Ab initio protein structure prediction – the necessary presence of external force field as it is delivered by Hsp40 chaperone

doi:10.21203/rs.3.rs-3212848/v1

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Research Article

Ab initio protein structure prediction – the necessary presence of external force field as it is delivered by Hsp40 chaperone

https://doi.org/10.21203/rs.3.rs-3212848/v1

This work is licensed under a CC BY 4.0 License

Journal Publication

published 07 Nov, 2023

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Background

The aqueous environment directs the protein folding process towards the generation of micelle-type structures, which results in the exposure of hydrophilic residues on the surface (polarity) and the concentration of hydrophobic residues in the center (hydrophobic core). Obtaining a structure without a hydrophobic core requires a different type of external force field than those generated by a water. The examples are membrane proteins, where the distribution of hydrophobicity is opposite to that of water-soluble proteins. Apart from these two extreme examples, the process of protein folding can be directed by chaperones, resulting in a structure devoid of a hydrophobic core.

Results

The current work presents such example: DnaJ Hsp40 in complex with alkaline phosphatase PhoA-U (PDB ID − 6PSI) - the client molecule. The availability of WT form of the folding protein - alkaline phosphatase (PDB ID − 1EW8) enables a comparative analysis of the structures: at the stage of interaction with the chaperone and the final, folded structure of this biologically active protein. The fuzzy oil drop model in its modified FOD-M version was used in this analysis, taking into account the influence of an external force field, in this case coming from a chaperone.

Conclusions

The FOD-M model identifies the external force field introduced by chaperon influencing the folding proces. The identified specific external force field can be applied in Ab Initio protein structure prediction as the environmental conditioning the folding proces.

chaperone

Hsp40

DnaJ

alkaline phosphatase

folding

client molecule

Chaperone proteins play a significant role in a control of protein folding process [1]. Their function relies on preventing the formation of internal interactions unfavorable for the final structure of proteins. The risk of misfolding increases when the temperature increases. The heat shock proteins are a group of chaperone proteins, the production of which is increased under conditions of thermal stress [2]. Based on the size of the chaperon molecule, the following classes are distinguished: Hsp90, Hsp70 and Hsp40, where the number at the end is the number of kilodaltons of a given group of heat shock proteins. The most frequently identified proteins in the Hsp group are Hsp70 and Hsp40, also referred to as DnaK and DnaJ, respectively [3]. The structures of proteins supporting the folding process, including the prevention of inappropriate aggregation, as well as the potential interaction with the membrane, are the subject of numerous studies, as the mechanism of action of these proteins is not fully recognized [4, 5]. In order for chaperone proteins to perform their functions, it is necessary to identify the sites of chaperone-client interactions [6, 7]. Very often, in the activity of chaperone proteins, a specific synergy involving both Hsp40 and Hsp70 is observed [8–10].

The availability of chaperone’s structure tog eter with the structure of the folding protein in a complex is a valuable source of information on the relationships between these two types of proteins during the folding process. The object of analysis in the current work is the complex of two Hsp40 chaperone chains (ttHsp40 – tt-Thermus thermophilus) with a pre-folded Alkaline Phosphatase (PhoA) chain. This complex (PDB ID 6PSI - [11]) and its components (two chaperone chains and a partially folded "client" protein) are analyzed individually as independent structural units. For comparative purposes, the final structure of the folded client protein (PDB ID 1EW8 – [12]) is also used in this work.

The aim of the current work is to quantify the impact of different environmental factors, including the chaperone’s one, on the folding process of the aforementioned client protein. The paper presents a proposal for expressing the external force field for the representation of environmental conditions for folding proces in ab initio approach. This proposal relies on the assumption that a polypeptide chain butli-up of bi-polar amino acids with different proportions of polar to hydrophobic parts in a polar water environment tends to obtain a micelle-like structure. This means the concentration of hydrophobic residues in the center of the molecule with the exposure of polar ones on the surface. The hydrophobicity distribution resulting from such idealized structuring can be described by 3DGaussian function. This function is proposed to represent the external force field directing the folding proces. Real proteins, each with a specific sequence can obtain a micelle-like structure to a full or limited extent which can be expressed by a local mismatch of the observed hydrophobicity distribution to the idealized one. The status of the hydrophobicity distribution present in a given structure is determined on the basis of the hydrophobic interactions as dependent on the distances between the interacting residues and their different intrinsic hydrophobicities.

A specific form and degree of maladjustment of the hydrophobicity distribution in the protein in relation to the idealized one is a form of recording the specific activity of a given protein. Local maladjustment carries information about the specificity of a potential partner in a chemical reaction. In the case of enzymes, the local "deficit" of hydrophobicity expresses the presence of cavity ready to interact with the ligand/substrate. Local exposure ("excess") of hydrophobicity on the surface may in turn be the form of preparation to complexation of another protein [13].

