An overview of descriptors to capture protein properties – Tools and perspectives in the context of QSAR modeling

Abstract

Proteins are important ingredients in food and feed, they are the active components of many pharmaceutical products, and they are necessary, in the form of enzymes, for the success of many technical processes. However, production can be challenging, especially when using heterologous host cells such as bacteria to express and assemble recombinant mammalian proteins. The manufacturability of proteins can be hindered by low solubility, a tendency to aggregate, or inefficient purification. Tools such as in silico protein engineering and models that predict separation criteria can overcome these issues but usually require the complex shape and surface properties of proteins to be represented by a small number of quantitative numeric values known as descriptors, as similarly used to capture the features of small molecules. Here, we review the current status of protein descriptors, especially for application in quantitative structure activity relationship (QSAR) models. First, we describe the complexity of proteins and the properties that descriptors must accommodate. Then we introduce descriptors of shape and surface properties that quantify the global and local features of proteins. Finally, we highlight the current limitations of protein descriptors and propose strategies for the derivation of novel protein descriptors that are more informative.

Graphical Abstract

1. Introduction

Proteins are important components of food and feed, providing amino acids that facilitate growth and maintain health [1], [2]. Many active pharmaceutical ingredients (APIs) are also proteins, including subunit vaccines, antibodies, blood products and replacement enzymes [3], [4], [5], [6]. Furthermore, numerous industrial processes rely on enzymes for the catalysis of chemical reactions that are too complex and/or expensive for total chemical synthesis, such as the production of paclitaxel [7], [8]. Unfortunately, the manufacturability of proteins can be hindered by low solubility, a tendency to aggregate or inefficient separation from other proteins, nucleic acids or small molecules [9], [10]. Several in silico approaches have therefore been developed to address these challenges, including rational protein engineering and model-based bioprocess development [11], [12], [13].

The approaches typically require the quantification of properties such as protein surface charge distribution to facilitate in silico screening and optimization. The quantitation can be achieved using descriptors that are discrete scalars (e.g., the number of positive surface charges), continuous scalars (e.g., the isoelectric point, pI), or vectors that capture molecular features and thus act as surrogates for actual properties [14], i.e. they reduce the dimensionality of an object, here: a protein. For example, instead of using the explicit charge of each surface-expose functional group of a protein at a given pH (e.g. 19 negative and 3 positive charges at pH 8.5) one can use the isoelectric point or net charge (e.g. 16 negative at pH 8.5) as global charge descriptors.

A key limitation of this dimensionality reduction is that, depending on their definition, descriptors may fail to capture protein complexity and the properties relevant for a specific application, e.g. the prediction of chromatographic protein separation. Specifically, the use of descriptors is characterized by an information loss. In particular, the complex interactions between different protein properties, such as shape and surface charge, can be challenging to capture in a descriptor. Hence, it is advisable to choose or develop descriptors using domain knowledge about the underlying molecular mechanisms of a specific application to ensure that the relevant information is maintained after dimensionality reduction.

The descriptor concept is well established in chemometrics, where it is used to characterize small-molecule compounds with a mass of less than 5000 kDa [15], [16], [17]. For example, typical small-molecule descriptors include the number of nitrogen atoms, the number of phenol rings, and the number of hydroxyl groups. Several suggestions for adapting the concept to proteins have been made [18], [19], [20] and discussing all of them in detail is beyond the scope of this review.

One main application of descriptors in case of proteins is quantitative structure–activity relationship (QSAR) modeling [21], [22]. QSAR models correlate molecular properties (e.g., descriptors such as the isoelectric point) with experimental data reporting measurable properties such as solubility, ligand interaction, or oligomerization [23], [24], [25]. If descriptors can be calculated ab initio, for example based on the protein’s shape and surface properties, such correlations can facilitate a priori predictions about molecular properties that have not been determined experimentally. Accordingly, manufacturability can be assessed during early product design and bioprocess development so that resources can be allocated to the most promising candidates.

Whereas descriptors provide meaningful information about small molecules, they quickly become ambiguous and thus irrelevant as the molecular mass and complexity increase. The ambiguity is more pronounced in proteins because they are polymers composed of a limited number of different but repeating monomeric building blocks. For example, two proteins like endo-beta-1,4-glucanase B (UniProt ID O74706) and glyceraldehyde-3-phosphate dehydrogenase A (UniProt ID P0A9B2) may have a similar atomic composition (3112 vs 3126 carbon atoms) and molecular mass (69.9391 kDa vs 70.8043 kDa) but adopt completely different structures because of differences in the primary sequence, whereas two proteins with different compositions but a limited degree of sequence homology may form similar structures [26], [27], [28]. Accordingly, descriptors must be tailored for proteins and the specific process or application problem. In the context of chromatography, the problem may be the determination of protein–ligand interactions that can in turn be used to predict isotherm parameters and, ultimately, separation conditions [29]. Protein descriptors can be discriminated into various types depending on the application context. Here, we classify protein descriptors into two main groups: surface descriptors and those related to shape, size or structure (for brevity, we describe these as surface descriptors and shape descriptors hereafter). These categories are useful in the context of modeling protein separation, e.g. during chromatography, as, for example, shape will determine diffusion whereas surface properties will determine sorption processes. However, other classifications may be more suitable in a different context and some descriptors are ambiguous because they could be assigned to more than one group. For example, the isoelectric point captures aspects of the protein surface charge and the (solvent) accessible surface area ((S)ASA), which is related to shape.

