My PhD relates to the use of flow-cell optical biosensors to
indirectly study the dynamics of biomolecular interactions. This led to
interest in variety of problems.

This concept lurks wherever we wish to “calibrate” a model structure
(estimate parameters from data) so that we can proceed to make
predictions.

Often we can represent a physical system by a structure of
“state-space” systems. These relate state variables
(**x**), observables (**y**) and possibly
inputs (**u**) through parametric expressions in the
parameters \(\boldsymbol{\theta}\):
\[\begin{gather}
\dot{\bf x}({\bf x}, {\bf u}, t; {\boldsymbol{\theta}}) = {\bf f}({\bf
x}, {\bf u}, t; {\boldsymbol{\theta}}) \, , \quad {\bf x}(0) = {\bf
x_{0}}(\boldsymbol{\theta}) \\
{\bf y}({\bf x}, {\bf u}, t; {\boldsymbol{\theta}}) = {\bf g}({\bf x},
{\bf u}, t; {\boldsymbol{\theta}}) \, .
\end{gather}\] Suppose we have an infinite, error-free record of
data, and a correctly specified model structure (composed of parametric
relationships between variables). Is it possible to obtain a unique
estimate for each parameter? If not, and if alternative parameter
estimates produce very different predictions, we cannot make predictions
with confidence. This may cause our study to be an unproductive use of
time, effort, and resources.

I have considered the problem for model structures used in various biological settings.

Optical biosensor experiments^{1} provide a means of
indirectly observing the interactions of biomolecular species in real
time. The experimental setup features an *immobilised analyte*
bound to a sensor surface, and an *analyte* in solution made to
flow over this surface. A series of “kinetic” experiments aim to
determine the rate constants of interactions. Experiments typically
consist of two or more phases, delineated by a change in experimental
conditions. For example, in the *association* phase, some
concentration of analyte is made to flow over the surface for a
specified time. In the *dissociation* phase, the solution is
changed to buffer (zero analyte concentration).

In certain cases, the experimental output is appropriately modelled by a linear switching system (LSS). A LSS is a collection of linear time-invariant state-space systems, with a switch that determines which system is in effect at each time point. A schematic of the LSS output is shown in Figure 2 below.

As standard methods in identifiability testing and parameter estimation are not appropriate for an LSS structure, it is necessary to design other methods.

See the abstract of my PhD thesis:^{2}

“Global
*a priori* identifiability of models of flow-cell optical
biosensor experiments”, Bulletin of the Australian Mathematical
Society 98, no. 2 (2018): 350-352.

Whyte, Jason M.

**“Branching out into Structural Identifiability Analysis with Maple: Interactive Exploration of Uncontrolled Linear Time-Invariant Structures.”**in “Maple in Mathematics Education and Research. MC 2020”, pp. 410–428, 2021. Communications in Computer and Information Science, vol 1414. Springer, Cham. (The arXiv preprint is available here)Whyte, Jason M.

**“Model Structures and Structural Identifiability: What? Why? How?”**, in 2019-20 MATRIX Annals, MATRIX Book Series, 2021, 185–213.

Zaloumis, Sophie G., Jason M. Whyte, Joel Tarning, Sanjeev Krishna, James M. McCaw, Pengxing Cao, Michael T. White et al.

**“Development and validation of an in silico decision-tool to guide optimisation of intravenous artesunate dosing regimens for severe falciparum malaria patients.”**, Antimicrobial Agents and Chemotherapy 65, no. 6 (2021).Alahmadi, Amani, Sarah Belet, Andrew Black, Deborah Cromer, Jennifer A. Flegg, Thomas House, Pavithra Jayasundara et al.

**“Influencing public health policy with data-informed mathematical models of infectious diseases: Recent developments and new challenges.”**, Epidemics 32 (2020): 100393.

Whyte, J. M.,

**“Maple 2020 procedures and a dashboard for interactive testing of uncontrolled linear-time-invariant structures for structural global identifiability”**, available online March 31st 2021.Whyte, J. M.,

**“Drawing a compartmental diagram for an uncontrolled linear, time-invariant structure”**, software for Maple Conference 2020, Dec 30 2020.

**Approaches to analysing jump dynamical systems in
biomolecular kinetics (and elsewhere?)“**, talk presented at the
ANZIAM Mathematical Biology Special Interest Group (MBSIG) meeting,
February 14th, 2022.

**“Structural
identifiability analysis for switching system structures: towards a
toolkit for changing times”**, talk presented at Dynamical
Systems Applied to Biology and Natural Sciences (DSABNS 2022 Virtual),
February 10th, 2022. (DSABNS Contributed Talk Award.)

**“Numerical
investigation of structural minimality for structures of uncontrolled
linear switching systems with Maple”**, talk presented at the
Maple Conference 2021 (virtual), November 2021.

**“My
Enemy, My Ally: how useful is this mathematical model?”**,
talk presented at the ARC Centre of Excellence for Mathematical &
Statistical Frontiers (ACEMS) Early-Career Researcher Retreat, November
3rd, 2020.

*Talk begins with a brief comparison of mathematics
and science fiction.*

**“Branching out into structural identifiability analysis with
Maple”**, Maple Conference 2020 (online), Nov 2nd 2020.

**“Frustrated mathematical modelling and changeable destinies:
Structural identifiability analysis of models to support useful
results”**, Seminario de Investigación Interdisciplinar para la
Innovación en Ciencia y Tecnología, (SICTE Interdisciplinary research,
Catholic University of the North, Chile), invited oral presentation
online, Oct 20th 2020.

**“An introduction to the testing of model structures for
global a priori identifiability (with examples drawn from Plasmodium
falciparum malaria modelling)”**, invited oral presentation for
Influencing Public Health Policy with Data-informed Mathematical Models
of Infectious Diseases, Creswick, Victoria, July 1st 2019.

**“Biological modelling, and rarely asked questions of the 21st
century”**, poster presentation, BioInfoSummer, University of
Western Australia, Perth, December 3rd 2018.

**“Biological modelling, and rarely asked questions of the 21st
century”**, poster presentation, Australian Bioinformatics and
Computational Biology Society Conference, Melbourne, November 26th
2018.

Whyte, J. M. **“Structural minimality of linear swtiching
system structres, as motivated by flow-cell optical biosensors and
biomolecular interactions”**