Markov propagation of allosteric effects in biomolecular systems: application to GroEL–GroES

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Abstract
We introduce a novel approach for elucidating the potential pathways of allosteric communication in biomolecular systems. The methodology, based on Markov propagation of ‘information’ across the structure, permits us to partition the network of interactions into soft clusters distinguished by their coherent stochastics. Probabilistic participation of residues in these clusters defines the communication patterns inherent to the network architecture. Application to bacterial chaperonin complex GroEL–GroES, an allostery‐driven structure, identifies residues engaged in intra‐ and inter‐subunit communication, including those acting as hubs and messengers . A number of residues are distinguished by their high potentials to transmit allosteric signals, including Pro33 and Thr90 at the nucleotide‐binding site and Glu461 and Arg197 mediating inter‐ and intra‐ring communication, respectively. We propose two most likely pathways of signal transmission, between nucleotide‐ and GroES‐binding sites across the cis and trans rings, which involve several conserved residues. A striking observation is the opposite direction of information flow within cis and trans rings, consistent with negative inter‐ring cooperativity. Comparison with collective modes deduced from normal mode analysis reveals the propensity of global hinge regions to act as messengers in the transmission of allosteric signals. ### Synopsis A central goal in structural biology is to understand the mechanism of allosteric communication in supramolecular systems. Allostery is the cooperative process by which local effects propagate across the structure, often to regions spatially distant from initiation sites. Although several experimental and computational studies point to the importance of the topology of inter‐residue contacts in a network representation of biomolecular structures, no systematic computational method to derive the potential pathways of signal transduction favored by the complex molecular architecture has been developed to date. A new methodology is introduced in the present study to address this issue and elucidate the pathways of allosteric communication in large biomolecular systems. The allostery‐driven system we explore here is the bacterial chaperonin system GroEL–GroES ([Thirumalai and Lorimer, 2001][1]; [Saibil and Ranson, 2002][2]; [Horovitz and Willison, 2005][3]). GroEL has a cylindrical structure, consisting of 14 identical chains organized in two back‐to‐back stacked rings of seven subunits each ([Xu et al , 1997][4]). Each chain is composed of three domains, equatorial (E), intermediate (I) and apical (A). During the allosteric cycle that mediates protein folding, the rings alternate between open ( cis ) and closed ( trans ) forms in an ATP‐regulated manner, providing access to, or release from, the central cavity where the folding of encapsulated (partially folded or misfolded) protein/peptide is assisted. The chaperonin function requires an efficient communication between distant locations on the complex. For example, ATP binding to E‐domains is accompanied by a cooperative conformational change that facilitates the binding of co‐chaperonin GroES at the A‐domains in the same ( cis ) ring, whereas substrate binding and ATP binding to opposite ( trans ) ring triggers the release of GroES, substrate protein and ADP from the cis ring. Although several studies have been undertaken to unravel the mechanism of allostery in GroEL–GroES ([Xu et al , 1997][4]; [Ma and Karplus, 1998][5]; [Sigler et al , 1998][6]; [de Groot et al , 1999][7]; [Ma et al , 2000][8]; [Thirumalai and Lorimer, 2001][1]; [Kass and Horovitz, 2002][9]; [Keskin et al , 2002][10]; [Horovitz and Willison, 2005][3]), the underlying pathways of allosteric communication remain to be elucidated, as well as the key interactions that mediate the intra‐ring (positive) and inter‐ring (negative) cooperativity. Motivated by the recent success of network‐based approaches in determining the structural motifs/mechanisms for allosteric communication ([Keskin et al , 2002][10]; [Xu et al , 2003][11]), we model structures as networks of residues ([Bahar et al , 1997][12]; [Haliloglu et al , 1997][13]; [Hinsen, 1998][14]; [Doruker et al , 2000][15]; [Atilgan et al , 2001][16]) and study the Markov propagation of information over the network of interactions. This approach permits us to reduce the original complex structure into a collection of ‘soft clusters’ at different levels of resolution ([Figure 2][17]). Each cluster probabilistically ‘owns’ groups of residues obeying coherent signal propagation stochastics ([Figure 3][18]). Those residues ‘shared’ more or less equally by adjoining clusters are instrumental in transmitting information across clusters and serve as messengers, whereas those almost completely owned by a given cluster serve as hubs. This description greatly simplifies our understanding of the dominant mechanisms and key elements that mediate the communication across distant regions in complex structures. Application of this framework to the chaperonin system GroEL–GroES shows that GroES mobile loop Glu18–Ala33 play a key role in achieving the communication between the cis ring and the co‐chaperonin. At the trans ring, we observe that inter‐subunit communication is achieved by inter‐subunit I–A domain couplings. This may be a functional requirement, to ensure the coherence of the trans ring that lacks, compared to the cis ring, the stabilizing effect of the bound co‐chaperonin cap. Our analysis reveals that inter‐subunit, intra‐ring communication is achieved by an equatorial domain segment of 10–15 residues that inserts into the neighboring cluster, bridging adjacent subunits. In this regard, a most...