'GeneVyuha' tab simulates a circuit with a specific parameter set. Once the circuit is loaded from the 'Circuit' or 'Database' tab, a random set of parameters is generated. If the circuit from the database has its own parameter set, that set is used. The parameter set contains two paramters for each gene and three parameters for each interactions. The gene parameters are production (G_'gene') and degradation (k_'gene') rate whereas the parameters for each interaction ('source'_'target') are 'threshold' (TH_), 'hill coefficient of cooperativity' and 'fold change'. These parameters can be modified using the dropdown box given below. The default value of the parameter is dispalyed when a parameter is selected. Edit the 'value' and click 'Update' to modify this value. Repeat these steps if other parameters are to be modified. Other simulation paramters can also be modified.

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One can compare the simulated expression with other simulated or experimental expression. The simulated expression can be uploaded from a file or from the RACIPE tab. The reference data is clustered into the specified number of clusters. Then each simulated data sample is compared with each sample of the cluster to find the cluster most similar to its expression pattern. Gene permutation is used to generate the null hypothesis. The percentage of samples belonging to each cluster in the reference and simulated expressions as well as the overall Kullback–Leibler divergence between the two distributions is reported. Heatmaps of both simulated and reference expressions as well as sample-sample correaltion is also plotted. Cluster 0 is the null cluster and by default we add one sample belonging to null cluster to the reference samples
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# Overview

Gene Circuit Explorer (GeneEx) is a systems-biology tool to visualize and simulate gene regulatory circuits (GRCs). It can simulate a single model with specific kinetic parameters or an ensemble of models using the random circuit perturbation approach with and without stochastic effects (sRACIPE/RACIPE) for a comprehensive understanding of the structure and function of the GRCs in cell populations. The randomization-based methods (RACIPE/sRACIPE) enable study of the effects of both the gene expression noise and the parametric variation on any GRC using only its topology by simulating an ensemble of models with random kinetic parameters at multiple noise levels. Statistical analysis of the generated gene expressions reveal the basin of attraction and stability of various phenotypic states generated by the GRC. Thus, GeneEx provides a holistic picture to evaluate the effects of both the stochastic nature of cellular processes and the parametric variation on GRCs.

GeneEx can also be used inside R by calling sracipeGeneEx function after installing sRACIPE R package from BioConductor. Additional tutorials on sRACIPE and GeneEx are available here.

# Citation

If you find this website helpful in your reserach, please consider citing the papers Interrogating the topological robustness of gene regulatory circuits by randomization published in PLoS computational biology 13 (3), e1005456 and Role of noise and parametric variation in the dynamics of gene regulatory circuits published in npj Systems Biology and Applications, 4, 40 (2018).

# Tutorial

## Introduction

GeneEx employs a differential equation based approach to model the genes and their interactions. The dynamics of an isolated gene is modeled using the differential equation $$\dot{X_t} = G_X - K_XX_t$$ where $$X_t$$ represents the expression level of a gene at time $$t$$, $$\dot{X}$$ represents the rate of change of $$X_t$$ and $$G_X$$, $$K_X$$ are the two parameters representing the production rate and degradation rate of the gene. In this simple case, the steady state is simply the expression level at which $$\dot{X}=0$$ or $$X_s = G/k$$. If gene $$X$$ is regulated by another gene $$Y$$, then the interaction between them is modeled using the shifted Hill function, $H_s(Y_t,T_{YX},N_{YX},\lambda_{YX}) = \lambda + \frac{1-\lambda }{1+\big( \frac{Y_t}{T_{YX}}\big)^{N_{YX}}}$ where $$T_{YX}$$ is the threshold of regulation, $$N_{YX}$$ (integer) is the Hill coefficient of regulation, and $$\lambda_{YX}$$ is the fold change of the regulation. We multiply the production rate of the gene $$X$$ by regulation factor given by, $$H(Y_t,T_{YX},N_{YX},\lambda_{YX})/\lambda_{YX}$$ if the $$Y \to X$$ regulation is excitatory and $$H(Y_t,T_{YX},N_{YX},\frac{1}{\lambda_{YX}})$$ if the regulation is inhibitory. If a gene is regulated by multiple genes, then the production rate is multipled by the regulation factor of all the interactions regulating this gene. For example, if gene $$X$$ in a stochastic environment with noise level $$\eta$$ is activated by gene $$Y$$ and inhibited by gene $$Z$$, then the stochastic differential equation for $$X$$ can be written as, $\dot{X_t} = G_X\frac{H_s(Y_t,T_{YX},N_{YX},\lambda_{YX})}{\lambda_{YX}}H_s(Z_t,T_{ZX},N_{ZX},\frac{1}{\lambda_{ZX}}) -K_XX_t + \eta_t$ Thus, in this modeling method, there are two parameters for each gene - the production and degradation rate of the gene, and three parameters for each interaction between two gene - the threshold, fold change and Hill coefficient of regulation. For a circuit with $$N_g$$ genes and $$N_{reg}$$ regulations, the total number of parameters is $$2N_g+3N_{reg}$$. Varying these parameters generates different time trajectories and steady state gene expression values. Using GeneVyuha, one can simulate and visualize a circuit with random parameter values and then interactively change any parameter value and observe the effect on the time trajectory of gene expression values. Further, bifurcation diagrams for any parameter can be plotted and stochastic effects can be incorporated by changing the noise levels.

