Disulfide bonds and disorder in granulin‐3: An unusual handshake between structural stability and plasticity

Granulins (GRNs) are a family of small (～6 kDa) proteins generated by the proteolytic processing of their precursor, progranulin (PGRN), in many cell types. Both PGRN and GRNs are implicated in a plethora of biological functions, often in opposing roles to each other. Lately, GRNs have generated significant attention due to their implicated roles in neurodegenerative disorders. Despite their physiological and pathological significance, the structure‐function relationships of GRNs are poorly defined. GRNs contain 12 conserved cysteines forming six intramolecular disulfide bonds, making them rather exceptional, even among a few proteins with high disulfide bond density. Solution NMR investigations in the past have revealed a unique structure containing putative interdigitated disulfide bonds for several GRNs, but GRN‐3 was unsolvable due to its heterogeneity and disorder. In our previous report, we showed that abrogation of disulfide bonds in GRN‐3 renders the protein completely disordered (Ghag et al., Prot Eng Des Sel 2016). In this study, we report the cellular expression and biophysical analysis of fully oxidized, native GRN‐3. Our results indicate that both E. coli and human embryonic kidney (HEK) cells do not exclusively make GRN‐3 with homogenous disulfide bonds, likely due to the high cysteine density within the protein. Biophysical analysis suggests that GRN‐3 structure is dominated by irregular loops held together only by disulfide bonds, which induced remarkable thermal stability to the protein despite the lack of regular secondary structure. This unusual handshake between disulfide bonds and disorder within GRN‐3 could suggest a unique adaptation of intrinsically disordered proteins towards structural stability.     

To lyse or not to lyse: transient-mediated stochastic fate determination in cells infected by bacteriophages

Cell fate determination is usually described as the result of the stochastic dynamics of gene regulatory networks (GRNs) reaching one of multiple steady-states each of which corresponds to a specific decision. However, the fate of a cell is determined in finite time suggesting the importance of transient dynamics in cellular decision making. Here we consider cellular decision making as resulting from first passage processes of regulatory proteins and examine the effect of transient dynamics within the initial lysis-lysogeny switch of phage λ. Importantly, the fate of an infected cell depends, in part, on the number of coinfecting phages. Using a quantitative model of the phage λ GRN, we find that changes in the likelihood of lysis and lysogeny can be driven by changes in phage co-infection number regardless of whether or not there exists steady-state bistability within the GRN. Furthermore, two GRNs which yield qualitatively distinct steady state behaviors as a function of phage infection number can show similar transient responses, sufficient for alternative cell fate determination. We compare our model results to a recent experimental study of cell fate determination in single cell assays of multiply infected bacteria. Whereas the experimental study proposed a "quasi-independent" hypothesis for cell fate determination consistent with an observed data collapse, we demonstrate that observed cell fate results are compatible with an alternative form of data collapse consistent with a partial gene dosage compensation mechanism. We show that including partial gene dosage compensation at the mRNA level in our stochastic model of fate determination leads to the same data collapse observed in the single cell study. Our findings elucidate the importance of transient gene regulatory dynamics in fate determination, and present a novel alternative hypothesis to explain single-cell level heterogeneity within the phage λ lysis-lysogeny decision switch.     

Diversity of temporal correlations between genes in models of noisy and noiseless gene networks

Gene regulatory networks (GRNs) are parallel information processing systems, binding past events to future actions. Since cell types stably remain in restricted subsets of the possible states of the GRN, they are likely the dynamical attractors of the GRN. These attractors differ in which genes are active and in the amount of information propagating within the network. Using mutual information (I) as a measure of information propagation between genes in a GRN, modeled as finite-sized Random Boolean Networks (RBN), we study how the dynamical regime of the GRN affects I within attractors (I(A)). The spectra of I(A) of individual RBNs are found to be scattered and diverse, and distributions of I(A) of ensembles are non-trivial and change shape with mean connectivity. Mean and diversity of I(A) values maximize in the chaotic near-critical regime, whereas ordered near-critical networks are the best at retaining the distinctiveness of each attractor's I(A) with noise. The results suggest that selection likely favors near-critical GRNs as these both maximize mean and diversity of I(A), and are the most robust to noise. We find similar I(A) distributions in delayed stochastic models of GRNs. For a particular stochastic GRN, we show that both mean and variance of I(A) have local maxima as its connectivity and noise levels are varied, suggesting that the conclusions for the Boolean network models may be generalizable to more realistic models of GRNs.     

