1
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Christoffer C, Harini K, Archit G, Kihara D. Assembly of Protein Complexes in and on the Membrane with Predicted Spatial Arrangement Constraints. J Mol Biol 2024; 436:168486. [PMID: 38336197 PMCID: PMC10942765 DOI: 10.1016/j.jmb.2024.168486] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2023] [Revised: 01/17/2024] [Accepted: 02/05/2024] [Indexed: 02/12/2024]
Abstract
Membrane proteins play crucial roles in various cellular processes, and their interactions with other proteins in and on the membrane are essential for their proper functioning. While an increasing number of structures of more membrane proteins are being determined, the available structure data is still sparse. To gain insights into the mechanisms of membrane protein complexes, computational docking methods are necessary due to the challenge of experimental determination. Here, we introduce Mem-LZerD, a rigid-body membrane docking algorithm designed to take advantage of modern membrane modeling and protein docking techniques to facilitate the docking of membrane protein complexes. Mem-LZerD is based on the LZerD protein docking algorithm, which has been constantly among the top servers in many rounds of CAPRI protein docking assessment. By employing a combination of geometric hashing, newly constrained by the predicted membrane height and tilt angle, and model scoring accounting for the energy of membrane insertion, we demonstrate the capability of Mem-LZerD to model diverse membrane protein-protein complexes. Mem-LZerD successfully performed unbound docking on 13 of 21 (61.9%) transmembrane complexes in an established benchmark, more than shown by previous approaches. It was additionally tested on new datasets of 44 transmembrane complexes and 92 peripheral membrane protein complexes, of which it successfully modeled 35 (79.5%) and 15 (16.3%) complexes respectively. When non-blind orientations of peripheral targets were included, the number of successes increased to 54 (58.7%). We further demonstrate that Mem-LZerD produces complex models which are suitable for molecular dynamics simulation. Mem-LZerD is made available at https://lzerd.kiharalab.org.
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Affiliation(s)
- Charles Christoffer
- Department of Computer Science, Purdue University, West Lafayette, IN 47907, USA
| | - Kannan Harini
- Department of Biotechnology, Bhupat and Jyoti Mehta School of Biosciences, Indian Institute of Technology Madras, Chennai 600036, India; Department of Biological Sciences, Purdue University, West Lafayette, IN 47907, USA
| | - Gupta Archit
- Department of Biological Sciences, Purdue University, West Lafayette, IN 47907, USA; Department of Genetic Engineering, SRM Institute of Science and Technology, Kattankulathur 603203, India
| | - Daisuke Kihara
- Department of Computer Science, Purdue University, West Lafayette, IN 47907, USA; Department of Biological Sciences, Purdue University, West Lafayette, IN 47907, USA; Purdue University Center for Cancer Research, Purdue University, West Lafayette, IN 47907, USA.
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2
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Zhang Y, Wang X, Zhang Z, Huang Y, Kihara D. Assessment of Protein-Protein Docking Models Using Deep Learning. Methods Mol Biol 2024; 2780:149-162. [PMID: 38987469 DOI: 10.1007/978-1-0716-3985-6_10] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/12/2024]
Abstract
Protein-protein interactions are involved in almost all processes in a living cell and determine the biological functions of proteins. To obtain mechanistic understandings of protein-protein interactions, the tertiary structures of protein complexes have been determined by biophysical experimental methods, such as X-ray crystallography and cryogenic electron microscopy. However, as experimental methods are costly in resources, many computational methods have been developed that model protein complex structures. One of the difficulties in computational protein complex modeling (protein docking) is to select the most accurate models among many models that are usually generated by a docking method. This article reviews advances in protein docking model assessment methods, focusing on recent developments that apply deep learning to several network architectures.
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Affiliation(s)
- Yuanyuan Zhang
- Department of Computer Science, Purdue University, West Lafayette, IN, USA
| | - Xiao Wang
- Department of Computer Science, Purdue University, West Lafayette, IN, USA
| | - Zicong Zhang
- Department of Computer Science, Purdue University, West Lafayette, IN, USA
| | - Yunhan Huang
- Department of Computer Science, Purdue University, West Lafayette, IN, USA
| | - Daisuke Kihara
- Department of Computer Science, Purdue University, West Lafayette, IN, USA.
- Department of Biological Sciences, Purdue University, West Lafayette, IN, USA.
