The setup of the model is for a generic gene encoding organelle machinery. The gene may be encoded in the organelle, or in the nucleus of the cell, in which case it must be transported to the organelle through the cytosol. We assume that there is no systematic difference in the intrinsic properties of this representative gene between the two possible encoding compartments, neglecting, for example, differences in genetic code that may be required for the different locations [7 (link)]. Working at a coarse-grained level, we will use this general picture to describe both mitochondria and plastids. The model has two dynamic variables: xm(t) is the available amount of functional gene product in the organelle at time t (for example, the various protein subunits of electron transport chain complexes) and xc(t) is the available amount of gene product in the cytosol at time t.
The parameters of the model for the cellular processes include the following non-negative constant rates: λ is the baseline synthesis rate of gene product (which will be scaled by the cell’s response to the environment, see below), D is the import or transport rate of gene product from the cytosol to the organelle, νm, νc are the degradation rates of gene product in the organelle and in the cytosol, respectively. We also include a parameter p, the proportion of wild-type oDNA which allows the synthesis of functional gene product in the organelle. This parameter is required to capture the potential for oDNA damage, which occurs on longer (evolutionary) time scales than the cell biological processes above. Instead of modelling both gene expression and mutation time scales explicitly, which would require a rather more involved simulation setup, we coarse-grain the effect of mutation into this expected oDNA damage load which stays constant over a cell lifetime. This damage can be pictured as arising from mutation in the history of the lineage of the cell; the purpose of our study here is to characterize the balance between this potential accumulation of oDNA damage and the selective pressure favouring oDNA encoding. Lower p corresponds to more oDNA damage, compromising the expression of functional organelle machinery; p = 1 corresponds to perfect oDNA and hence the maximum possible expression capacity. The propensity for oDNA damage in an organism, both within a lifetime and across generations, will act to reduce p. The cell processes and properties described by these parameters are illustrated infigure 1 a.
The parameters D and νc describe the ability of a nuclear-encoded gene product to translocate to its required position in the organelle. These can be used to model different mechanisms proposed for the hydrophobicity hypothesis. One mechanism is that hydrophobic gene products cannot readily be unpacked to import into the organelle [1 (link),22 (link)], corresponding to a high value of the degradation rate in the cytosol νc, as the gene product is merely lost and hence can be considered as degraded. Another mechanism is that the gene product is mistargeted, usually to the endoplasmic reticulum [17 (link),23 (link)], so that the import to the organelle takes a much longer time: corresponding to a low value of the transport rate D.
The parameters of the model for the cellular processes include the following non-negative constant rates: λ is the baseline synthesis rate of gene product (which will be scaled by the cell’s response to the environment, see below), D is the import or transport rate of gene product from the cytosol to the organelle, νm, νc are the degradation rates of gene product in the organelle and in the cytosol, respectively. We also include a parameter p, the proportion of wild-type oDNA which allows the synthesis of functional gene product in the organelle. This parameter is required to capture the potential for oDNA damage, which occurs on longer (evolutionary) time scales than the cell biological processes above. Instead of modelling both gene expression and mutation time scales explicitly, which would require a rather more involved simulation setup, we coarse-grain the effect of mutation into this expected oDNA damage load which stays constant over a cell lifetime. This damage can be pictured as arising from mutation in the history of the lineage of the cell; the purpose of our study here is to characterize the balance between this potential accumulation of oDNA damage and the selective pressure favouring oDNA encoding. Lower p corresponds to more oDNA damage, compromising the expression of functional organelle machinery; p = 1 corresponds to perfect oDNA and hence the maximum possible expression capacity. The propensity for oDNA damage in an organism, both within a lifetime and across generations, will act to reduce p. The cell processes and properties described by these parameters are illustrated in
The parameters D and νc describe the ability of a nuclear-encoded gene product to translocate to its required position in the organelle. These can be used to model different mechanisms proposed for the hydrophobicity hypothesis. One mechanism is that hydrophobic gene products cannot readily be unpacked to import into the organelle [1 (link),22 (link)], corresponding to a high value of the degradation rate in the cytosol νc, as the gene product is merely lost and hence can be considered as degraded. Another mechanism is that the gene product is mistargeted, usually to the endoplasmic reticulum [17 (link),23 (link)], so that the import to the organelle takes a much longer time: corresponding to a low value of the transport rate D.
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