In this review, we describe the complex features of proteins that must be captured by descriptors and the introduce the various families of shape and surface descriptors that are used, highlighting their applications and limitations, specifically in the context of QSAR models. Finally, we discuss properties that are underrepresented by current descriptors and opportunities to cover them when creating novel descriptors. We focus our discussion on bioprocess development, specifically downstream processing, such as chromatographic purification. We will not cover membrane proteins or the methods of descriptor selection because this must be carried out in the context of specific QSAR applications [30]. Also, descriptors covering biological function will not be discussed.

2. Determinants of protein structure complexity that have to be covered by descriptors

The purpose of protein descriptors is to capture chemical information and relevant properties of the three-dimensional structure in a simple, often one-dimensional form, for example as a scalar or set of scalars like the k largest positively charged surface patches. Therefore, in an abstract sense, calculating the numeric value of a descriptor is a complexity reduction task. The challenge is to minimize the information loss when extracting the important aspects of protein properties, for example the surface charge (distribution), while reducing the dimensionality of the original object [31].

To illustrate the challenge of complexity reduction, we will briefly describe the important structural elements of proteins. The four well-known structural levels are the primary structure (amino acid sequence), the secondary structure (repeating local configurations such as α-helices, β-sheets and β-turns, generally held together by hydrogen bonds) or lack thereof (random coil), the tertiary structure (overall configuration or “fold”, defined by the path of the polypeptide backbone through space, which is stabilized by disulfide and hydrogen bonds as well as ionic and hydrophobic interactions) and the quaternary structure (assembly of polypeptide subunits into a higher-order structure) [32]. The quaternary structure is also described as oligomerization and may comprise multiple copies of the same polypeptide (homomultimer) or different polypeptides (heteromultimer) [33]. Various degrees of oligomerization exist, starting with the monomer (e.g., bovine serum albumin; UniProt ID P02769) and dimer (e.g., human alcohol dehydrogenase class 3; UniProt ID P11766), but building to complex assemblies such as hetero-16-mers (e.g., ribulose-1,5-bisphosphate carboxylase-oxygenase (RuBisCO); UniProt IDs P00876 and P69249) and hetero-24-mers (e.g., human ferritin; UniProt IDs P02792 and P02794). Importantly, oligomerization can change the properties of the monomeric unit compared to the free monomer. The oligomer always has a larger mass and size, but the monomeric shape and surface charge may also change. For example, human ferritin monomers have a mass of 20–21 kDa and a size of ∼4 nm, whereas the 24-mer has a mass of ∼400 kDa and a diameter of ∼10 nm [34]. In addition, the free monomers have a flattened shape whereas the oligomer is a hollow sphere. Similarly, monomers of antibodies are composed of globular domains (e.g., immunoglobulin gamma heavy chain constant region 2B; UniProt ID P01867) but assemble into a Y-shaped tetramer, and in some cases higher-order structures with additional components. Even without considering oligomerization, the tertiary structure of proteins can adopt diverse shapes, including dense spheres (e.g., bovine chymotrypsinogen A; UniProt ID P00766), barrels (e.g., red fluorescent protein drFP583; UniProt ID Q9U6Y8), rods (e.g., human fibrinogen; UniProt ID P02675) and hooks (e.g., integrin α-E; UniProt ID P38570). Surface properties are also affected by oligomerization. For example, the (structure-based) isoelectric points of the tobacco RuBisCO large and small subunits of are 5.60 and 6.51 respectively, whereas the isoelectric point of the hetero-16-mer is 6.21.

Post-translational modifications can also alter both the shape and surface properties of proteins. Glycosylation significantly increases the mass of a protein (e.g., by ∼1.9 kDa per site or 5–10% of a protein [35]), and affects the surface properties in a number of ways. On one hand, carbohydrates can shield the surface and prevent certain areas interacting with other molecules, for example to modify or suppress recognition by the immune system [36]. On the other hand, many carbohydrates feature charged monomers that alter the protein surface charge (distribution) [37]. Other post-translational modifications may be smaller but can nevertheless alter the surface properties of a protein dramatically. For example, a phosphate group has a diameter of less than 0.4 nm [38], but adds two negative charges (depending on the pH of the surrounding medium). Similarly, methylation and acetylation remove a potential hydrogen bonding site and increase the hydrophobicity of the surface [39]. Protein databases such as UniProt (https://www.uniprot.org/) provide annotated information about potential and reported post-translational modifications, but the set of modifications present on a given protein may vary and is difficult to predict a priori, especially if a protein is produced in a heterologous host that may not create native modifications authentically. For example, human proteins expressed in yeast often contain high-mannose glycans lacking the charged, terminal N-acetylneuraminic acid residues normally found in the native protein [40]. This makes it difficult to account for post-translational modifications when calculating descriptors, especially if samples of purified, authentic protein are not available for analysis. Nevertheless, all these layers of structural complexity should be considered when designing and calculating descriptors of protein surface and protein shape properties in order to obtain values that are representative of the actual protein.