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3
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Asim A. Approaches to Backbone Flexibility in Protein-Protein Docking. Methods Mol Biol 2024; 2780:45-68. [PMID: 38987463 DOI: 10.1007/978-1-0716-3985-6_4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/12/2024]
Abstract
Proteins are the fundamental organic macromolecules in living systems that play a key role in a variety of biological functions including immunological detection, intracellular trafficking, and signal transduction. The docking of proteins has greatly advanced during recent decades and has become a crucial complement to experimental methods. Protein-protein docking is a helpful method for simulating protein complexes whose structures have not yet been solved experimentally. This chapter focuses on major search tactics along with various docking programs used in protein-protein docking algorithms, which include: direct search, exhaustive global search, local shape feature matching, randomized search, and broad category of post-docking approaches. As backbone flexibility predictions and interactions in high-resolution protein-protein docking remain important issues in the overall optimization context, we have put forward several methods and solutions used to handle backbone flexibility. In addition, various docking methods that are utilized for flexible backbone docking, including ATTRACT, FlexDock, FLIPDock, HADDOCK, RosettaDock, FiberDock, etc., along with their scoring functions, algorithms, advantages, and limitations are discussed. Moreover, what progress in search technology is expected, including not only the creation of new search algorithms but also the enhancement of existing ones, has been debated. As conformational flexibility is one of the most crucial factors affecting docking success, more work should be put into evaluating the conformational flexibility upon binding for a particular case in addition to developing new algorithms to replace the rigid body docking and scoring approach.
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Affiliation(s)
- Ayesha Asim
- Department of Synthesis and Chemical Technology of Pharmaceutical Substances with Computer Modeling Laboratory, Faculty of Pharmacy, Medical University of Lublin, Lublin, Poland
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4
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Christoffer C, Harini K, Archit G, Kihara D. Assembly of Protein Complexes In and On the Membrane with Predicted Spatial Arrangement Constraints. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.10.20.563303. [PMID: 37961264 PMCID: PMC10634698 DOI: 10.1101/2023.10.20.563303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/15/2023]
Abstract
Membrane proteins play crucial roles in various cellular processes, and their interactions with other proteins in and on the membrane are essential for their proper functioning. While an increasing number of structures of more membrane proteins are being determined, the available structure data is still sparse. To gain insights into the mechanisms of membrane protein complexes, computational docking methods are necessary due to the challenge of experimental determination. Here, we introduce Mem-LZerD, a rigid-body membrane docking algorithm designed to take advantage of modern membrane modeling and protein docking techniques to facilitate the docking of membrane protein complexes. Mem-LZerD is based on the LZerD protein docking algorithm, which has been constantly among the top servers in many rounds of CAPRI protein docking assessment. By employing a combination of geometric hashing, newly constrained by the predicted membrane height and tilt angle, and model scoring accounting for the energy of membrane insertion, we demonstrate the capability of Mem-LZerD to model diverse membrane protein-protein complexes. Mem-LZerD successfully performed unbound docking on 13 of 21 (61.9%) transmembrane complexes in an established benchmark, more than shown by previous approaches. It was additionally tested on new datasets of 44 transmembrane complexes and 92 peripheral membrane protein complexes, of which it successfully modeled 35 (79.5%) and 15 (16.3%) complexes respectively. When non-blind orientations of peripheral targets were included, the number of successes increased to 54 (58.7%). We further demonstrate that Mem-LZerD produces complex models which are suitable for molecular dynamics simulation. Mem-LZerD is made available at https://lzerd.kiharalab.org.
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Affiliation(s)
- Charles Christoffer
- Department of Computer Science, Purdue University, West Lafayette, IN, 47907, USA
| | - Kannan Harini
- Department of Biotechnology, Bhupat and Jyoti Mehta School of Biosciences, Indian Institute of Technology Madras, Chennai 600036, India
- Department of Biological Sciences, Purdue University, West Lafayette, IN, 47907, USA
| | - Gupta Archit
- Department of Biological Sciences, Purdue University, West Lafayette, IN, 47907, USA
- Department of Genetic Engineering, SRM Institute of Science and Technology, Kattankulathur 603203, India
| | - Daisuke Kihara
- Department of Computer Science, Purdue University, West Lafayette, IN, 47907, USA
- Department of Biological Sciences, Purdue University, West Lafayette, IN, 47907, USA
- Purdue University Center for Cancer Research, Purdue University, West Lafayette, IN, 47907, USA
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5
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Christoffer C, Kihara D. Modeling protein-nucleic acid complexes with extremely large conformational changes using Flex-LZerD. Proteomics 2023; 23:e2200322. [PMID: 36529945 PMCID: PMC10448949 DOI: 10.1002/pmic.202200322] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2022] [Revised: 12/08/2022] [Accepted: 12/13/2022] [Indexed: 12/23/2022]
Abstract
Proteins and nucleic acids are key components in many processes in living cells, and interactions between proteins and nucleic acids are often crucial pathway components. In many cases, large flexibility of proteins as they interact with nucleic acids is key to their function. To understand the mechanisms of these processes, it is necessary to consider the 3D atomic structures of such protein-nucleic acid complexes. When such structures are not yet experimentally determined, protein docking can be used to computationally generate useful structure models. However, such docking has long had the limitation that the consideration of flexibility is usually limited to small movements or to small structures. We previously developed a method of flexible protein docking which could model ordered proteins which undergo large-scale conformational changes, which we also showed was compatible with nucleic acids. Here, we elaborate on the ability of that pipeline, Flex-LZerD, to model specifically interactions between proteins and nucleic acids, and demonstrate that Flex-LZerD can model more interactions and types of conformational change than previously shown.
