Helen Byrne is a Professor of Applied Mathematics in the School of Mathematical Sciences and Director of the Centre for Mathematical Medicine and Biology at the University of Nottingham.

Helen Byrne’s homepage

Centre Research | Virtual Root

Helen Byrne's homepage

Scientific background

I studied for my D.Phil (Ph.D) under Dr Peter Howell and Dr Chris Breward at the Oxford Centre for Industrial and Applied Mathematics. My project was based on an industrial coating process used within the paper industry, where I modelled the pigment-containing fluid flows involved. I used techniques from fluid mechanics and asymptotic methods; in particular exploiting the geometry of the flow to simplify the governing equations. This project was sponsored by ArjoWiggins via a CASE studentship, and therefore involved a high degree of multidisciplinarity including spending time on-site with them and discussions with their scientists.

CPIB research

My main role within CPIB was to model the mechanical aspects of root growth, at both cellular and organ scale. I use mathematical modelling techniques such as asymptotic analysis to formulate models which can be tackled analytically, in addition to giving mathematical back up to the hyperelastic models which are solved using finite element methods. In particular, we wish to incorporate the mechanical anisotropy of the call wall, which has been mainly neglected in previous models of plant cells.

My plant work is focused on cell growth within the elongation zone of the root, in which the cell undergoes rapid anisotropic expansion; increasing in length around 30 fold whilst displaying minimal radius change.   Growth is driven by high internal turgor pressure causing viscous stretching of the cell wall.  Cellulose microfibrils embedded within the wall give strongly anisotropic mechanical properties, which are under biochemical control and are modified by the cell during growth.  We have derived and analysed the governing system for this process

.  Representing the cell as a thin axisymmetric fibre-reinforced viscous sheet between rigid end plates, we performed a systematic reduction of the governing equations, under simple sets of assumptions about fibre and wall properties, to derive the governing system. This extension of the Trouton model for extensional flow of a Newtonian fluid to a fibre-reinforced fluid was in itself a novel and challenging piece of mathematics, which may have other applications to other areas as well as plant growth. We found variants of the traditional Lockhart equation, which relates the axial cell growth rate to the internal pressure and is currently used by many plant biologists to model growth.  The model provides insights into the geometric and biomechanical parameters underlying bulk quantities such as wall extensibility and shows how either dynamical changes in wall material properties or passive fibre reorientation may suppress cell elongation.

Current Position

Rosemary Dyson is now a Lecturer in the School of Mathematics, University of Birmingham. She continues to work closely with CPIB.

Centre Research | Root SAT-NAV: uncovering the molecular mechanisms guiding root angle in soil | Hormone Regulation of Plant Growth | Virtual Root

Rosemary Dyson's homepage

Oliver Jensen was Professor of Applied Mathematics at the University of Nottingham and the Manager of Strand 4 of the CPIB virtual root project.

He has particular interests in biomechanical aspects of plant growth and function. He remains a member of CPIB and is currently Professor of Applied Mathematics at the University of Manchester.

Contact details, research interests and publications may be found here.

Centre Research | Root SAT-NAV: uncovering the molecular mechanisms guiding root angle in soil | Integrative approaches to understanding and improving nutrient uptake efficiencies of crop species | FUTUREROOTS: Redesigning Root Architecture for Improved Crop Performance | 3D Canopy Architecture Modelling | Lateral Root Emergence | Virtual Root

Oliver Jensen's homepage

I joined CPIB in September 2008 as the Strand 3 Plant Scientist. My main focus was on studying the development of the lateral root primordium (LRP), and more precisely, on the patterning events driving the construction of its 3D tissue structure.

Mikaël left CPIB in July 2010.

Centre Research | Virtual Root

My primary role within CPIB was to develop mathematical models of hormone perception. This involved interacting closely with experimentalists (in particular Tara Holman, Benjamin Péret and Susana Úbeda-Tomás) to integrate their latest results into my models, and suggest novel experiments that validated my predictions. I also interacted with other mathematicians (Leah Band and Rosemary Dyson) to integrate my models into theirs, and with statisticians and computer scientists (Kim Kenobi, Claudio Lima and Jianyong Sun) to fit my models to the data generated in the lab. I also co-supervised PhD student Nathan Mellor (who was looking at LAX3 regulation) and summer student Fred Hoffman (who was looking at stochastic effects on the Aux/IAA negative feedback loop).