3. Descriptor availability, redundancy and applicability

Given the structural complexity of proteins, many descriptors have been developed to cover different properties. Some descriptors were designed for the characterization of small molecules and capture atomic properties such the number of specific nitrogen atoms or chemical groups such as aromatic rings [21]. These are often of limited use for proteins because they are unlikely to capture the surface and shape properties in a meaningful way and their values can be similar even for proteins lacking structural homology (see the carbon atom example above). Others have been developed specifically to quantify protein shape and surface properties, such as the number, shape and size of surface patches (contiguous protein surface areas with a consistent property, like hydrophobicity or positive charge) [41], [42]. However, the underlying property (e.g., positive charge) is typically a continuous parameter and it is difficult to define the boundaries and thus the size and number of patches. A given position on the protein surface is unlikely to have an exactly zero net charge but will instead exhibit a slight charge due to the combined effects of positively and negatively charged amino acid side chains near that position [43]. A common workaround is to define thresholds for the patch boundaries, for example the minimal positive charge could be 10 eV. However, this means the boundary condition of a patch is defined arbitrarily, and the relevance of the threshold with respect to applications such as protein binding to a charged chromatography ligand would be unclear [24], [44]. This is often addressed by creating sets of similar descriptors that use different thresholds, e.g. the k largest patches. But even this creates new difficulties because introducing sets of similar descriptors substantially inflates the total number of descriptors. Furthermore, the descriptors within such a set are highly redundant and collinear by design, aggravating the selection of the most relevant descriptors during subsequent QSAR model building [45]. An informed threshold selection and/or descriptor pre-selection by experts with domain knowledge (e.g., in chromatography) can reduce the number of descriptors but will rely on personal experience and may be unintentionally biased. Therefore, a more rational definition of thresholds and descriptors would be helpful in this context as was also recently discussed in the context of small molecules and when comparing self-supervised and manually selected features [46], [47].

Another major limitation of many protein descriptors is their averaging effect. For example, calculating the dipole momentum of a protein will integrate polarity over the entire molecule, which can mask distinct differences both on the surface and between surfaces. Indeed, molecules with different partial charge distributions may have the same dipole momentum (Fig. 1). Accordingly, the descriptor will not properly capture the intramolecular heterogeneity. The inability of Pearson’s correlation coefficient to distinguish between different types of (non-randomly) scattering data can be regarded as an analogy in this context. Therefore, novel descriptors may be required that maintain information about the heterogeneity of properties such as shape and charge distribution.

Fig. 1.

Descriptor ambiguity. A. Schematic representation of a protein (black ellipse) with positive (red) and negative (blue) surface charges creating a net zero dipole moment. B. Alternative schematic for a different protein (black circle) with the same net zero dipole moment as in A but different surface charge distribution, i.e. a central patch of negative surface charge. C. Schematic representation of protein domains (green dots) and the corresponding minimum volume-enclosing ellipsoid use to calculate eccentricity (black ellipse). D. Alternative protein with the same minimum volume-enclosing ellipsoid as in C, but substantially different domain architecture and mass.

The various types of descriptors can be calculated based on either the amino acid sequence or the protein structures such as those from the Protein Data Bank (PDB) using many different commercial or free-to-use software tools (Table 1). Some of these tools have recently been reviewed [45], and tool selection may be driven by the subsequent application of the descriptors and resulting QSAR model (e.g., the prediction of protein separation or solubility [48], [49]).

Table 1.

Overview of software packages used for descriptor calculation. A similar overview has been published before [45].

