Protein sequences as random fractals

Protein intrinsically disordered regions have a non-random, modular architecture

MOTIVATION

Protein sequences can be broadly categorized into two classes: those which adopt stable secondary structure and fold into a domain (i.e. globular proteins), and those that do not. The sequences belonging to this latter class are conformationally heterogeneous and are described as being intrinsically disordered. Decades of investigation into the structure and function of globular proteins has resulted in a suite of computational tools that enable their sub-classification by domain type, an approach that has revolutionized how we understand and predict protein functionality. Conversely, it is unknown if sequences of disordered protein regions are subject to broadly generalizable organizational principles that would enable their sub-classification.

RESULTS

Here, we report the development of a statistical approach that quantifies linear variance in amino acid composition across a sequence. With multiple examples, we provide evidence that intrinsically disordered regions are organized into statistically non-random modules of unique compositional bias. Modularity is observed for both low and high-complexity sequences and, in some cases, we find that modules are organized in repetitive patterns. These data demonstrate that disordered sequences are non-randomly organized into modular architectures and motivate future experiments to comprehensively classify module types and to determine the degree to which modules constitute functionally separable units analogous to the domains of globular proteins.

AVAILABILITY AND IMPLEMENTATION

The source code, documentation, and data to reproduce all figures are freely available at https://github.com/MWPlabUTSW/Chi-Score-Analysis.git. The analysis is also available as a Google Colab Notebook (https://colab.research.google.com/github/MWPlabUTSW/Chi-Score-Analysis/blob/main/ChiScore_Analysis.ipynb).

Capturing molten globule state of α-lactalbumin through constant pH molecular dynamics simulations

The recently developed methods of constant pH molecular dynamics directly captures the correlation between protonation and conformation to probe protein structure, function, and dynamics. In this work, we investigate the effect of pH on the conformational properties of the protein human α-lactalbumin. Constant pH simulations at both acidic and alkaline medium indicate the formation of the molten globule state, which is in accordance with the previous experimental observations (especially, in acidic medium). The size of the protein measured by its radius of gyration (RG) exhibits a marked increase in both acidic and alkaline medium, which matches with the corresponding experimentally observed value of RG found in the molten globule. The probability of native contacts is also considerably reduced at acidic and basic pH as compared to that of native structure crystallized at neutral pH. The mean fractal dimension D2 of the protein records a sharp increase in basic medium as compared to those in neutral and acidic solutions implying a significant pH induced conformational change. The mean square fluctuations of all residues of the entire protein are found to increase by several folds in both acidic and basic medium, which may be correlated with the normalized solvent accessibility of the residues indicating role of solvent accessible surface area on protein internal dynamics. The helices comprising the α-domain of the protein are moderately preserved in the acidic and alkaline pH. However, the β-sheet structures present in the β-domain are completely disrupted in both acidic as well as basic pH.

Fractal symmetry of protein interior: what have we learned?

The application of fractal dimension-based constructs to probe the protein interior dates back to the development of the concept of fractal dimension itself. Numerous approaches have been tried and tested over a course of (almost) 30 years with the aim of elucidating the various facets of symmetry of self-similarity prevalent in the protein interior. In the last 5 years especially, there has been a startling upsurge of research that innovatively stretches the limits of fractal-based studies to present an array of unexpected results on the biophysical properties of protein interior. In this article, we introduce readers to the fundamentals of fractals, reviewing the commonality (and the lack of it) between these approaches before exploring the patterns in the results that they produced. Clustering the approaches in major schools of protein self-similarity studies, we describe the evolution of fractal dimension-based methodologies. The genealogy of approaches (and results) presented here portrays a clear picture of the contemporary state of fractal-based studies in the context of the protein interior. To underline the utility of fractal dimension-based measures further, we have performed a correlation dimension analysis on all of the available non-redundant protein structures, both at the level of an individual protein and at the level of structural domains. In this investigation, we were able to separately quantify the self-similar symmetries in spatial correlation patterns amongst peptide-dipole units, charged amino acids, residues with the π-electron cloud and hydrophobic amino acids. The results revealed that electrostatic environments in the interiors of proteins belonging to 'α/α toroid' (all-α class) and 'PLP-dependent transferase-like' domains (α/β class) are highly conducive. In contrast, the interiors of 'zinc finger design' ('designed proteins') and 'knottins' ('small proteins') were identified as folds with the least conducive electrostatic environments. The fold 'conotoxins' (peptides) could be unambiguously identified as one type with the least stability. The same analyses revealed that peptide-dipoles in the α/β class of proteins, in general, are more correlated to each other than are the peptide-dipoles in proteins belonging to the all-α class. Highly favorable electrostatic milieu in the interiors of TIM-barrel, α/β-hydrolase structures could explain their remarkably conserved (evolutionary) stability from a new light. Finally, we point out certain inherent limitations of fractal constructs before attempting to identify the areas and problems where the implementation of fractal dimension-based constructs can be of paramount help to unearth latent information on protein structural properties.