Alistair left CPIB in April 2010, and is currently working at the University of Heidelberg.

Centre Research | Virtual Root

Alistair Middleton's homepage

Nick Monk is Associate Professor and Reader in Applied Mathematics and the Manager of Strand 2 of the CPIB virtual root project. His research centres on the use of theoretical and mathematical modelling to gain insight into basic mechanisms of cellular signalling networks in animal and plant tissues.

Further information can be found at Nick Monk’s homepage.

Centre Research | Virtual Root

Nick Monk's homepage

I joined CPIB as a mathematician in September 2009. My role is to undertake deterministic (differential-equations based) modelling of gene and signalling networks involved in lateral root initiation. In particular, I am developing models of hormone interactions regulating the priming of founder cells in lateral root initiation at a cellular and multi-cellular scale. The model formulation requires working in collaboration with a biologist, [[ute-vos]], and other mathematicians of the centre, [[alistair middleton]] and Leah Band.

Centre Research | Virtual Root

Daniele Muraro's homepage

I joined CPIB in July 2009. My role was to further develop image analysis techniques specifically the RootTrace program, modifying it to characterise root systems architecture, which was published in


Asad is a CPIB affiliate, having left in September 2010 for the Air University, Islamabad, Pakistan.

Centre Research | Virtual Root

Asad Naeem's homepage

Marie Curie Research Fellow (Intra European Fellowship)

Lateral Root Emergence

Lateral root (LR) formation is a major determinant of root systems architecture. LRs originate deep within the parental root from a small number of founder cells at the periphery of vascular tissues (Péret et al, 2009a) and must emerge through intervening layers of tissues. This process has been defined as “Lateral Root Emergence” (Péret et al, 2009).

A schematic cross-section of the Arabidopsis root

A schematic cross-section of the Arabidopsis root

The Auxin Influx Transporter LAX3 Regulates LR Emergence

The hormone auxin, which originates from the developing lateral root, acts as a local inductive signal which re-programmes adjacent cells. Auxin induces the expression of the auxin influx carrier LAX3 in cortical and epidermal cells directly overlaying new primordia. Increased LAX3 activity reinforces the auxin-dependent induction of a selection of cell-wall-remodelling enzymes, which are likely to promote cell separation in advance of developing lateral root primordia (Swarup et al. (2008)).

A schematic of the lateral root emergence network model

A schematic of the lateral root emergence network model

A confocal microscope image of the lateral root primordia

A confocal microscope image of the lateral root primordia

Building a Regulatory Network for Lateral Root Emergence

As a Marie Curie Fellow, I interacted with CPIB modellers to build a regulatory network of lateral root emergence. This included: – developing tools to induce LR emergence and study gene expression – identifying new components of the LR emergence pathway – producing quantitative data to feed mathematical models – engineering auxin content in planta to study the spatial regulation of LR emergence – using chemical genetics to decipher LR emergence (Antoine Larrieu) – identifying important transcription factors (Wei Hseng Chan, PhD Student). As part of Strand 3, I collaborated with other aspects of LR formation such as LR patterning ([[ute-vos]] and Mikaël Lucas).


  • auxin synthesis and homeostasis (Karin Ljung, Umea, Sweden)
  • nutrient regulation (Philippe Nacry, INRA Montpellier, France and Laurent Nussaume, CEA Cadarache, France)
  • biomechanical aspects (Christophe Maurel, INRA Montpellier, France and Anton Schaffner, Muenchen, Germany)
  • LR initiation (Tom Beeckman and Bert de Rybel, Ghent, Belgium)
  • LR formation (Reidunn Aalen and Robert Kumpf, University of Oslo, Norway)
  • root vascular patterning (Yka Helariutta, University of Helsinki, Finland)
  • auxin perception (Mark Estelle, University of California San Diego, USA)


This work was funded by a Marie Curie Intra-European Fellowship within the 7th European Community Framework Programme (PIEF-GA-2008-220506).

Centre Research | Virtual Root

Benjamin Péret's homepage