Genotype-phenotype mapping in a post-GWAS world

Understanding how metabolic reactions, cell signaling, and developmental pathways translate the genome of an organism into its phenotype is a grand challenge in biology. Genome-wide association studies (GWAS) statistically connect genotypes to phenotypes, without any recourse to known molecular interactions, whereas a molecular biology approach directly ties gene function to phenotype through gene regulatory networks (GRNs). Using natural variation in allele-specific expression, GWAS and GRN approaches can be merged into a single framework via structural equation modeling (SEM). This approach leverages the myriad of polymorphisms in natural populations to elucidate and quantitate the molecular pathways that underlie phenotypic variation. The SEM framework can be used to quantitate a GRN, evaluate its consistency across environments or sexes, identify the differences in GRNs between species, and annotate GRNs de novo in non-model organisms.     

The evolution of gene regulatory networks controlling Arabidopsis thaliana L. trichome development

Background

The variation in structure and function of gene regulatory networks (GRNs) participating in organisms development is a key for understanding species-specific evolutionary strategies. Even the tiniest modification of developmental GRN might result in a substantial change of a complex morphogenetic pattern. Great variety of trichomes and their accessibility makes them a useful model for studying the molecular processes of cell fate determination, cell cycle control and cellular morphogenesis. Nowadays, a large number of genes regulating the morphogenesis of A. thaliana trichomes are described. Here we aimed at a study the evolution of the GRN defining the trichome formation, and evaluation its importance in other developmental processes.

Results

In study of the evolution of trichomes formation GRN we combined classical phylogenetic analysis with information on the GRN topology and composition in major plants taxa. This approach allowed us to estimate both times of evolutionary emergence of the GRN components which are mainly proteins, and the relative rate of their molecular evolution. Various simplifications of protein structure (based on the position of amino acid residues in protein globula, secondary structure type, and structural disorder) allowed us to demonstrate the evolutionary associations between changes in protein globules and speciations/duplications events. We discussed their potential involvement in protein-protein interactions and GRN function.

Conclusions

We hypothesize that the divergence and/or the specialization of the trichome-forming GRN is linked to the emergence of plant taxa. Information about the structural targets of the protein evolution in the GRN may predict switching points in gene networks functioning in course of evolution. We also propose a list of candidate genes responsible for the development of trichomes in a wide range of plant species.

     

Are Quasi-Steady-State Approximated Models Suitable for Quantifying Intrinsic Noise Accurately?

Large gene regulatory networks (GRN) are often modeled with quasi-steady-state approximation (QSSA) to reduce the huge computational time required for intrinsic noise quantification using Gillespie stochastic simulation algorithm (SSA). However, the question still remains whether the stochastic QSSA model measures the intrinsic noise as accurately as the SSA performed for a detailed mechanistic model or not? To address this issue, we have constructed mechanistic and QSSA models for few frequently observed GRNs exhibiting switching behavior and performed stochastic simulations with them. Our results strongly suggest that the performance of a stochastic QSSA model in comparison to SSA performed for a mechanistic model critically relies on the absolute values of the mRNA and protein half-lives involved in the corresponding GRN. The extent of accuracy level achieved by the stochastic QSSA model calculations will depend on the level of bursting frequency generated due to the absolute value of the half-life of either mRNA or protein or for both the species. For the GRNs considered, the stochastic QSSA quantifies the intrinsic noise at the protein level with greater accuracy and for larger combinations of half-life values of mRNA and protein, whereas in case of mRNA the satisfactory accuracy level can only be reached for limited combinations of absolute values of half-lives. Further, we have clearly demonstrated that the abundance levels of mRNA and protein hardly matter for such comparison between QSSA and mechanistic models. Based on our findings, we conclude that QSSA model can be a good choice for evaluating intrinsic noise for other GRNs as well, provided we make a rational choice based on experimental half-life values available in literature.     

