Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins. To faithfully capture this combinatorial process in a mathematical model is an important challenge in systems biology. Exploiting the limited context on which most binding and modification events are conditioned, attempts have been made to reduce the combinatorial complexity by quotienting the reachable set of molecular species into species aggregates while preserving the deterministic semantics of the thermodynamic limit. Recently,  proposed a quotienting that also preserves the stochastic semantics and that is complete in the sense that the semantics of individual species can be recovered from the aggregate semantics. ,  prove that this quotienting yields a sufficient condition for ak lumpability (that is to say that the quotient system is still Markovian for a given set of initial distributions) and that it gives rise to a backward Markov bisimulation beten the original and aggregated transition system (which means that the conditional probability of being in a given state in the original system knowing that  are in its equivalence class is an invariant of the system).  illustrate the framework on a case study of the epidermal growth factor (EGF)/insulin receptor crosstalk.
['Jérôme Feret', 'Thomas A. Henzinger', 'Heinz Koeppl', 'Tatjana Petrov']
I am writing a research paper on a idea Lumpability abstractions of rule-based systems
[{"from": "human", "value": "I am writing a research paper on a idea Lumpability abstractions of rule-based systems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins. To faithfully capture this combinatorial process in a mathematical model is an important challenge in systems biology. Exploiting the limited context on which most binding and modification events are conditioned, attempts have been made to reduce the combinatorial complexity by quotienting the reachable set of molecular species into species aggregates while preserving the deterministic semantics of the thermodynamic limit. Recently,  proposed a quotienting that also preserves the stochastic semantics and that is complete in the sense that the semantics of individual species can be recovered from the aggregate semantics. ,  prove that this quotienting yields a sufficient condition for ak lumpability (that is to say that the quotient system is still Markovian for a given set of initial distributions) and that it gives rise to a backward Markov bisimulation beten the original and aggregated transition system (which means that the conditional probability of being in a given state in the original system knowing that  are in its equivalence class is an invariant of the system).  illustrate the framework on a case study of the epidermal growth factor (EGF)/insulin receptor crosstalk."}]