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Interdiction of Protein Folding for Therapeutic Drug Development in SARS CoV-2

In this article, we predict the folding initiation events of the ribose phosphatase domain of protein Nsp3 and the receptor binding domain of the spike protein from the severe acute respiratory syndrome (SARS) coronavirus-2. The calculations employ the sequential collapse model and the crystal structures to identify the segments involved in the initial contact formation events of both viral proteins. The initial contact locations may provide good targets for therapeutic drug development. The proposed strategy is based on a drug binding to the contact location, thereby aiming to prevent protein folding. Peptides are suggested as a natural choice for such protein folding interdiction drugs.


INTRODUCTION
Understanding the biochemistry of the new coronavirus SARS-CoV-2 has become an issue of prime importance and urgency as the virus spread has triggered an ongoing pandemic that has already cost thousands of lives and large economic disruption. 1−3 Many therapeutic strategies are being considered including monoclonal antibodies 4,5 that rely on targeting selected virus proteins based on their native structure. Considerable work has been developed against coronaviruses in the past in this direction, and the experience gained is now being deployed against SARS-CoV-2 based on the crystal structures already available of several of the virus' proteins. 6−9 The purpose of this paper is to introduce a distinct possible new therapy route by (a) presenting predictions of the earliest events along the folding pathway of two of the virus' proteins and (b) building on this foundation to propose an alternative drug development strategy based on reducing the functionality of the virus by interdicting in the folding process of its proteins.
In order to fulfill goal (a) of the article, we will focus on the folding initiation events of two of the SARS-CoV-2 proteins: (1) the ADP ribose phosphatase domain of the nonstructural NsP3 protein 10,11 and (2) the receptor binding domain of the spike protein. 7,12,13 The earliest folding initiation event in both cases will be predicted employing the sequential collapse model (SCM). 14,15 In the SCM, the multistate folding process of proteins longer than ∼100 amino acids is initiated by formation of specific nonlocal contacts called primary contacts. These primary contacts help constrain the folding process by dividing the protein into several smaller domains. In this way, overall folding becomes vastly more efficient than a purely random statistical search, resulting in what we have referred to as "Nature's shortcut" to the native structure. 15 Nucleation of the folding process by the primary contacts then constitutes a potential set of emergent natural physical constraints that sidestep Levinthal's paradox. 15 In the case of misfolded protein-based diseases, the SCM has been applied to investigate some general properties of the folding dynamics of neuropathogenic proteins. 16,17 In order to unequivocally determine the folding initiation events, we will support the SCM predictions with structural information from the crystal structures of both proteins.
Goal (b) of this article will be addressed utilizing the SCM predictions to provide potential target (intraprotein) regions for the development of therapeutic drugs able to interdict the folding initiation event. Various possible therapeutic drugs could be considered, but peptides 18 form a natural class for target region binding, ideally preventing subsequent folding, although other molecular categories could also be similarly employed. This therapeutic drug development strategy based on folding interdiction of target regions (FITRs) is similar to an earlier proposal to develop drugs to interfere in protein folding. 19,20 The novelty in the present work lies in the SCM's ability to predict critical target regions for folding initiation from the primary sequence. The broader potential of the FITR strategy and possible development hurdles will also be discussed. In particular, it will be explained that the proposed FITR drug strategy could be extended to other proteins of SARS-CoV-2 as well as to other diseases in which the presence of specific proteins plays a decisive role.

METHODS: THE SCM MODEL
The physical basis of the SCM and its most up-to-date formulation have been recently explained in full detail. 15,17 Here, only a brief summary of the main concepts is presented that are relevant to the issues investigated in the present paper.
