The biphasic behavior of incoherent feed-forward loops in biomolecular regulatory networks

An incoherent feed-forward loop (FFL) is one of the most-frequently observed motifs in biomolecular regulatory networks. It has been thought that the incoherent FFL is designed simply to induce a transient response shaped by a 'fast activation and delayed inhibition'. We find that the dynamics of various incoherent FFLs can be further classified into two types: time-dependent biphasic responses and dose-dependent biphasic responses. Why do the structurally identical incoherent FFLs play such different dynamical roles? Through computational studies, we show that the dynamics of the two types of incoherent FFLs are mutually exclusive. Following from further computational results and experimental observations, we hypothesize that incoherent FFLs have been optimally designed to achieve distinct biological function arising from different cellular contexts. Additional Supporting Information may be found in the online version of the article.     

Reduction, integration and emergence in biochemical networks

Most studies of molecular cell biology are based upon a process of decomposition of complex biological systems into their components, followed by the study of these components. The aim of the present paper is to discuss, on a physical basis, the internal logic of this process of reduction. The analysis is performed on simple biological systems, namely protein and metabolic networks. A multi-sited protein that binds two ligands x and y can be considered the simplest possible biochemical network. The organization of this network can be described through a comparison of three systems, i.e. XY, X and Y. X and Y are component sub-systems that collect states x(i) and y(j), respectively, i.e. protein states that have bound either i molecules of x (whether or not these states have also bound y), or j molecules of y (whether or not these states have bound x). XY is a system made up of the specific association of X and Y that collects states x(i)y(j). One can define mean self-informations per node of the network, , and . Reduction of the system XY into its components is possible if, and only if, ,is equal to the sum of and . If is smaller than the sum of and , the system is integrated, for it has less self-information than the set of its components X and Y. It can also occur that , be larger than the sum of and . Hence, the system XY displays negative integration and emergence of self-information relative to its components X and Y. Such a system is defined as complex. Positive or negative integration of the system implies it cannot be reduced to its components. The degree of integration can be measured by a function , called mutual information of integration. In the case of enzyme networks, emergence of self-information is associated with emergence of catalytic activity. Moreover, if the enzyme reaction is part of a metabolic sequence, its mutual information of integration can be increased by an effect of context of this sequence.     

The incoherent feed‐forward loop can generate non‐monotonic input functions for genes

Gene regulation networks contain recurring circuit patterns called network motifs. One of the most common network motif is the incoherent type 1 feed‐forward loop (I1‐FFL), in which an activator controls both gene and repressor of that gene. This motif was shown to act as a pulse generator and response accelerator of gene expression. Here we consider an additional function of this motif: the I1‐FFL can generate a non‐monotonic dependence of gene expression on the input signal. Here, we study this experimentally in the galactose system of Escherichia coli, which is regulated by an I1‐FFL. The promoter activity of two of the gal operons, galETK and galP, peaks at intermediate levels of the signal cAMP. We find that mutants in which the I1‐FFL is disrupted lose this non‐monotonic behavior, and instead display monotonic input functions. Theoretical analysis suggests that non‐monotonic input functions can be achieved for a wide range of parameters by the I1‐FFL. The models also suggest regimes where a monotonic input‐function can occur, as observed in the mglBAC operon regulated by the same I1‐FFL. The present study thus experimentally demonstrates how upstream circuitry can affect gene input functions and how an I1‐FFL functions within its natural context in the cell.     

Evolutionary modelling of feed forward loops in gene regulatory networks

Feed forward loops (FFLs) are gene regulatory network motifs. They exist in different types, defined by the signs of the effects of genes in the motif on one another. We examine 36 feed forward loops in Escherichia coli, using evolutionary simulations to predict the forms of FFL expected to evolve to generate the pattern of expression of the output gene. These predictions are tested using likelihood ratios, comparing likelihoods of the observed FFL structures with their likelihoods under null models. The very high likelihood ratios generated, of over 10(11), suggest that evolutionary simulation is a valuable component in the explanation of FFL structure.     