Just as the external environment provides the conditions for proper folding, the already folded protein can provide a local external force field for the course of a given reaction in the active site of the enzyme. The protein body is much larger than the active center, constituting an external force field for a specific reaction. The degree and type of separateness of the hydrophobicity distribution from the idealized one is a kind of recording the specificity of the environment and its impact on the ongoing process in the active center. The structure of the protein, including its local maladjustment to the micelle-like system, is the result of the influence of the external environment. The order/disorder of the hydrophobicity distribution in the folded protein, in turn, constitutes an external force field for the active site and thus an environment for a specific reaction.

In the Fuzzy oil drop (FOD) model [14], the external force field for proteins folding in an aqueous environment is described by the 3DGauss function. Proteins with an ordered hydrophobicity distribution in this way are known [15]. A different specificity is expressed by the membrane environment in which numerous proteins are active. The modification of the FOD model was introduced in the FOD-M model [15], where the possibility of changing the characteristics of the environment is taken into account. In addition to the factors such as the cell membrane, other factors are used to guide the process of protein folding. Such factors are chaperones, which - as it is generally interpreted - prevent misfolding by imposing the appropriate structuring.

In the present study the assessment of the form and degree of influence of the chaperone on the protein folding process was carried out by analyzing the native form of bacterial alkaline phosphatase [12] with the form that this protein represents in a complex with the chaperone Hsp40 - DnaJ2 [11]. The available structures, both native and partially folded with the help of a chaperone, enables the comparative analysis to track the structural changes during folding.

It is also possible to identify the specificity of an external force field provided by a chaperon. The status of the hydrophobicity distribution in the native form revealing significant deviations from the distribution typical for the aquatic environment allows to determine the influence of the external force field introduced by a chaperone. In turn. the availability of the structure of the chaperone-client molecule’s complex, enables the evaluation of the chaperone itself as a provider of a specific external force field for the folding of the enzyme in question.

The FOD-M model is assumed to deliver the expression of environmental conditions directing the folding process toward the aim-oriented results in biologicaly active form.

Data

Table 1

shows the proteins analyzed with the identifiers introduced for the present work.
PDB – ID	SKŁAD	NAME	ID in this paper
6PSI [11]	Chain A – chaperone Chain C – chaperone Chain B - client	Hsp40-A Hsp40-C PhoA	HspA-Comp (complex)
6PSI	Chain A – chaperone Chain C - chaperone	Hsp40-A Hsp40-C	HspA-AC
6PSI	Chain A - chaperone	Hsp40-A	Hsp40-A
6PSI	Chain C – chaperone	Hsp40-C	Hsp40-C
6PSI	Chain B - client	PhoA	PhoA-U (unfolded)
1EW8 [12]	Chain A Chain B	PhoA-A PhoA-B	PhoA-WT-AB
1EW8	Chain A	PhoA	PhoA-WT-A

Table 1. Proteins with structural units analyzed in the work and identifiers introduced for the purpose of this work. The right column gives the identification system for structural units as described in this paper.

Programs used

The program allowing calculation of RD is accessible upon request on CodeOcean platform: https://codeocean.com/capsule/3084411/tree. Please contact the corresponding author to get access to your private program instance (accessed June 10, 2023).

The application – implemented in collaboration with the Sano Centre for Computational Medicine (https://sano.science) and running on resources contributed by ACC Cyfronet AGH (https://www.cyfronet.pl) in the framework of the PL-Grid Infrastructure (https://plgrid.pl) – provides a web wrapper for the abovementioned computational component and is freely available at https://hphob.sano.science (accessed June 10, 2023).

The VMD program was used to present the 3D structures [16, 17] (accessed June 10, 2023).

The FOD-M Model

The FOD model assumes that the structure of proteins folding in a polar water environment leads to the formation of forms corresponding to a spherical micelle with a hydrophobic, centrally located hydrophobic core and a polar surface that guarantees a favorable entropic-enthalpy state towards the water environment. The description of the hydrophobicity distribution in the micelle-like form is expressed by the 3DGaussian function spanned over a protein molecule. The size of the ellipsoid (expressed by the appropriate values of σ_X, σ_Y and σ_Z) is adjusted to the size of the protein molecule encapsulating it.

The value of the 3DGaussian function for the positions of effective atoms (average position of atoms included in a given amino acid) expresses the level of hydrophobicity treated as theoretical, completely consistent with the micelle-like system, and is denoted by T_i (Fig. 1.A).