Application	Tool name	Type of descriptors	Input format	Output	Software Type	Open access	Web address	Ref.
General	CDK	Topological, constitutional, geometric, electronic, hybrid descriptors, fingerprints (ECFP, Daylight, MACCS, and others)	SMILES, SDF, InChI, MOL2, CML, and others	One or more values of varying types (Boolean, Double, Integer)	Java Library	yes	http://cdk.github.io	[50]
	MOE	2d, 3d descriptors, topological, physical properties, structural keys	PDB, SDF, SMILES, and others	n.a.	Software	no	www.chemcomp.com	n.a.
	PyDPI	Amino acid, di-, and tri-peptide composition, autocorrelation descriptors, CTD descriptors, sequence order coupling, quasi-sequence order descriptors, pseudo amino acid composition, descriptors, amphiphilic pseudo amino acid composition descriptors, conjoint triad features	n.a.	Binary, integer and continuous scalars, group of scalars descriptors can be interpreted as 1D, 2D, or 3D arrays* *	Python toolkit	yes	https://pypi.org/project/pydpi/#description	[51]
	Rcpi	Amino acid composition, autocorrelation, CTD descriptors, quasi-sequence order, pseudo-amino acid composition, PSSM profile, molecular descriptors (2D/3D), including constitutional, topological, geometrical, electronic descriptors, molecular fingerprints (PCM, GO similarity, sequence similarity)	SMILES, DF files, FASTA, PDB	n.a.	R package	yes	https://bioconductor.org/packages/release/bioc/vignettes/Rcpi/inst/doc/Rcpi.html; http://research.chem.psu.edu/pcjgroup/adapt.html	[52]
Small molecules	ADAPT 260 *	Topological, geometrical, electronic	n.a.	n.a.	n.a.	n.a.	n.a.	n.a.
	ADMET predictor	Constitutional, functional group counts, topological, E-state, 3d descriptors, molecular patterns, acid-base ionization, empirical estimates of quantum	SDF	n.a.	software	no	www.simulations-plus.com	n.a.
	ADRIANA. Code	Constitutional, functional group counts, Lipinski rule-of-five, topological, E-state, Moriguchi, Meylan flags, 3d descriptors, molecular patterns	n.a.	n.a.	software	no	http://www.akosgmbh.de/molnet/adriana.htm	n.a.
	ALOGPS2.1 *	logP, logS	n.a.	n.a.	n.a.	yes	www.vcclab.org	n.a.
	BioChem	Constitution, topology, connectivity, kappa, estate, autocorrelation, molecular properties, charge, moe-type descriptors	SMILES, SDF, SMI-file	Integer and continuous scalars, groups can be interpreted as arrays* *	Web-server	yes	http://biotriangle.scbdd.com	[53]
	BlueDesc	Constitutional descriptors, topological descriptors, connectivity indices, 2d-autocorrelation, topological charges indices, geometrical descriptors, WHIM descriptors, functional groups, molecular properties	3D-structures	Integer and continuous scalars, groups can be interpreted as arrays* *	Java-Tool	yes	http://www.ra.cs.uni-tuebingen.de/software/bluedesc/welcome_e.html	n.a.
	ChemDes	Molecular descriptors	SMILES, SDF, SMI-file	Integer and continuous scalars, groups can be interpreted as arrays* *	web-based platform	yes	www.scbdd.com/chemdes	[54]
	Chemopy	Constitution, topology, connectivity, E-state, kappa, Basak, Burden, autocorrelation (Moreau-Broto, Moran, Geary), charge, property, moe-type, geometric, CPSA, RDF, MoRSE, WHIM, fingerprints	SMILES, MOL	Integer and continuous scalars, groups can be interpreted as arrays* *	Python Package	free	https://code.google.com/archive/p/pychem/downloads	[55]
	CODESSA	Constitutional, topological geometrical, charge-related, semi-empirical, thermodynamical	n.a.	Numerical characteristics	Software	no	www.codessa-pro.com	n.a.
	DRAGON	Constitutional, topological 2d- autocorrelations, geometrical, WHIM, GETAWAY, RDF, functional groups, etc.	MDL, Sybyl, SMILES, CML, and others	Integer and continuous scalars, groups can be interpreted as arrays* *	Software	no	www.talete.mi.it	n.a.
	E-DRAGON*	Molecular descriptors	n.a.	n.a.	Software	yes	www.vcclab.org/lab/edragon/	n.a.
	JOELib	Counting, topological, geometrical properties	SMILES, SDF, CML, CTX, FLAT, MOL2, and others (PDB in progess)	n.a.	Java-Package	yes	http://www.ra.cs.uni-tuebingen.de/software/joelib/introduction.html	n.a.
	KRAKENX	Quantum chemical, atomic charge-based, CPSA, EVA/EEVA, shape, geometry, topographical, Coulomb matrix, graph energy	SDF	Integer and continuous scalars, groups can be interpreted as arrays* *, vectors, matrices	Software	yes	https://gitlab.com/vishsoft/krakenx	[56]
	MODEL*	Molecular descriptors	n.a.	n.a.	Web-server	yes	http://jing.cz3.nus.edu.sg/cgi-bin/model/model.cgi	n.a.
	MOLCONN-Z	Topological	SMILES, SDF, MOL2	Integer and continuous scalars, groups can be interpreted as arrays* *	Software	no	www.edusoft-lc.com/molconn	n.a.
	MOLD2	1d, 2d	n.a.	Integer and continuous scalars, groups can be interpreted as arrays* *	Software	yes	https://www.fda.gov/science-research/bioinformatics-tools/mold2	[57]
	MOLGEN-QSPR	Constitutional, topological, geometrical	SDF	n.a.	Software	no	www.molgen.molgenqspr.html	n.a.