2.1. SCM Entropic Cost of Loop Formation. The SCM considers early specific nonlocal contacts based on the entropy of formation of the resultant protein loops. The SCM has successfully predicted many of the observed features of protein folding pathways. 15 In the SCM, two different loop regimes are considered when analyzing early nonlocal contacts: short loops for which the gyration radius, R g (n), is smaller than the average side chain length £(n) [i.e., R g (n) < £(n)], and long loops for which R g (n) > £(n). The loop length at which the transition between the short and long loops takes place [i.e., the length for which R g (n) ≈ £(n)] is called the optimal loop length n op . The optimal loop length has been estimated to be n op ≈ 65 amino acids for typical protein sequences for £(n) ≈ 7.9 Å, 17 although some sequence variability exists and n op is expected to be shorter for highly disordered proteins that contain few of the bulky hydrophobic amino acids. 21 This value for n op is consistent with experimental data showing the behavior of poly-alanine, a polypeptide with smaller side chains than the average globular protein, in this case £(n) ≈ 6.7 Å, 17 which exhibits deviations from Gaussian statistics because of steric hindrance when n < 50 amino acids. 22 The long loop regime is physically equivalent to the classical Flory−Jacobson−Stockmayer (FJS) picture and the entropic cost of forming protein loops is well represented, assuming that the amino acids can be taken to be solid ball-like by a simple logarithmic function of the form 23 This is clearly an approximation, as for example, the side chains would be better represented by solid spheres of different sizes according to the primary sequence. In the SCM short loop regime, however, the internal degrees of freedom of the side chains cannot be neglected, and the entropic cost of forming short loops must be higher than when the amino acids are taken to be solid spheres. Moreover, because most of the degrees of freedom are in the side chains, we expect the contribution of the side chains to the overall entropic cost to be dominant with respect to that of any constraints imposed by loop formation on the backbone.
Thus, in the SCM it is expected that for a short loop, the entropic cost of loop formation ΔS loop approximately becomes with ΔS side-chain-crowding ≪ 0, opposing folding. When R g (n) ≥ £(n), we have ΔS side-chain-crowding ≈ 0 and the standard FJS regime is recovered. The side chain crowding term ΔS side-chain-crowding will appear as a correction to the JS results for shorter loops. It is extremely difficult to obtain an analytical expression for the side chain crowding term, and in the SCM it has been presented in generic Boltzmann−Gibbs form 15 where f 0 (n,£) is the average configurational freedom per amino acid in the unfolded chain and f loop (n,£) is the average configurational freedom of an amino acid in a loop. Consideration of modifying the homogeneous Flory-like representation of the protein chain to take into fuller account the microscopic details of the protein−solvent system is not exclusive to the SCM and has been employed before to account, for example, for the effects of the solvent. 24 Based on the model developed above, in the SCM, the folding of proteins with more than ∼100 amino acids likely involves the formation of an early nonlocal contact, called the primary contact within the SCM, that defines the earliest folding phase with n ≥ n op ≈ 65 amino acids. As only a few primary contacts can be established at most in proteins of length n ≥ n op , most of the tertiary structure contacts will still be defined by contacts at a shorter range established in later folding phases. 14 Formation of the primary contact in the SCM defines the primary loop, which subsequently collapses through two-state kinetics. 15 Because proteins longer than ∼100 amino acids do not generally undergo two-state collapse 15 but rather fold through multistep pathways, consistent simple physical reasoning implies that there is a limit to the size of the primary loop that can successfully lead to the native SCM folding pathway of ∼100 amino acids.
The concept of folding nucleated by nonlocal contacts is not exclusive to the SCM, having arisen earlier in the context of the diffusion−collision model 25 and in the energy landscape picture. 26 It also has appeared in simulations of the transition state of two-state folding proteins. 27 Also, protein topology has been considered an essential element of folding mechanisms in a number of theoretical efforts. 28−32 The particular feature in the SCM is that the early nonlocal contacts are highly specific as in the loop hypothesis, 33 and a methodology is developed to derive their location from primary sequence information. 