The actual level of hydrophobicity resulting from interactions is determined using the function proposed by Levitt [18]. The observed level of hydrophobicity assigned to a given effective atom - referred to as O_i - depends on the distance between adjacent effective atoms (cutoff distance = 9 Å) and the intrinsic hydrophobicity of each interacting amino acid.

$H_{i}^{O}=\frac{1}{{H_{{sum}}^{O}}}\sum\limits_{j} {\left\{ \begin{gathered} \left( {H_{i}^{r}+H_{j}^{r}} \right)\left( {1 - \frac{1}{2}\left( {7{{\left( {\frac{{{r_{ij}}}}{c}} \right)}^2} - 9{{\left( {\frac{{{r_{ij}}}}{c}} \right)}^4}+5{{\left( {\frac{{{r_{ij}}}}{c}} \right)}^6} - {{\left( {\frac{{{r_{ij}}}}{c}} \right)}^8}} \right)} \right)\quad for\;{r_{ij}} \leqslant c \hfill \\ 0,\quad \quad for\;{r_{ij}}>c \hfill \\ \end{gathered} \right.}$

Both T and O distributions after normalization can be compared by evaluating to what extent the O distribution reflects the T one. In other words, how close is the O distribution to the distribution of an idealized spherical micelle (Fig. 1. AND).

In order to quantify this distance, the D_KL entropy divergence introduced by Kullback-Leibler [19] was used. The D_KL value expresses the amount of entropy for the assessment of the differences between the two compared distributions P_i (the analyzed distribution - in our case the O distribution) and Q_i - the reference distribution (in our case the T distribution)

$${D}_{KL}\left(P|Q\right)=\sum _{i=1}^{N}{P}_{i}{\text{log}}_{2}\frac{{P}_{i}}{{Q}_{i}}$$

The value of D_KL determined in this way cannot be interpreted as expressing entropy. Thus, a second reference distribution was introduced in the form of the R distribution, where each residue is described by the same level of hydrophobicity equal to R_i = 1/N where N is the number of amino acids in the protein. Such a distribution represents a status devoid of any variation in hydrophobicity levels within the protein and thus devoid of a hydrophobic core.

Each protein is described by the two parameters: D_KL for the O|T and for the O|R relationships, respectively. To avoid the necessity of using two parameters to describe one object, the RD (Relative Distance) parameter was introduced, expressed as:

The value of RD < 0.5 means the presence of a hydrophobic core (good approximation of the O distributiton the T one), while RD > 0.5 means the absence of a hydrophobic core (the O distribution similar to uniform R distribution) (Fig. 1.C).

The RD parameter can be determined for any given structural unit: complex, single chain or domain. In this case, the corresponding 3DGaussian function is defined for each of the listed structural units.

It is also possible to assess the contribution to the construction of a given distribution of any selected section (or other component, e.g. a single protein within a complex, or a domain within a protein, but also a chain fragment within a given structural unit). For this purpose, the Oi and Ti values of the selected fragment are normalized and the calculation of the D_KLs and RD values becomes possible. Interpretation of the RD value is as above: RD < 0.5 means the participation of a given fragment in the construction of a central hydrophobic nucleus. An RD value > 0.5 for a given fragment means a local disorder of the structure of the micelle-like system.

The water environment is not the only one where proteins are active. In particular, membrane proteins function in an environment that expects a different distribution of hydrophobicity. The hydrophobicity is expected to be exposed on the surface for stabilization in the hydrophobic environment of the membrane. Therefore, the idealized hydrophobicity distribution in a membrane protein is described by a function that is the complement of the 3DGaussian function:

$${M}_{i}={T}_{MAX}-{T}_{i}$$

On the basis of previous analyses, the description of the distribution of hydrophobicity in the membrane protein is a combination of the distribution of 3DGauss and [1-3DGauss], with the share of the latter turning out to be varied. Therefore, the final form of the hydrophobicity distribution turns out to be:

$${M}_{i}={\left[{T}_{i}+{K*\left({T}_{MAX}-{T}_{i}\right)}_{n}\right]}_{n}$$

where the index n means a normalization. Parameter K determines the degree to which the micelle-like system has been modified by the external factors, including the hydrophobicity coming from an environment in particular. The choice of the values of parameter K is determined on the basis of the minimum D_KL value calculated for the O|M relation, which means that the given modified M distribution was „reproducer” to the highest degree by the O distribution (Fig. 1.B).

Therefore, each protein analyzed here is determined by two parameters: RD – the assessment of proximity to/far from the idealized micelle-like distribution and K, which determines the degree of participation of environmental factors other than polar water affecting the structure of the protein in question. Thus, the RD value characterizes the structuring of the protein, while the K parameter characterizes the environment.