In RACIPE, we randomize these parameters and by default their values are chosen from a uniform distribution with range $$(1,100)$$ for the production rate, $$(0.1,1)$$ for the degradation rate, $$(1,100)$$ for fold change, and $$[1,6]$$ for the Hill coefficient of regulation. The range of the thresholds for each interaction is calculated based on the circuit topology. Statistical analysis of gene expression simulation of a large ensemble of models with such randomized parameters yields distinct clusters that resemble typical phenotypic states corresponding to the simulated circuit. For further details, please refer to Citation.

We are also curating (see Database) simulations of selected circuits demonstrating the utility of GeneEx in generating known time trajectories (steady states or oscillations) and phenotypic clusters for typical circuits. Users can upload their simulated datasets and circuit to the database. Note that the uploaded data will not be available in the database immediately and it will be verified manually to maintain the integrity of the database.

## Circuit

At the minimum, the GeneEx user needs to provide a cicuit topology mentioning the regulator (source) gene, regulated (target) gene and the type of regulation (acitvation or inhibition). Such topology can be uploaded or the information can be entered in the editable table. A sample topology file can be downloaded from the Choose Circuit File section. Below we show the topology file for a toggle switch circuit with two genes, A and B, inhibiting each other.

Source Target Type
A      B    2
B      A    2

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## GeneVyuha

GeneVyuha (Vyuha - a sanskrit origin word meaning pattern/formation) tab can be used to simulate the trajectory/time series of a gene regulatory circuit for a given set of parameters and explore the effect of change in parameter values. Initially a random parameter set is generated for the circuit. The Parameter is a dropdown menu populated by the parameters of the circuit being simulated. It lists the parameters in the follwing order:

• Production rate of genes
• Thresholds for the interactions
• Hill coefficients of regulation for interactions
• Fold change of regulations As the production rate (G) and degradation rate (K) are gene specific parameters, they are indicated by the letter G_(K_) followed by the gene name. Similarly, as the other parameters are interaction specific, they are labeled as TH_ (threshold), N_ (Hill coefficient), and FC_ (fold change) followed by the name of the source gene and target gene separated by an underscore. The Value is a numeric input to replace the randomly generated value of the parameter. Every parameters can be changed by selecting the parameter to be changed from the dropdown menu and modifying its value. Other options for simulations like simulation time, step size, noise level etc can also be changed. Clicking Simulate will generate and display the time trajectories of the gene expression values as shown below.

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Clicking the Randomize Parameters button will generate a new set of parameter values . Multiple new buttons like Download Data, Upload Options, Parametric Perturbations, etc are visible now. Clicking the Simulate button will perform a new simulation of the circuit with these modified parameters.

Clicking Parametric Perturbation button at the bottom will show other inputs like Parameter, Min value, Max value, Simulation Points. Here, GeneEx generates a large number of models with parameters used in the previous simulation and selects the value of the parameter selected in the Parameter input from a uniform distribution specified by the range (Min value, Max value). By default, these values are populated by (0.9P,1.1P) where P denotes the value of the parameter in the previous simulation. All the models are simulated and their final gene expressions are plotted against the selected parameter to generate the parametric perturbation diagram. For a recorded demo, please click on the image below to watch a video on youtube.

## RACIPE

RACIPE (random circuit perturbation) approach generates a large number of models with random parameters to mimic the parameters in a cell population. The models with these parameters are simulated and the final gene expressions obtained for each model are used for further statistical analysis. RACIPE tab shows the statistical behavior of models mimicking a cell population. The data can be filtered for various parameters so that one can observe how a change in parameter value affects the gene expression patterns. For example, limiting the production rate of a gene can be considered as knockdown of that particular gene. sRACIPE (stochastic random circuit perturbation) approach incorporates stochastic effects in the RACIPE approach to better model a cell population. The statistiics are calculated at multiple noise levels using two simulation schemes: (a) constant noise based method which estimates the basin of attraction of various phenotypic states and (b) annelaing based method which provides an estimate of the relative stability of the different phenotypic states. For further details please see Citation.

Once the circuit is successfully loaded, parameters like Number of Models representing the models to be simulated for RACIPE, Parameter Range representing the range (1-100) of parameters with respect to the default range (100), Simulation Time, Integration Time Step etc. Clicking Simulate button will simulate the circuit for specified parameters and display the hierarchical clustering and prinicpal components plots of the simulated gene expressions. Note that the gene expressions are normalized and log transformed for downstream analysis including the clustering analysis. Another button Parametric Analysis will be visible now which can be used for studying the effect of parameters on the gene expression clusters. Clicking Parametric Analysis will show three inputs Parameter with corresponding slider bars Parameter Range. These three filters can be used to filter the simulated data for specified range of parameters. Similar to GeneVyuha, the Parameter is a dropdown menu populated by the parameters of the circuit being simulated. It lists the parameters in the follwing order:

1. Production rate of genes
Clicking the Stochastic RACIPE button shows the inputs for stochastic simulations. Stochastic Simulation Type is two option button with options Constant Noise and Annealing. With Constant Noise simulations are carried out by incoporating stochastic effects whose strength is proportional to the value selected in the Noise Level slider. With Annealing, the ensemble of models are simulated for a large $$(\sim20)$$ number of noise levels differing by a small amount. Note that due to large number of simulations in annealing, it can be much slower. Cicking Perform Stochastic Simuations will simulate the circuit and display the hierarchical clustering and principle components.