Mechanistic modelling of treatment resistance in cancer

Despite advances in targeted medicine, most patients with advanced cancer will experience drug resistance, treatment failure and, ultimately, disease recurrence. This drug resistance, long thought to result from genetic heterogeneity and Darwinian evolution, is increasingly understood as the result of non-genetic evolutionary adaptations to therapy. Recent experimental studies identifies the importance of reversible drug-tolerant phenotypes in driving drug resistance to anti-cancer therapy. This phenotypic adaptation is modulated by a number of complex physiological factors, including the current state of the tumour population and microenvironment, as well as the life history of the parental cell. As systems-level experiments of the complex interactions driving treatment resistance are currently intractable, mathematical models are integral to our understanding of how therapeutic selection pressure shapes the epigenetic evolution of malignant tumours. The proposed research will advance the development of mathematical models to understand the reversible epigenetic resistance observed experimentally. <br /> <br /> Many of the existing mathematical models of intra-tumour dynamics extensively use the theoretical framework of evolutionary game theory. There, treatment-driven evolution is typically modelled as a multi-species replicator equation describing clonal dynamics over fixed genetic landscapes. In these models, tumour dynamics are entirely determined by clonal frequency and pre-determined sensitivity to therapy. However, these evolutionary games are incompatible with the continuous phenotypic adaptation to therapy that is increasingly observed in experiments. Thus, the proposed research will develop a mathematical framework to characterise this continuous adaptation and techniques to calibrate the resulting mathematical models to appropriate data.

<p>Potential areas for further investigation are:</p> <p>1) In a population of genetically identical non-small cell lung cancer cells, a reversible drug-tolerant phenotype expands during anti-cancer targeted therapies and drives tumour rebound during treatment. Existing mathematical model consider this evolutionary adaptation by using a phenomelogical models that enforce discrete “sensitive” and “resistance” states. Here, we could consider the more biologically realisitc case of continuous or stochastic phenotypic adaptation and the extension of this model to understand cooperation during in vitro experiments.</p> <p>2) Roughly 50% of melanoma cases harbour an activating mutation in the Mitogen Activated Protein Kinase (MAPK) pathway that drives tumour growth. Inhibitors targeting this pathway represented a breakthrough in the treatment of melanoma with over 65% of patients showing clinical benefit during continuous treatment. However, treatment resistance inevitably develops and leads to disease progression. Recent experimental evidence suggests that including period of no treatment -so called drug holidays- can delay the onset of treatment resistance. Here, we could develop mathematical models to understand the evolutionary dynamics leading to development of resistance to MAPK inhibitors.</p> <p>3) Drug resistance results from changes at the cellular scale. However, the results of this resistance, namely treatment failure and tumour growth, are only observed at a much larger scale. Bridging the in vitro experimental results with clinical scale measurements requires a deep understanding of biological mechanisms and multi-scale models. Here, we could investigate modelling techniques to bridge the inherent multi-scale nature of treatment resistance and the generation of clinically relevant virtual populations.</p>

<p>Formal applications for research degree study should be made online through the <a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University's website</a>. Please state clearly in the Planned Course of Study section that you are applying for <em><strong>PHD Applied Mathematics FT</strong></em> and in the research information section that the research degree you wish to be considered for is <em><strong>Mechanistic modelling of treatment resistance in cancer</strong></em> as well as <a href="https://eps.leeds.ac.uk/maths/staff/11895/dr-tyler-cassidy">Dr Tyler Cassidy</a> as your proposed supervisor and in the finance section, please state clearly <em><strong>the funding that you are applying for, if you are self-funding or externally sponsored</strong></em>.</p> <p>If English is not your first language, you must provide evidence that you meet the University's minimum English language requirements (below).</p> <p><em>As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.</em></p> <p class="MsoNoSpacing">Applications will be considered after the closing date.  Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application. We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed.</p> <p style="margin-bottom:11px"><strong>Please note that you must provide the following documents in support of your application by the closing date of Monday 6 January 2025 if applying for the China Scholarship Council-University of Leeds Scholarship, Monday 3 February 2025 if applying for Leeds Doctoral Scholarship or Tuesday 1 April 2025 for Leeds Opportunity Research Scholarship.</strong></p> <p><strong>If you are applying for the School of Mathematics Scholarship 2025/26, or with external sponsorship or you are funding your own study, please ensure you provide your supporting documents at the point you submit your application:</strong></p> <ul> <li>Full Transcripts of all degree study or if in final year of study, full transcripts to date</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul>

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid. Some schools and faculties have a higher requirement.

<p style="margin-bottom:12px"><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p><strong>UK</strong> – The <a href="https://phd.leeds.ac.uk/funding/138-leeds-doctoral-scholarship-2025-faculty-of-engineering-and-physical-sciences#:~:text=Key%20facts&text=One%20Leeds%20Doctoral%20Scholarship%20is,rata%20for%20part%2Dtime%20study.">Leeds Doctoral Scholarship</a> <strong>(closing date: Monday 3 February 2025)</strong>, <a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a><strong> (closing date: Tuesday 1 April 2025) </strong>and <a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship-2025-26">School of Mathematics Scholarship 2025/26</a> <strong>(open from October 2024)</strong> are available to UK applicants.</p> <p>Non-UK – <a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship-2025-26">School of Mathematics Scholarship 2025/26</a> <strong>(open from October 2024)</strong> are available to all International applicants.  The <a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a> <strong>(closing date: Monday 6 January 2025) </strong>is available to nationals of China. The <a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a> is available to support US citizens. <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p>You will be responsible for paying the overtime fee in full in your writing up/overtime year (£320 in Session 2024/25), but the scholarship maintenance allowance will continue to be paid for up to 6 months in the final year of award.</p> <p><strong>Important: </strong>Please note that that the award does <em><strong>not</strong></em> cover the costs associated with moving to the UK.  All such costs (<a href="https://www.leeds.ac.uk/international-visas-immigration/doc/applying-student-visa">visa, Immigration Health Surcharge</a>, flights etc) would have to be met by yourself, or you will need to find an alternative funding source. </p> <p>Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.</p>

<p>For questions about this research project, please contact Dr Tyler Cassidy by email to <a href="mailto:t.cassidy1@leeds.ac.uk">t.cassidy1@leeds.ac.uk</a></p> <p>For further information about your application, please contact PGR Admissions by email to <a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a></p>