High-dimensional switches and the modeling of cellular differentiation

Many genes have been identified as driving cellular differentiation, but because of their complex interactions, the understanding of their collective behaviour requires mathematical modelling. Intriguingly, it has been observed in numerous developmental contexts, and particularly hematopoiesis, that genes regulating differentiation are initially co-expressed in progenitors despite their antagonism, before one is upregulated and others downregulated. We characterise conditions under which 3 classes of generic "master regulatory networks", modelled at the molecular level after experimentally-observed interactions (including bHLH protein dimerisation), and including an arbitrary number of antagonistic components, can behave as a "multi-switch", directing differentiation in an all-or-none fashion to a specific cell-type chosen among more than 2 possible outcomes. bHLH dimerisation networks can readily display coexistence of many antagonistic factors when competition is low (a simple characterisation is derived). Decision-making can be forced by a transient increase in competition, which could correspond to some unexplained experimental observations related to Id proteins; the speed of response varies with the initial conditions the network is subjected to, which could explain some aspects of cell behaviour upon reprogramming.The coexistence of antagonistic factors at low levels, early in the differentiation process or in pluripotent stem cells, could be an intrinsic property of the interaction between those factors, not requiring a specific regulatory system

Generalized, switch-like competitive heterodimerization networks

High-dimensional switches have been proposed as a way to model cellular differentiation, particularly in the context of basic Helix-Loop-Helix (bHLH) competitive heterodimerization networks. A previous study derived a simple rule showing how many elements can be co-expressed, depending on the rate of competition within the network. A limitation to that rule, however, is that many biochemical parameters were considered to be identical. Here, we derive a generalized rule. This in turns allows one to study more ways in which these networks could be regulated, linking intrinsic cellular differentiation determinants to extra-cellular cues

Clocks, gradients, and molecular networks: mathematical models for morphogenesis.

The acquisition of a spatial structure during embryo development involves the differentiation of cells, often according to positional information. The complexity of the molecular networks regulating differentiation and of the mechanisms generating positional information makes it necessary to study them by means of mathematical modeling. Vertebrate embryos also acquire a segmented structure during somitogenesis this requires spatial and temporal variations in gene expression, which mathematical modeling can also help understand. A molecular mechanism for the somitogenesis clock is proposed, which accounts for inter-cellular synchronisation, and is based on positive feedback, even though it is compatible with all experimental data interpreted as showing that the clock is based on negative feedback. Experiments proposed to test this model involve real-time clock reporters, as well as inducible systems to induce spatially-controlled perturbations. Theoretical and experimental results have led to conflicting ideas as to how useful positional information can be established. In particular, it has been pointed out that some models of extracellular diffusion of morphogen exhibit inadequate traveling waves of receptor saturation. Two alternative (but not mutually exclusive) models are proposed, which are based on recent experimental results highlighting the roles of extracellular glycoproteins and morphogen oligomerization. The readout of positional information is translated to a discrete set of gene expression patterns. Intriguingly, it has been observed in numerous contexts that genes regulating differentiation are initially co-expressed in progenitors despite their antagonism. We characterise conditions under which three classes of generic "master regulatory networks" can behave as a "multi-switch", directing differentiation in an all-or-none fashion to a specific cell-type chosen among more than two possible outcomes. bHLH dimerisation networks can readily display coexistence of many antagonistic factors when competition is low. Decision-making can be forced by a transient increase in competition, which could correspond to some unexplained experimental observations related to Id proteins

Converting genetic network oscillations into somite spatial pattern

In most vertebrate species, the body axis is generated by the formation of repeated transient structures called somites. This spatial periodicity in somitogenesis has been related to the temporally sustained oscillations in certain mRNAs and their associated gene products in the cells forming the presomatic mesoderm. The mechanism underlying these oscillations have been identified as due to the delays involved in the synthesis of mRNA and translation into protein molecules [J. Lewis, Current Biol. {\bf 13}, 1398 (2003)]. In addition, in the zebrafish embryo intercellular Notch signalling couples these oscillators and a longitudinal positional information signal in the form of an Fgf8 gradient exists that could be used to transform these coupled temporal oscillations into the observed spatial periodicity of somites. Here we consider a simple model based on this known biology and study its consequences for somitogenesis. Comparison is made with the known properties of somite formation in the zebrafish embryo . We also study the effects of localized Fgf8 perturbations on somite patterning.Comment: 7 pages, 7 figure