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Affiliation(s)
- Charles Christoffer
- Department of Computer Science, Purdue University, West Lafayette, Indiana, USA
| | - Daisuke Kihara
- Department of Computer Science, Purdue University, West Lafayette, Indiana, USA
- Department of Biological Sciences, Purdue University, West Lafayette, Indiana, USA
- Purdue University Center for Cancer Research, Purdue University, West Lafayette, Indiana, USA
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6
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Christoffer C, Kihara D. Domain-Based Protein Docking with Extremely Large Conformational Changes. J Mol Biol 2022; 434:167820. [PMID: 36089054 PMCID: PMC9992458 DOI: 10.1016/j.jmb.2022.167820] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2022] [Revised: 08/31/2022] [Accepted: 09/03/2022] [Indexed: 11/17/2022]
Abstract
Proteins are key components in many processes in living cells, and physical interactions with other proteins and nucleic acids often form key parts of their functions. In many cases, large flexibility of proteins as they interact is key to their function. To understand the mechanisms of these processes, it is necessary to consider the 3D structures of such protein complexes. When such structures are not yet experimentally determined, protein docking has long been present to computationally generate useful structure models. However, protein docking has long had the limitation that the consideration of flexibility is usually limited to very small movements or very small structures. Methods have been developed which handle minor flexibility via normal mode or other structure sampling, but new methods are required to model ordered proteins which undergo large-scale conformational changes to elucidate their function at the molecular level. Here, we present Flex-LZerD, a framework for docking such complexes. Via partial assembly multidomain docking and an iterative normal mode analysis admitting curvilinear motions, we demonstrate the ability to model the assembly of a variety of protein-protein and protein-nucleic acid complexes.
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Affiliation(s)
- Charles Christoffer
- Department of Computer Science, Purdue University, West Lafayette, IN 47907, USA
| | - Daisuke Kihara
- Department of Computer Science, Purdue University, West Lafayette, IN 47907, USA; Department of Biological Sciences, Purdue University, West Lafayette, IN 47907, USA; Purdue University Center for Cancer Research, Purdue University, West Lafayette, IN 47907, USA.
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7
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Aderinwale T, Christoffer C, Kihara D. RL-MLZerD: Multimeric protein docking using reinforcement learning. Front Mol Biosci 2022; 9:969394. [PMID: 36090027 PMCID: PMC9459051 DOI: 10.3389/fmolb.2022.969394] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2022] [Accepted: 08/08/2022] [Indexed: 11/24/2022] Open
Abstract
Numerous biological processes in a cell are carried out by protein complexes. To understand the molecular mechanisms of such processes, it is crucial to know the quaternary structures of the complexes. Although the structures of protein complexes have been determined by biophysical experiments at a rapid pace, there are still many important complex structures that are yet to be determined. To supplement experimental structure determination of complexes, many computational protein docking methods have been developed; however, most of these docking methods are designed only for docking with two chains. Here, we introduce a novel method, RL-MLZerD, which builds multiple protein complexes using reinforcement learning (RL). In RL-MLZerD a multi-chain assembly process is considered as a series of episodes of selecting and integrating pre-computed pairwise docking models in a RL framework. RL is effective in correctly selecting plausible pairwise models that fit well with other subunits in a complex. When tested on a benchmark dataset of protein complexes with three to five chains, RL-MLZerD showed better modeling performance than other existing multiple docking methods under different evaluation criteria, except against AlphaFold-Multimer in unbound docking. Also, it emerged that the docking order of multi-chain complexes can be naturally predicted by examining preferred paths of episodes in the RL computation.