	Mordred	2d, 3d	SMILES, SDF	Integer and continuous scalars, boolean, groups can be interpreted as arrays* *	Python Package	yes	https://github.com/mordred-descriptor/mordred	[21]
	OEChem TK	166-bit MACCS, LINGO, circular, path (Daylight-like)	FASTA, SMILES, PDB, andothers	n.a.	programming library	no	www.eyesopen.com	n.a.
	OpenBabel	MOLPRINT2D, 166-bit MACCS, Daylight fingerprint (FP2), structural key fingerprints	SMILES, PDB, MOL2, CML., InChl, and other (84 formats)	Numerical and textual descriptors	Python Modul / Software	yes	www.openbabel.org	[58]
	PADEL*	1d, 2d, 3d descriptors, molecular fingerprints	n.a.	1d, 2d, and 3d descriptors	n.a.	yes	www.padel.nus.edu.sg	[59]
	PowerMV	Constitutional, atom pairs, fingerprints, BCUT	MDL, SDF	Bit strings, continuous, collections, and counts	Software	yes	www.niss.org/PowerMV	[60]
	PreADMET	Constitutional, topological, geometrical, physicochemical, etc.	n.a.	n.a.	Web-server	yes	http://preadmet.bmdrc.org	n.a.
	QikProp	Topological descriptors, Mopac Descriptors, QikProp	n.a.	n.a.	Software	no	https://www.schrodinger.com/products/qikprop	n.a.
	QuBiLS‐MAS	Topological molecular descriptors based	MOL, SDF, MDL	Continuous scalars, groups can be interpreted as arrays* *	Software	yes	http://tomocomd.com/software/qubils-mas	[22]
	RDKit	2d, 3d descriptors, fingerprints	SDF, MOL2, PDB, and others	Integer and continuous scalars, vectors, dict	Toolkit	yes	https://www.rdkit.org	n.a.
	Sarchitect*	Constitutional, 2d, 3d	n.a.	n.a.	n.a.	no	www.strandls.com/sarchitect/index.html	n.a.
	VolSurf+	ADME relevant descriptors	n.a.	Quantitative numerical descriptors	Software	no	https://www.moldiscovery.com/software/vsplus/	n.a.
Protein	AAindex	No direct descriptor	n.a.	Integer and continuous scalars, group of scalars descriptors can be interpreted as 1d, 2d, or 3d arrays* *	Database of amino acid indices	yes	https://pypi.org/project/pydpi/#description	[61]
	BioProt	Amino acid, di-, and tri-peptide composition, CTD descriptors, M-B, Moran, Geary autocorrelation, conjoint triad features, quasi-sequence order descriptors, sequence order coupling number, pseudo amino acid composition 1 / 2	raw aa sequence, FASTA	Integer and continuous scalars, group of scalars descriptors can be interpreted as 1d, 2d, or 3d arrays* *	Web-server	yes	http://biotriangle.scbdd.com	[53]
	DescribePROT	Database of 13 complementary descriptors for 83 complete proteomes	n.a.	Binary, integer and continuous scalars, group of scalars can be interpreted as arrays* *	Database of descriptors	yes	http://biomine.cs.vcu.edu/servers/DESCRIBEPROT/main.php	[62]
	iFeature	Amino acid composition, grouped amino acid composition, CTD descriptors, M-B, Moran, Geary autocorrelation, conjoint triad, quasi-sequence-order, pseudo-amino acid composition, PseKRAAC, AAindex, BLOSUM62, Z-scale	FASTA	n.a.	Python Package / Web-server	yes	https://ifeature.erc.monash.edu	[63]
	MuLiMs-MCoMPAs*	n.a.	n.a.	n.a.	n.a.	yes	http://mumbailocalinference.net/MCoMPAS/MCoMPAS.html	[64]
	ProFeat-SS*	n.a.	n.a.	n.a.	n.a.	yes	http://bidd.cz3.nus.edu.sg/software/ProFeat-SS/*	n.a.
	PROFEAT*	n.a.	n.a.	n.a.	n.a.	yes	http://bidd.cz3.nus.edu.sg/software/PROFEAT/*	n.a.
	ProPred*	n.a.	n.a.	n.a.	n.a.	yes	https://web.kuicr.kyoto-u.ac.jp/supp/propred/	n.a.
	ProtDCal*	n.a.	PDB, FASTA	n.a.	n.a.	yes	https://webs.iiitd.edu.in/raghava/protdcal/	[65]
	PROTEIN RECON*	n.a.	n.a.	n.a.	n.a.	yes	http://bioinf.modares.ac.ir/software/protein-recon/	n.a.
	Protparam	Molecular weight, theoretical pI, amino acid composition, atomic composition, extinction coefficient, estimated half-life, instability index, aliphatic index, grand average of hydropathicity (GRAVY)	raw aa sequence, Swiss-Prot/TrEMBL accession number (AC)	Integer and continuous scalars, group of scalars descriptors can be interpreted as 1d, 2d, or 3d arrays* *	Web-server	yes	https://web.expasy.org/protparam/	[66]
	protr	Amino acid composition, grouped amino acid composition, CTD descriptors, M-B, Moran, Geary autocorrelation, conjoint triad, sequence order coupling number, quasi-sequence-order, pseudo-amino acid composition, amphiphilic pseudo-amino acid composition, pseudo amino acid compositions	raw aa sequence, FASTA	Integer and continuous scalars, group of scalars descriptors can be interpreted as 1d, 2d, or 3d arrays* *	R Package	yes	https://nanx.app/protr/	[67]
	PseAAC	n.a.	FASTA	Integer and continuous scalars, group of scalars descriptors can be interpreted as 1d, 2d, or 3d arrays* *	Web-server	yes	http://www.csbio.sjtu.edu.cn/bioinf/PseAAC/	[68]
	PyBioMed (PyProtein)	Amino acid, di-, and tri-peptide composition, CTD descriptors, M-B, Moran, Geary autocorrelation, conjoint triad features, quasi-sequence order descriptors, sequence order coupling number, pseudo amino acid composition 1 / 2	PDB ID, UniprotID	Integer and continuous scalars, group of scalars descriptors can be interpreted as 1d, 2d, or 3d arrays* *	Python Package	yes	https://pybiomed.readthedocs.io/en/latest/	[69]

