A Generalized Michaelis–Menten Equation in Protein Synthesis: Effects of Mis-Charged Cognate tRNA and Mis-Reading of Codon

Dutta, Annwesha; Chowdhury, Debashish

doi:10.1007/s11538-017-0266-5

Cited by 4 publications

(5 citation statements)

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“…Here, V0 is a single vertex corresponding to the unbound enzyme and there are multiple bound enzyme conformations which change or fluctuate along a sequence, from which irreversible transitions can return to the single vertex in V0. Second, they have been used in studies of the ribosome (17)(18)(19), in which the MM formula was found for the average ribosome velocity as a function of aminoacyl tRNA concentration. Here, V0 is a single vertex corresponding to the bare ribosome conformation and tRNA binding gives irreversible outgoing edges from this vertex.…”

Section: Resultsmentioning

confidence: 99%

Structural conditions on complex networks for the Michaelis–Menten input–output response

Wong

Dutta

Chowdhury

et al. 2018

Proc. Natl. Acad. Sci. U.S.A.

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The Michaelis-Menten (MM) fundamental formula describes how the rate of enzyme catalysis depends on substrate concentration. The familiar hyperbolic relationship was derived by timescale separation for a network of three reactions. The same formula has subsequently been found to describe steady-state input-output responses in many biological contexts, including single-molecule enzyme kinetics, gene regulation, transcription, translation, and force generation. Previous attempts to explain its ubiquity have been limited to networks with regular structure or simplifying parametric assumptions. Here, we exploit the graph-based linear framework for timescale separation to derive general structural conditions under which the MM formula arises. The conditions require a partition of the graph into two parts, akin to a "coarse graining" into the original MM graph, and constraints on where and how the input variable occurs. Other features of the graph, including the numerical values of parameters, can remain arbitrary, thereby explaining the formula's ubiquity. For systems at thermodynamic equilibrium, we derive a necessary and sufficient condition. For systems away from thermodynamic equilibrium, especially those with irreversible reactions, distinct structural conditions arise and a general characterization remains open. Nevertheless, our results accommodate, in much greater generality, all examples known to us in the literature.

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Section: Resultsmentioning

confidence: 99%

Structural conditions on complex networks for the Michaelis–Menten input–output response

Wong

Dutta

Chowdhury

et al. 2018

Proc. Natl. Acad. Sci. U.S.A.

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“…To each of the directed spanning trees T µ i , we assign a numerical value, A(T µ i ), which is defined as the product of the |V | − 1 = 6 transition rates in the tree, with transitions i → j defined along the orientation (i, j). The steady state probability distributions are then given by (20) with the normalization factor (21). As a result of this construction, all unnormalized steady state probabilitiesP i = M µ=1 A(T µ i ) for the 7state model are a sum of 39 monomials.…”

Section: Step 4: Steady-state Solution In Terms Of Contributions Frommentioning

confidence: 99%

“…Using the decomposition (20) of the stationary probabilities into contributions from the directed spanning trees one obtains the decomposition…”

Section: Appendix B: Graphical Representations Of Transition and Cyclmentioning

confidence: 99%

“…Over the last few decades, enormous progress has been made in characterizing the structure of the ribosome and its dynamics during the process of translation by X-ray crystallography, cryo-electron microscopy and combinations of biochemical and biophysical single molecule techniques such as smFRET, [3][4][5][6][7][8]. There are many theoretical studies of the translation process based on these experimental revelations [9][10][11][12][13][14][15][16][17][18][19][20] but, to our knowledge, there is no report on any study of the stochastic thermodynamics and operational modes of ribosome. * Corresponding author; e-mail: debch@iitk.ac.in…”

Section: Introductionmentioning

confidence: 99%

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Stochastic thermodynamics and modes of operation of a ribosome: A network theoretic perspective

