Download pdf - Accelerating the drug discovery process with mathematical … · 1 Accelerating the drug discovery process with mathematical modelling and MATLAB David Gavaghan . University of Oxford

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Accelerating the drug discovery process with mathematical

modelling and MATLAB

David Gavaghan University of Oxford

[email protected]

Presenter

Presentation Notes

Director of the EPSRC DTC Head of Computational Biology Group which has grown from around 7 people when formed in 2005 to over 70 today including 7 faculty. Previously we were part of the Numerical Analysis Group in Oxford.

Overview • The increasing need for mathematical training in the life

sciences – Predictive and quantitative modelling of biological systems

• What is a Doctoral Training Centre? – The Oxford DTC Programmes – Role of MATLAB within our programmes

• Development of the Chaste software package – Links to industry, particularly Pharma

• Making Chaste available through MATLAB

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Multi-scale, multi-physics

• Biological systems are

– Multiscale: involve interdependent processes occurring on multiple spatial and temporal scales

– Multiphysics: involve multiple physical mechanisms (transport, signalling, reaction….)

– Complex: self-healing, adaptive, plastic, self-organising, reactive

Presenter

Presentation Notes

Two key points. 1. Physical processes and scales are intertwined. Processes cannot be decoupled and scales cannot be separated using our usual applied mathematics toolbox (asymptotics, perurbation theory, homogenisation etc). This has huge implications for the computational complexity of the modelling task. 2. Systems can change themselves and adapt to changes in their environment in ways that may not be obvious.

Courtesy of Peter Kohl (Harefields)

Normal beating Fibrillation

Model complexity is dependent on the scientific questions being asked…….

Pras Pathmanathan (FDA)

• Scientific questions: what is the optimal shock strength to reverse this process? What is the precise effect of a drug?

• Aiming for predictive, quantitative understanding in biology • Requires a new approach to scientific training

Presenter

Presentation Notes

If we look at the previous slide, if we simply want to model the action of a drug on an ion channel, or the integrative effect of drug block at a cellular level, then our models can be quite simple (in these cases typically non-linear odes which can be solved very efficiently in MATLAB) If, however, we want to simulate a complex process such as the initiation of a life threatening arrhythmia (as shown in middle panel) the we may need to include all components from ion channel dynamics right up the full complexity of the cardiac geometry in our model. On left is normal beating and opening and closing of the heart valves. A diseased heart may go into fibrillation which is often a precursor to heart failure. How are processes such as fibrillation initiated and in particular how can drugs influence this process? We can only gain an understanding of these processes through an iterative interplay between experiment, mathematical modelling and very computationally expensive computer simulation using HPC resources. Movie on the right was generated on a large cluster (>1000 processors) and solves on a realistic heart geometry in the left ventricle with over 4million tetrahedral elements in the Finite Element mesh. Scientific questions we might ask

• Quantitative and Systems Pharmacology in the Post-genomic Era: New Approaches to Discovering Drugs and Understanding Therapeutic Mechanisms

• An NIH White Paper by the QSP Workshop Group – October, 2011.

• Peter K. Sorger (co-chair), Sandra R.B. Allerheiligen (co-chair), Darrell R. Abernethy, et al

Why is this important to the Pharmaceutical industry?

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• Quantitative and Systems Pharmacology in the Post-genomic Era: New Approaches to Discovering Drugs and Understanding Therapeutic Mechanisms

• An NIH White Paper by the QSP Workshop Group – October, 2011.

• Peter K. Sorger (co-chair), Sandra R.B. Allerheiligen (co-chair), Darrell R. Abernethy, et al

Definition: The goal of QSP is to understand, in a precise, predictive manner, how drugs modulate cellular networks in space and time and how they impact human pathophysiology. QSP aims to develop formal mathematical and computational models that incorporate data at several temporal and spatial scales; these models will focus on interactions among multiple elements (biomolecules, cells, tissues etc.) as a means to understand and predict therapeutic and toxic effects of drugs.