*the websites were not accessible during the time of writing, which is why little information was retrievable; * * some descriptors represent amino acid or heavy atom counts, which can be regarded as sets of individual descriptors or as a single 1D-array. Additionally, there are descriptors that count pairs and triples, which can be represented as 2D or 3D-arrays accordingly.

Regardless of which software tool is used to calculate the descriptors, the values can vary substantially based on the hydrogen atom addition and energy minimization operations applied to the structures before descriptor calculation. For example, we obtained electric dipole moments of catalase (UniProt ID P00432, pdb ID 3re8) ranging from 371 to 812 Debye (1.237 ×10^-27 to 2.708 ×10^-27 C m) when using Molecular Operating Environment (MOE; Chemical Computing Group, Canada) for the calculation. In contrast, an open access server provided a value of 121 Debye (0.404 ×10^-27 C m) [70]. At best, this variability can be accommodated by calculating the descriptors of a protein several times for structures derived from individual hydrogen atom addition and energy minimization procedures or using slightly different parameters for the latter (e.g., force field, pH and temperature).

4. Protein shape descriptors

Protein shape descriptors often simplify the overall complexity of a protein structure by reporting sum parameters such as the molecular mass, the van der Waals (vdW) area or (S)ASA and corresponding volumes [71]. Similarly, protein properties may be averaged and represented through convex hulls [72] or equivalent spheres that share a certain feature with the protein of interest. Accordingly, the radii of such spheres are descriptors too: for example, the hydrodynamic radius (also called the Stokes radius, equivalent to diffusion properties, [73]) or the radius of gyration (equivalent to the moment of inertia, [74], [75]), which can be used to predict polymer-induced precipitation and/or diffusion in porous media as well as potential sites of molecular interactions [76], [77], [78], [79]. Recently, models have been developed that correlate the hydrodynamic radius and radius of gyration for unstructured proteins [80]. Furthermore, the radii of gyration and eccentricity are measures of compactness [19], [81], and thus indicate how well a protein complies with the frequent assumption of a sphere-like shape made by many predictive models. Indeed, predictions about friction or sedimentation often assume smooth spheres [82] and so do models predicting unstructured regions of proteins. Eccentricity and the principal axes of inertia are interesting indicators of molecular anisotropy and are linked to ligand-binding sites [76]. They can mask distinct structural differences between proteins because molecules differing in shape may have the same eccentricity. Specifically, eccentricity is based on the minimum volume-enclosing ellipsoid [19], which can be identical even between proteins that occupy substantially different fractions of the volume of that ellipsoid (Fig. 1).

Shape descriptors can also account for the number of secondary structures and their relative abundance in a protein. This is important because motifs featuring, for example, up to four α-helices often mediate protein–protein interactions [83], [84]. The descriptor calculation typically uses propensities derived from theoretical considerations or generalized experimental observations, as proposed by Chou and Fasman [85], and can be improved if data from actual protein three-dimensional structures are available from X-ray crystallography, nuclear magnetic resonance spectroscopy or homology modeling studies. Furthermore, the relative orientation of secondary structures, which is important for the formation of binding motifs, is not captured by these descriptors.

The protein shape is also affected by intrinsically unstructured, disordered or natively unfolded regions, which facilitate flexible and context-specific binding [86], [87]. These are described as intrinsically disordered regions (IDRs) if they are found within an otherwise structured protein, or intrinsically disordered proteins (IDPs) if the entire protein is affected. IDRs can be predicted based on propensities similar to those of helices and sheets, for example using neural networks [87], [88]. Accordingly, the corresponding descriptors share similar limitations such as the reliance on biased datasets over-representing globular proteins while neglecting other shapes [89].

At the level of primary structure, proteins can be described using graph theory approaches, such as the connectivity index and Wiener index. These indices facilitate primary sequence alignments [90] as well as the design of protein interaction networks [91], [92], but are more likely to be relevant for small molecules. For example, the Wiener index is the sum of the shortest path between all pairs of vertices (e.g., atoms on the protein surface), yet the number of such pairs m increases as a function of the number of vertices n according to the equation m = n × (n – 1)/2, so that values can be large for proteins but differences between proteins may be small despite substantial differences in shape. Interestingly, protein size and oligomerization, as well as structural elements such as linker sequences, seem to correlate with the relative abundance of amino acids like alanine, which may also be useful as a descriptor [93], [94].

In contrast, global, rotation-invariant descriptors of protein shape may be derived from a series expansion of three-dimensional functions. Although these descriptors are based on the global shape of a protein, they account for distinct local features and therefore circumvent some of the shortcomings described above for conventional descriptors. One successful example is the so-called Zernike 3D descriptor, which allows the rapid identification of similar protein shapes and surfaces involved in protein–protein interactions [19], [95], [96]. Zernike 3D descriptors are vectors of, for example, 121 entries. Each entry represents a norm of a vector of coefficients derived from the expansion series of a three-dimensional function formulated on an orthogonal basis [96], and different three-dimensional functions can be used [95]. Accordingly, protein shape similarity can be quantified by calculating the difference in the Euclidian norms of the Zernike 3D descriptors of two proteins or using similar distance measures such as the Manhattan metric. In addition to this tensor algebra-based approach, linear algebra and other forms can be used as well [97]. The topic of 3D molecular descriptors for proteins has recently been applied and reviewed elsewhere [97], [98], [99]. In this context, the Laplace-Beltrami operator may be used as an alternative option to describe protein shapes invariant to rotation and translation [100], [101]. Specifically, this operator can be used to calculate local geometric descriptors, such as the heat kernel signature [102], which can be used to create a fingerprint-like map for each node on a discretized, polygonal surface, for example of a protein. A challenge of this approach is the definition of meaningful time points at which a surface is to be evaluated, potentially creating a large number of (partially) redundant descriptors. There are various methods to reduce the dimensionality of the high-dimensional local descriptors and condense them into predefined global descriptors, e.g. by calculating the covariance matrix or aggregating eigenfunctions [101], [103]. When combining Laplace-Beltrami operator-derived descriptors with methods such as bag-of-features [104], it may become possible to simultaneously capture protein shape and surface properties, for example by correlating protein properties with a heat kernel signature [102]. (Fig. 2).

Fig. 2.

Discretized polygonal surface of plastocyanin B'/B'' (UniProt ID P35477) colored according to its heat kernel signature [102] at various time points. The heat kernel signature of each vertex reflects a theoretical heat dissipation over time and serves as a tool to elucidate distinct local geometry determined by the intrinsic properties of the protein surface that can be used as a descriptor.

5. Protein surface property descriptors

The functionality of the protein surface comprises various important properties that affect solubility and interactions with other molecules, including proteins, substrates, or ligands during chromatographic separation. These surface properties are defined by the functional groups of amino acid side chains exposed on the protein surface, including charged, polar or hydrophobic residues (among other classifications [105]), and may constitute patches on the surface if several amino acids of the same type cluster together [12]. The corresponding protein surface regions may partially overlap, making it difficult to define boundaries as discussed above. Protein surface descriptors typically report properties as counts (e.g., number of positively charged surface patches) or sums (e.g., total positively charged surface area), both of which can be normalized against another property such as the (S)ASA. Sets of descriptors can capture the same property using different thresholds (also known as gates), defined by a minimum number, size, or other parameter. Like shape descriptors, surface descriptors can capture properties globally and locally as discussed below for charged, polar and hydrophobic descriptors.