15 2.2. Determining the Primary Contact. Based on the model presented in the previous sections, whether there is a nonlocal contact in an otherwise unfolded state is dependent upon the stability of the potential contact candidates at loop lengths of n ≥ n op amino acids. In the SCM, the stability of a contact formed by the number n cont of amino acids, ΔG contact (n cont ,n loop ), can be written as Here, ΔG loop represents the entropic free energy cost of the loop as discussed in Section 2.1. The term ΔG int,H denotes all the enthalpic interactions that help stabilize the contact, possibly including hydrophobic interactions, van der Waals interactions, hydrogen bonds, disulfide bonds, and salt bridges, 34 and its value satisfies ΔG int < 0. The term ΔG cont,S > 0 represents the entropic cost of constraining the side chains of the amino acids defining the contact such that the contact is stable and it opposes contact formation. A segment-specific determination of the value ΔG cont,S (n cont ) for a given contact would require detailed molecular dynamics techniques. However, a heuristic estimate can be made from earlier work within the SCM, which showed that the average entropic cost The Journal of Physical Chemistry B pubs.acs.org/JPCB Article of folding per amino acid for a sample of 13 proteins was ΔG folding/residue,S ≈ 0.85kT/residue, 35 and the maximum was ΔG folding/residue,S ≈ 1.09kT/residue. As these are estimates for the entropic cost for folding per residue of complete proteins that include highly buried as well as flexible exposed regions, it is then reasonable to expect that the entropic cost of a contactforming region must be closer to the highest calculated values for ΔG f o l d i n g / r e s i d u e , S . Here, we will assume that ΔG contact,S (n contact ) for a contact including n cont amino acids is approximately ΔG folding/residue,S determined by the number of residues defining the contact, such that ΔG cont,S (n cont ) ≈ 1.09n cont . This result is clearly an approximation, but in Section 3 it will be shown to suffice for establishing a cut-off in the number of possible contacts that is consistent with the available structural data. Hydrophobic interactions are well understood to constitute the main driving force of the folding process. 34 Other interactions such as hydrogen bonds are weaker 34 or like disulfide bonds and salt bridges form later along the folding pathway. 36 Thus, for an early contact forming from the unfolded state, we can take ΔG int (n op ) ≈ ΔG hyd (n op ), where ΔG hyd (n op ) represents the stabilizing effect of hydrophobicity in the early contacts, and eq 4 can be written as As the hydrophobic stabilization energy of the contact ΔG hyd is determined by the hydrophobicity of the segments involved, the hydrophobicity values h k are obtained from the Fauchere− Pliska scale 37 and assigned to each residue in accord with previous calculations within the SCM.
Because the amino acid side chains are significantly larger than the typical peptide bond length, early contacts between two hydrophobic amino acids will inherently involve segments including several amino acids, adjacent to the initial contact. The stability of this early hydrophobic contact will determine where the folding process is initiated. This picture is not unlike the zapping model of Dill and collaborators. 38 Here the typical early contact segment size will be taken to be ∼5 amino acids in line with previous calculations within the SCM. 14 The 5amino acid window size is based on the geometric considerations underlying the SCM: with an average effective fluctuating width of the unfolded protein chain of w ∼ 2£(n) ≈ 15.8 Å, and a peptide bond length of 3.5 Å, the minimum number n cont of amino acids that can define a contact in the open fluctuating chain should be n cont ∼ int[2£(n)/3.5] = 5 amino acids. The results for the location of the most stable primary contact were seen to be robust to the employment of five and six-amino acid windows, while some deviations were observed when the window was reduced to four amino acids. In practice within the SCM, the hydrophobicity h k of each residue is added over a segment contact window of five amino acids centered at residue i, resulting in a segment hydrophobicity h i , 5 (a value of ∼0.45 is equivalent to a change in energy of kT, with the margin of error being ∼0.1kT 35 ).
In order to determine the best contact, the h i,5 values of a segment centered at residue i is added to the h j value of a segment centered at residue j, located at a distance n ij at least n op amino acids apart along the sequence, and no longer than the maximum primary loop length of ∼100 amino acids, to give a contact stability of

RESULTS
We have chosen to focus in this paper on two domains of two major functional proteins of SARS-CoV-2: (a) the nonstructural ADP ribose phosphatase domain of protein NsP3; 10 and (b) the structural receptor binding domain of the spike protein. 12 This choice was made based on two distinct considerations: (1) to study both a structural and a nonstructural protein that have a direct involvement in the viral infection mechanism, thus providing options for drug discovery; and (2) to employ the SCM within the boundaries of its demonstrated applicability, that is, on proteins long enough that a multi-state folding pathway is expected, but not so long that degeneracies in the results might cloud any definite conclusions. 15

Primary Contact for the ADP Ribose Phosphatase Domain (X Domain) of Protein NsP3 of SARS-CoV-2.