Definition: The goal of QSP is to understand, in a precise, predictive manner, how drugs modulate cellular networks in space and time and how they impact human pathophysiology. QSP aims to develop formal mathematical and computational models that incorporate data at several temporal and spatial scales; these models will focus on interactions among multiple elements (biomolecules, cells, tissues etc.) as a means to understand and predict therapeutic and toxic effects of drugs.

The report also makes the overarching recommendation:

Because industry has an acute need for trainees with strong skills in quantitative reasoning, network biology, and animal and human pharmacology, industry should

be engaged in education as well as research.

Presenter

Presentation Notes

In 2010 only 17 new compounds were approved for phase III clinical trials by the FDA – something needs to change…..

EPSRC Life Sciences Interface Doctoral Training Centres

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What is a Doctoral Training Centre? • Introduced by EPSRC’s Life Sciences Interface Programme in 2002

• Address need for scientists capable of quantitative and predictive research in biological and medical sciences

• Typically fund centre costs plus 5 cohorts each of ten students

• Min of 25% taught training, strong emphasis on “transferable skills”

• Oxford LSI DTC was one of the first two (other being in Edinburgh)

• Three years ago rolled out across EPSRC portfolio (£300M) 2002 and 2012

cohorts

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The Oxford DTC Programmes

• Three current Programmes – Life Sciences Interface (2002) – Systems Biology (2007) – Systems Approaches to Biomedical Science (2009, Industrial)

• Industry partners include GSK, AZ, Roche, Novartis, Pfizer

• Total of ~300 students to date, ~120 completed PhDs

• ~25% go into industry, 75% into academic research

Strong focus on mathematical training (regardless of background) largely facilitated by MATLAB

Presenter

Presentation Notes

Explain differences between programmes

Use of MATLAB within the Programmes

• Gain understanding and insight in the mathematical courses (basic to advanced)

• Data analysis – basic graphical tool through to advanced statistical, image

processing and data visualisation

• Computational modelling – Prototyping through to research software

• Toolboxes routinely used – Bioinformatics, Image processing, PDE, Statistics, [Parallel]

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Examples of MATLAB in DTC Research

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Chris Arthurs and David Kay Adaptive p-refinement

Tom Doel and Vicente Grau Lobe segmentation in the lung

Presenter

Presentation Notes

Can’t get movies to run yet – can always skip….

The majority of computational modelling research in the DTC is done in MATLAB but…

• Some problems are of a scale and complexity that bespoke scientific software must be developed

– anatomically detailed multiscale, multiphysics problems such as whole-organ modelling

– individual-based models bridging hybrid discrete/continuous, stochastic/deterministic such as cancer modelling

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Presenter

Presentation Notes

The image on the right shows the 4-million element finite element mesh that was used in the simulation I showed earlier. It has embedded fibre architecture and vasculature. The systems of equations solved over the mesh for the electrical potential typically have around 30-60 unknowns at each node.

CHASTE: a MATLAB-inspired software development project

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Presenter

Presentation Notes

Matlab is great but it can’t do everything……in particular it isn’t (yet) for the types of really complex problems such as the multi-scale, multi-physics research problems typically arising in systems biology and physiology and of increasing interest to the pharmaceutical industry, so, about 7 years ago we started to develop Chaste. Out goal at the outset was to make programming in Chaste as easy as programming in matlab so that we would get strong takeup from the community…..but it actually started as a training course within the DTC…..and has almost all been developed by DTC students (now post-docs)

What is Chaste?

“Cancer Heart and Soft Tissue

Environment”

http://www.cs.ox.ac.uk/chaste/

• Started in 2005 as a 4-week DTC course in Software Engineering

• Library of Open Source (BSD) code for large-scale biological problems

• Aim: produce a robust, extensible, reliable, re-usable and well-documented code base

• Functionality: coupled ODEs, PDEs, agent-based and hybrid on desktop and HPC

• Main applications: Cardiac and Cell-Based

http://web.comlab.ox.ac.uk/chaste/

http://web.comlab.ox.ac.uk/chaste/

Chaste development approach • Focus from the start on software engineering issues

– Object-oriented – C++

• Agile approach – Test-driven (test first) – Pair programming – Frequent refactoring – Team ownership

• Code base contains >300,000 lines of code and ~200,000 lines of test

• Growing user base – has been downloaded well over 1000 times from over 400 unique IP addresses including by FDA and NASA

J. Pitt-Francis, et al. Chaste: a test-driven approach to software development for biological modelling. Comp Phys Comm 180:2452-2471, 2009.