Mechanistic Explanations for Restricted Evolutionary Paths That Emerge from Gene Regulatory Networks

The extent and the nature of the constraints to evolutionary trajectories are central issues in biology. Constraints can be the result of systems dynamics causing a non-linear mapping between genotype and phenotype. How prevalent are these developmental constraints and what is their mechanistic basis? Although this has been extensively explored at the level of epistatic interactions between nucleotides within a gene, or amino acids within a protein, selection acts at the level of the whole organism, and therefore epistasis between disparate genes in the genome is expected due to their functional interactions within gene regulatory networks (GRNs) which are responsible for many aspects of organismal phenotype. Here we explore epistasis within GRNs capable of performing a common developmental function – converting a continuous morphogen input into discrete spatial domains. By exploring the full complement of GRN wiring designs that are able to perform this function, we analyzed all possible mutational routes between functional GRNs. Through this study we demonstrate that mechanistic constraints are common for GRNs that perform even a simple function. We demonstrate a common mechanistic cause for such a constraint involving complementation between counter-balanced gene-gene interactions. Furthermore we show how such constraints can be bypassed by means of “permissive” mutations that buffer changes in a direct route between two GRN topologies that would normally be unviable. We show that such bypasses are common and thus we suggest that unlike what was observed in protein sequence-function relationships, the “tape of life” is less reproducible when one considers higher levels of biological organization.     

Evolving modular genetic regulatory networks with a recursive,top-down approach

Being able to design genetic regulatory networks (GRNs) to achieve a desired cellular function is one of the main goals of synthetic biology. However, determining minimal GRNs that produce desired time-series behaviors is non-trivial. In this paper, we propose a ‘top-down’ approach to evolving small GRNs and then use these to recursively boot-strap the identification of larger, more complex, modular GRNs. We start with relatively dense GRNs and then use differential evolution (DE) to evolve interaction coefficients. When the target dynamical behavior is found embedded in a dense GRN, we narrow the focus of the search and begin aggressively pruning out excess interactions at the end of each generation. We first show that the method can quickly rediscover known small GRNs for a toggle switch and an oscillatory circuit. Next we include these GRNs as non-evolvable subnetworks in the subsequent evolution of more complex, modular GRNs. Successful solutions found in canonical DE where we truncated small interactions to zero, with or without an interaction penalty term, invariably contained many excess interactions. In contrast, by incorporating aggressive pruning and the penalty term, the DE was able to find minimal or nearly minimal GRNs in all test problems.     

Communication and complexity in a GRN-based multicellular system for graph colouring

Artificial Genetic Regulatory Networks (GRNs) are interesting control models through their simplicity and versatility. They can be easily implemented, evolved and modified, and their similarity to their biological counterparts makes them interesting for simulations of life-like systems as well. These aspects suggest they may be perfect control systems for distributed computing in diverse situations, but to be usable for such applications the computational power and evolvability of GRNs need to be studied. In this research we propose a simple distributed system implementing GRNs to solve the well known NP-complete graph colouring problem. Every node (cell) of the graph to be coloured is controlled by an instance of the same GRN. All the cells communicate directly with their immediate neighbours in the graph so as to set up a good colouring. The quality of this colouring directs the evolution of the GRNs using a genetic algorithm. We then observe the quality of the colouring for two different graphs according to different communication protocols and the number of different proteins in the cell (a measure for the possible complexity of a GRN). Those two points, being the main scalability issues that any computational paradigm raises, will then be discussed.     

