Developing efficient computational methods to change the state of a cell from an undesirable condition, e.g. diseased, into a desirable, e.g. healthy, condition is an important goal of systems biology. The identification of potential interventions can be achieved through mathematical modeling of the state of a cell by finding appropriate input manipulations in the model that represent external interventions. This paper focuses on quantifying the unwanted or unplanned changes that come along with the application of an intervention to produce a desired effect , which we define as the side effects of the intervention. The type of mathematical models that we will consider are discrete dynamical systems which include the widely used Boolean networks and their generalizations. The potential control targets can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system. This paper presents practical tools along with applications for the analysis and control of multistate networks. The first result is a polynomial normal form representation for discrete functionsthat provides a partition of the inputs of the function into canalizing and non-canalizing variables and, within the canalizing ones, we categorize the input variables into layers of canalization. The second theoretical result is a set of formulas for counting the maximum number of transitions that will change in the state space upon an edge deletion in the wiring diagram. These formulas rely on the stratification of the inputs of the target function where the number of changed transitions depends on the layer of canalization that includes the input to be deleted. Applications from using these formulas to estimate the number of changes in the state space and comparisons with the actual number of changes are also presented .
Developing efficient computational methods to change the state of a cell from an undesirable condition, e.g. diseased, into a desirable, e.g. healthy, condition is an important goal of systems biology. The identification of potential interventions can be achieved through mathematical modeling of the state of a cell by finding appropriate input manipulations in the model that represent external interventions. This paper focuses on quantifying the unwanted or unplanned changes that come along with the application of an intervention , which we define as the total effect of the intervention. The type of mathematical models that we will consider are discrete dynamical systems which include the widely used Boolean networks and their generalizations. The potential control targets can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system. Regulatory rules that appear in published models tend to have special features such as the property of being nested canalizing, a concept inspired by the concept of canalization in evolutionary biology. We provide a polynomial normal form based on the canalizing properties of regulatory functions. This polynomial normal form provides a partition of the inputs of the function into canalizing and non-canalizing variables and, within the canalizing ones, we categorize the input variables into layers of canalization. Using this polynomial normal form, we provide a set of formulas for counting the maximum number of transitions that will change in the state space upon an edge deletion in the wiring diagram. These formulas rely on the canalizing structure of the target function where the number of changed transitions depends on the canalizing layer that includes the input to be deleted. We applied our methods to two published models to compare the accuracy of the upper bounds and shown that the bounds are sharp .
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to produce a desired effect
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side effects
total effect
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This paper presents practical tools along with applications for the analysis and control of multistate networks. The first result is
Regulatory rules that appear in published models tend to have special features such as the property of being nested canalizing, a concept inspired by the concept of canalization in evolutionary biology. We provide
R
representation for discrete functionsthat
based on the canalizing properties of regulatory functions. This polynomial normal form
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The second theoretical result is
Using this polynomial normal form, we provide
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stratification of the inputs of the
canalizing structure of the
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layer of canalization
canalizing layer
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Applications from using these formulas to estimate the number of changes in the state space and comparisons with the actual number of changes are also presented
We applied our methods to two published models to compare the accuracy of the upper bounds and shown that the bounds are sharp