5.1. Charge

A prominent global descriptor of a protein’s surface charge properties is the isoelectric point (pI). This can be calculated from the primary sequence alone [106] or by accounting for structural information reflecting the functional groups accessible on the protein surface [107]. Databases with proteome-wide isoelectric point information are now available [108] and this metric can be used, for example, as a predictor of crystallization efficiency [109] whereas it may be insufficient to predict protein–ligand interactions in a chromatography setting [110]. A property related to the isoelectric point is the overall net charge of a protein in a buffer with a given pH. In molecular dynamics simulations, this property correlates well with the colloidal interaction strength between proteins [111].

Protein surface charge can also be characterized by the number and size of positively and/or negatively charged patches, and thresholds for the minimum patch size (e.g., in Ų or nm²) and charge (e.g., in eV) can be applied. Additional constraints may be formulated to specify the surface charge descriptors. For example, the charged surface area may be limited to the k largest patches or counting can be restricted to certain protein domains or parts thereof, such as the complementarity determining regions (CDRs) of an antibody. Such charge-based descriptors have been used in QSAR models for the successful prediction of retention on different types of charged chromatography resin [24], [48]. Locally, descriptors may report residue pKa values, which can be combined with a protein’s pseudo amino acid composition to discriminate between mesophilic and thermophilic proteins [112].

Other descriptors relate surface charge to the behavior of proteins in suspension. Specifically, the ζ-potential is the electric potential of a protein at its slipping plane when moving through a suspension. The ζ-potential can be calculated for different conditions, such as bulk suspensions or confined environments like pores [113], [114], and depends on properties such as pH and conductivity, which must be specified accordingly [115]. The ζ-potential can be used to predict the likelihood of protein aggregation, with values close to zero indicating a high propensity and values< –40 or> 40 mV typically indicating colloidal stability [116]. A closely related descriptor is the Debye (screening) length (κ^-1), which is a measure of how quickly (in terms of distance) the effects of the electric potential of a protein decline in the surrounding suspension. Accordingly, the Debye length depends on the salt type and concentration as well as temperature, and can be used to describe the effect of suspension properties on the formation of a protein–polyelectrolyte complex [117].

5.2. Polarity

Whereas charge is defined by the presence of ions of opposing charge, polarity concerns partial charges that arise when the electronegativity differs between two covalently bound atoms [118]. Accordingly, polarity-based descriptors may account for surface properties based on charge, non-charged but polar features, or a combination of both, blurring the boundary between charge and polarity-based descriptors. Dipole moments exemplify a family of global, polarity-based descriptors, capturing the overall anisotropy of the surface (partial) charge distribution of a protein. On one hand, this family consists of the dipole direction and dipole moment of a protein, the latter distinguishing between proteins that are likely to precipitate in the presence of either ammonium sulfate or polyethylene glycol [18]. The (charge) separation distance and (charge) shape regularity are descriptors with a similar information content, which also applies to the ζ-dipole moment derived from the ζ-potential described above. On the other hand, dipole moments may also be calculated for each of the three axes of a Cartesian coordinate system or for the principal axes of inertia of the protein as discussed above. More selective measures of polarity can also be applied, for example by calculating the charge symmetry of variable regions of antibodies, providing useful descriptors for the in silico prediction of antibody solubility [25].

The polarity of a protein may also be predicted from the primary sequence based on polarity propensities of the individual amino acids [119], [120], but this approach neglects any structural information and is limited in value. The same applies to descriptors such as hydrophilicity indices, as well as the number of hydrogen-bond donors and acceptors, which are probably more relevant for small molecules because, for example, there are fewer donors per molecule compared to proteins, and differences thus facilitate better discrimination.

5.3. Hydrophobicity

Surface hydrophobicity is important for protein–protein recognition [121], aggregate formation [122], solubility, and proteolytic stability [123]. Many descriptors therefore encode hydrophobic properties. The total hydrophobicity of surface-exposed and solvent-accessible amino acid side chains is a global descriptor [124], which can be refined by applying a quadratic model to these values [125]. This modified descriptor was successfully used to predict protein retention times during hydrophobic interaction chromatography. Similarly, partitioning coefficients, for example in octanol–water two-phase systems (logP(o/w)), can be used to describe the overall hydrophobicity/lipophilicity of a protein. However, such descriptors may be difficult to predict ab initio and the overall hydrophobicity does not reveal the distribution of hydrophobic patches on the protein surface. Similar to global charge descriptors, the hydrophobic dipole moment is a metric that quantifies the degree of asymmetry in surface hydrophobicity [126].

The hydrophobic dipole moment can also be calculated for fractions of a protein, such as a domain or secondary structure, as an indicator for intramolecular and intermolecular interactions [126]. However, information about the spatial distribution and relative orientation of the individual moments is not stored in these descriptors. Similarly, hydrophobicity can be calculated for the k largest patches, a certain number of patches, or a number of patches above a certain threshold, as discussed for surface charge above. It is important to note that if threshold selection is arbitrary and many thresholds are used, the number of collinear descriptors increases, which also increases the risk of overfitting QSAR models if the size of the training set is small compared to the number of descriptors [127].