An Ethnography of Brand Piracy in Guatemala

An important dimension of contemporary capitalism is the global spread of intellectual property rights law, drawing new attention by governments and media to the unauthorized copying of fashion brands. In this dissertation, I draw on sixteen months of ethnographic research with small-scale, indigenous Maya garment manufacturers to examine the cultural and moral context of brand piracy in Guatemala. I analyze what practices of copying and imitation, some of which qualify as piracy under national and international law, among Maya manufacturers reveal about two aspects of the social field: first, changing economic and cultural conditions following waves of neoliberal economic and legal reform, and, second, the nonlinear reproduction of forms of moral and legal reckoning at the margins of the global economy and amidst mounting insecurities that include rising violent crime rates and legal impunity for violent crime. I examine how practices of copying and imitation among manufacturers and competitive behavior more generally are evaluated locally in light of kin relations that promote the sharing of knowledge and resources within a somewhat loose property regime and given ideologies of race and nation that encourage class-based solidarity among Maya people. I find that the normative models and business practices evident among these manufacturers parochialize official portraits of progress, business ethics, and development promoted in neoliberal policy agendas and international law. In addition, I analyze significant gaps between what fashion and branding mean in Guatemalan Maya communities and how they are understood in international projects of legal harmonization that are also about re-branding and re-imagining the Guatemalan nation. Neoliberal statecraft following a long internal armed conflict in Guatemala involves policy approaches that amplify the presence of global brands while compounding conditions of social and economic inequality that limit Maya men and women’s access to authorized goods. Meanwhile, Maya people are invited to participate in a modernist vision of citizenship and social progress that encourages a privatized model of indigenous identity mediated by branded commodities and formal market transactions. The brand emerges as a powerful medium through which claims to legitimacy and authority and senses of belonging are negotiated at national and local levels.Anthropolog

Sign patterns for chemical reaction networks

Most differential equations found in chemical reaction networks (CRNs) have the form $dx/dt=f(x)= Sv(x)$, where $x$ lies in the nonnegative orthant, where $S$ is a real matrix (the stoichiometric matrix) and $v$ is a column vector consisting of real-valued functions having a special relationship to $S$. Our main interest will be in the Jacobian matrix, $f'(x)$, of $f(x)$, in particular in whether or not each entry $f'(x)_{ij}$ has the same sign for all $x$ in the orthant, i.e., the Jacobian respects a sign pattern. In other words species $x_j$ always acts on species $x_i$ in an inhibitory way or its action is always excitatory. In Helton, Klep, Gomez we gave necessary and sufficient conditions on the species-reaction graph naturally associated to $S$ which guarantee that the Jacobian of the associated CRN has a sign pattern. In this paper, given $S$ we give a construction which adds certain rows and columns to $S$, thereby producing a stoichiometric matrix $\widehat S$ corresponding to a new CRN with some added species and reactions. The Jacobian for this CRN based on $\hat S$ has a sign pattern. The equilibria for the $S$ and the $\hat S$ based CRN are in exact one to one correspondence with each equilibrium $e$ for the original CRN gotten from an equilibrium $\hat e$ for the new CRN by removing its added species. In our construction of a new CRN we are allowed to choose rate constants for the added reactions and if we choose them large enough the equilibrium $\hat e$ is locally asymptotically stable if and only if the equilibrium $e$ is locally asymptotically stable. Further properties of the construction are shown, such as those pertaining to conserved quantities and to how the deficiencies of the two CRNs compare.Comment: 23 page

Glycine-rich RNA binding protein of Oryza sativa inhibits growth of M15 E. coli cells

<p>Abstract</p> <p>Background</p> <p>Plant glycine-rich RNA binding proteins have been implicated to have roles in diverse abiotic stresses.</p> <p>Findings</p> <p><it>E. coli </it>M15 cells transformed with full-length rice glycine-rich RNA binding protein4 (OsGR-RBP4), truncated rice glycine-rich RNA binding protein4 (OsGR-RBP4ΔC) and rice FK506 binding protein (OsFKBP20) were analyzed for growth profiles using both broth and solid media. Expression of OsGR-RBP4 and OsGR-RBP4ΔC proteins caused specific, inhibitory effect on growth of recombinant M15 <it>E. coli </it>cells. The bacterial inhibition was shown to be time and incubation temperature dependent. Removal of the inducer, IPTG, resulted in re-growth of the cells, indicating that effect of the foreign proteins was of reversible nature. Although noted at different levels of dilution factors, addition of purified Os-GR-RBP4 and OsGR-RBP4ΔC showed a similar inhibitory effect as seen with expression inside the bacterial cells.</p> <p>Conclusions</p> <p>Expression of eukaryotic, stress-associated OsGR-RBP4 protein in prokaryotic <it>E. coli </it>M15 cells proves injurious to the growth of the bacterial cells. <it>E. coli </it>genome does not appear to encode for any protein that has significant homology to OsGR-RBP4 protein. Therefore, the mechanism of inhibition appears to be due to some illegitimate interactions of the OsGR-RBP4 with possibly the RNA species of the trans-host bacterial cells. The detailed mechanism underlying this inhibition remains to be worked out.</p

The interplay of intrinsic and extrinsic bounded noises in genetic networks

After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a genetic network. The influence of intrinsic and extrinsic noises on genetic networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: $(i)$ the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, $(ii)$ a model of enzymatic futile cycle and $(iii)$ a genetic toggle switch. In $(ii)$ and $(iii)$ we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possibile functional role of bounded noises