Non-structural proteins of coronaviruses have been the object of intense study, concerning both their structures and their functionality. 39,40 The multi-domain non-structural protein 3 (Nsp3) is the largest protein encoded by the coronavirus' genome. 10 It includes up to sixteen domains, of which eight domains and two transmembrane regions are conserved. 41,42 One of the conserved domains is the macrodomain (also called the X domain), which includes 173 amino acids. 7 The first available crystal structure of a NsP3 domain of any coronavirus was the unliganded X domain of SARS-CoV, obtained in 2005. 43 The crystal structure for the SARS-CoV-2 variant of the X domain is known. 11 It has the typical X domain organization, with seven β-strands defining a central β-sheet, surrounded by six α-helices. 11 One of the functions of the X domain is to bind ADP-ribose and poly-(ADP-ribose). 43−45 The X domains of coronaviruses, also show ADP-ribose-1″phosphate phosphatase activity. 43,44,46 It has been observed that this property is linked to the ability of the virus to compromise the immune system of the host. 47,48 Our calculations predict that the best possible primary contact for the X domain (i.e., the best folding initiation contact) is established between segments ( 35 PTVVV 39 ) centered at V37, and ( 125 LLAPL 129 ) centered at A127, with a stability of ΔG cont ≈ −6.3kT. The predicted primary contact is in clear proximity in the crystal structure of the protein (PDB code 6VXS), and we have represented the two segments in Figure 1a. 49 The next-best possible contacts with energies within ∼1kT of the best primary contact (37, 127) are shown in Table 1. None of the possible alternatives to contact (37, 127) is a good native contact on the crystal structure. None of the side chains of the two segments defining these alternative contacts appear within the van der Waals interaction distance in the crystal structure. The issue of the multiplicity of possible primary contacts in the SCM has been considered in previous work. 50 Because no major rearrangements of the protein core are expected post-collapse, it is generally assumed within the model that primary contacts that are non-native on the 3D folded structure are likely not to correspond to native pathways leading to the functional folded structure. 51,52 In all the proteins studied to date within the SCM it has been observed that the most stable primary contact is native-like. 15 Thus, our result implies that the majority of the protein molecules are The Journal of Physical Chemistry B pubs.acs.org/JPCB Article expected to fold through the initiation event defined by the primary contact predicted here. In this regard, it is a prediction of the model that primary contact (37−127) is the gateway to "Nature's shortcut" 15 to the folding of the ADP ribose phosphatase domain of SARS-CoV-2.
3.2. Primary Contact of the Receptor Binding Domain of the Spike Protein of SARS-CoV-2. The receptor recognition mechanisms of coronaviruses have been extensively studied. 53,54 In particular, for SARS-CoV-2 7 and its earlier viral variant SARS-CoV, 53 entry into the host's cells is mediated by a virus-surface spike protein that includes a specific receptor-binding domain (RBD). 54−56 The RBD recognizes angiotensin-converting enzyme 2 (ACE2) as its specific receptor. 55 The structure of SARS-CoV RBD is well known, 56 and the structure of SARS-CoV-2 RBD is similar, 7 albeit with some specific mutations in the ACE2 binding ridge that enhance the ability of SARS-CoV-2 to bind human ACE2. 7 The spike protein of SARS-CoV-2 is a natural therapeutic target given its critical biological role in facilitating the virus entry in the cell. The search for inhibitors, including peptides, that actively block RBD-ACE2 binding of coronavirus has been an active field of investigation for many years. 57−59 The RBD of SARS-CoV-2 is 223 amino acids long, making it the longest protein investigated within the SCM to date. 14,15,17 The best possible contacts with energies within ∼1kT of the best primary contact (37, 127) are shown in Table 2. Our calculations predict that the best possible primary contact is established between segments ( 114 CVIAW 118 ) centered at I116,and ( 193 VVLSF 197 ) centered at L195, 79 residues apart, with a stability of ΔG cont ≈ −11.5kT. The predicted contact is in clear proximity in the crystal structure of the protein (PDB code 6M0J), and we have represented the two segments defining the contact in Figure 1b. 49 The second-best possible contact is defined by segments ( 17 LCPFG 21 ), centered at P19, and ( 114 CVIAW 118 ), 97 residues apart, with a stability of ΔG cont ≈ −10.8kT. Contact (19, 116) is not as good a contact on the native structure. Thus, our result implies that the majority of the protein molecules will fold through the initiation event defined by the best primary contact (116, 195) predicted here.

