differential amplification of choice depending on behavioral type. The model accounts for recent experimental results on social caterpillars not only confirming this coexistence, but also showing the relationship between the two types of regime and the ratio of active to inactive individuals.

Kinetics of aggregate formation in social insects.

A model for the kinetics of aggregation in social insects which accounts for stochastic effects arising from individual variability and covers both the early and the mature stages of the process is developed. Different aggregation scenarios are studied, depending on the degree of cooperativity and the mean population density. It is shown that under certain conditions, the system evolves slowly to a single cluster incorporating all individuals, or to two coexisting clusters of similar sizes.

Optimality of collective choices: a stochastic approach.

Amplifying communication is a characteristic of group-living animals. This study is concerned with food recruitment by chemical means, known to be associated with foraging in most ant colonies but also with defence or nest moving. A stochastic approach of collective choices made by ants faced with different sources is developed to account for the fluctuations inherent to the recruitment process. It has been established that ants are able to optimize their foraging by selecting the most rewarding source. Our results not only confirm that selection is the result of a trail modulation according to food quality but also show the existence of an optimal quantity of laid pheromone for which the selection of a source is at the maximum, whatever the difference between the two sources might be. In terms of colony size, large colonies more easily focus their activity on one source. Moreover, the selection of the rich source is more efficient if many individuals lay small quantities of pheromone, instead of a small group of individuals laying a higher trail amount. These properties due to the stochasticity of the recruitment process can be extended to other social phenomena in which competition between different sources of information occurs.

Sox2 regulatory sequences direct expression of a (beta)-geo transgene to telencephalic neural stem cells and precursors of the mouse embryo, revealing regionalization of gene expression in CNS stem cells.

Sox2 is one of the earliest known transcription factors expressed in the developing neural tube. Although it is expressed throughout the early neuroepithelium, we show that its later expression must depend on the activity of more than one regionally restricted enhancer element. Thus, by using transgenic assays and by homologous recombination-mediated deletion, we identify a region upstream of Sox2 (-5.7 to -3.3 kb) which can not only drive expression of a (beta)-geo transgene to the developing dorsal telencephalon, but which is required to do so in the context of the endogenous gene. The critical enhancer can be further delimited to an 800 bp fragment of DNA surrounding a nuclease hypersensitive site within this region, as this is sufficient to confer telencephalic expression to a 3.3 kb fragment including the Sox2 promoter, which is otherwise inactive in the CNS. Expression of the 5.7 kb Sox2(beta)-geo transgene localizes to the neural plate and later to the telencephalic ventricular zone. We show, by in vitro clonogenic assays, that transgene-expressing (and thus G418-resistant) ventricular zone cells include cells displaying functional properties of stem cells, i.e. self-renewal and multipotentiality. We further show that the majority of telencephalic stem cells express the transgene, and this expression is largely maintained over two months in culture (more than 40 cell divisions) in the absence of G418 selective pressure. In contrast, stem cells grown in parallel from the spinal cord never express the transgene, and die in G418. Expression of endogenous telencephalic genes was similarly observed in long-term cultures derived from the dorsal telencephalon, but not in spinal cord-derived cultures. Thus, neural stem cells of the midgestation embryo are endowed with region-specific gene expression (at least with respect to some networks of transcription factors, such as that driving telencephalic expression of the Sox2 transgene), which can be inherited through multiple divisions outside the embryonic environment.

UFD1L, a developmentally expressed ubiquitination gene, is deleted in CATCH 22 syndrome.

The CATCH 22 acronym outlines the main clinical features of 22q11.2 deletions (cardiac defects, abnormal facies, thymic hypoplasia, cleft palate and hypocalcemia), usually found in DiGeorge (DGS) and velo-cardio-facial (VCFS) syndromes. Hemizygosity of this region may also be the cause of over 100 different clinical signs. The CATCH 22 locus maps within a 1.5 Mb region, which encompasses several genes. However, no single defect in 22q11.2 hemizygous patients can be ascribed to any gene so far isolated from the critical region of deletion. We have identified a gene in the CATCH 22 critical region, whose functional features and tissue-specific expression suggest a distinct role in embryogenesis. This gene, UFD1L, encodes the human homolog of the yeast ubiquitin fusion degradation 1 protein (UFD1p), involved in the degradation of ubiquitin fusion proteins. Cloning and characterization of the murine homolog (Ufd1l) showed it to be expressed during embryogenesis in the eyes and in the linear ear primordia. These data suggest that the proteolytic pathway that recognizes ubiquitin fusion proteins for degradation is conserved in vertebrates and that the UFD1L gene hemizygosity is the cause of some of the CATCH 22-associated developmental defects.

Immortalization of multipotent growth-factor dependent hemopoietic progenitors from mice transgenic for GATA-1 driven SV40 tsA58 gene.

The transcription factor GATA-1 is required for the normal development of erythroid cells. GATA-1 is also expressed in other hemopoietic cells, suggesting that it might be initially activated in a multipotent progenitor. To immortalize GATA-1-expressing progenitors, we generated mice transgenic for a thermosensitive SV40 T gene, driven by the GATA-1 promoter-enhancer. Immortalized marrow cells grow in culture at 32 degrees C but not at 38 degrees C, and are dependent on erythropoietin (Epo) or interleukin 3 (IL-3). Epo dependent cells express hemoglobin, high levels of GATA-1, GATA-2 and NF-E2 p45 mRNAs, and are positive for stem cell antigen 2 (Sca-2) and the early myeloid marker ER-MP12. IL-3 dependent cells can be derived from Epo dependent lines, and are hemoglobin-, Sca-2- and ER-MP12-negative, have low GATA-1 and NF-E2 p45 mRNA levels, and express myeloid markers Mac-1, F4/80 and Gr-1. Brief treatment of Epo dependent cells with myeloid growth factors (plus Epo) leads to the induction of Mac-1, F4/80 and Gr-1, concomitant with the disappearance from most cells of Sca-2, ER-MP12 and GATA-1 driven T antigen nuclear expression. Thus, the immortalized Epo dependent cells have the property of a progenitor capable of differentiation towards either the erythroid or myeloid lineages. These cells initiate transcription of a proportion of GATA-1 RNA molecules at an upstream promoter, previously known to be expressed only in testis cells.