Proteins with a high degree of micelle-like order with low R and K values have been identified. Proteins characterized by the K = 0 parameter are: down-hill, fast-folding, and antifreeze type II proteins. Also, the vast majority of domains present in proteins show structures with a micelle-like order of hydrophobicity [15]. Membrane proteins including channels in particular show significantly elevated RD and K values (even K levels as high as 3) [20, 21].

The analysis of protein complexation models showing compliance with the FOD model, based on the use of superficial hydrophobic interactions to build the interface, is a point of reference for the example analyzed in the present work. In [22] it has been shown that if the purpose of the complex is only to stabilize and maintain the system, then the construction of an interface is based on a common hydrophobic core for the interacting proteins. The interface is built of hydrophobic residues of interacting proteins exposed on the monomers surface. A local deviation of the O distribution from the T one in the form of a local excess of hydrophobicity indicates a potential site of complexation of another. A local hydrophobicity deficit indicates the presence of a cavity. The type of incompatibility determines the specificity towards a potential interaction partner. This is clearly seen in a significant proportion of enzymes [23].

The main aim of the prezent study is to characterize the chaperone protein DnaJ Hsp40 in a complex with the protein referred to as the "client" using FOD-M model as well as the folded client protein In its native form.

The description of the results obtained in the current work covers the following issues.

The non-micelle-like structuring in PhoA-WT-Aprotein.
Tracking structural changes during PhoA-U folding into PhoA-WT-A.
Determining the specifics of the external force field introduced by the chaperone –HspA-Comp and HspA-AC
Speculations on how the chaperone chain obtains the structure – HspA-A

Comparative analysis of PhoA-U and PhoA-WT structures: assessment of changes in the hydrophobicity distribution

Evaluation of the homodimer status of the active form of PhoA-AB reveals a high degree of maladjustment of the observed distribution to micelle-like one. A very high value of the K parameter indicates a significant contribution of environmental modifying factors to the polar water environment (Table 2). The status of PhoA-A and PhoA-B chains treated as components of the complex turns out to be comparable to the status of a complete complex with equally high K values.

PhoA-A and PhoA-B chains treated as individual units show slightly lower RD and K values, although they are far from those typical of micelle-like ones. On the other hand, the status of the PhoA-U chain is described by very high RD and K values - much higher than for the PhoA-WT. This is due to the very low packing of the structure caused by the cleavage of the PhoA-U chain between Hsp40-A and Hsp40-C (Fig. 2). It should be noted that the value of K = 1.7 is one of the highest values observed for polypeptide chain structures.

Tab. 2. The set of parameters describing the status of the chains in the dimer and the monomers in the PhoA-WT structure. Two values given in the COMPLEX column – the status of the chains A and B considered as components of PhoA-WT. The columns COMPLEX/ INDIVIDUAL – 3D Gauss function stretched over a complex/chain. Values after the // sign – status in the form of PhoA-U. CAT ± 5 denotes the status of the catalytic residue along with a stretch of immediate surroundings ± 5 adjacent residues. SS – segments defined by Cyx positions building the appropriate disulfide bond. P-P – the status of the residues included in the interface, NoP-P – the status of the rest of the chain after elimination of the interface residues.

1EW8

PhoA-WT

COMPLEX

PhoA-WT-A / PhoA-WT-B

INDIVIDUAL

PhoA-WT-A / PhoA-WT-B // PhoA-U

PhoA-AB

PhoA-A/PhoA-B

CAT 102 ± 5

CAT 166 ± 5

SS 168-178

SS 286-336

P-P

NO P-P

0.689

0.691 / 0.688

0.485 / 0.487

0.610 / 0.605

0.471 / 0.471

0.572 / 0.597

0.678

0.672

1.1

1.0 / 1.1

0.596 /0.596 // 0.778

0.274 / 0.289 // 0.564

0.539 / 0.537 // 0.518

0.484 / 0.483 // 0.521

0.480 /0.476 // 0.592

0.718 / 0.720

0.574 / 0.577

0.6 / 0.6 // 1.7

The visualization of the RD and K parameters (Fig. 3) reveals a clearly better fit of the T and O distributions for the PhoA-WT-A form compared to the PhoA-U. The M distribution for K=0.6 partially reproduces the T distribution. Obtaining the value RD < 0.5 requires the removal of numerous residues (showing a significant deviation of both T and O distributions), which also show a significant dispersion along the entire chain. Such a situation indicates inconsistent micelle-like protein folding.

The M distribution is important here, which for the PhoA-U form takes the form of a horizontal line, i.e. similar to the R distribution. The R distribution means complete independence from the influence of the polar water environment, introducing an almost uniform distribution of hydrophobicity along the entire chain.

