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 .
Developing efficient computational methods to assess the impact of external interventions on the dynamics of a network model is an important problem in systems biology. This paper focuses on quantifying the global changes that result from the application of an intervention to produce a desired effect , 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 interventions can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system. We use a class of regulatory rules called nested canalizing functions that frequently appear in published models and were inspired by the concept of canalization in evolutionary biology. In this paper, we provide a polynomial normal form based on the canalizing properties of regulatory functions. Using this polynomial normal form, we give 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 since the number of changed transitions depends on the canalizing layer that includes the input to be deleted. We also present computations on random networks to compare the exact number of changes with the upper bounds provided by our formulas. Finally, we provide statistics on the sharpness of these upper bounds in random networks .
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change the state of a cell from an undesirable condition, e.g. diseased, into a desirable, e.g. healthy, condition
assess the impact of external interventions on the dynamics of a network model
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goal of
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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.
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unwanted or unplanned changes that come along with
global changes that result from
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to produce a desired effect
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total effect
total effect
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control targets
interventions
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Regulatory rules that
We use a class of regulatory rules called nested canalizing functions that frequently
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tend to have special features such as the property of being nested canalizing, a concept
and were
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In this paper, we
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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.
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provide
give
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where
since
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applied our methods to two published models to compare the accuracy of
also present computations on random networks to compare
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exact number of changes with the
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and shown that the bounds are sharp
provided by our formulas. Finally, we provide statistics on the sharpness of these upper bounds in random networks