Able with an associated probability distribution. The probability distribution used in this work is either the exponential distribution or Gaussian distribution. Thus a memory reaction has a corresponding non-memory reaction in the non-memory time period. However, certain non-memory reactions such as 1326631 (Eq. 2) may not be capable of Title Loaded From File firing during the memory time period. To realize the firing capacity of different types of reactions, we introduced memory species that exist only in the memory time period. A chemical species is a normal species (Sj ) during the nonmemory time period and may be a memory species M(Sj ) in the memory time period. For a memory reaction, at least one reactant and one product should be memory species; however, it is not necessary to define all species involving in a memory reaction as memory species. For example, the memory reaction for TF binding to the promoter site is represented by Memory reaction : M(DNA)zTFkM(DNA-TF), ??Methods Chemical memory reactionThis work first proposed a novel theory to model biological systems with chemical memory reactions. Chemical reactions in the system are classified into (non-memory) reactions and memory reactions; and each category contains elementary reactions and delayed reactions. Defined as chemical reaction firing in the path of a molecular memory event, memory reaction may occur during particular time-periods and/or under specific system conditions. An example of the memory events is the refractory time period during which an organ or cell is incapable of repeating a particular action. In gene expression, one of the refractory states is the chromatin epigenetic process, such as silencing by DNA methylation and structural changes in chromatin [39,40]. Since silencing molecules are recruited by an autocatalytic mechanism, this can lead to a long periods of reactivation, as exemplified by the ON/ OFF switching in the epigenetic silencing by Sir3 [41] and a refractory period of transcriptional inactivation close to 3 h in mammalians [42]. During the time period of transcriptional activation, both the transcriptional factor (TF) and RNA polymerase (RNAP) can bind to the corresponding promoter site, which has been modeled by the following elementary reactionswhere M(DNA) and M(DNA-TF) are memory species of DNA and DNA-TF, respectively. Thus the propensity functions of both memory reactions and non-memory reactions can be calculated simultaneously. Like the non-memory reaction, the memory reaction is also subject to stochastically distributed times between reaction instances. The time between reaction instances of both non-memory reaction and memory reaction can be determined in the same framework of the SSA. Memory reactions normally are able to fire after a specific reaction occurs (e.g. the disassociation of RNAP from the promoter sites after the Title Loaded From File synthesis of the first transcript in a transcription cycle). This specific reaction is called the trigger reaction and its firing represents the start of a memory time period. Note that one trigger reaction may lead to two or more memory reaction time periods. When a trigger reaction fires, the finishing time points of the memory time periods are determined. The index of the memory reaction and finishing time point are stored in a 12926553 queue structure that also saves the index and manifesting time point of delayed reactions. A key issue in describing memory reaction is the transition between memory and non-memory species at the beginning.Able with an associated probability distribution. The probability distribution used in this work is either the exponential distribution or Gaussian distribution. Thus a memory reaction has a corresponding non-memory reaction in the non-memory time period. However, certain non-memory reactions such as 1326631 (Eq. 2) may not be capable of firing during the memory time period. To realize the firing capacity of different types of reactions, we introduced memory species that exist only in the memory time period. A chemical species is a normal species (Sj ) during the nonmemory time period and may be a memory species M(Sj ) in the memory time period. For a memory reaction, at least one reactant and one product should be memory species; however, it is not necessary to define all species involving in a memory reaction as memory species. For example, the memory reaction for TF binding to the promoter site is represented by Memory reaction : M(DNA)zTFkM(DNA-TF), ??Methods Chemical memory reactionThis work first proposed a novel theory to model biological systems with chemical memory reactions. Chemical reactions in the system are classified into (non-memory) reactions and memory reactions; and each category contains elementary reactions and delayed reactions. Defined as chemical reaction firing in the path of a molecular memory event, memory reaction may occur during particular time-periods and/or under specific system conditions. An example of the memory events is the refractory time period during which an organ or cell is incapable of repeating a particular action. In gene expression, one of the refractory states is the chromatin epigenetic process, such as silencing by DNA methylation and structural changes in chromatin [39,40]. Since silencing molecules are recruited by an autocatalytic mechanism, this can lead to a long periods of reactivation, as exemplified by the ON/ OFF switching in the epigenetic silencing by Sir3 [41] and a refractory period of transcriptional inactivation close to 3 h in mammalians [42]. During the time period of transcriptional activation, both the transcriptional factor (TF) and RNA polymerase (RNAP) can bind to the corresponding promoter site, which has been modeled by the following elementary reactionswhere M(DNA) and M(DNA-TF) are memory species of DNA and DNA-TF, respectively. Thus the propensity functions of both memory reactions and non-memory reactions can be calculated simultaneously. Like the non-memory reaction, the memory reaction is also subject to stochastically distributed times between reaction instances. The time between reaction instances of both non-memory reaction and memory reaction can be determined in the same framework of the SSA. Memory reactions normally are able to fire after a specific reaction occurs (e.g. the disassociation of RNAP from the promoter sites after the synthesis of the first transcript in a transcription cycle). This specific reaction is called the trigger reaction and its firing represents the start of a memory time period. Note that one trigger reaction may lead to two or more memory reaction time periods. When a trigger reaction fires, the finishing time points of the memory time periods are determined. The index of the memory reaction and finishing time point are stored in a 12926553 queue structure that also saves the index and manifesting time point of delayed reactions. A key issue in describing memory reaction is the transition between memory and non-memory species at the beginning.