On the x-axis the residues engaged in the interaction in PhoA-U are marked: with chain Hsp40-A (blue) and Hsp40-C (blue). Top line – red – catalytic residues, blue – residues eliminated from PhoA-WT to reach the RD < 0.5

The discrepancies in the T and O distributions in proteins are of a different nature. There are examples of proteins with RD values > 0.5 (e.g. lysozyme [13]), where the elimination of several residues results in RD < 0.5. The common spatial location of these residues turns out to build an active center. This is not the case in the discussed PhoA-WT protein. Here, obtaining the value RD < 0.5 requires the elimination of a large number of residues located in a significant dispersion along the chain (Fig. 2 - top line, Fig. 4). This means a different folding strategy, where the chain adapts to a non-aquatic environment. The micelle-like arrangement in PhoA-WT is present to a negligible extent. This may be explained by the involvement of the chaperone in the folding of this protein. In the discussed system, the chaperone is treated as a supplier of the external force field, actively participating in the folding process by isolating the folding chain completely from the influence of the polar water environment.

Residues distinguished : red space filling – residues eliminated to reach status expressed by RD < 0.5, green – catalytic residues, yellow – residues engaged in P-P interaction in final PhoA-WT; black – residues engaged in P-P inreaction and simultaneously emgaged in P-P interaction.

It is important to analyze the status of catalytic residues and their immediate surroundings. The catalytic residue 102S ± 5 (together with the immediate vicinity of ± adjacent residues in the chain sequence) shows a status described by the RD < 0.5 in all forms discussed. In the case of PhoA-U, this value is slightly above the threshold 0.5, while the residue 166R ± 5 in all forms shows a status far from micelle-like order. It can be speculated that this common status of catalytic residues is already imposed in the form of PhoA-U.

The presence of disulfide bonds is important for tertiary structure stabilization. The disulfide-bonded chain fragment 168-178 appears to represent a micelle-like arrangement in PhoA-WT. The SS-binding of 286-336 in the PhoA-WT-AB homodimer structure shows RD > 0.5. However, from the point of view of the structure of a single chain, its status is determined by the value of RD < 0.5. The status of both segments in the case of PhoA-U is described by RD values > 0.5 (Tab. 2, Fig. 5).

Residues that build the interface play a specific role in protein complexes. These residues - if the complexation is based on the hydrophobic interactions - very often show a local excess of hydrophobicity. The exposure of hydrophobicity promotes the complexation of another protein, thus disturbing the 3DGaussian distribution within the monomeric unit. In such a situation, the stepwise elimination of residues for the rest of the chain except those included in the interface results in the significant reduction of the interface’s RD value [22]. In the example discussed here, this is not the case. The increased RD value for interface building residues is observed for a single PhoA-WT chain. The remaining part of the chain (after eliminating the residues that build the interface) is described by the reduced value of RD. This means that the interface is partially encoded in the monomer structure, although the formation of a homodimer does not result in the appearance of the micelle-like arrangement for the dimer. Here one should refer to the interfaces, that only stabilize the complex. This is the case, for example, in distrophin, where the purpose of the domain with a clearly defined hydrophobic core is to stabilize the system subjected to numerous external stresses, and where the stable hydrophobic core prevents destabilization of the system [22].

The analysis of the status of individual fragments of the chain with a specific secondary structure in PhoA-WT in comparison with the form represented by these segments in PhoA-U reveals a significant increase in the RD value. Their location is shown in Fig. 6 indicating the mismatch of the centrally located part of the β-sheet.

In summary: the analysis of the structure of PhoA-WT protein chains, it should be emphasized that their status is far from micelle-like, indicating the presence of a factor significantly reducing the influence of polar water as a supplier of external force field. This is indicated by a large number of residues showing maladjustments between T and O distributions distributed along the entire chain. The inability to identify one common location of such maladjustments proves the need for the presence of an environment other than polar water in the folding process.

The status of the PhoA-U (Hsp40-B) chain shows a specific, very far from micelle-like order, of O distribution with a significantly high value of K parameter. This allows to assess the influence of the immediate environment introduced by the chaperone on the folding of the chain. The M distribution for this chain is similar to that of R one, indicating almost complete isolation from the influence of the polar water environment.