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Affiliation(s)
- Tunde Aderinwale
- Department of Computer Science, Purdue University, West Lafayette, IN, United States
| | - Charles Christoffer
- Department of Computer Science, Purdue University, West Lafayette, IN, United States
| | - Daisuke Kihara
- Department of Computer Science, Purdue University, West Lafayette, IN, United States
- Department of Biological Sciences, Purdue University, West Lafayette, IN, United States
- *Correspondence: Daisuke Kihara,
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8
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Verburgt J, Kihara D. Benchmarking of structure refinement methods for protein complex models. Proteins 2022; 90:83-95. [PMID: 34309909 PMCID: PMC8671191 DOI: 10.1002/prot.26188] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Revised: 06/24/2021] [Accepted: 07/22/2021] [Indexed: 01/03/2023]
Abstract
Protein structure docking is the process in which the quaternary structure of a protein complex is predicted from individual tertiary structures of the protein subunits. Protein docking is typically performed in two main steps. The subunits are first docked while keeping them rigid to form the complex, which is then followed by structure refinement. Structure refinement is crucial for a practical use of computational protein docking models, as it is aimed for correcting conformations of interacting residues and atoms at the interface. Here, we benchmarked the performance of eight existing protein structure refinement methods in refinement of protein complex models. We show that the fraction of native contacts between subunits is by far the most straightforward metric to improve. However, backbone dependent metrics, based on the Root Mean Square Deviation proved more difficult to improve via refinement.
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Affiliation(s)
- Jacob Verburgt
- Department of Biological Sciences, Purdue University, West Lafayette, IN, 47907, USA
| | - Daisuke Kihara
- Department of Biological Sciences, Purdue University, West Lafayette, IN, 47907, USA
- Department of Computer Science, Purdue University, West Lafayette, IN, 47907, USA
- Purdue University Center for Cancer Research, Purdue University, West Lafayette, IN, 47907, USA
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9
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Christoffer C, Bharadwaj V, Luu R, Kihara D. LZerD Protein-Protein Docking Webserver Enhanced With de novo Structure Prediction. Front Mol Biosci 2021; 8:724947. [PMID: 34466411 PMCID: PMC8403062 DOI: 10.3389/fmolb.2021.724947] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2021] [Accepted: 07/21/2021] [Indexed: 01/25/2023] Open
Abstract
Protein-protein docking is a useful tool for modeling the structures of protein complexes that have yet to be experimentally determined. Understanding the structures of protein complexes is a key component for formulating hypotheses in biophysics regarding the functional mechanisms of complexes. Protein-protein docking is an established technique for cases where the structures of the subunits have been determined. While the number of known structures deposited in the Protein Data Bank is increasing, there are still many cases where the structures of individual proteins that users want to dock are not determined yet. Here, we have integrated the AttentiveDist method for protein structure prediction into our LZerD webserver for protein-protein docking, which enables users to simply submit protein sequences and obtain full-complex atomic models, without having to supply any structure themselves. We have further extended the LZerD docking interface with a symmetrical homodimer mode. The LZerD server is available at https://lzerd.kiharalab.org/.
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Affiliation(s)
- Charles Christoffer
- Department of Computer Science, Purdue University, West Lafayette, IN, United States
| | - Vijay Bharadwaj
- Department of Computer Science, Purdue University, West Lafayette, IN, United States
| | - Ryan Luu
- Department of Computer Science, Purdue University, West Lafayette, IN, United States
| | - Daisuke Kihara
- Department of Computer Science, Purdue University, West Lafayette, IN, United States.,Department of Biological Sciences, Purdue University, West Lafayette, IN, United States
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10
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Christoffer C, Chen S, Bharadwaj V, Aderinwale T, Kumar V, Hormati M, Kihara D. LZerD webserver for pairwise and multiple protein-protein docking. Nucleic Acids Res 2021; 49:W359-W365. [PMID: 33963854 PMCID: PMC8262708 DOI: 10.1093/nar/gkab336] [Citation(s) in RCA: 34] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2021] [Revised: 04/13/2021] [Accepted: 04/19/2021] [Indexed: 12/13/2022] Open
Abstract
Protein complexes are involved in many important processes in living cells. To understand the mechanisms of these processes, it is necessary to solve the 3D structures of the protein complexes. When protein complex structures have not yet been determined by experiment, protein-protein docking tools can be used to computationally model the structures of these complexes. Here, we present a webserver which provides access to LZerD and Multi-LZerD protein docking tools. The protocol provided by the server have performed consistently among the top in the CAPRI blind evaluation. LZerD docks pairs of structures, while Multi-LZerD can dock three or more structures simultaneously. LZerD uses a soft protein surface representation with 3D Zernike descriptors and explores the binding pose space using geometric hashing. Multi-LZerD performs multi-chain docking by combining pairwise solutions by LZerD. Both methods output full-atom docked models of the input proteins. Users can also input distance constraints between interacting or non-interacting residues as well as residues that locate at the interface or far from the interface. The webserver is equipped with a user-friendly panel that visualizes the distribution and structures of binding poses of top scoring models. The LZerD webserver is available at https://lzerd.kiharalab.org.