IQCELL: A platform for predicting the effect of gene perturbations on developmental trajectories using single-cell RNA-seq data

The increasing availability of single-cell RNA-sequencing (scRNA-seq) data from various developmental systems provides the opportunity to infer gene regulatory networks (GRNs) directly from data. Herein we describe IQCELL, a platform to infer, simulate, and study executable logical GRNs directly from scRNA-seq data. Such executable GRNs allow simulation of fundamental hypotheses governing developmental programs and help accelerate the design of strategies to control stem cell fate. We first describe the architecture of IQCELL. Next, we apply IQCELL to scRNA-seq datasets from early mouse T-cell and red blood cell development, and show that the platform can infer overall over 74% of causal gene interactions previously reported from decades of research. We will also show that dynamic simulations of the generated GRN qualitatively recapitulate the effects of known gene perturbations. Finally, we implement an IQCELL gene selection pipeline that allows us to identify candidate genes, without prior knowledge. We demonstrate that GRN simulations based on the inferred set yield results similar to the original curated lists. In summary, the IQCELL platform offers a versatile tool to infer, simulate, and study executable GRNs in dynamic biological systems.     

Two antagonistic gustatory receptor neurons responding to sweet-salty and bitter taste in Drosophila

In Drosophila, gustatory receptor neurons (GRNs) occur within hair-like structures called sensilla. Most taste sensilla house four GRNs, which have been named according to their preferred sensitivity to basic stimuli: water (W cell), sugars (S cell), salt at low concentration (L1 cell), and salt at high concentration (L2 cell). Labellar taste sensilla are classified into three types, l-, s-, and i-type, according to their length and location. Of these, l- and s-type labellar sensilla possess these four cells, but most i-type sensilla house only two GRNs. In i-type sensilla, we demonstrate here that the first GRN responds to sugar and to low concentrations of salt (10-50 mM NaCl). The second GRN detects a range of bitter compounds, among which strychnine is the most potent; and also to salt at high concentrations (over 400 mM NaCl). Neither type of GRN responds to water. The detection of feeding stimulants in i-type sensilla appears to be performed by one GRN with the combined properties of S+L1 cells, while the other GRN detects feeding inhibitors in a similar manner to bitter-sensitive L2 cells on the legs. These sensilla thus house two GRNs having an antagonistic effect on behavior, suggesting that the expression of taste receptors is segregated across them accordingly.     

Two antagonistic gustatory receptor neurons responding to sweet‐salty and bitter taste in Drosophila

In Drosophila, gustatory receptor neurons (GRNs) occur within hair‐like structures called sensilla. Most taste sensilla house four GRNs, which have been named according to their preferred sensitivity to basic stimuli: water (W cell), sugars (S cell), salt at low concentration (L1 cell), and salt at high concentration (L2 cell). Labellar taste sensilla are classified into three types, l‐, s‐, and i‐type, according to their length and location. Of these, l‐ and s‐type labellar sensilla possess these four cells, but most i‐type sensilla house only two GRNs. In i‐type sensilla, we demonstrate here that the first GRN responds to sugar and to low concentrations of salt (10–50 mM NaCl). The second GRN detects a range of bitter compounds, among which strychnine is the most potent; and also to salt at high concentrations (over 400 mM NaCl). Neither type of GRN responds to water. The detection of feeding stimulants in i‐type sensilla appears to be performed by one GRN with the combined properties of S + L1 cells, while the other GRN detects feeding inhibitors in a similar manner to bitter‐sensitive L2 cells on the legs. These sensilla thus house two GRNs having an antagonistic effect on behavior, suggesting that the expression of taste receptors is segregated across them accordingly. © 2004 Wiley Periodicals, Inc. J Neurobiol, 2004     

A New Asynchronous Parallel Algorithm for Inferring Large-Scale Gene Regulatory Networks