Chaperone Hsp40 as a force field supplier in PhoA folding

The presence of the Hsp40 chaperone can be regarded as an external force field provider in the folding process of PhoA. The assessment of its impact on the basis of the FOD-M model is given in Tab. 3. The analysis of the status of the PhoA-U chain residues involved in the interaction with the relevant chaperone chains may answer the question about the contribution of the chaperone to the folding process. In the final structural form of PhoA-WT, the status of the sections involved in the PhoA-U structure in interaction with the chaperone (chain A and C) turns out to be far from the micelle-like status. On the other hand, the part of the chain not involved in the interaction with the chaperone chains shows the status closest to the micelle-like status (Tab. 3), although also at the level with RD > 0.5.

Tab. 3. The values of RD and K parameters for the part of the PhoA-WT chain involved in the interaction with the chains (A and C) in the Hsp40-Compl complex

INTERACTION	RD	K
with Chain A	0.638	0.8
with Chain C	0.604	0.7
Not engaged	0.584	0.5

The location of these segments in the 3D structure of the PhoA-WT form reveals the role of the residues involved in the interaction with the Hsp40-A chain in the interchain interface area of the PhoA-AB complex. In contrast, the residues involved in the PhoA-U form in the interaction with the C chain (Hsp40-C) show surface localization in the PhoA-WT form. In other words, the chaperone determined the form of the interface and the specificity of the surface in the final form of PhoA-WT (Fig.7).

Comparing the forms of PhoA-U with PhoA-WT ( Fig. 8.A) one can notice a change in the T values of individual residues. Low T values indicate a surface location, far from the center. On the other hand, high T values indicate a central position. Therefore, changing the low T values in PhoA-U to high T values in PhoA-WT indicates a shift towards the center of the final structure. Fig. 8.B reveals that PhoA-U (and thus PhoA-WT) residues being in contact with Hsp40-C contribute the most to this rearrangement. On the other hand, the residues located on the surface in the PhoA-U that have migrated to the center are most involved in contact with the Hsp40-A chain. The residues that did not change their location in relation to the center of the molecule are mainly the residues without the contact with the chaperone chains.

The results given above allow us to speculate on the folding mechanism of the protein in question. Sections involved in interactions with A and C chains (PDB ID - 6PSI) in the final structure show a status far from micelle-like organization with high RD and K values (Tab. 3). The structure of the relevant segments, frozen by interactions with the chaperone, enables the interaction-free part of the chain to fold according to the rules applicable in the aqueous environment, leading to a structuring similar to the micelle-like form (the lowest RD and K values for the compared sections of the PhoA-U protein chain).

The structure of Hsp40 complex

The use of the FOD-M model to analyze the Hsp40-Comp complex (DnaJ homodimer + client protein) reveals the high RD and K values (Tab. 4), and when analyzing the T, O and M profiles, significant discrepancies between the O and T distributions can be observed (Fig. 9.). The M distribution obtained for a high value of K is expressed in the form of a line parallel to the x-axis, which means an approximation to the R distribution. This means an approximation of the force field devoid of the specificity of the aquatic environment. Thus, the folding process takes place in an anhydrous environment. The R distribution, which is similar to the M distributions for the entire complex, suggests that this structure is located in a kind of „water-vacuum". The presence of a polar external force field characteristic of a polar water environment is not revealed.

The statuses of individual units treated as components of the complex expressed by the values of RD and K are very close to the description of the entire complex.

The highest value of RD and K, which is shown by PhoA-U treated as a component of the complex, is noteworthy. This is interpreted as imposing a structuring far removed from that which the chain obtains in an aqueous environment. Similarly, an M distribution similar to the R one reveals structuring in the „water-vacuum" (Fig. 9).

The high RD value of the interface residues (P-P and NoP-P) in the discussed complex suggests that this complex was not formed as a result of interactions directed by the aquatic environment. Using the FOD-M model, the mechanism of formation of protein complexes can be explained as an interaction of surface-exposed hydrophobic residues, which in turn gives the interface the status of a hydrophobic core component [22]. This is not the case in given example.

Tab.4. A set of parameters describing the status of the Hsp40-Complex complex (chaperone homodimer + "client" protein)

Chains – składniki kompleksu- chain	RD	K	PP interaction RD	No P-P interaction RD
Hsp40-A, Hsp40-C, PhoA-U (chain B)	0.738	1.3	0.658	0.728
Hsp40-Dimer A+C in complex	0.738	1.3	0.682	0.743
Hsp40-A in complex	0.738	1.2	0.641	0.743
Hsp40-C in complex	0.698	0.9	0.643	0.642
PhoA–U in complex	0.749	1.4	0.651	0.766

The status expressed by the values of RD and K (Tab. 4) visualizes a set of T, O and M profiles for the discussed units. The 3D Gaussian function was generated for a complex containing all three chains.

Looking ate Fig. 9 one can observe that the distributions O and T are significantly different, but the M distributions are comparable for All chains.

How a chaperone chain folds?

