Computational Random Mutagenesis to Investigate RAS Mutant Signaling

Abstract

This chapter will describe how mathematical models can be used to investigate the possible range of behaviors for mutant forms of a protein. A mathematical model of the RAS signaling network that has previously been developed and applied to specific RAS mutants will be adapted for the process of computational random mutagenesis. By using this model to computationally investigate the range of RAS signaling outputs that would be anticipated over a wide range of the relevant parameter space one can gain intuition about the types of behaviors that would be demonstrated by biological RAS mutants.

1. Introduction

Mutations within the RAS genes KRAS, NRAS, and HRAS are among the most common acquired activating mutations that promote cancer [1]. Many different RAS mutant alleles have been observed in human cancer, and the specific alleles observed can vary largely between tumor type [2]. A variety of experiments suggest that there is significant selection for which specific mutations have the potential to promote cancer, and suggest that this selection may vary between genetic and tissue contexts [3,4]. The specific factors that influence which mutant alleles are capable of generating a tumor in a given tissue or genetic background remain undetermined.

A variety of methods have been applied to studying different RAS mutant alleles. Structures of a variety of mutant forms have been solved [5,6]. Biochemical kinetics have been measured for a variety of RAS mutants [6,7]. Isogenic cell lines that include different RAS alleles have helped illuminate cell biological differences [8–12]. Cell line models have also been useful for characterizing, at scale, a wide variety of RAS mutations expressed ectopically [13,14]. Organoids that express different RAS alleles are an important emerging approach, and such organoids have demonstrated the ability to reproduce mutant-allele specific effects including responses to targeted therapies [15]. Mouse models that compare different mutant alleles have also been useful for revealing differences in the ability to promote cancer [15,16]. This chapter will focus on mathematical modeling as an alternative approach that can also enable exploration of the potential behaviors of mutant proteins.

The mathematical model is used to study how the biochemical consequences of a mutation influence biochemical phenotypes. When a protein is mutated, it may have an altered sequence of amino acids and/or altered expression levels. These changes can influence protein-protein interaction kinetics and/or the absolute abundance of the mutated protein. These quantifiable biological properties are also often properties of a mechanistic computational model. With such a model, computational exploration of how the model outputs change in response to parameter variation may be able to give insight into the behaviors that would be realized in an actual biological experiment (Note 1).

2. Materials

2.1. RAS model

Just as one would need to determine which mouse model or cell line model they would like to use for a specific experimental study, one must also determine which computational model to use for a theoretical study. As with experimental studies, one could either utilize an existing model system or one could generate a new model system. For the demonstration of this method, we will use an existing model of the RAS signaling network [17–19] (Note 2). This model has proven useful for investigating a variety of problems involving RAS signaling, and this model has made a variety of prospective predictions about pathogenic RAS mutants that were non-obvious and were then experimentally observed [17,20,21,11,12]. The model is limited to RAS (separate pools of WT and mutant RAS), GAPs, GEFs, and effectors.

This RAS model used was developed at the same “resolution” as available biochemical characterizations of RAS proteins and their mutant forms. In other words, the parameters of the model are the same biochemical rate constants and enzymatic parameters that biochemists and biophysicists had measured for RAS GTPases. For example, GAP activity on RAS is modeled with Michaelis-Menten kinetics because experimentalists often measure and provide K_m and k_cat values. WT RAS and mutant RAS proteins can have different values for these rate constants because a reaction may proceed faster (or slower) for a mutant relative to the reaction speed for WT RAS. The outputs of the model are quantities like total RAS-GTP and total RAS-GTP-Effector complex, which generally and intuitively correspond to signaling outputs. The RAS model used here, and that we have used most commonly in the literature, has one pool of WT RAS, one pool of mutant RAS, and a single pool of each of GAP, GEF, and effector species.

2.2. Parameter variation plan for computational random mutagenesis

Computational models generally have many different parameters. To perform a computational random mutagenesis, one must first determine which parameters are likely to vary with mutation (Note 3). The RAS model being used in this example is limited to the reactions that directly regulate RAS. The model is subdivided into wild-type and mutant RAS pools (Note 4). In this demonstration of a computational random mutagenesis, we will vary all parameters that involve modeled reactions that involve of the mutant RAS. In this way, we will be attempting to explore the full range of behaviors that RAS mutants could potentially exhibit (Note 5). For this demonstration, we will vary all parameters simultaneously. We will specify the values of each mutant parameter as a multiple of the wild-type parameter, where the scalar multiplying the wild-type parameter is a random number chosen from a log-normal distribution (Note 6).