DISCUSSION: A POSSIBLE AVENUE TO PROTEIN FOLDING-INTERDICTING THERAPEUTIC DRUGS AGAINST SARS-COV-2
The identification of the primary contacts along the folding pathway of viral proteins constitutes an important result for at least two reasons: (a) the sequences of the specific segments involved in the primary contacts provide a template to specify candidate peptide drugs of inhibitory effect with the maximum possible contact affinity to compete with the natural folding mechanism; and (b) it provides insight for further investigation into the subsequent folding steps leading to a fully functional viral protein, potentially providing for additional FITRs.
The fact that the primary contact is defined by the interaction between two well defined amino acid sequences suggests that a strategy to develop FITR-based therapeutic drugs could be one utilizing trial peptide drugs as suggested above. Peptide drugs offer several advantages versus other more classical approaches such as function-blocking monoclonal antibodies. In particular, being much smaller and flexible, peptide drugs can much more easily cross the cellular membrane to reach their intended targets. 60 However, designing therapeutically effective peptide drugs remains an important challenge. 61 There are several reasons why effective peptide drugs are hard to discover: (1) the potential space of peptide candidates is very large; (2) ensuring delivery at the right location on the target molecule is a considerable challenge; and (3) making a peptide drug that is contact-site  49 The color code reflects the location from the Nterminus (dark blue) to the C-terminus (yellow). Only the side chains corresponding to the segments that define the primary contacts are shown.  The Journal of Physical Chemistry B pubs.acs.org/JPCB Article specific is not an easy task. As a consequence, no more than ∼60 effective peptide drugs are in use today, 18 although there is active investigation of many more. 18 The SCM might prove of assistance in addressing at least difficulty (1) above, and maybe also (2) and (3), through the utilization of the predicted primary contact sequence as a template to search for an effective therapeutic peptide capable of inhibiting primary contact formation. Also, other non-peptide molecules have shown potentially therapeutic capabilities by binding to mostly unfolded states of proteins. For example, ceftriaxone binds specifically to the C-terminal region of the intrinsically disordered protein α-synuclein, 62 generally understood to be involved in triggering Parkinson's disease, 63 and has shown therapeutic potential. Also, recent experimental results suggest that the folding kinetics of proteins with two-state transitions can be modulated by the employment of suitable peptides that mimic specific segments of the protein chain. 64 Although the purpose of the experiment was the opposite of the one sought for here, as the goal was to speed up the folding transition, the results provide general support for the contention presented that specific peptide molecules can interfere and alter the folding kinetics of globular proteins. The proposed therapeutic strategy is depicted in Figure 2.
To summarize, we have presented a target-specific strategy to develop folding-interdicting drugs. Such folding-interdicting drugs would function by specifically inhibiting the earliest folding events. In order to do so, we propose to rely on the a priori capabilities to identify FITRs embedded within the SCM. This strategy is generally similar to earlier proposals to develop therapeutic peptide folding inhibitors relying on protein folding information. 65 Our expectation is that by developing such SCM-based folding-interdicting drugs as Figure 2. Proposed inhibitory mechanism of viral functionality based on the employment of specific peptides in order to interdict the initial folding event of the viral proteins. The effect on the viral structure of the employment of such folding inhibitory peptides on the spike proteins of SARS-Cov-2 is illustrated in generic form as its precise effect on the overall configuration of the virion is not known. Additionally, multiple spike proteins would need to be inhibited simultaneously to fully disrupt the functionality of the virion. Whether folding interdiction through inhibition of just the dominant folding initiation event suffices to preempt the onset of disease is a matter that calls for experimental assessment.

CONCLUSIONS
In this article we presented theoretical predictions for the folding initiation events of two functionally relevant proteins of the SARS-CoV-2 virus. The predicted folding initiation events were shown to map into good contacts on the 3D structure of the proteins. We proposed that knowledge of the protein segments involved in the folding initiation event, opens an attractive route to developing new therapeutic drugs intended to prevent the successful folding of key viral proteins. Such reduction of the population of properly folded viral proteins could lead to a decreased level of viral spread, thus reducing the lethality of the infection. On the basis of these findings, we proposed a general therapeutic drug development strategy based on interdicting the folding process through the identification of SCMpredicted FITRs. The FITR strategy could be generally used to approach other diseases where specific proteins play an essential role.