The reconstruction of gene regulatory networks (GRNs) from high-throughput experimental data has been considered one of the most important issues in systems biology research. With the development of high-throughput technology and the complexity of biological problems, we need to reconstruct GRNs that contain thousands of genes. However, when many existing algorithms are used to handle these large-scale problems, they will encounter two important issues: low accuracy and high computational cost. To overcome these difficulties, the main goal of this study is to design an effective parallel algorithm to infer large-scale GRNs based on high-performance parallel computing environments. In this study, we proposed a novel asynchronous parallel framework to improve the accuracy and lower the time complexity of large-scale GRN inference by combining splitting technology and ordinary differential equation (ODE)-based optimization. The presented algorithm uses the sparsity and modularity of GRNs to split whole large-scale GRNs into many small-scale modular subnetworks. Through the ODE-based optimization of all subnetworks in parallel and their asynchronous communications, we can easily obtain the parameters of the whole network. To test the performance of the proposed approach, we used well-known benchmark datasets from Dialogue for Reverse Engineering Assessments and Methods challenge (DREAM), experimentally determined GRN of Escherichia coli and one published dataset that contains more than 10 thousand genes to compare the proposed approach with several popular algorithms on the same high-performance computing environments in terms of both accuracy and time complexity. The numerical results demonstrate that our parallel algorithm exhibits obvious superiority in inferring large-scale GRNs.     

On multistability of delayed genetic regulatory networks with multivariable regulation functions

Many genetic regulatory networks (GRNs) have the capacity to reach different stable states. This capacity is defined as multistability which is an important regulation mechanism. Multiple time delays and multivariable regulation functions are usually inevitable in such GRNs. In this paper, multistability of GRNs is analyzed by applying the control theory and mathematical tools. This study is to provide a theoretical tool to facilitate the design of synthetic gene circuit with multistability in the perspective of control theory. By transforming such GRNs into a new and uniform mathematical formulation, we put forward a general sector-like regulation function that is capable of quantifying the regulation effects in a more precise way. By resorting to up-to-date techniques, a novel Lyapunov-Krasovskii functional (LKF) is introduced for achieving delay dependence to ensure less conservatism. New conditions are then proposed to ensure the multistability of a GRN in the form of linear matrix inequalities (LMIs) that are dependent on the delays. Our multistability conditions are applicable to several frequently used regulation functions especially the multivariable ones. Two examples are employed to illustrate the applicability and usefulness of the developed theoretical results.     

Understanding the dynamic behavior of genetic regulatory networks by functional decomposition

A number of mechanistic and predictive genetic regulatory networks (GRNs) comprising dozens of genes have already been characterized at the level of cis-regulatory interactions. Reconstructions of networks of 100's to 1000's of genes and their interactions are currently underway. Understanding the organizational and functional principles underlying these networks is probably the single greatest challenge facing genomics today. We review the current approaches to deciphering large-scale GRNs and discuss some of their limitations. We then propose a bottom-up approach in which large-scale GRNs are first organized in terms of functionally distinct GRN building blocks of one or a few genes. Biological processes may then be viewed as the outcome of functional interactions among these simple, well-characterized functional building blocks. We describe several putative GRN functional building blocks and show that they can be located within GRNs on the basis of their interaction topology and additional, simple and experimentally testable constraints.     

Ensemble Inference and Inferability of Gene Regulatory Networks

The inference of gene regulatory network (GRN) from gene expression data is an unsolved problem of great importance. This inference has been stated, though not proven, to be underdetermined implying that there could be many equivalent (indistinguishable) solutions. Motivated by this fundamental limitation, we have developed new framework and algorithm, called TRaCE, for the ensemble inference of GRNs. The ensemble corresponds to the inherent uncertainty associated with discriminating direct and indirect gene regulations from steady-state data of gene knock-out (KO) experiments. We applied TRaCE to analyze the inferability of random GRNs and the GRNs of E. coli and yeast from single- and double-gene KO experiments. The results showed that, with the exception of networks with very few edges, GRNs are typically not inferable even when the data are ideal (unbiased and noise-free). Finally, we compared the performance of TRaCE with top performing methods of DREAM4 in silico network inference challenge.