2020

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The ribosome is one of the largest and most complex macromolecular machines in living cells. It polymerizes a specific protein in a step-by-step manner as directed by the corresponding template messenger RNA (mRNA) and this process is referred to as 'translation' of the genetic message encoded in the sequence of mRNA transcript. In each successful chemo-mechanical cycle during the (protein) elongation stage, the ribosome elongates the protein by a single subunit, called amino acid, and steps forward on the template mRNA by three nucleotides called a codon. Therefore, a ribosome is also regarded as a molecular motor for which the mRNA serves as the track, its step size is that of a codon and two molecules of GTP hydrolyzed in that cycle serve as its fuel. What adds further complexity is the existence of branched pathways and futile consumption of fuel that leads neither to elongation of the nascent protein nor forward stepping of the ribosome on its track. We investigate a model based on the network of the seven discrete chemo-mechanical states of a ribosome using a graph-theoretic approach to derive the exact solution of the corresponding master equations. We identify the various possible modes of operation of a ribosome in terms of its average velocity and mean rate of GTP hydrolysis. We also discuss the stochastic thermodynamics of a ribosome by computing entropy production as functions of the rates of the interstate transitions. arXiv:1906.08154v1 [cond-mat.stat-mech] 19 Jun 2019 J a = (k 12 k 23 k 31 − k 13 k 21 k 32 )(k 45 k 51 + k 43 (k 51 + k 54 ))(k 67 k 71 + k 63 (k 71 + k 76 ))/Z J b = (k 12 k 23 k 34 k 45 k 51 − k 15 k 21 k 32 k 43 k 54 )(k 67 k 71 + k 63 (k 71 + k 76 ))/Z J c = (k 45 k 51 + k 43 (k 51 + k 54 ))(k 12 k 23 k 36 k 67 k 71 − k 17 k 21 k 32 k 63 k 76 )/Z J d = (k 21 + k 23 )(k 45 k 51 + k 43 (k 51 + k 54 ))(k 13 k 36 k 67 k 71 − k 17 k 31 k 63 k 76 )/Z J e = (k 21 + k 23 )(k 13 k 34 k 45 k 51 − k 15 k 31 k 43 k 54 )(k 67 k 71 + k 63 (k 71 + k 76 ))/Z J f = (k 21 + k 23 )(k 17 k 34 k 45 k 51 k 63 k 76 − k 15 k 36 k 43 k 54 k 67 k 71 )/Z (C1)In the equations (C1),

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“…These suppressor mutations result in an error-prone variant of IF2 that has been shown to initiate with non-formylated Met-tRNA fMet , with elongator aa-tRNAs, and with no tRNA at all in vitro and, presumably, in vivo [18,19]. Almost all of the kinetic models of translation that have been reported so far [29][30][31][32][33][34], have mainly focused on the details of the elongation stage of protein synthesis and have represented the initiation stage of protein synthesis using a single effective rate constant. Here, we have developed a kinetic model that focuses exclusively on the multi-step assembly of the canonical, pseudo, and non-canonical 70S ICs during the initiation stage of protein synthesis.…”

Section: Mechanism and Regulation Of Translation Initiationmentioning

confidence: 99%

Fidelity of bacterial translation initiation: a stochastic kinetic model

Ghanti,

Caban,

Frank

et al. 2018

Preprint

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During the initiation stage of protein synthesis, a ribosomal initiation complex (IC) is assembled on a messenger RNA (mRNA) template. In bacteria, the speed and accuracy of this assembly process are regulated by the complementary activities of three essential initiation factors (IFs). Selection of an authentic N-formylmethionyl-transfer RNA (fMet-tRNA fMet ) and the canonical, triplet-nucleotide mRNA start codon are crucial events during assembly of a canonical, ribosomal 70S IC. Mis-initiation due to the aberrant selection of an elongator tRNA or a non-canonical start codon are rare events that result in the assembly of a pseudo 70S IC or a non-canonical 70S IC, respectively. Here, we have developed a theoretical model for the stochastic kinetics of canonical-, pseudo-, and non-canonical 70S IC assembly that includes all of the major steps of the IC assembly process that have been observed and characterized in ensemble kinetic-, single-molecule kinetic-, and structural studies of the fidelity of translation initiation. Specifically, we use the rates of the individual steps in the IC assembly process and the formalism of first-passage times to derive exact analytical expressions for the probability distributions for the assembly of canonical-, pseudo-and non-canonical 70S ICs. In order to illustrate the power of this analytical approach, we compare the theoretically predicted first-passage time distributions with the corresponding computer simulation data. We also compare the mean times required for completion of these assemblies with experimental estimates. In addition to generating new, testable hypotheses, our theoretical model can also be easily extended as new experimental 70S IC assembly data become available, thereby providing a versatile tool for interpreting these data and developing advanced models of the mechanism and regulation of translation initiation.

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A Generalized Michaelis–Menten Equation in Protein Synthesis: Effects of Mis-Charged Cognate tRNA and Mis-Reading of Codon

Cited by 4 publications

References 46 publications

Structural conditions on complex networks for the Michaelis–Menten input–output response

Structural conditions on complex networks for the Michaelis–Menten input–output response

Stochastic thermodynamics and modes of operation of a ribosome: A network theoretic perspective

Fidelity of bacterial translation initiation: a stochastic kinetic model

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