One can also ask about the way of obtaining the structure by the Hsp40-A and Hsp40-C chains. The status of these chains (dimer) treated as individual structural units is characterized by the values of RD = 0.778 and K = 1.7. So this is a status far from the form obtained spontaneously in the aquatic environment. The status of single chain Hsp40-A is described by RD=0.646 and K=0.8. It suggests no water-directed folding. In the structure of a single chain of the Hsp40 chaperone, the presence of domains according to the CATH criteria was not identified [24, 25]. However, for the purposes of the present work, the components of this protein structure – pseudo-domains - can be distinguished on the basis of visual analysis (Fig. 10).

Tab. 5. The values of RD and K parameters describing the status of domains distinguished in a single Hsp40 chain. Column on right – number of residues eliminated to reach RD < 0.5

DOMAIN	FRAGMENT	RD	K	Number of Residues eliminated
1. (BLUE)	1-107	0.514	0.4	4
2. (BLUE)	1-115	0.499	0.4
3. (BLUE)	(1-115)+(163-170)	0.519	0.4	7
4. (RED)	(116-162)+(171-182)	0.353	0.1
5. (VIOLET)	(183-257)	0.595	0.7	15
6. (CYAN)	(262-280)	0.592	0.4	3
7. VIOLET+HELIX	(183-280)	0.563	0.5	13

The pseudo-domain status shows relatively very low K values suggesting a relatively low contribution of non-aqueous factors. RD values are slightly above the limit of RD=0.5. The exception is the pseudo-domain 183-280. This part of the chain is involved in the interaction with the second monomer. The reason for this disorder may therefore result from the mutual influence of both chains in the interaction area. However, this complexation is also not based on hydrophobic interactions. In the structure of the dimer limited to these two pseudo-domains, there is a significant deviation from the micelle-like arrangement (RD=0.676, for the P-P part RD=0.561 and for the NoP-P RD=0.682).

For the remaining pseudo-domains, however, it can be assumed that they folded based on the influence of the aquatic environment.

In our previous works related to protein’s structure, a hydrophobic core stabilizing the tertiary structure was repeatedly identified using the FOD-M model. This structure can be found in numerous proteins like down-hill, fast-folding, ultra-fast-folding and antifreeze type II ones [15]. The structures having a hydrophobic core can be found in the vast majority of domains identified in the PDB database [26]. This phenomenon can be interpreted as the effect of the active participation of water environment, which directs the localisation of hydrophobic residues to the center of a protein molecule with the exposure of polar ones on the surface. Very often the participation of disulfide bonds in the stabilization of protein’s tertiary structure favors the arrangement of a hydrophobic core, but it can be also the only factor responsible for its stabilization [27]. Proteins with a longer than 150 aa chain (being the limit for a domain) without a hydrophobic core are stabilized by the disulfide bonds. Undoubtedly, the presence/absence of a hydrophobic core imposes appropriate dynamics and allowable structural changes, including those related to a [22] function.

The water-based external force field can be modified by the presence of chaperones as discussed in the present work. The specificity of the hydrophobicity distribution obtained in this way relies on „imposing” uniform distribution.

To illustrate this, the reference enzyme lysozyme can be used (RD value = 0.529). Exceeding the threshold value RD = 0.5 is caused only by the 3 residues. These are the two catalytic residues 35E and 53D and the residue 128C. The location of 128C in the immediate vicinity of the substrate binding cavity should be emphasized, which gives the specificity of this site related to enzymatic activity. Eliminating these three residues results in the obtaining a status with RD < 0.5, so In this way a part of the protein was identified which, arranged according to the micelle-like scheme, ensures not only the solubility of the protein, but probably also the appropriate dynamics, including local one, related to biological activity. The folding of this protein can therefore be treated as a synergy effect of non-binding interactions and the active participation of an external force field from water [13]. Identification of the part with micelle-like order in the protein (PhoA-WT) discussed in the present work requires the elimination of numerous residues significantly distributed along the chain. [13]. This means the effect of deliberately preventing micelle-like ordering, which is ensured by the chaperone environment. Folding of the PhoA-U chain has a common feature with the process taking place in the endoplasmic reticulum, where the N-terminal fragment is rigidly anchored in the membrane [28–34]. However, the conclusions drawn here cannot be generalized due to the very diverse structures of chaperones with the folding proteins. The only thing that can be generalized is the form of the environmental imposition for the folding protein. This environment is different from the aquatic environment and can be expressed In the FOD-M model by the high RD and K values for both the folding protein and the surrounding chaperone. The role of section 1–22 in the PhoA-U chain should also be emphasized, as it is almost entirely involved in the interaction with the Hsp40-Compl A chain and is removed leading to the final structure of the enzyme. This section, together with the A chain of the chaperone, is a factor referred to as a component of external conditioning, i.e. a factor modifying the external force field for the folding protein. The status of the PhoA-U chain with respect to the entire Hsp40 complex (Fig. 3.B and C) shows an M distribution close to the horizontal line (almost uniform distribution). Such a system can be defined as a specific „water-vacuum" devoid of any influence of the aquatic environment (K value > 1). The status of catalytic residues seems to be already defined in the form of PhoA-U, which means its purposefulness for obtaining the final form leading to obtaining a biologically active structure.

