A computational framework to empower probabilistic protein design

MOTIVATION: The task of engineering a protein to perform a target biological function is known as protein design. A commonly used paradigm casts this functional design problem as a structural one, assuming a fixed backbone. In probabilistic protein design, positional amino acid probabilities are used to create a random library of sequences to be simultaneously screened for biological activity. Clearly, certain choices of probability distributions will be more successful in yielding functional sequences. However, since the number of sequences is exponential in protein length, computational optimization of the distribution is difficult. RESULTS: In this paper, we develop a computational framework for probabilistic protein design following the structural paradigm. We formulate the distribution of sequences for a structure using the Boltzmann distribution over their free energies. The corresponding probabilistic graphical model is constructed, and we apply belief propagation (BP) to calculate marginal amino acid probabilities. We test this method on a large structural dataset and demonstrate the superiority of BP over previous methods. Nevertheless, since the results obtained by BP are far from optimal, we thoroughly assess the paradigm using high-quality experimental data. We demonstrate that, for small scale sub-problems, BP attains identical results to those produced by exact inference on the paradigmatic model. However, quantitative analysis shows that the distributions predicted significantly differ from the experimental data. These findings, along with the excellent performance we observed using BP on the smaller problems, suggest potential shortcomings of the paradigm. We conclude with a discussion of how it may be improved in the future.     

Computational framework to model and design surgical meshes for hernia repair

Surgical procedures for hernia surgery are usually performed using prosthetic meshes. In spite of all the improvements in these biomaterials, the perfect match between the prosthesis and the implant site has not been achieved. Thus, new designs of surgical meshes are still being developed. Previous to implantation in humans, the validity of the meshes has to be addressed, and to date experimental studies have been the gold standard in testing and validating new implants. Nevertheless, these procedures involve long periods of time and are expensive. Thus, a computational framework for the simulation of prosthesis and surgical procedures may overcome some disadvantages of the experimental methods. The computational framework includes two computational models for designing and validating the behaviour of new meshes, respectively. Firstly, the beam model, which reproduces the exact geometry of the mesh, is set to design the weave and determine the stiffness of the surgical prosthesis. However, this implies a high computational cost whereas the membrane model, defined within the framework of the large deformation hyperelasticity, is a relatively inexpensive computational tool, which also enables a prosthesis to be included in more complex geometries such as human or animal bodies.     

F-IND: A framework to design fuzzy indices of environmental conditions

Multivariable indices of environmental conditions summarize the information provided by several biotic or abiotic variables into a single value of immediate interpretability. Thus they are important instruments for monitoring. Developing new indices that combine different variables is not a trivial task: variables may be qualitative, or measured in different units, and the relationship between primitive components and quality may be ambiguous. Fuzzy logic has been repeatedly proposed as an effective technique to cope with such problems; however, the variety of choices that exist at each stage of the development of fuzzy models may present a problem for the index designer. In this paper we present F-IND, a framework to create fuzzy indices by means of a simplified and intuitive procedure. It allows to capture the expert knowledge of the system under study (air, soil, water) to easily generate a multivariable index of environmental conditions. F-IND is implemented in Java, to achieve an optimal portability on any operating system.     

A maximum likelihood framework for protein design

Background  

The aim of protein design is to predict amino-acid sequences compatible with a given target structure. Traditionally envisioned as a purely thermodynamic question, this problem can also be understood in a wider context, where additional constraints are captured by learning the sequence patterns displayed by natural proteins of known conformation. In this latter perspective, however, we still need a theoretical formalization of the question, leading to general and efficient learning methods, and allowing for the selection of fast and accurate objective functions quantifying sequence/structure compatibility.     

A multiscale probabilisitic framework to model early steps in tumor metastasis

Tumor metastasis is the leading cause of nearly all cancer related deaths. While several experimental and computational studies have addressed individual stages of the complex metastasis process, a comprehensive systems-biology model that links various stages of metastasis has not been put forth as of yet. In this paper we discuss the formulation and application of such a model that utilizes basic principles of cell biology, physics and mechanics to study the migratory patterns of tumor cells as they move from the parent tumor site to the connective tissue via the basement membrane. The model is first of its kind in capturing the essential early features of metastasis in a single simulation and shows good agreement with recent experimental studies.     

