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

Abstract

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),

Entropy production rates for different notions of partial information

“…T denotes the probability vector to find the system in the respective states at time t. The system reaches a steady state at the long-time limit, denoted by the state probabilities vector π , which can be obtained from solving Wπ = 0. The distributions at steady state can also be obtained directly from the transition rates using the matrix-tree theorem [23,52]. The stationary current between states i and j is defined by J π ji = w ji π i − w ij π j .…”

A model for ribosome translocation based on the alternated displacement of its subunits

“…The ribosome can be regarded as a molecular motor for which the mRNA template serves as a track [15]; the motor is fuelled by GTP and/or ester bond hydrolysis and its step size on the track is a single codon, whose length is close to 1 nm. Given the relevance of thermal fluctuations in the dynamics of a molecular motor, modeling the ribosome translocation cycle needs to take into account the randomness present in each molecular event occurring during the whole process and, in particular, the stochastic nature of ribosome conformational changes established in the previous section.…”

“…A succession of possible molecular events substantiates the model presented in this work, as explained in section 2, giving rise to a cycle of ribosomal configurations. Following [14,15], this cycle is mathematized in section 3 as a Markov network of discrete ribosomal states. The model aims to calculate ribosome translocation dynamics in terms of the kinetics of the interaction among the different conformations resulting from the proposed ribosome subunits motions, as shown in sections 3 and 4.…”

A model for ribosome translocation based on the alternated displacement of its subunits

“…A succession of possible molecular events substantiates the model presented in this work, as explained in section 2, giving rise to a cycle of ribosomal configurations. Following [14,15], this cycle is mathematized in section 3 as a Markov network of discrete ribosomal states. The model aims to calculate ribosome translocation dynamics in terms of the kinetics of the interaction among the different conformations resulting from the proposed ribosome subunits motions, as shown in sections 3 and 4.…”