Based on current understanding of a biological system, bioengineers predict how the system will respond to designed perturbations. One important manifestation of this process is predicting whether exposing a patient to a drug with a pre-defined target will result in a favorable clinical outcome. This approach works well when few relevant components of the system are considered. However, it is more difficult to propagate possible effects through a complex system using intuition alone, which hinders the capability for reliable prediction.
To aid intuition, a broad spectrum of mathematical and computational models have been developed [1
]. For example, “theory-driven” differential equations (DEs) based on physico-chemical mechanisms have been used to model and make predictions in biological systems ranging from virus population dynamics in a host organism [3
] to receptor trafficking through cellular compartments [4
] to enzymatic phosphorylation cascades [5
]; at the other end of the spectrum, “data-driven” algebraic and statistical algorithms have been used to understand the integrated influence of multiple signaling pathways on cell phenotypic outcomes [6
]. While these approaches have proven useful in biological and pharmaceutical contexts, their ability to make reliable predictions depends heavily on a large amount of appropriate experimental data for determining relationships, topologies, and parameter values. This critical dependence creates a high barrier-to-entry for using mathematical models to guide scientific decisions on a day-to-day basis. Furthermore, using these methods to describe relationships between different biological scales, such as the exchange of a molecule from tissues to individual cells and subsequent molecular interactions within the cell, is a significant challenge and an active area of research [8
Logic-based models are an attractive alternative because they are readily derivable from either a theory-driven or data-driven foundation [11
] and have been successfully used to predict the response of a biological system to perturbation (e.g., [12
]). In discrete (e.g., Boolean) logic models, all species are found categorically in one of a few levels of activity. However, this description is often too simple to adequately describe biological systems, and feedback in these models can result in oscillations which convolute interpretation of their results. Recently, some have proposed transforming discrete logic models into either ordinary or piecewise linear differential equations [14
]. While some software tools for building and simulating models of these types exist (reviewed in [11
]), changes to parameters of such models affect the differential equations governing each species, and it is not immediately evident how such changes affect the quantitative relationships among the species in the system. Moreover, use of these tools to determine the effect of perturbations to species or parameters requires familiarity with the particular software and is not straightforward.
To alleviate these difficulties, we present a new analysis framework for asking questions of logic-based models, which we term “querying quantitative logic models” (Q2LM). We use the constrained fuzzy logic (cFL) formalism recently developed for training a logic model to data [17
], but here demonstrate the ability to make predictions with models based solely on prior knowledge of the biological system. Additionally, we introduce a simulation procedure that is able to solve for the steady state of a system even when feedback results in oscillatory behavior. This logic formalism allows species in a biological system to be modeled with a continuous range between zero and one using mathematical functions that directly relate input and output species (transfer functions). Importantly, the Q2LM approach facilitates querying these models for efficient prediction of the behavior of biological systems in response to perturbation. Q2LM is a MATLAB toolbox freely available at http://sites.google.com/site/saezrodriguez/software.
Because we use a simple logic-based framework, Q2LM is flexible enough to concomitantly incorporate multiple scales of biology-from molecular species to whole organisms. We illustrate the use of Q2LM to build and query a logic model with a simple example intracellular signaling model. Subsequently, we investigate a logic model of multiscale pharmacokinetics and pharmacodynamics (PK/PD) of granulocyte colony stimulating factor (G-CSF) with the objective of predicting the molecular-level alterations that would best stimulate maturation of precursor neutrophils.