Chaste projects with Industry • EPSRC Integrative Biology e-Science (2004-7)

– IBM

• EU FP7 preDiCT project: prediction of Drug Cardiac Toxicity (2008-11) – Fujitsu Laboratories of Europe (UK), GlaxoSmithKline (UK), Novartis (Switzerland),

F. Hoffman-La Roche, AstraZeneca, Pfizer

• EPSRC 2020 Science Project (2011-2015) – Microsoft Research

• GSK embedding Chaste in the drug development pipeline with the intention of replacing some animal tests

• Collaborations with AZ/Medimmune in cancer modelling

• Collaboration with Mathworks in building a MATLAB front end to Chaste

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Embedding Chaste Functionality into Matlab

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Problem statement • Cell-based version of Chaste requires strong C++ skills

• The process of running simulations very time-consuming

• Not easy to interact with Chaste simulations “on-the-fly”

• Makes Chaste much less attractive to end users, particularly in industry

Presenter

Presentation Notes

MATLAB is a language that facilitates quick development and may be more familiar to (or at least more easily picked up by) a non-expert programmer. Particularly useful for experimentalists who may wish to try their hand at simulations. Good C++ skills are harder to find amongst life scientists. Tweaking simulations or modifying them based on the outcome is not an easy process at the moment. Using the interpreted coding style of MATLAB without the need for compilation will speed up this process, provided it can be done without compromising on speed. By opening up Chaste’s simulation engine to MATLAB, a greater level of interactivity can be achieved�

• Developed earlier this year via a Mathworks-funded 3-month internship for Tom Dunton (3rd Year DTC student)

• Aim – build a MATLAB front-end to Chaste for a cell-based application problem giving greater control of the simulations

• Provides the user with the modelling capability of Chaste and the visualisation and analytical power of MATLAB

Prototype solution

The Crypt Renewal Cycle (turnover in 4-6 days)

1. Proliferation of stem cells (bottom of crypt)

2. Transit cells divide 2-3 times (lower third of crypt)

3. Cells migrate to the surface

4. Transit cells differentiate (midcrypt region)

5. Senile cells removed from surface (midpoint between crypts) 1

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Colorectal cancer is the result of multiple genetic mutations which disrupt the normal processes of cell

proliferation, cell differentiation and cell death

Presenter

Presentation Notes

Explain why Pharma might be interested in this – cancer drugs often work well in vitro (in a test tube) but often fail in the later stages of development. This is often because the drug doesn’t get to the target, or doesn’t stay at the target for long enough. By modelling the process in a realistic environment we can assess the likelihood of efficacy.

Cell-based modelling of tumour development

• Sub-cellular level: typically cell-cycle models (deterministic ode, stochastic), interacts with tissue level (e.g. via WNT signalling)

• Tissue level: continuous field equations describing e.g. inter-cellular signalling, nutrient uptake (cells act as source/sinks), transport phenomena

Presenter

Presentation Notes

So how do we model this? We need to model how individual cells interact with each other (in terms of the forces they exert on each other), and signal to each other (continuous field equations). We also need to model the subcellular control mechanisms (cell cycle models) – these are the processes that typically get disrupted through mutations leading to cancer.

Test problem • Want to look at how the

location and type of mutation (cell properties) affects – the number of cells in the crypt – persistence of mutation

Method: • Initialize a crypt and simulate

until it has equilibrated • Introduce a set of mutations • Simulate the progression of

the mutation

Presenter

Presentation Notes

The system is one of the test-tubed shaped crypts in the colon. The figures show the representation of that system in Chaste. The test tube is unwrapped into a 2D sheet, with a fixed boundary at the bottom, periodic boundaries along the sides, and an open top edge, where cells are killed once they reach a certain height – representing transition to the walls of the colon. The grey cells have differing mutations, with the ones on the right have greater intercellular adhesion (modelled by an increase in the drag coefficient).

