Multiple Perspectives, Multiple Goals

There are many ways to characterize the multiple perspectives displayed by predictive models of functional protein structure. One can crudely dis-tinguish between physical, chemical, and biological perspectives. These are loosely correlated with different contexts in which proteins are studied: in silico, in vitro, and in vivo, respectively. The three perspectives each pro-vide partial and not completely overlapping accounts of the phenomenon.

Learning about protein structure from the physics perspective, consider-ing the basic atomic components of proteins and forces actconsider-ing on them, will inform, but not determine, what is detected from an investigation of the protein’s chemical structure. Knowing the chemical details, in turn, informs, but does not completely specify, biogenesis, interaction, and the biological functions of the macromolecule. At the beginning of advances in the study of protein structure in the 1950s, it was believed that a reduc-tive approach, that is, ab initio modeling the thermodynamic features of atomic components of the amino acid sequence of a protein, would be sufficient for predicting the tertiary, biologically functional structure. As Francis Crick proposed, “it is of course possible that there is a special mechanism for folding up the chain, but the more likely hypothesis is that the folding is simply a function of the order of the amino acids” ( Crick 1958 , 144). This view contains two inferential steps: that protein sequence contains all the information necessary to determine structure and that protein structure is sufficient to determine its function ( Berg, Tymoczko, and Stryer 2002 ; Dill, Ozkan, Weikl, Choder, and Voelz 2007 ).

However, developments in protein science have revealed a more com-plex story. Anfinsen’s discovery ( Sela, White, and Anfinsen 1957 ) of the spontaneous refolding of a denatured protein in vitro seemed to support the reductionist hopes that nothing more than the interatomic interactions of the atoms making up the primary structure of a protein were required to

determine the thermodynamically lowest energy state in a particular envi-ronment and that would allow inferences to biological function. Indeed, it was on the basis of Anfinsen’s discovery in support of the “thermody-namic hypothesis” ( Anfinsen 1973 ) that he was awarded a Nobel Prize in 1972. Yet in 1969 Levinthal offered a thought experiment that generated a “paradox” for this hypothesis. The number of possible configurations a protein could acquire is astronomical (10 ¹⁴³ ). If configurations were sampled sequentially, it would take longer than the age of the universe for a protein to find its energetically minimum structure. However, proteins fold sometimes in milliseconds. Levinthal claimed that protein structure is not a simple derivation from the physics of the component parts find-ing their native state: “if the final folded state turned out to be the one of lowest configurational energy, it would be a consequence of biological evolution and not of physical chemistry” ( Levinthal 1968 , 44).

Some scientists today still hope to find the holy grail of a reductive algorithm that will predict a protein’s functional structure. But that hope has not been realized ( Mitchell and Gronenborn 2017 ). Instead there is a proliferation of models, methods, and representations aiming to provide the means to predict protein structure. Rather than viewing the physics models of proteins reductively, I suggest we consider them perspectivally.

How can one model protein transformation from a string of amino acids into a functional three-dimensional structure? On the basis of what features can its structure be predicted? These questions have been inves-tigated by looking at the phenomenon from different perspectives, but the answer cannot be obtained from any one alone. The functional struc-ture is not a consequence of the atomic arrangements in the amino acid sequence alone, nor of the hydrophobic and hydrophilic responses of the atoms of a protein with the surrounding molecules in its environment alone, nor of the complex interactions with other proteins that are impli-cated in the biogenesis of complex proteins in the messy environment of a cell. All three perspectives are needed.

The physics perspective targets the thermodynamic features of folded and unfolded proteins, that is, their mean free energy, and the kinetics of change from denatured through intermediate states to the native state.

Coarse-grained and all-atom approaches are used to calculate atomic interactions and to simulate energy landscapes. The unique amino acid string specifies the atomic components of the protein, and the energy con-tent of all possible configurations is computationally sampled to deter-mine which structure possesses the lowest free energy. Thus, the physics perspective investigates protein folding in silico. In answer to Levinthal’s paradox, if the energy surface on which the atoms of a protein move is appropriately biased, then even a stochastic search can lead to native structures in realistic times (computationally, as well as in vitro or in vivo). For some proteins, intermediate states act as local minima between the denatured and native states, constituting kinetic traps that can stall

the search or prohibit reaching the stable native structure ( Bryngelson, Onuchic, Socci, and Wolynes 1995 ). But where does information about the bias of the energy surface come from? It is not exclusively found in the atomic components of the amino acid sequence; it may be the result of activities of other molecules in the protein’s cellular context.

One track through the chemistry perspective targets the detectable three-dimensional structure of a protein by experimentally manipulating an actual protein (chemically or thermally denaturing it, for example) and allowing it to fold in a simplified environment in vitro. The solution con-ditions of the protein, like temperature, pH, and salt concentration, can be varied to be more or less similar to what would be found in a living cell.