The isoelectric region of proteins: a systematic analysis

Background

Binding of proteins in ion exchange chromatography is dominated by electrostatic interactions and can be tuned by adjusting pH and ionic strength of the solvent. Therefore, the isoelectric region (IER), the pH region of almost zero charge near the pI, has been used to predict the binding properties of proteins.

Principal findings

Usually the IER is small and binding and elution is carried out at pH values near to the pI. However, some proteins with an extended IER have been shown to bind and elute far away from its pI. To analyze factors that mediate the size of the IER and to identify proteins with an extended IER, two protein families consisting of more than 7000 proteins were systematically investigated. Most proteins were found to have a small IER and thus are expected to bind or elute near to their pI, while only a small fraction of less than 2% had a large IER.

Conclusions

Only four factors, the number of histidines, the pI, the number of titratable amino acids and the ratio of acidic to basic residues, are sufficient to reliably classify proteins by their IER based on their sequence only, and thus to predict their binding and elution behaviour in ion exchange chromatography.

Methods for improving simulations of biological systems: systemic computation and fractal proteins

Modelling and simulation are becoming essential for new fields such as synthetic biology. Perhaps the most important aspect of modelling is to follow a clear design methodology that will help to highlight unwanted deficiencies. The use of tools designed to aid the modelling process can be of benefit in many situations. In this paper, the modelling approach called systemic computation (SC) is introduced. SC is an interaction-based language, which enables individual-based expression and modelling of biological systems, and the interactions between them. SC permits a precise description of a hypothetical mechanism to be written using an intuitive graph-based or a calculus-based notation. The same description can then be directly run as a simulation, merging the hypothetical mechanism and the simulation into the same entity. However, even when using well-designed modelling tools to produce good models, the best model is not always the most accurate one. Frequently, computational constraints or lack of data make it infeasible to model an aspect of biology. Simplification may provide one way forward, but with inevitable consequences of decreased accuracy. Instead of attempting to replace an element with a simpler approximation, it is sometimes possible to substitute the element with a different but functionally similar component. In the second part of this paper, this modelling approach is described and its advantages are summarized using an exemplar: the fractal protein model. Finally, the paper ends with a discussion of good biological modelling practice by presenting lessons learned from the use of SC and the fractal protein model.

Pair-preferences: a quantitative measure of regularities in protein sequences

We present here the results obtained by applying several different methods to quantitatively measure regularities in protein sequences based on pair-preferences. We have studied the distribution of amino acid residues, singly as well as in pairs in a large data base and have attempted this task. We confirmed the existence of well-defined pair-preferences in proteins which were shown to be remarkably absent in simulated random sequences of similar amino acid distribution. The analysis of the sequences from the SWISS-PROT data base using simple statistical tests. Fourier analysis, fractal analysis and statistical thermodynamical tests were used to derive parameters to define a natural sequence. As a consequence of the existence of pair-preferences, parameters like fractal dimension (D), spectral exponent (beta), scaling parameter (H) and entropy (statistical) were found to be characteristic for natural sequences. For a reference state we chose a randomised state devoid of any pair-preference. The pair-preferences qualified well to be used as quantitative measures of regularities in protein sequences.