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Affiliation(s)
- Charles Christoffer
- Department of Computer Science, Purdue University, West Lafayette, IN 47907, USA
| | - Siyang Chen
- Department of Computer Science, Purdue University, West Lafayette, IN 47907, USA
| | - Vijay Bharadwaj
- Department of Computer Science, Purdue University, West Lafayette, IN 47907, USA
| | - Tunde Aderinwale
- Department of Computer Science, Purdue University, West Lafayette, IN 47907, USA
| | - Vidhur Kumar
- Department of Computer Science, Purdue University, West Lafayette, IN 47907, USA
| | - Matin Hormati
- Department of Computer Science, Purdue University, West Lafayette, IN 47907, USA
| | - Daisuke Kihara
- Department of Computer Science, Purdue University, West Lafayette, IN 47907, USA.,Department of Biological Sciences, Purdue University, West Lafayette IN, 47907, USA.,Purdue University Center for Cancer Research, Purdue University, West Lafayette, IN 47907, USA
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11
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Kurcinski M, Kmiecik S, Zalewski M, Kolinski A. Protein-Protein Docking with Large-Scale Backbone Flexibility Using Coarse-Grained Monte-Carlo Simulations. Int J Mol Sci 2021; 22:ijms22147341. [PMID: 34298961 PMCID: PMC8306105 DOI: 10.3390/ijms22147341] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2021] [Revised: 07/03/2021] [Accepted: 07/04/2021] [Indexed: 12/21/2022] Open
Abstract
Most of the protein–protein docking methods treat proteins as almost rigid objects. Only the side-chains flexibility is usually taken into account. The few approaches enabling docking with a flexible backbone typically work in two steps, in which the search for protein–protein orientations and structure flexibility are simulated separately. In this work, we propose a new straightforward approach for docking sampling. It consists of a single simulation step during which a protein undergoes large-scale backbone rearrangements, rotations, and translations. Simultaneously, the other protein exhibits small backbone fluctuations. Such extensive sampling was possible using the CABS coarse-grained protein model and Replica Exchange Monte Carlo dynamics at a reasonable computational cost. In our proof-of-concept simulations of 62 protein–protein complexes, we obtained acceptable quality models for a significant number of cases.
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12
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Jain A, Terashi G, Kagaya Y, Maddhuri Venkata Subramaniya SR, Christoffer C, Kihara D. Analyzing effect of quadruple multiple sequence alignments on deep learning based protein inter-residue distance prediction. Sci Rep 2021; 11:7574. [PMID: 33828153 PMCID: PMC8027171 DOI: 10.1038/s41598-021-87204-z] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2021] [Accepted: 03/25/2021] [Indexed: 12/12/2022] Open
Abstract
Protein 3D structure prediction has advanced significantly in recent years due to improving contact prediction accuracy. This improvement has been largely due to deep learning approaches that predict inter-residue contacts and, more recently, distances using multiple sequence alignments (MSAs). In this work we present AttentiveDist, a novel approach that uses different MSAs generated with different E-values in a single model to increase the co-evolutionary information provided to the model. To determine the importance of each MSA's feature at the inter-residue level, we added an attention layer to the deep neural network. We show that combining four MSAs of different E-value cutoffs improved the model prediction performance as compared to single E-value MSA features. A further improvement was observed when an attention layer was used and even more when additional prediction tasks of bond angle predictions were added. The improvement of distance predictions were successfully transferred to achieve better protein tertiary structure modeling.
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Affiliation(s)
- Aashish Jain
- Department of Computer Science, Purdue University, West Lafayette, IN, 47907, USA
| | - Genki Terashi
- Department of Biological Sciences, Purdue University, West Lafayette, IN, 47907, USA
| | - Yuki Kagaya
- Graduate School of Information Sciences, Tohoku University, Sendai, Japan
| | | | - Charles Christoffer
- Department of Computer Science, Purdue University, West Lafayette, IN, 47907, USA
| | - Daisuke Kihara
- Department of Computer Science, Purdue University, West Lafayette, IN, 47907, USA.
- Department of Biological Sciences, Purdue University, West Lafayette, IN, 47907, USA.
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