Logic-based models are predictive tools that can be leveraged in the absence of reliable parameter information or mechanistic details needed for more quantitatively precise methods, such as ODE models. Importantly, the predictive power of logic methods is dependent on the nature of the logic network model constructed. In this review, we have pointed out important factors to consider when building predictive logic-based models. We have emphasized the importance of using descriptive logic network diagrams and provided biologically motivated example networks. Most significantly, we have emphasized the need to properly characterize the nature of all interactions in the network and to understand the implicit meaning of logic functions used to integrate multiple input signals.
As we have seen, the use of AND
logical operators produce very different results for the same input conditions (, and ). We strongly encourage the creation of truth tables to verify that the output of each logic function is reasonable and in qualitative agreement with experimental data, if available. When the nature of the interaction modelled by a logic function is not known (e.g.
, whether an activator will trump an inhibitor, if both are active, or vice versa
), then the logic model can be used to test hypothesized mechanisms for the uncertain interaction. The use of “incomplete truth tables”, a computational approach for analysing the effect of logical uncertainty in a logic network, has also been proposed for these cases.72
Despite their advantages, resistance to the use of logic-based models in biology exists. Some resistance is related to the idea that a molecule’s state can be reduced to discrete ON
values. In actuality, experimental molecular states are often qualitatively described in binary terms. Genes may be characterized as up-regulated or down-regulated in microarray experiments and proteins are often referred to as activated or inactivated to indicate their functional state. Given the stochastic variation in gene and protein expression across cells, biological molecular networks are remarkably robust.73
The presence of growth factors in the local environment, for example, will almost invariably result in the induction of proliferative pathways within a population of cells, despite the heterogeneity in the molecular expression across individual cells in the population. This deterministic output from a given cellular input has been compared to cellular digital computation.74
Fundamentally, the basis of digital readouts are 0’s and 1’s–at least at the computational level. Another point of concern with logic-based Boolean models is that time is unrelated to physiological time and can provide only a qualitative chronology of molecular activations.3
While this is true, Boolean models can provide qualitative predictive values, which allow biomedical scientists to gain unique insights into molecular network dynamics that may otherwise be out of reach.
For those interested in using logic models to study large networks, the use of asynchronous updating is generally recommended.2,45
A variety of algorithms exist for introducing asynchronous updates in a logic model.45
For most purposes, the repeated random order asynchronous45
update method (which is similar to a statistical Monte Carlo simulation) will be sufficient. This is the algorithm used for the asynchronous simulations in this review. Some attractors found with the simpler synchronous updating scheme may be artifacts of uniform timescales. In contrast, an asynchronous scheme introduces stochastic variation in timescales. Moreover, asynchronous methods can produce qualitative readouts that are more representative of biological readouts ( and ) and can easily facilitate in silico
perturbations, such as knock downs and constitutive activations.
We view logic models as complementary to other network analysis methods in systems biology and consider them to be an important tool for making biological inferences about the dynamics of intracellular networks. A number of software tools for logic-based network analysis are available.12,43,72,75
The appropriate software tool to use will depend on the nature of the network model and objectives of the analysis.7
For asynchronous simulations and in silico
molecular perturbation studies, we recommend Boolean Net, 12
which is a relatively easy to use open source tool developed in Python. Needless to say, the implementation of logic-based models requires computational and mathematical proficiency. As a consequence, collaboration between integrative biologists and computational scientists will play a pivotal role in the successful development, analysis, and interpretation of logic-based models.
Importantly, logic-based models are also a powerful approach for constructing models of biological networks that can ultimately be integrated into multiscale models–models that consider the integration between different scales and phenomena in a biological system or process–to provide an integrative view of biological systems.76
In the literature, multiscale models of cancer growth have been developed that account for the cellular, genetic, and environmental factors regulating tumour growth.54,77
These models have implemented genetic and signalling networks as Boolean models to regulate cell cycle progression where the response to signals from the intracellular gene network determines whether a cell will proliferate or die and, therefore, directly influences the cellular and the extracellular tissue level of the model.
In conclusion, it is never feasible to create a model that is an exact replica of a complex system and, as a consequence, compromises must be made between the predictive power of a model and the complexity of a model. The discrete nature of a Boolean model sacrifices quantitative dynamics for qualitative dynamics. In exchange, a parameter-free modelling framework can be used to investigate complex intracellular networks.