Environmental selection of the feed-forward loop circuit in gene-regulation networks

Gene-regulation networks contain recurring elementary circuits termed network motifs. It is of interest to understand under which environmental conditions each motif might be selected. To address this, we study one of the most significant network motifs, a three-gene circuit called the coherent feed-forward loop (FFL). The FFL has been demonstrated theoretically and experimentally to perform a basic information-processing function: it shows a delay following ON steps of an input inducer, but not after OFF steps. Here, we ask under what environmental conditions might the FFL be selected over simpler gene circuits, based on this function. We employ a theoretical cost-benefit analysis for the selection of gene circuits in a given environment. We find conditions that the environment must satisfy in order for the FFL to be selected over simpler circuits: the FFL is selected in environments where the distribution of the input pulse duration is sufficiently broad and contains both long and short pulses. Optimal values of the biochemical parameters of the FFL circuit are determined as a function of the environment such that the delay in the FFL blocks deleterious short pulses of induction. This approach can be generally used to study the evolutionary selection of other network motifs.     

Emergence and biological complexity

Biological networks possess an organization that expresses their potential information. A function, I(X:Y)N, called mutual information of integration, define, on a quantitative basis, three types of organization. If I(X:Y)N=0, the properties of the global system XY can be reduced to the properties of its component sub-systems X and Y. Hence, XY is not a real system displaying collective properties but the mere collection of X and Y. Its properties are the properties of the sub-systems X and Y. If I(X:Y)N>0, the system is integrated. Although it behaves as a coherent whole, it does not possess many collective properties. Last, if I(X:Y)N<0, the system possesses emergent collective properties and can be considered complex for it possesses many collective properties that cannot be predicted from the independent study of component sub-systems X and Y. In a biological system, the emergence of information usually means the emergence of a novel function. This is probably what is occurring with enzymes. If a protein binds two ligands able to interact, and if the condition above is fulfilled, then the protein behaves as an enzyme able to allow a catalytic reaction between the two reagents.     

A DPP-mediated feed-forward loop canalizes morphogenesis during Drosophila dorsal closure

Development is robust because nature has selected various mechanisms to buffer the deleterious effects of environmental and genetic variations to deliver phenotypic stability. Robustness relies on smart network motifs such as feed-forward loops (FFLs) that ensure the reliable interpretation of developmental signals. In this paper, we show that Decapentaplegic (DPP) and JNK form a coherent FFL that controls the specification and differentiation of leading edge cells during Drosophila melanogaster dorsal closure (DC). We provide molecular evidence that through repression by Brinker (Brk), the DPP branch of the FFL filters unwanted JNK activity. High-throughput live imaging revealed that this DPP/Brk branch is dispensable for DC under normal conditions but is required when embryos are subjected to thermal stress. Our results indicate that the wiring of DPP signaling buffers against environmental challenges and canalizes cell identity. We propose that the main function of DPP pathway during Drosophila DC is to ensure robust morphogenesis, a distinct function from its well-established ability to spread spatial information.     

Temporally incoherent magnetic fields mitigate the response of biological systems to temporally coherent magnetic fields

We have previously demonstrated that a weak, extremely-low-frequency magnetic field must be coherent for some minimum length of time (≈? 10 s) in order to affect the specific activity of ornithine decarboxylase (ODC) in L929 mouse cells. In this study we explore whether or not the superposition of an incoherent (noise) magnetic field can block the bioeffect of a coherent 60 Hz magnetic field, since the sum of the two fields is incoherent. An experimental test of this idea was conducted using as a biological marker the twofold enhancement of ODC activity found in L929 murine cells after exposure to a 60 Hz, 10 μT_rms magnetic field. We superimposed an incoherent magnetic noise field, containing frequencies from 30 to 90 Hz, whose rms amplitude was comparable to that of the 60 Hz field. Under these conditions the ODC activity observed after exposure was equal to control levels. It is concluded that the superposition of incoherent magnetic fields can block the enhancement of ODC activity by a coherent magnetic field if the strength of the incoherent field is equal to or greater than that of the coherent field. When the superimposed, incoherent noise field was reduced in strength, the enhancement of ODC activity by the coherent field increased. Full ODC enhancement was obtained when the rms value of the applied EM noise was less than one-tenth that of the coherent field. These results are discussed in relation to the question of cellular detection of weak EM fields in the presence of endogenous thermal noise fields. © 1994 Wiley-Liss, Inc.