Voronoi and Protein Science

Voronoi’s Scientific Advisory Board members:

Lillian L. Siu, MD, FRCPC, is a senior medical oncologist at Princess Margaret Cancer Centre and a Professor of Medicine at the University of Toronto. She directs the Phase I Program and the Cancer Genomics Program and is the clinical leader for the Tumor Immunotherapy Program at the Princess Margaret Cancer Centre. Dr. Siu is also the Principal Investigator of the Princess Margaret Phase I Consortium as part of the U.S. National Cancer Institute Experimental Therapeutics Clinical Trials Network. In addition to serving on the ASCO Board of Directors, Dr. Siu also serves on the Cancer Education Committee.

An ASCO member since 1997, Dr. Siu has served on the Editorial Board of the Journal of Clinical Oncology, Scientific Program Committee, and as Chair of the Grants Selection Committee, among other activities.

Dr. Siu has been actively involved in the American Association for Cancer Research, she currently is a member of the Nominating Committee and has served previously as Chair of the Annual Meeting Educational Program Committee and member of the Scientific Program Committee. She was the recipient of the U.S. National Cancer Institute Michaele C. Christian Award in Oncology Drug Development in 2010, and served as the co-chair of Investigational Drug Steering Committee in 2013-2014.

Dr. Siu obtained her medical degree at the University of Toronto, completed her fellowship at Princess Margaret Cancer Centre, and completed drug development fellowships at Princess Margaret Cancer Centre and the University of Texas Science Center San Antonio.

Revisiting the Voronoi description of protein–protein interfaces

Frédéric Cazals,1 Flavien Proust,1 Ranjit P. Bahadur,2 and Joël Janin2

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We developed a model of macromolecular interfaces based on the Voronoi diagram and the related alpha-complex, and we tested its properties on a set of 96 protein–protein complexes taken from the Protein Data Bank. The Voronoi model provides a natural definition of the interfaces, and it yields values of the number of interface atoms and of the interface area that have excellent correlation coefficients with those of the classical model based on solvent accessibility. Nevertheless, some atoms that do not lose solvent accessibility are part of the interface defined by the Voronoi model. The Voronoi model provides robust definitions of the curvature and of the connectivity of the interfaces, and leads to estimates of these features that generally agree with other approaches. Our implementation of the model allows an analysis of protein–water contacts that highlights the role of structural water molecules at protein–protein interfaces.

Keywords: protein–protein interaction, algorithmic geometry, alpha-complex, interface connectivity

Proteins make noncovalent interactions that are essential elements of their biological function. The study of such interactions relies in part on modeling the geometry and physical chemistry of the interfaces built by interacting proteins. When atomic coordinates are available, the Voronoi description of proteins is a useful geometric tool that has been applied in a variety of settings. The pioneering work of Richards (1974) used the Euclidean Voronoi diagram to analyze the atomic packing inside macromolecules, followed by the work of many other investigators (Harpaz et al. 1994; Gerstein et al. 1995; Pontius et al. 1996; Nadassy et al. 2001; McConkey et al. 2002; Tsai and Gerstein 2002). The Voronoi diagram associates to each atom its Voronoi cell, a convex polyhedron that contains all points of space closer to that atom than to any other atom. More recently, it has been used to define contacts in macromolecules without applying a distance cutoff: Two atoms are in contact if and only if their Voronoi cells have a facet in common. Similarly, Voronoi cells can be drawn around amino acid residues to define residue–residue contacts (Singh et al. 1996; Munson and Singh 1997; Soyer et al. 2000; Dupuis et al. 2005). Given this definition of a contact, the set of facets shared by atoms of two macromolecules forming a complex represents their interface. There is, however, a major difficulty: Atoms on the molecular surface have unbounded, or at least poorly defined, Voronoi cells. This may be circumvented by surrounding the protein with solvent molecules (Soyer et al. 2000), but their position must be fixed, which is not physically meaningful. An alternative is to use the alpha-complex, an extension of the Voronoi diagram proposed by Edelsbrunner and Mucke (1994). Applications of the alpha-complex to macromolecules, reviewed by Poupon (2004), include the computation of molecular surfaces (Akkiraju and Edelsbrunner 1996), and that of interfaces in an implementation in which the unbounded facets that extend out of the molecular surface are removed by an iterative process called retraction (Ban et al. 2004). Cazals and Proust (2006) recently offered a simpler, and possibly more natural, way to define the interface between molecules by removing facets based on purely geometric criteria. Here, we apply their procedure to a set of 96 protein–protein complexes taken from the Protein Data Bank (PDB) (Berman et al. 2002), and compare the results to those of the classical approach where interfaces are defined by changes in solvent accessibility (Chothia and Janin 1975; Janin and Chothia 1990; Jones and Thornton 1995, 1996; Lo Conte et al. 1999; Chakrabarti and Janin 2002).


