Differential methods for assessing sensitivity in biological models

Abstract

Differential sensitivity analysis is indispensable in fitting parameters, understanding uncertainty, and forecasting the results of both thought and lab experiments. Although there are many methods currently available for performing differential sensitivity analysis of biological models, it can be difficult to determine which method is best suited for a particular model. In this paper, we explain a variety of differential sensitivity methods and assess their value in some typical biological models. First, we explain the mathematical basis for three numerical methods: adjoint sensitivity analysis, complex perturbation sensitivity analysis, and forward mode sensitivity analysis. We then carry out four instructive case studies. (a) The CARRGO model for tumor-immune interaction highlights the additional information that differential sensitivity analysis provides beyond traditional naive sensitivity methods, (b) the deterministic SIR model demonstrates the value of using second-order sensitivity in refining model predictions, (c) the stochastic SIR model shows how differential sensitivity can be attacked in stochastic modeling, and (d) a discrete birth-death-migration model illustrates how the complex perturbation method of differential sensitivity can be generalized to a broader range of biological models. Finally, we compare the speed, accuracy, and ease of use of these methods. We find that forward mode automatic differentiation has the quickest computational time, while the complex perturbation method is the simplest to implement and the most generalizable.

Automatic differentiation and the optimization of differential equation models in biology

“…Many aspects of model interpretation depend on sensitivity (Mester et al, 2022). How much do model predictions change with a change in a parameter?…”

“…Because sensitivity often means the change in performance with respect to a change in parameters, one often evaluates sensitivity by the derivative of performance with respect to parameters. For models with many parameters, automatic differentiation provides computational benefits (Mester et al, 2022). In evolutionary analyses, the performance surface that defines sensitivity is the adaptive or fitness landscape (Stadler, 2002;Malan, 2021).…”

“…Slopes and curvatures calculated by differentiation also provide the basis for enhanced sensitivity analysis (Mester et al, 2022). In biology, sensitivity plays a key role in understanding robustness, variability, and evolutionary dynamics.…”

From Data to Knowledge: A Mini-Review on Molecular Network Modeling and Analysis for Therapeutic Target Discovery

“…For this purpose, regardless of the model type, a common analysis approach is to induce in silico mutations or molecular dysfunctionalities in the network and then compute the network response deviation from the normal response. Different forms of this approach are developed in different frameworks such as fault diagnosis or vulnerability analysis [39], and sensitivity analysis [74,75]. Fault diagnosis is a platform for finding selective targets by using computational and systems biology techniques that have been developed and optimized over the years [38][39][40][41].…”

Optimal Design of Galvanic Vestibular Stimulation for Patients with Vestibulopathy and Cerebellar Disorders

“…In addition, using a sensitivity analysis (SA) approach, the identification of key design parameters is implemented in design optimization [ 30 ]. SA is a system identification process that is carried out to construct a mathematical model based on input–output data measured in the real system, with steps including model structure selection, design of experiments, data collection, parameter optimization, and model validation [ 31 , 32 ].…”