A Stochastic Binary Model for the Regulation of Gene Expression to Investigate Responses to Gene Therapy

Abstract

Simple Summary Gene editing technologies reached a turning point toward epigenetic modulation for cancer treatment. Gene networks are complex systems composed of multiple non-trivially coupled elements capable of reliably processing dynamical information from the environment despite unavoidable randomness. However, this functionality is lost when the cells are in a diseased state. Hence, gene-editing-based therapeutic design can be viewed as a gene network dynamics modulation toward a healthy state. Enhancement of this control relies on mathematical models capable of effectively describing the regulation of stochastic gene expression. We use a two-state stochastic model for gene expression to investigate treatment response with a switching target gene. We show the necessity of modulating multiple gene-expression-related processes to reach a heterogeneity-reduced specific response using epigenetic-targeting cancer treatment designs. Our approach can be used as an additional tool for developing epigenetic-targeting treatments. In this manuscript, we use an exactly solvable stochastic binary model for the regulation of gene expression to analyze the dynamics of response to a treatment aiming to modulate the number of transcripts of a master regulatory switching gene. The challenge is to combine multiple processes with different time scales to control the treatment response by a switching gene in an unavoidable noisy environment. To establish biologically relevant timescales for the parameters of the model, we select the RKIP gene and two non-specific drugs already known for changing RKIP levels in cancer cells. We demonstrate the usefulness of our method simulating three treatment scenarios aiming to reestablish RKIP gene expression dynamics toward a pre-cancerous state: (1) to increase the promoter's ON state duration; (2) to increase the mRNAs' synthesis rate; and (3) to increase both rates. We show that the pre-treatment kinetic rates of ON and OFF promoter switching speeds and mRNA synthesis and degradation will affect the heterogeneity and time for treatment response. Hence, we present a strategy for reaching increased average mRNA levels with diminished heterogeneity while reducing drug dosage by simultaneously targeting multiple kinetic rates that effectively represent the chemical processes underlying the regulation of gene expression. The decrease in heterogeneity of treatment response by a target gene helps to lower the chances of emergence of resistance. Our approach may be useful for inferring kinetic constants related to the expression of antimetastatic genes or oncogenes and for the design of multi-drug therapeutic strategies targeting the processes underpinning the expression of master regulatory genes.