An integrated modelling approach for targeted degradation: insights on optimisation, data requirements and PKPD predictions from semi- or fully-mechanistic models and exact steady state solutions
Sofia Guzzetti, Pablo Morentin Gutierrez
AstraZeneca
Objectives:
This work proposes a novel pragmatic modelling approach for targeted protein degradation which captures the essence of the mechanism while retaining model simplicity. Examples of local sensitivity analysis or data fitting with fully mechanistic models are plenty (see, e.g., [1-2]), however understanding of their identifiability is still lacking and conclusions are limited to specific scenarios which may not be representative of the whole range of relevant physiological settings. On the other hand, simplified approaches lack evidence of predictivity [3] or are based on assumptions that may not hold true across biological models and, ultimately, patients [4]. In this context we propose a general integrated modelling approach which leverages benefits while mitigating limitations of each model type: (1) Exact mechanistic steady state solutions can (i) provide insight on each system parameter role regardless of its specific value, (ii) suggest which mechanistic knowledge can be confidently extracted from single time point data, (iii) which additional data needs to be collected, and (iv) ultimately, inform compound optimization, data generation and resource prioritization; (2) Global sensitivity analysis can help identify key drivers of the response. As a result, by incorporating insights from fully mechanistic models into simpler turnover models, the proposed pragmatic modelling approach enables acceleration of drug discovery programs and increased probability of success in the clinic.
Methods:
For monovalent degraders we assume that endogenous protein synthesis and degradation are zero- and first-order processes, respectively. When compound is added, binding kinetics leads to the formation of a binary complex, which induces degradation at a first order rate. For bivalent degraders (e.g. PROTACs), ternary complex formation can happen from a PROTAC-target or PROTAC-ligase binary complex, where the extent of the contribution of each pathway is dictated by binding affinities, PROTAC concentration, and target and E3 ligase levels. Upon degradation of the target protein, PROTAC and E3 ligase are recycled back into the system. The exact solution of each model was calculated with the method illustrated in [5], which applies thoughtful algebraic manipulations to leverage the linear component of the system while segregating the non-linear part to its core, which can then be solved numerically. Global sensitivity analysis of the PROTACs mechanistic model was evaluated using Sobol indices [6] to assess the fraction of total variability associated with each parameter, which is a random variable represented via Polynomial Chaos Expansions [7].
Results:
Exact solutions of monovalent degraders mechanistic models show how on/off binding rates and degradation rates are related to potency and maximal effect, which can be used to suggest a compound optimization strategy. For bivalent degraders, even the structure of convoluted exact steady state solutions suggests that the total remaining target at steady state, which is easily accessible experimentally, is insufficient to reconstruct the state of the whole system at equilibrium and observations on different species such as binary/ternary complexes are necessary. Furthermore, global sensitivity analysis of fully mechanistic models suggests that both target and ligase baselines (actually, their ratio) are the major source of variability in the response of non-cooperative systems, which speaks to the importance of characterizing their distribution in the target patient population. As a result, we propose a pragmatic modelling approach which incorporates the insights generated with fully mechanistic models into simpler turnover models to improve their predictive ability.
Conclusions:
In this work we show the value of an integrated modelling approach for degraders which combines the benefits of traditional turnover models and fully mechanistic models to address two key project questions in drug discovery programs, i.e. (i) how to drive compound optimization and (ii) how to predict pharmacology across line of sight models or the kinetics of in vivo degradation from in vitro data. For bivalent degraders, we suggest pathways to enrich (too) simplistic turnover models just enough to unlock their predictive capacity. The pragmatic approach we proposed here is being applied to PROTAC programs within AstraZeneca.
References:
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[2] Park, D., Izaguirre, J., Coffey, R., Xu, H.: Modeling the effect of cooperativity in ternary complex formation and targeted protein degradation mediated by heterobifunctional degraders. ACS Bio & Med Chem Au (2022)
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[7] Ghanem, R.G., Spanos, P.D.: Spectral techniques for stochastic finite elements. Archives of Computational Methods in Engineering. 1997 Mar 1;4(1):63.