A MATLAB interface to Chaste

• Use MEX as the way to integrate C++ and MATLAB

• Mirror Chaste classes in object-oriented MATLAB

• Create a functional interface to MATLAB classes – createmesh( myCrypt, ‘mesh’, 10, 6); – solvesystem( myCrypt, 20, 1);

• The evolution of the simulation can be visualised and the MATLAB graphical user interface enables interaction during the simulation

Presenter

Presentation Notes

This project was conceived as a proof of concept for the integration of Chaste and MATLAB. My work has shown that it is indeed possible, and that there are many benefits of such an integration that we can seek to exploit. There may be some areas for improvement, and scope for extension, but the groundwork has been done and this paves the way for a deeper integration

Structure of MATLAB-Chaste interface

GUI

Object-oriented MATLAB

MEX-functions

Chaste libraries C++ repository of Chaste functionality

MATLAB’s bridge to C/C++

Take advantage of MATLAB’s GUI support. OO MATLAB allows natural development of sophisticated GUIs

Modularity of the MATLAB code improves scalability and maintainability for larger software projects

Presenter

Presentation Notes

This is an overview of the project structure. The Chaste libraries are build in the same way they normally would be. The shared libraries are then made accessible to MATLAB using MEX-files, compiled into MEX-functions. This approach meant we can use the existing class structure of Chaste, and all the tools contained therein, to set up and run simulations. We use the MEX-functions to pass important simulation parameters to the Chaste objects, and are then able to use tools in Chaste to extract simulation data and pass this back to MATLAB.� We opted for a small MEX-file interface, with only two files. One for initializing the simulations and one for advancing the simulation a given amount. With a crypt simulation class, we can use its methods to set up and run simulations, and by appropriate use of set and get access methods, we can ensure that the parameters are of the correct form for the MEX-functions. The simulation can be printed to screen as it is running, and the user can select cells to mutate, or just label, by clicking on the cells that are displayed.

Basic test case with no user interaction

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User defined mutation of cells

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User defined mutation of cells

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Current Chaste Functionality (James Osborne and Sara-Jane Dunn)

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Self-organisation of the colorectal crypt

Tumour spheroid with a necrotic core Over-proliferation leading

to polyp formation

Summary and Future Work • Research and training at the LSI is an exciting and

rewarding area

• Project with Mathworks ongoing – looking at extending to encompass further functionality

• Work with Pharma on cardiotoxicity being extended (funding from NC3Rs and EPSRC)

• Cancer modelling work ongoing with AZ, MedImmune and Roche.

• DTC training at PhD level extended to post-doc level through 2020 Science programme

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Acknowledgements

• Tom Dunton, James Osborne

• Chaste cardiac team: Joe Pitt-Francis, Blanca Rodriguez, Pras Pathmanathan, Jon Cooper, Miguel Bernabeu, Gary Mirams, Alberto Corrias, Raf Bordas, Alan Garny, Nejib Zemzemi, Alfonso Bueno-Orovio

• Chaste cell-based team: Helen Byrne, Jon Whiteley, James Osborne, Alex Fletcher, Sara-Jane Dunn, Sophie Kershaw, Alex Walters, Philip Murray

• Numerics: David Kay, Jon Whiteley

• Funding: EPSRC, BBSRC, MRC, EU FP7, Wellcome Trust

Appendix of slides

• Some more slides from Tom’s presentation below

What do we want to control in Chaste?