In addition to the parameters of the model that vary for the computational random mutagenesis, it should be predetermined whether there are other parameters that need to vary as part of the computational experiment. For example, in a previous study we used computational random mutagenesis to evaluate the possible behaviors of RAS mutants when they occur in a cell with the full amount of GAP activity, and when they occur in a cell where the activity of a RAS GAP like NF1 has been lost to mutation [20]. This computational study involved us performing computational random mutagenesis on our baseline RAS model and on our baseline model with 50% of baseline GAP activity reduced to model the NF1/GAP impaired state. In another study, we evaluated the predicted drug-dose responses of cells containing computational random mutagenesis generated RAS mutants [12]. In this more complicated computational experiment, we generated computational random mutants, filtered out only the mutants that were within a range of activation similar to the common oncogenic RAS mutants, and then we used the model to find predicted levels of RAS-GTP for different levels of pathway activation.

2.3. Software to implement the model and hardware for simulations

MATLAB software was used to develop and simulate the RAS model. Previous versions of the RAS model can be downloaded as part of previous publications [22,12]. Implementation of the computational random mutagenesis can be implemented in MATLAB, as can data analysis. Simulations and analysis can be performed on a common laptop computer. Alternatively, one could code the same model into another programming language by utilizing the previously published supplemental methods and available code as references [17,20,22,11,12].

3. Methods

• 3.1Specify the parameters that will vary as part of the computational random mutagenesis.
• 3.2Specify the random number distribution. In our previous work we used a log-normal distribution [20].
• 3.3Generate the random parameters. In our previous instantiation, we generated a set of random numbers, where each random number in the vector of parameters for an individual computational random mutant was from a log-normal distribution.
• 3.4Generate the mutant parameters. For each computational random mutant, multiply the WT parameter value by the next random numbers to obtain the computational random mutant.
• 3.5Computationally find the output behavior of interest. We used steady-state levels of total RAS-GTP-effector complex as our metric of the signal strength that results from the computational mutant (Note 7).
• 3.7Plot results and evaluate the distribution of results.

4. Notes

Note 1. Whether the model gives good insights for the problem will depend on the quality of the model. Although modeling biochemical networks has been an active area of research for approximately two decades, detailed studies of pathogenic mutations with these models has received much less attention. The best practices for modeling pathogenic mutations remain to be determined.

Note 2. There are other available models of approximately similar scope and detail, and that have been applied to the study of pathogenic mutants [23–27]. A comparison and contrast of some of these models and their application to modeling pathogenic mutants has previously been published [28]. Just as one should be well-versed in the pros and cons of an experimental system, one should be well-versed in the pros and cons of the chosen computational model. For example, it is important to consider whether the question one is asking of a model is likely to be influenced by the simplifications of the model.

Note 3. In a large pathway model, it will only be a subset of parameters that vary with mutation. However, in a large pathway model each protein in the network may be modeled very simply and there may therefore be very few parameters that involve the mutated protein. In this case, the computational random mutagenesis is less likely to be informative with respect to the actual biological range of behaviors.

Note 4. There will not already be separate pools of wild-type and mutant protein in most currently available computational models. In that case, one may model all of the protein as mutated, or one may develop a derivative version of the model that includes wild-type and mutant pools of protein.

Note 5. One could envision a focused computational random mutagenesis, where mutations within one are of the protein are the focus, and where biophysical evidence suggests that the mutation would only disrupt specific protein-protein interactions and/or specific biochemical reactions. In such a situation, the computational random mutagenesis might focus on those parameters only and assume the mutations do not have any long-range interactions that influence other reactions of this protein.

Note 6. One could perform computational random mutagenesis in a variety of ways. One might only sample small changes from baseline parameters (+/− 10%) or one might use larger changes (multiple orders of magnitude). Experimenters may search local mutation space (DNA and peptide sequence mutation searches that look at only single substitutions) and they may search large mutation space (all n-mers). Just as the experimental approaches may offer different benefits, so, too, may different computational random mutagenesis schemes.

Note 7. RAS-GTP-effector may be the better measure of RAS activation than RAS-GTP when performing a computational random mutagenesis for RAS. This is because mutants that bind poorly to effectors, but are GAP insensitive, could result in high levels of RAS-GTP but still result in low levels of the RAS-GTP-effector complex and signal poorly.