Talk given at the Southern California Systems Biology Conference on January 31, 2015 entitled, "GRNmap and GRNsight: Open Source Software for Dynamical Systems Modeling and Visualization of Medium-Scale Gene Regulatory Networks". Abstract: A gene regulatory network (GRN) consists of genes, transcription factors, and the regulatory connections between them that govern the level of expression of mRNA and proteins from those genes. Our group has developed a MATLAB software package, called GRNmap, that uses ordinary differential equations to model the dynamics of medium-scale GRNs. The program uses a penalized least squares approach to estimate production rates, expression thresholds, and regulatory weights for each transcription factor in the network based on gene expression data, and then performs a forward simulation of the dynamics of the network. Parameters for a 21-gene network were optimized against DNA microarray data measuring the transcriptional response to cold shock in wild type and four transcription factor deletion strains of budding yeast, Saccharomyces cerevisiae. Model predictions fit experimental data well, within the 95% confidence interval. Open source code and a compiled executable that can run without a MATLAB license are available from <http: />. GRNsight is an open source web application for visualizing such models of gene regulatory networks. GRNsight accepts GRNmap- or user-generated spreadsheets containing an adjacency matrix representation of the GRN and automatically lays out the graph of the GRN model. The application colors the edges and adjusts their thicknesses based on the sign (activation or repression) and the strength (magnitude) of the regulatory relationship, respectively. Users can then modify the graph to define the best visual layout for the network. The GRNsight code and application are available from <http: />. This work was partially supported by NSF award 0921038.

1. GRNmap and GRNsight:
Open Source Software for Dynamical Systems
Modeling and Visualization of Medium-Scale
Gene Regulatory Networks
Kam D. Dahlquist, Ph.D.
Department of Biology
Loyola Marymount University
January 31, 2015
Southern California Systems Biology Conference

2. Outline
• Yeast respond to cold shock by changing gene
expression.
• But little is known about which transcription factors regulate
the response.
• GRNmap models the dynamics of “medium-scale”
gene regulatory networks using differential equations.
• A penalized least squares approach was used successfully to
estimate parameters from cold shock microarray data.
• GRNsight automatically generates weighted network
graphs from the spreadsheets produced by GRNmap.
• This facilitates visualization of the relative influence of each
transcription factor in controlling the cold shock response.

3. Yeast Respond to Cold Shock by Changing
Gene Expression
Alberts et al. (2004)
• Unlike heat shock, cold shock is not well-
studied.
• Cold shock temperature range for yeast is
10-18°C.
• Previous studies indicated that the cold shock
response can be divided into an early and late
response.
• General Environmental Stress Response (ESR)
genes are induced in the late response.
• Late response is regulated by the Msn2/Msn4
transcription factors.
• No “canonical” factor responsible for early
response.

4. Yeast Respond to Cold Shock by Changing
Gene Expression
Alberts et al. (2004)
• Which transcription factors control the early response?
• What is the extent of ESR pathway overlap?
• Which part of the early response is due to indirect
effects of other transcription factors?
• Unlike heat shock, cold shock is not well-
studied.
• Cold shock temperature range for yeast is
10-18°C.
• Previous studies indicated that the cold shock
response can be divided into an early and late
response.
• General Environmental Stress Response (ESR)
genes are induced in the late response.
• Late response is regulated by the Msn2/Msn4
transcription factors.
• No “canonical” factor responsible for early
response.

5. Systems Biology Approach to Understanding the
Regulation of the Cold Shock Response in Yeast

6. A “Medium-Scale” Gene Regulatory Network that
Regulates the Cold Shock Response
Assumptions made in our model:
• Each node represents one gene encoding a transcription factor.
• When a gene is transcribed, it is immediately translated into protein;
a node represents the gene, the mRNA, and the protein.
• Each edge represents a regulatory relationship, either activation or
repression, depending on the sign of the weight.

7. GRNmap: Gene Regulatory Network Modeling and
Parameter Estimation
• The user has a choice to model the dynamics based on a
sigmoidal (shown) or Michaelis-Menten function.
• Parameters are estimated from DNA microarray data from wild type
and transcription factor deletion strains subjected to cold shock
conditions.
• Weight parameter, w, gives the direction (activation or repression)
and magnitude of regulatory relationship.
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9. Optimization of the 92 Parameters Required
the Use of a Regularization (Penalty) Term
• Plotting the least squares error
function showed that not all the
graphs had clear minima.
• We added a penalty term so that
MATLAB’s optimization algorithm
would be able to minimize the
function.
• θ is the combined production
rate, weight, and threshold
parameters.
• a is determined empirically from
the “elbow” of the L-curve.
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10. Forward Simulation of the Model Fits
the Microarray Data

11. GRNmap Produces an Excel Spreadsheet with an
Adjacency Matrix Representing the Network
• However, GRNmap does not generate any visual
representation of the gene regulatory network.
• Illustrating the weights of edges to would allow us to
visualize the relative influence of individual TFs.

12. GRNsight Rapidly Generates GRN graphs Using Our
Customizations to the Open Source D3 Library
GRNsight: 10 milliseconds to generate,
5 minutes to arrange
Adobe Illustrator: several hours to create
GRNsight: colored edges for weights
reveal patterns in data

13. The First Round of Modeling Has Suggested Future
Experiments

14. Summary
• Yeast respond to cold shock by changing gene
expression.
• Through modeling and experiment we are starting to get a
handle on which transcription factors control the response.
• GRNmap models the dynamics of “medium-scale”
gene regulatory networks using differential equations
and a penalized least squares approach.
• Code and executable (no MATLAB license required) available.
• GRNsight automatically generates weighted network
graphs from the spreadsheets produced by GRNmap.
• The set of transcription factors in the densely connected core
of our current network model have the strongest influence on
other factors.

15. GRNsight: http://dondi.github.io/GRNsight/
GRNmap: http://kdahlquist.github.io/GRNmap/
• Faculty Collaborators
• Dr. John David N. Dionisio, (LMU EE/CS)
• Dr. Ben G. Fitzpatrick, (LMU Math)
• GRNsight
• Nicole A. Anguiano ’16
• Britain J. Southwick ’14
• Anindita Varshneya ’17
• GRNmap
• Juan S. Carrillo ’16
• Nicholas A. Rohacz ’13
• Katrina Sherbina ’14
• NSF-RUI 0921038
• Microarray Data
• Cybele Arsan ’11
• Wesley Citti ’08
• Kevin Entzminger ’09
• Andrew Herman ’12
• Heather King ’06
• Lauren Kubeck ’11
• Stephanie Kuelbs ’09
• Elizabeth Liu ’08
• Matthew Mejia ’07
• Kenny Rodriguez ’09
• Olivia Sakhon ’08
• Alondra Vega ’12
• New Lab Members
• Monica Hong ’17
• Grace Johnson ’17
• Trixie Roque ’17
• Natalie Williams ’17
• Kevin Wyllie ’16