• Simulation – cell centre or vertex, length of simulation

• Crypt parameters – width, height

• Cell parameters – cell-cycle model,

• Mutations – mutation type, mutation parameters

Presenter

Presentation Notes

Having decided on a route to take, we now had to decide what it was that we wanted to control within Chaste simulations. TALK THROUGH LIST Having decided on these options, it was decided to separate them into two distinct groups: Those that needed to be chosen at the beginning of a simulation Those that were introduced during a simulation With this in mind, we were then in a position to think about how to construct the MEX-files

MEX-file interface

• Two MEX-functions o Initialize.cpp → set up the simulation o Simulate.cpp → advance the simulation

• Use Chaste’s serialization to save the

simulation in its current state, then re-load it to continue the simulation

• Two time scales to the interface o Small time step used within Chaste to solve the

system

Presenter

Presentation Notes

I opted to use two MEX-functions one for setting up the simulation – where the cell-level model (mesh/vertex) was decided, along with the crypt geometry, and the subcellular model The second was used to advance the simulation by a given amount, and would also enable the creation of mutations within specific cells and also labelling cells in order to track all the daughter cells. This approach makes frequent use of Chaste’s serialization tools. There is always going to be an issue with persistence when using external simulation tools. To avoid having to pass every single parameter back to MATLAB following each call of a MEX-function, we are able to save the state of the simulation object, then reload it at the next MEX-function call This brings us to the dual nature of the timescales of simulations using this MATLAB interface to Chaste. Firstly there is a small time step, over which Chaste solves the system of differential equations describing the system, usually on the order of tens of seconds of simulation time�2) Secondly there is a large time step, which defines how often MATLAB interacts with the Chaste simulation, this would commonly be in the region of every hour in the simulation.� With the overhead associated with saving and loading a file, the more frequently MATLAB interacts, the slower it will be. However, when interacting every hour there is only a 40% increase in simulation time, and without any interaction at all, this is reduced a less than 10% slow down, when compared to Chaste running on its own.

MEX-file interface

• Many options in Chaste are templated, so are set at compile time

• To solve this problem we have to use a switch in the MEX-file

• Parameters of interest are passed back to MATLAB o cells → structure array with information for

each cell d matri ith location of the nodes in the

Presenter

Presentation Notes

When writing the MEX-function we have to be careful. Chaste is written so that most of the options are set at compile-time. Meshes, cell cycle models, forces, mutations are all template classes. This introduced some issues as to how to best incorporate modification of these properties at run-time. The only sensible, if slightly un attractive, option was to use a switch condition to choose between the various template class options. So, during each large time step, MATLAB calls the MEX-function, which loads the simulation in its current state. Modification to properties are made as desired using the methods available within Chaste. The simulation is then advanced by one time step, and archived. This process is looped over in MATLAB to achieve the on-the-fly simulation visualization, which I have just shown you. To get the output that I demonstrated to you at the beginning

MATLAB crypt class

• Simulations are set up using a MATLAB crypt class

• crypt’s methods control all aspects of the simulation: verifying input parameters, calling the MEX-functions and controlling GUI

Presenter

Presentation Notes

To make sure that simulation are set up correctly, and parameters are passed to the MEX-functions in the correct form and combinations, it was necessary to hide the MEX-function interface from the user.

Designing the crypt class

• The methods implemented in the crypt class mirror the structure of simulations in Chaste

• Set and get access methods are employed to ensure parameters are correct

• Needs to exercise some control over the directories that Chaste writes to (avoid overwriting etc.)

Presenter

Presentation Notes

It was decided to design the crypt class, so that it’s methods mimicked the construction procedure for setting up simulations in Chaste. The class is constructed, taking only an output directory as a parameter. Then the createmesh method sets the simulation mesh type And the createcells method sets the subcellular model The system can now be solved using the solve system method, specifying the length of the simulation, and the value of the large time step (which determined the frequency of interation with MATLAB). The parameter values are verified using set access methods. This ensures that sensible parameters are passed, and that they are of the correct form. It also enables some control over the output directory for chaste – avoids overwriting archive and output data for other crypt simulation objects that are instantiated.

A few simple GUI elements

• Gives on-the-fly visualizations of the crypt state

• Can be easily extended to display various crypt parameters during the simulation

• As a demonstration of how to collect user input, mutations and labels can be applied with the mouse

Presenter

Presentation Notes

READ THE SLIDE Uses the ginput function in MATLAB to capture mouse clicks, and thus choose which cells to mutate or label.