The structure is detected by means of x-ray crystallography or nuclear magnetic resonance spectroscopy, with the relative positions or distances between the atoms in the protein computed from x-ray diffraction pat-terns or spectra shifts. The chemical, experimental perspective that tracks protein interactions in vitro will be discussed in detail in section 4.

The biology perspective studies the protein in the cells in which it is born, functions, and dies—that is, in vivo. The cellular habitat is densely populated, consisting of tens of millions of molecules, and it is in this environment that small and large proteins alike have to fold into their native three-dimensional structures to realize their biological function.

Fluorescence microscopy can be used to “see” inside the cell, but it can-not resolve anything at very fine detail or in a very fast time frame. How-ever, evidence of interactions of an unfolded protein with other proteins, chaperones and chaperonins for example, has been detected in the pro-cess of folding ( Hartl and Hayer-Hartl 2009 ).

When proteins are made on the ribosome, the leading portion of the polypeptide chain is produced prior to the completion of the anterior por-tion. This affords the opportunity of the initial portion of the sequence to bind aberrantly to other molecules in the cell, prior to the formation of the anterior region that may be required for interactions that lead to correct folding. Some molecules, called chaperones, bind to the amino terminus of the growing polypeptide chain, stabilizing it in a partially folded configuration (safe from any interfering molecules) until synthesis of the polypeptide is completed. Release of the posterior sequence from the ribosome and detachment of the chaperones then permits anterior and posterior portions of the chain to bind and thus for the protein to fold into its functional three-dimensional conformation.

Each of the three perspectives investigates the problem of predicting protein structure. But they differ in the features targeted for study, the habitat in which the system is studied, and the methods and the repre-sentations used to describe what is known about the system. No single approach targets all the features that are relevant to predicting struc-ture. If no representational model is complete, then why should one adopt a particular perspective with its target features, methods, and

representations? It is here that pragmatic interests enter. What the inves-tigator wants to do provides the source of criteria for judging representa-tional model adequacy. Different models can each correctly describe the same complex system and yet not be reducible to a single representation from a single perspective. Empirical confirmation warrants correctness, while pragmatic concerns decide adequacy. For example, if one wants to determine the relative energetic stability of different conformations of a protein under different conditions, without regard to the specific set of conditions that are found in a living cell, then the physics perspective may deliver results that are both correct and adequate. However, if the goal is to use knowledge of the structure to explore therapies for misfolding dis-eases, then it will be necessary to go beyond the boundaries of the physics perspective ( Karplus 1997 ).

Ab initio physics models provide insight into the physical constraints and dynamics protein conformations must meet. When the final folded conformation of a protein is thermodynamically stable, that is, has the least free energy, then to move to that conformation from the initial unfolded state is theoretically spontaneous. Chemical processes follow paths toward least free energy. Thus in ideal circumstances, predicting the functional structure of a protein would be finding the thermodynamically stable conformation for that string of amino acids.

However, kinetic factors will decide whether the thermodynamically stable state occurs in fact, under specific environmental conditions, as well as which pathway or pathways through the energy landscape the process of folding is likely to take, and whether it will trapped in a local minima or reach the least energetic conformation. These features of protein fold-ing are targeted by chemical and biological perspectives. The conditions under which proteins fold might be under the control of other molecules, the chaperones, which are part of the cellular environment, the in vivo habitat that is not modeled by either physics in silico or chemistry in vitro methods. “Protein folding occurs in vivo in the environment quite unlike that under experimental, in vitro conditions. A large fraction of newly synthesized protein chains do not fold spontaneously but are assisted by molecular chaperones” ( Kmiecik and Kolinski 2011 , 10283). This study showed that periodic distortion of the polypeptide chains by chaperone interactions can promote rapid folding and lead to a decrease in folding temperature, changing the conditions under which thermodynamic sta-bility would be defined. It also demonstrated how chaperone interactions can prevent kinetically trapped conformations, thus providing a mecha-nism for reaching a pathway to the least energy conformation.

In summary, the relationships among the three perspectives for study-ing protein structure is not one of reduction but rather one of integra-tion. Each provides a partial grasp of the phenomenon, and each requires input and ongoing engagement with the other perspectives, especially if the aims are real-world complex, like finding therapies for misfolding

diseases like Alzheimer’s and Parkinson’s disease. This is how the partial-ity of perspectival models that leave some factors out (interactions with other molecules in the example above) can be informed and corrected by the perspectives that target those very features. But what if two perspec-tives target the very same features of the phenomenon and predict what appear to be incompatible models?