A model management systems approach to manufacturing systems design

Manufacturing systems design involves the solution of a complex series of interrelated problems. This complexity will increase in the future as manufacturing practices change to meet increased global competition. Research within manufacturing systems design has mainly been focused on finding improved models for solving particular problems, or extending existing modeling techniques. This has resulted in numerous modeling tools being available to support manufacturing systems design. However, little research work has been carried out into consolidating the existing theories and models. As a result, a large body of this work has not been applied in industry. Model management has evolved as a research area which investigates methods for storing, modifying, and manipulating models. This article describes a prototype model management system for manufacturing systems design. The objective here is not to develop “another” decision support system for manufacturing design, but to illustrate, through the development of a prototype system, a number of key ideas of how concepts from the area of model management systems can be used to support manufacturing systems design. The prototype model management system utilizes the structured modeling framework and uses an extended version of the structured modeling language. An important aspect of the prototype model management system is the incorporation of the model development task, thus allowing the system to be easily updated and adapted. The prototype system was evaluated using a range of queueing network models for manufacturing systems design.     

Monte Carlo model framework to simulate settlement dynamics

We developed an open source Monte Carlo based model to simulate Settlement Dynamics in Drylands (SeDD). The model assigns partial probabilities to each pixel within a grid region, based on several factors that can influence the establishment and subsistence of settlements: groundwater depth, vegetation type, proximity to rivers, paved roads, old river beds, and existing settlements. Partial probabilities are considered to be independent from each other, and therefore multiplied to calculate an overall probability for each pixel. Settlements are assigned by maximum probabilities or randomly, according to pre-established threshold probability values. We also modeled the gradual reduction of vegetation caused by a new settlement in neighboring pixels, decreasing the probabilities related to vegetation type. The final distribution of settlements is given by an average over multiple Monte Carlo simulations. The model is computationally efficient and could be used to rapidly explore different scenarios of settlement dynamics and vegetation degradation in arid environments, and other environmental factors that can be added to the framework without performing changes in the source code.     

A computational framework for the design of optimal protein synthesis

Despite the establishment of design principles to optimize codon choice for heterologous expression vector design, the relationship between codon sequence and final protein yield remains poorly understood. In this work, we present a computational framework for the identification of a set of mutant codon sequences for optimized heterologous protein production, which uses a codon-sequence mechanistic model of protein synthesis. Through a sensitivity analysis on the optimal steady state configuration of protein synthesis we are able to identify the set of codons, that are the most rate limiting with respect to steady state protein synthesis rate, and we replace them with synonymous codons recognized by charged tRNAs more efficient for translation, so that the resulting codon-elongation rate is higher. Repeating this procedure, we iteratively optimize the codon sequence for higher protein synthesis rate taking into account multiple constraints of various types. We determine a small set of optimized synonymous codon sequences that are very close to each other in sequence space, but they have an impact on properties such as ribosomal utilization or secondary structure. This limited number of sequences can then be offered for further experimental study. Overall, the proposed method is very valuable in understanding the effects of the different properties of mRNA sequences on the final protein yield in heterologous protein production and it can find applications in synthetic biology and biotechnology.     

PocketOptimizer 2.0: A modular framework for computer-aided ligand-binding design

The ability to design customized proteins to perform specific tasks is of great interest. We are particularly interested in the design of sensitive and specific small molecule ligand-binding proteins for biotechnological or biomedical applications. Computational methods can narrow down the immense combinatorial space to find the best solution and thus provide starting points for experimental procedures. However, success rates strongly depend on accurate modeling and energetic evaluation. Not only intra- but also intermolecular interactions have to be considered. To address this problem, we developed PocketOptimizer, a modular computational protein design pipeline, that predicts mutations in the binding pockets of proteins to increase affinity for a specific ligand. Its modularity enables users to compare different combinations of force fields, rotamer libraries, and scoring functions. Here, we present a much-improved version––PocketOptimizer 2.0. We implemented a cleaner user interface, an extended architecture with more supported tools, such as force fields and scoring functions, a backbone-dependent rotamer library, as well as different improvements in the underlying algorithms. Version 2.0 was tested against a benchmark of design cases and assessed in comparison to the first version. Our results show how newly implemented features such as the new rotamer library can lead to improved prediction accuracy. Therefore, we believe that PocketOptimizer 2.0, with its many new and improved functionalities, provides a robust and versatile environment for the design of small molecule-binding pockets in proteins. It is widely applicable and extendible due to its modular framework. PocketOptimizer 2.0 can be downloaded at https://github.com/Hoecker-Lab/pocketoptimizer .     