The three-dimensional structure of a protein can be modeled by a set of polyhedra drawn around its atoms or residues. The tessellation invented by Voronoi in 1908, and other tessellations of space derived from it, provide versatile representations of three-dimensional structures. In recent years, they have been used to investigate a series of issues relating to proteins: atom and residue volumes, packing, folding, interactions and binding.


. 1998;14(3):295-308.

doi: 10.1093/bioinformatics/14.3.295.

New scoring schemes for protein fold recognition based on Voronoi contacts

R Zimmer 1, M Wöhler, R Thiele

Affiliations expand


Motivation: The genome projects produce a wealth of protein sequences. Theoretical methods to predict possible structures and functions are needed for screening purposes, large-scale comparisons and in-depth analysis to identify worthwhile targets for further experimental research. Sequence-structure alignment is a basic tool for the identification of model folds for protein sequences and the construction of crude structural models. Empirical contact potentials (potentials of mean force) are used to optimize and evaluate such alignments.

Results: We propose new scoring schemes based on a contact definition derived from Voronoi decompositions of the three-dimensional coordinates of protein structures. We demonstrate that Voronoi potentials are superior to pure distance-based contact potentials with respect to recognition rate and significance for native folds. Moreover, the scoring scheme has the potential to provide a reasonable balance of detail and ion such that it is also useful for the recognition of distantly related (both homologous and non-homologous) proteins. This is demonstrated here on a set of structural alignments showing much better correspondence of native and model scores for the Voronoi potentials as compared to conventional distance-based potentials.

Availability: The potentials are made available via the program system ToPLign (URL: http://cartan.gmd.de/ToPLign.html).


Prof. Dr. Ralf Zimmer

1971-1980 Vinzenz-Pallotti-Kolleg, Rheinbach
05/1980 Abitur
1981-1986 Studies of Computer Science, Minor subject Operations Research at Rheinische Friedrich-Wilhelms-Universität Bonn
05/1986 Diploma degree in Computer Science (M.sc equiv.)
1987-1990 PhD-Studies Computer Science, Minor subjects Mathematical Logic and Practical Mathematics at Christian-Albrechts-Universität (CAU) Kiel
05/1990 PhD Computer Science (summa cum laude)
12/1990 Dissertation prize of the CAU
Working experience
1980-1981 Obligatory military service
1982-1986 Software developer and project manager at SIEMENS AG, Bonn
1984 Teaching assistant at the Institute of Computer Science, Rheinische Friedrich-Wilhelms-Universität Bonn
1985-1986 Software developer and project manager at SIEMENS AG, Bonn
1986-1990 Researcher, National Research Center for Information Technology (GMD), Institut für methodological foundations (Prof. Carl-Adam Petri) Sankt Augustin, Germany
1987-1990 research Assistant, CAU Kiel
1991-1992 Research Assistant, GMD, Institut for Algorithms and Scientific Computing (Prof. Thomas Lengauer)
1992-2004 Group Leader and Project Leader, GMD, Institut for Algorithms and Scientific Computing (Prof. Thomas Lengauer)
1995 Visiting Researcher, Laboratory for Mathematical Biology (Prof. R. Nussinov), National Cancer Institute (NCI), National Institutes of Health (NIH), Bethesda&Frederick, MD, USA
1997 Visiting Faculty, Beckman Center for Molecular and Genetic Medicine(Prof. D. Brutlag), School of Medicine, Stanford University, Palo Alto, CA, USA
2001 Offers for chairs for bioinformatics at the LMU, the Saarland University, and the Heinrich Heine Düsseldorf/caesar Bonn
since 2001 Full Professor, Chair for Practical Informatics and Bioinformatics, LMU Munich
since 2001 Director of the Steering Commitee, DFG Bioinformatics Center MunichBIM
since 2009 LMU Spokesperson of the DFG International Research Training Group RECESS
since 2011 Member of the senate of the LMU LMU Senat



Guided Folding of Life’s Proteins in Integrate Cells with Holographic Memory and GM-Biophysical Steering



Dirk K F Meijer at University of Groningen

Dirk K F Meijer

Hans J. H. Geesink at Independent Researcher

Hans J. H. Geesink


Patent number : 5753611
Type: Grant
Filed : Nov 4, 1994
Date of Patent : May 19, 1998
Assignee : Rijksuniversiteit Groningen (Groningen)
Inventors : Erik J. F. Franssen (Groningen), Frits Moolenaar (Stitswerd), Dirk K. F. Meijer (Groningen), Dick De Zeeuw (Groningen)
Primary Examiner : Gollamudi S. Kishore
Law Firm : Oliff & