Regulatory Dynamics on Random Networks: Asymptotic Periodicity and Modularity

We study the dynamics of discrete-time regulatory networks on random digraphs. For this we define ensembles of deterministic orbits of random regulatory networks, and introduce some statistical indicators related to the long-term dynamics of the system. We prove that, in a random regulatory network, initial conditions converge almost surely to a periodic attractor. We study the subnetworks, which we call modules, where the periodic asymptotic oscillations are concentrated. We proof that those modules are dynamically equivalent to independent regulatory networks.Comment: 23 pages, 3 figure

Hierarchy and Feedback in the Evolution of the E. coli Transcription Network

The E.coli transcription network has an essentially feedforward structure, with, however, abundant feedback at the level of self-regulations. Here, we investigate how these properties emerged during evolution. An assessment of the role of gene duplication based on protein domain architecture shows that (i) transcriptional autoregulators have mostly arisen through duplication, while (ii) the expected feedback loops stemming from their initial cross-regulation are strongly selected against. This requires a divergent coevolution of the transcription factor DNA-binding sites and their respective DNA cis-regulatory regions. Moreover, we find that the network tends to grow by expansion of the existing hierarchical layers of computation, rather than by addition of new layers. We also argue that rewiring of regulatory links due to mutation/selection of novel transcription factor/DNA binding interactions appears not to significantly affect the network global hierarchy, and that horizontally transferred genes are mainly added at the bottom, as new target nodes. These findings highlight the important evolutionary roles of both duplication and selective deletion of crosstalks between autoregulators in the emergence of the hierarchical transcription network of E.coli.Comment: to appear in PNA

Topological Evolution of Dynamical Networks: Global Criticality from Local Dynamics

We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average connectivity of the network towards the critical value $K_c =2$ in the limit of large system size $N$. How this principle could generate self-organization in natural complex systems is discussed for two examples: neural networks and regulatory networks in the genome.Comment: 4 pages RevTeX, 4 figures PostScript, revised versio

Dynamical modeling of syncytial mitotic cycles in Drosophila embryos

Immediately following fertilization, the fruit fly embryo undergoes 13 rapid, synchronous, syncytial nuclear division cycles driven by maternal genes and proteins. During these mitotic cycles, there are barely detectable oscillations in the total level of B-type cyclins. In this paper, we propose a dynamical model for the molecular events underlying these early nuclear division cycles in Drosophila. The model distinguishes nuclear and cytoplasmic compartments of the embryo and permits exploration of a variety of rules for protein transport between the compartments. Numerical simulations reproduce the main features of wild-type mitotic cycles: patterns of protein accumulation and degradation, lengthening of later cycles, and arrest in interphase 14. The model is consistent with mutations that introduce subtle changes in the number of mitotic cycles before interphase arrest. Bifurcation analysis of the differential equations reveals the dependence of mitotic oscillations on cycle number, and how this dependence is altered by mutations. The model can be used to predict the phenotypes of novel mutations and effective ranges of the unmeasured rate constants and transport coefficients in the proposed mechanism

Adherence to intermittent preventive treatment for malaria in Papua New Guinean infants: A pharmacological study alongside the randomized controlled trial.

The intermittent preventive treatment in infants (IPTi) trial that took place in Papua New Guinea showed an overall reduction of 29% of the risk of malaria when delivering single-dose sulfadoxine-pyrimethamine (SP) associated to 3 days of amodiaquine (AQ) every three months to children during the first year of life. The aim of the present study was to assess if the last two doses of AQ were truly administered as prescribed by the parents at home based on drug level measurement and PK modelling, which is a good proxy of medication adherence. It provides also important information to discuss the efficacy of the intervention and on feasibility of self-administered preventive malaria treatment. During the three-arm randomized double-blinded IPTi trial, each child was prescribed one dose of SP (day 0) and 3 doses of either AQ or artesunate (AS) at day 0, 1 & 2 adjusted to weight or placebo. Treatments were given at 3, 6, 9 and 12 months of age. The first day of treatment was delivered by nursing staff (initiation under directly observed treatment (DOT)) and the two last doses of AQ or AS by parents at home without supervision. For this cross-sectional study, 206 consecutive children already involved in the IPTi trial were enrolled over a 2-month period. At the time of the survey, allocation of the children to one of the three arms was not known. Blood samples for drug level measurement were collected from finger pricks one day after the planned last third dose intake. Only children allocated to the SP-AQ arm were included in the present analysis. Indeed, the half-life of AS is too short to assess if drugs were given on not. Because of the short half-life of AQ, desethyl-AQ (metabolite of AQ (DAQ)) measurements were used to investigate AQ medication adherence. Two PK (PK) models from previously published studies in paediatric populations were applied to the dataset using non-linear mixed effect modelling (NONMEM) to estimate the number of doses really given by the parents. The study nurse reported the administration time for the first AQ dose while it was estimated by the parents for the remaining two doses. Out of 206 children, 64 were in the SP-AQ arm. The adjusted dosing history for each individual was identified as the one with the lowest difference between observed and individual predicted concentrations estimated by the two PK models for all the possible adherence schemes. The median (range) blood concentration AQ in AQ arm was 9.3 ng/mL (0-1427.8 ng/mL), (Quartiles 1-3: 2.4 ng/mL -22.2 ng/mL). The median (range) for DAQ was 162.0 ng/mL (0-712 ng/mL), (Quartiles 1-3: 80.4 ng/mL-267.7 ng/mL). Under the assumption of full adherence for all participants, a marked underprediction of concentrations was observed using both PK models. Our results suggest that only 39-50% of children received the three scheduled doses of AQ as prescribed, 33-37% two doses and 17-24% received only the first dose administered by the study nurse. Both models were highly congruent to classify adherence patterns. Considering the IPTi intervention, our results seem to indicate that medication adherence is low in the ideal trial research setting and is likely to be even lower if given in day-to-day practice, questioning the real impact that this intervention might have. More generally, the estimation of the number of doses truly administered, a proxy measure of adherence and an assessment of the feasibility of the mode of administration, should be more thoroughly studied when discussing the efficacy of the interventions in trials investigating self-administered malaria preventive treatments

Genetic noise control via protein oligomerization

Gene expression in a cell entails random reaction events occurring over disparate time scales. Thus, molecular noise that often results in phenotypic and population-dynamic consequences sets a fundamental limit to biochemical signaling. While there have been numerous studies correlating the architecture of cellular reaction networks with noise tolerance, only a limited effort has been made to understand the dynamic role of protein-protein interactions. Here we have developed a fully stochastic model for the positive feedback control of a single gene, as well as a pair of genes (toggle switch), integrating quantitative results from previous in vivo and in vitro studies. We find that the overall noise-level is reduced and the frequency content of the noise is dramatically shifted to the physiologically irrelevant high-frequency regime in the presence of protein dimerization. This is independent of the choice of monomer or dimer as transcription factor and persists throughout the multiple model topologies considered. For the toggle switch, we additionally find that the presence of a protein dimer, either homodimer or heterodimer, may significantly reduce its random switching rate. Hence, the dimer promotes the robust function of bistable switches by preventing the uninduced (induced) state from randomly being induced (uninduced). The specific binding between regulatory proteins provides a buffer that may prevent the propagation of fluctuations in genetic activity. The capacity of the buffer is a non-monotonic function of association-dissociation rates. Since the protein oligomerization per se does not require extra protein components to be expressed, it provides a basis for the rapid control of intrinsic or extrinsic noise

Simulating the Mammalian Blastocyst - Molecular and Mechanical Interactions Pattern the Embryo

Mammalian embryogenesis is a dynamic process involving gene expression and mechanical forces between proliferating cells. The exact nature of these interactions, which determine the lineage patterning of the trophectoderm and endoderm tissues occurring in a highly regulated manner at precise periods during the embryonic development, is an area of debate. We have developed a computational modeling framework for studying this process, by which the combined effects of mechanical and genetic interactions are analyzed within the context of proliferating cells. At a purely mechanical level, we demonstrate that the perpendicular alignment of the animal-vegetal (a-v) and embryonic-abembryonic (eb-ab) axes is a result of minimizing the total elastic conformational energy of the entire collection of cells, which are constrained by the zona pellucida. The coupling of gene expression with the mechanics of cell movement is important for formation of both the trophectoderm and the endoderm. In studying the formation of the trophectoderm, we contrast and compare quantitatively two hypotheses: (1) The position determines gene expression, and (2) the gene expression determines the position. Our model, which couples gene expression with mechanics, suggests that differential adhesion between different cell types is a critical determinant in the robust endoderm formation. In addition to differential adhesion, two different testable hypotheses emerge when considering endoderm formation: (1) A directional force acts on certain cells and moves them into forming the endoderm layer, which separates the blastocoel and the cells of the inner cell mass (ICM). In this case the blastocoel simply acts as a static boundary. (2) The blastocoel dynamically applies pressure upon the cells in contact with it, such that cell segregation in the presence of differential adhesion leads to the endoderm formation. To our knowledge, this is the first attempt to combine cell-based spatial mechanical simulations with genetic networks to explain mammalian embryogenesis. Such a framework provides the means to test hypotheses in a controlled in silico environment

Boolean Dynamics with Random Couplings

This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N Boolean elements at a given time is given a value which depends upon K elements in the previous time step. We review the work of many authors on the behavior of the models, looking particularly at the structure and lengths of their cycles, the sizes of their basins of attraction, and the flow of information through the systems. In the limit of infinite N, there is a phase transition between a chaotic and an ordered phase, with a critical phase in between. We argue that the behavior of this system depends significantly on the topology of the network connections. If the elements are placed upon a lattice with dimension d, the system shows correlations related to the standard percolation or directed percolation phase transition on such a lattice. On the other hand, a very different behavior is seen in the Kauffman net in which all spins are equally likely to be coupled to a given spin. In this situation, coupling loops are mostly suppressed, and the behavior of the system is much more like that of a mean field theory. We also describe possible applications of the models to, for example, genetic networks, cell differentiation, evolution, democracy in social systems and neural networks.Comment: 69 pages, 16 figures, Submitted to Springer Applied Mathematical Sciences Serie

Delay-Induced Transient Increase and Heterogeneity in Gene Expression in Negatively Auto-Regulated Gene Circuits

A generic feature in all intracellular biochemical processes is the time required to complete the whole sequence of reactions to yield any observable quantity-from gene expression to circadian rhythms. This widespread phenomenon points towards the importance of time delay in biological functions. Theoretically time delay is known to be the source of instability, and has been attributed to lead to oscillations or transient dynamics in several biological functions. Negative feedback loops, common in biochemical pathways, have been shown to provide stability and withstand considerable variations and random perturbations of biochemical parameters. The interaction of these two opposing factors-of instability and homeostasis-are features that are widespread in intracellular processes. To test the effect of these divergent forces in the dynamics of gene expression, we have designed and constructed simple negatively auto-regulated gene circuits consisting of a basic regulator and transcriptional repressor module, and compared it with one, which has delayed repression. We show, both theoretically and experimentally, that delayed repression induces transient increase and heterogeneity in gene expression before the gain of stability effected by the negative feedback. This design, therefore, seems to be suitable for conferring both stability and variability in cells required for adaptive response to a noisy environment