The role of an external force field as an active participant in the folding process directly affects the aquatic environment. Changing the structure and ordering of water molecules turns out to be critical for the course of numerous reactions, including protein folding in particular [35–41], the phenomenon of accelerating the reaction on the surface [42–46], the process of wetting hydrophobic surfaces [47–50] indicated as important for the course of numerous processes. This also applies to amyloid transformation, which proceeds with an increased air-water interphase (effect of shaking) [51]. Therefore, the participation of the immediate environment as an active player in the protein folding process, the characteristics of which are expressed by the K parameter in the FOD-M model, seems to be important for the consideration of protein structuring, including amyloid transformation [52]. The discussed example of the role of a chaperone as an external force field provider is closely related to the participation of prefoldins in the process of folding supported by other proteins [53].

The use of the FOD-M model allows for a quantitative assessment of the change in the folding environment in relation to the aqueous environment, thus determining the role of the chaperone as the supplier of the external force field for the protein folding process. The tertiary structure of PhoA-WT is stabilized by disulfide bonds in the absence of a hydrophobic core. The mismatch of the hydrophobicity distribution towards the micelle-like system applies to the entire chain (as opposed to the proteins, where the few residues showing such a mismatch are located in a 3D structure in a common place, often creating a precisely defined active center). This means that the uniform distribution of hydrophobicity is deliberate and is obtained by the environment of the external force field created in the discussed example by the chaperone. The chaperone’s environment can be defined as a kind of a „water-vacuum" enabling the distribution of hydrophobicity in accordance with the uniform distribution.

The introduction of an external M-distributed field to the in Silico simulation of the protein folding process should direct this process towards the presence of the chaperone. The current work is another example of treating the presence of a factor other than the aqueous environment (membrane [15], prefoldin [53]) as a form of external force field actively participating in the protein folding process.

The generated structure of the PhoA-WT enzyme formed as a result of the external force field provided by the chaperone, in turn, creates an external field for the catalysis process. The characteristics of this field can be determined by the parameter K, which specifies the degree of change to the aqueous environment directing the folding process towards the construction of a central hydrophobic core.

The FOD-M model treats the distribution of hydrophobicity (internal hydrophobic force field) as the effect of external force field (chaperone) influencing the folding proces. This is why the M function (3DGauss function modified by K parameter) is assumed to be the definition of the external force field for prtein folding simulation in Ab initio model. The folding simulation controled by the energy (non-bonding interaction) optimisation shall also take the external force field inluence as optimisation factor under consideration. The simulation shall follow the step-wise adaptation to the directing role of environemntal influence. The Ab Initio folding simulation of alkaline phosphatase folding shall be posssible in the presence of external force field expressed with K = 0.6 modification of 3DGauss function.

Ethics approval and consent to participate – neither human nor animals data are used in the presented research

Consent for publication – All Authors declare consent for publication

Data Availability Statement: All data can be available on request addressed to the corresponding author. The program allowing calculation of RD is accessible on GitHub platform: https://github.com/KatarzynaStapor/FODmodel and on the platform https://hphob.sano.science.

Competing interests - The authors declare no conflict of interest

Funding: This research was funded by Jagiellonian University Medical College grant number N41 / DBS / 000722.

Author Contributions: Conceptualization: IR and LK; methodology: KS; software: KS; validation: KS, formal analysis: IR, LK; investigation: IR; resources: IR; data curation: KS,; writing — original draft preparation: KS and IR; writing — review and editing. KS and IR; visualization. IR; supervision. IR; project administration: IR; funding acquisition: IR .All authors have read and agreed to the published version of the manuscript.

Acknowledgments: Many thanks to Anna Śmietańska and Zdzisław Wiśniowski for technical suport. This research was partially supported by the European Union's Horizon 2020 program under grant Sano No 857533. and Sano project carried out within the International Research Agendas program of the Foundation for Polish Science. co-financed by the European Union under the European Regional Development Fund.

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Ab initio protein structure prediction – the necessary presence of external force field as it is delivered by Hsp40 chaperone

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