At the primary sequence level, the hydrophobicity index of each amino acid in a protein can be aggregated to an overall hydrophobicity. However, many different definitions of this index have been developed over time [128], 24 of which are implemented in ProtScale, a protein identification and analysis tool on the Expasy server [129]. The definitions are based on either theoretical calculations or empirical data [130], such as the accessible surface of amino acids, the fraction of the number of different amino acids buried within proteins, the amino acid free energy of transfer from ethanol to water, and peptide retention times during reversed-phase chromatography [125]. Accordingly, the ranges and dimensions of hydrophobicity indices differ substantially. Nevertheless, 19 of the 24 indices in ProtScale are strongly connected, with an average Pearson’s correlation coefficient of r = 0.81 (Fig. 3, Table S1). The remaining five indices still have an average Pearson’s correlation coefficient of r = 0.62. They are negatively correlated with the first group of indices (r = –0.72), indicating an inversion of the direction of the scales compared to the other indices.

Fig. 3.

Comparison of hydrophobicity scales. A. The hydrophobic propensities of the 24 hydrophobicity scales used in ProtScale are plotted for each of the 20 canonical amino acids. Mean (red), frequently referenced scales (Kyte & Doolittle, green), the scale ordered in reverse (Parker, orange), and the scale with the lowest absolute correlation to the other scales (Welling, blue) are highlighted in color. B. Same hydrophobicity scales as in A but with standardized values. C. Maximum spanning tree of the absolute correlations between hydrophobicity scales with inversion number (IN) to average scale and value range of scale (RoS). The r values at edges indicate the Pearson correlation coefficient between the connected scales. D. Color code of the boxes in C. according to the inversion number of the corresponding hydrophobicity scale. The inversion number quantifies the similarity of the order of amino acid hydrophobicity between the different hydrophobicity scale. Specifically, each scale is compared to the average amino acid order of hydrophobicity scaled between 0 and 1, e.g. an IN of 0 would indicate a perfect match with average whereas a value of n⋅(n-1)/2 (here:190) indicates a fully inverted order. E. Amino acid hydrophobicity averaged over all scales. The five inverted hydrophobicity scales (blue) were reverted when calculating the average to ensure a uniform direction in hydrophobicity. Amino acids are given in three-letter code in A, B and E.

Ultimately, the selection of hydrophobicity descriptors will depend on the application. Whereas a dedicated tag-based hydrophobicity descriptor predicts the binding of tagged proteins during hydrophobic interaction chromatography more accurately than an index variant describing the entire surface, the accessible surface hydrophobicity can be used successfully to describe protein partitioning in aqueous two-phase systems [130].

5.4. Aggregation

Charge, polarity and hydrophobicity affect protein properties at the same time, and a holistic investigation should therefore account for combinations of these factors and their interactions. Calculating such combinations may be difficult a priori due to complex mutual interferences, including shape effects and environmental effects due to solvent and buffer properties. Therefore, a set of descriptors has been developed based on empirical polypeptide aggregation data to predict the tendency of proteins to form aggregates [131], [132]. Although this approach can resolve differences caused by single amino acid substitutions, it depends on an empirical dataset for calibration and is therefore laborious to augment (including a lack of standardization between laboratories when generating such data) and is inherently biased in favor of polypeptides/proteins available in sufficient quantities. Alternative approaches include the Zyggregator family of descriptors based on more fundamental properties that can be updated quickly from the ever-growing protein structure databases, such as the α-helical propensities of amino acids [133]. Additional approaches to predict aggregation are statistical thermodynamic algorithms like TANGO [11], the spatial distribution of patches [12], [111], [134] or explicit molecular interactions [135].

6. Conclusion – need for and potentials of novel protein descriptors

Developing meaningful protein descriptors is a major challenge because it requires the integration of domain/application knowledge and has to balance information loss against redundancy and high dimensionality. Therefore, alternatives to commonly used aggregation functions such as mean, maxima, or thresholds have been proposed and include fuzzy measures to create global descriptors considering interdependencies for molecular descriptors [136], [137]. These approaches seem promising in improving protein descriptors, especially as advanced structure prediction tools such as alpha-fold and ESM models provide access to an ever increasing number of protein structures [138], [139].

Many descriptors currently used to capture protein shape and surface properties fail to account for the complexity of proteins, such as the relative position of charged surface patches or the anisotropy of properties in general. This can be a major limitation if distinct shape and surface properties strongly influence protein behavior in a given application. For example, close proximity between charged and hydrophobic surface patches can be required for protein binding to multimodal chromatography ligands [140], whereas the absolute number, size or strength of these patches may be much less important. Accordingly, descriptors should be cross-correlated and co-contextualized for each application using domain knowledge about the underlying molecular mechanisms. This approach helps to avoid excessive gating (i.e., the imposition of many threshold conditions for individual descriptors) and alternative descriptors can be defined on a rational basis. In this context, it can be valuable to use descriptors originating beyond the protein and biological molecule domain. For example, descriptors developed or first used for the analysis of cell images [141] or computer vision have been adapted to small molecules but not yet to proteins [103]. Three-dimensional functions such as the Laplace-Beltrami operator can also provide a good source of novel descriptors [142].

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Consent for publication

All authors have seen a draft version of the manuscript and concur with its submission to the journal.

Code availability (software application or custom code)

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Funding

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CRediT authorship contribution statement

JB planned the study. JE and JB conducted the literature review, analyzed the data, prepared the figures and wrote the manuscript. JB revised the manuscript.

Appendix A. Supplementary material

Supplementary material

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Data Availability

Data can be made available upon request to the corresponding author.