A probabilistic model of reserve design

We develop a probabilistic approach to optimum reserve design based on the species-area relationship. Specifically, we focus on the distribution of areas among a set of reserves maximizing biodiversity. We begin by presenting analytic solutions for the neutral case in which all species have the same colonization probability. The optimum size distribution is determined by the local-to-regional species richness ratio k. There is a critical k(t) ratio defined by the number of reserves raised to the scaling exponent of the species-area relationship. Below k(t), a uniform area distribution across reserves maximizes biodiversity. Beyond k(t), biodiversity is maximized by allocating a certain area to one reserve and uniformly allocating the remaining area to the other reserves. We proceed by numerically exploring the robustness of our analytic results when departing from the neutral assumption of identical colonization probabilities across species.     

A universal combinatorial design of antibody framework to graft distinct CDR sequences: a bioinformatics approach

Antibody (Ab) humanization is crucial to generate clinically relevant biologics from hybridoma-derived monoclonal antibodies (mAbs). In this study, we integrated antibody structural information from the Protein Data Bank with known back-to-mouse mutational data to build a universal consensus of framework positions (10 heavy and 7 light) critical for the preservation of the functional conformation of the Complimentarity Determining Region of antibodies. On the basis of FR consensus, we describe here a universal combinatorial library suitable for humanizing exogenous antibodies by CDR-grafting. The six CDRs of the murine anti-human EGFR Fab M225 were grafted onto a distinct (low FR sequence similarity to M225) human FR sequence that incorporates at the 17 FR consensus positions the permutations of the naturally observed amino acid diversities. Ten clones were selected from the combinatorial library expressing phage-displayed humanized M225 Fabs. Surprisingly, 2 of the 10 clones were found to bind EGFR with stronger affinity than M225. Cell-based assays demonstrated that the 10 selected clones retained epitope specificity by blocking EGFR phosphorylation and thus hindering cellular proliferation. Our results suggest that there is a universal and structurally rigid near-CDR set of FR positions that cooperatively support the binding conformation of CDRs.     

A hierarchical biology concept framework: a tool for course design

A typical undergraduate biology curriculum covers a very large number of concepts and details. We describe the development of a Biology Concept Framework (BCF) as a possible way to organize this material to enhance teaching and learning. Our BCF is hierarchical, places details in context, nests related concepts, and articulates concepts that are inherently obvious to experts but often difficult for novices to grasp. Our BCF is also cross-referenced, highlighting interconnections between concepts. We have found our BCF to be a versatile tool for design, evaluation, and revision of course goals and materials. There has been a call for creating Biology Concept Inventories, multiple-choice exams that test important biology concepts, analogous to those in physics, astronomy, and chemistry. We argue that the community of researchers and educators must first reach consensus about not only what concepts are important to test, but also how the concepts should be organized and how that organization might influence teaching and learning. We think that our BCF can serve as a catalyst for community-wide discussion on organizing the vast number of concepts in biology, as a model for others to formulate their own BCFs and as a contribution toward the creation of a comprehensive BCF.     

A model of weak selection in the infinite alleles framework

Ewens (1972) proposed a model in the infinite allele framework for populations with neutrality of all alleles at a particular locus. This paper proposes a generalisation of Ewens' result for situations where there is a form of weak selection. The models considered here are continuous time, discrete state space Markov processes.     

A region-based model framework for the rat urine concentrating mechanism

The highly structured organization of tubules and blood vessels in the outer medulla of the mammalian kidney is believed to result in preferential interactions among tubules and vessels; such interactions may promote solute cycling and enhance urine concentrating capability. In this study, we formulate a new model framework for the urine concentrating mechanism in the outer medulla of the rat kidney. The model simulates preferential interactions among tubules and vessels by representing two concentric regions and by specifying the fractions of tubules and vessels assigned to each of the regions. The model equations are based on standard expressions for transmural transport and on solute and water conservation. Model equations, which are derived in dynamic form, are solved to obtain steady-state solutions by means of a stable and efficient numerical method, based on the semi-Lagrangian semi-implicit method and on Newton’s method. In this application, the computational cost scales as O(N ²), where N is the number of spatial subintervals along the medulla. We present representative solutions and show that the method generates approximations that are second-order accurate in space and that exhibit mass conservation.     

A statistical framework to evaluate virtual screening

Background  

Receiver operating characteristic (ROC) curve is widely used to evaluate virtual screening (VS) studies. However, the method fails to address the "early recognition" problem specific to VS. Although many other metrics, such as RIE, BEDROC, and pROC that emphasize "early recognition" have been proposed, there are no rigorous statistical guidelines for determining the thresholds and performing significance tests. Also no comparisons have been made between these metrics under a statistical framework to better understand their performances.