Taming Complex Quantitative Systems Pharmacology Models with Model Reduction

Taming Complex Quantitative Systems Pharmacology Models with Model Reduction

Quantitative systems pharmacology (QSP) combines computational modeling and experimental data to examine the relationships between a drug, the biological system, and the disease process. This emerging discipline integrates quantitative drug data with knowledge of its mechanism of action. QSP models predict how drugs modify cellular networks in space and time and how they impact and are impacted by human pathophysiology. Additionally, QSP facilitates evaluating complex, heterogeneous diseases such as cancer, immunological, metabolic, and central nervous system diseases that probably will require combination therapies to fully control them.

As with any approach, QSP has its challenges:

  • Parameterization of very large models
  • Model validation and parameter identifiability in the context of limited data
  • Knowing where to draw the line on what to include in a complex model in terms of target scale dynamics and what not to include

All of these challenges have their roots in model complexity. In this blog post, I’ll discuss why QSP models are so complex and explain why model reduction can help address this challenge.

What do we mean by model complexity?

By seeking to describe target scale dynamics systemically, QSP grapples with the issue of model complexity. Quoting Ribba and coworkers in a recent CPT: Pharmacometrics & Systems Pharmacology paper,

“In the design of QSP models, finding the right granularity is notoriously difficult. Granularity is the level of detail in which biological and pharmacological processes are represented and is associated with higher expected predictive power. But granularity comes with a cost, which is the difficulty of building, running, communicating, and maintaining a model with a vast number of components and parameters which—for the purpose of this discussion—will be summarized as complexity. One particular aspect of this complexity is the difficulty in parameter estimation, potentially resulting in large uncertainty in parameter estimates.”

QSP models are complex for four major reasons:

  • The high dimensionality of modeled species, reactions and complexes in these models
  • The high degree of nonlinearity, including both positive and negative feedback loops commonly connecting components of such models
  • The common use of complex mathematical expressions to describe specific phenomena such as oscillatory behavior in these models
  • Finally, common properties of a high degree of model stiffness and sensitivity of particular components of the model

Issues with complexity

Taken in combination, these model properties make it difficult to predict how perturbations to one part of the model will ripple throughout the entire network, and this complexity causes difficulty in traditional modeling approaches in several ways.

Firstly, the “curse of dimensionality” is a phenomenon wherein as the number of features, variables, or dimensions grows, the data becomes sparse relative to the volume of the model’s state-space. Thus, traditional applications of data in modeling—model identification, validation, etc.—will often become untenable with such high dimensional models.

Secondly, structural identifiability. Due to the complex model structure and limited endpoint data, the model can become unidentifiable. This means that it can be impossible, even assuming the capture of infinite data, to identify the parameters of the system we’re studying. Additionally, in terms of computational speed, very complex systems can result in unacceptably long model runtimes due to both the stiffness and the dimensionality of the system.

Finally, complex systems can simply be unintuitive in terms of their model structures. Thus, identifying and understanding which parts of molecular pathways are critical to the physiological mechanisms of interest can be difficult in complex models.

Methods of model reduction as an approach to alleviate complexity

Other fields, such as engineering or computational physics, have used model reduction methods to address the problem of model complexity. While these methods are relatively well established in other fields, they have only recently been employed in the field of systems pharmacology.

The goal of model reduction is to create a reduced system that reproduces the behavior of the original model, within some reasonable error, whilst reducing the number of species, reactions, or complexes represented in the network.

To learn more about how model reduction can help you get more out of your models, please watch a webinar I gave on this topic.

Tom Snowden

About the Author

Tom Snowden

Research Scientist, Certara

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Tom Snowden received his PhD in applied mathematics and quantitative systems pharmacology from the University of Reading in 2015. He was then awarded and completed an EPSRC doctoral prize fellowship at the university, continuing his research at the interface of mathematics and pharmacology. In October 2016, Tom joined Certara QSP as a research scientist working on a range of QSP consultancy projects.