# Day 5: Friday 2nd Oct.

## Networks Inference

Constructing network models (often unconciously as sketches) is usually the first step in the conceptual part of the scientific process. This is due to the fact that any system can be dissected into components and the relations the components have with each other. But such models need to be verfied on the base of experimental data. It is clear that there is a hidden relationship between the conceptual network framework and the way data are created or processed. On this day we like to discuss relationships between graphical models as used in statistics, parameter estimation methods and non-linear dynamical processes defined on networks. The day is closely related to a previous symposium workshop: **Information extraction from complex data sets**, (INF).

**10:00am - 10:15am** Welcome Tea & Coffee, Mathematics Common Room.

**10:15am - 12:30am**

Chris Ladroue Warwick) - * Recent extensions of Granger Causality for network inference*, 45min

David Gilbert (Brunel) - * Model checking and its use in network inference*, 45min

Sach Mukherjee (Warwick) - * Probabilistic network models in cancer biology*, 45min

**12:30am - 1:30pm** Lunch Break, Mathematics Common Room.

**1:30pm - 3:00pm**

Guido Sanguinetti (Sheffield) - * Switching Regulatory Models of Cellular Stress Reaction, *45 min

Ed Morissey (Warwick) -* Inferring gene regulatory network topology using a non linear sparse Dynamic Bayesian Network model, *45min

**3:00pm - 3:30pm** Tea Break, Mathematics Common Room.** **

**3:30pm - 4:30pm
**

Jim Smith (Warwick) -* Network Inference, *45min

**Discussion on network inference**

Abstracts:

**Model checking and its use in network inference**

by David Gilbert

We describe how model checking can be used in Systems Biology and also Synthetic Biology to aid the analysis and construction of models of biological systems, as well as to help guide the design of the synthetic systems.

We illustrate this tutorial by reference to the simulative MC2 Model Checker which operates over properties written in Probabilistic Linear-time Temporal Logic with numerical constraints (PLTLc), and which can handle descriptions ranging from highly qualitative to fully quantitative.

We also introduce the concept of Model Engineering, which is a systematic approach for designing, constructing and analyzing computational models of biological systems, and takes some inspiration from efficient software engineering strategies.

Special thanks to Robin Donaldson, University of Glasgow, who developed the MC2 model checker (www.brc.dcs.gla.ac.uk/software/mc2/ and created the MC2 model checking slides in this presentation.

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**Probabilistic network models in cancer biology**

by Sach Mukerjee

Networks of proteins called “signalling networks” play a key role in the control of diverse cellular processes; their aberrant functioning is heavily implicated in many diseases, including cancer. Aberrations in cancer cells are thought to perturb the normal connectivity of these networks, with important biological and therapeutic implications. Yet tumour-specific signalling connectivity remains poorly understood, especially at the level of relevant post-translational protein modifications. Modern high-throughput proteomic technologies are now able to make measurements on components of these systems, and can, in principle, shed light on a variety of open questions concerning signalling in cancer. I will discuss approaches for interpreting these data, in particular how a class of stochastic models known as “probabilistic graphical models” can be used to integrate biochemical data and prior knowledge of signalling biology to facilitate the discovery process.

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**Switching Regulatory Models of Cellular Stress Reaction**

by Guido Sanguinetti

**Abstract:** We present a novel approach to inferring transcription factor (TF) activities and kinetic rates in transcriptional networks from mRNA expression time courses. Within a Bayesian framework, we place a switching stochastic process prior on the TF activity profile, and derive a likelihood from the ODEs governing mRNA transcription. We use a variational inference approach that allows us to determine both the posterior TF process and the kinetic parameters (production/ decay rates). More importantly, we show that, given sufficient data and some partial information about the connectivity of the transcriptional network, the method is capable of handling the situation when transcription is governed by a set of non-linearly interacting TFs.

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**Inferring gene regulatory network topology using a non linear sparse Dynamic Bayesian Network model**

by Ed Morissey

**Abstract:** It is a well known fact that genes do not act alone, rather they form part of complex interacting

networks. Specialised genes called transcription factors codify proteins that drive the dynamics

of other genes, these in turn codify proteins that perform a number of essential functions (DNA repair,

signalling molecules, ...). Depending on the structure of these networks, certain behaviour can emerge

such as oscillating gene expression dynamics, switch-like behaviour, etc. Although all this is known, currently

few networks are fully characterised. Given that we can measure the activity of these genes, the challenge is

to try to predict the structure of the network from the gene activity.

Several methods have been put forward, most of them relying on a linear approximation to explain the

relation between genes. Although this approximation strikes a good balance between complexity/accuracy,

thanks to molecular modeling we know that these interactions are better represented by non linear

montone functions.

We propose a fully Bayesian semi-parametric model, based on penalised splines. The model is compared to

the equivalent linear model with a number of synthetic and real examples.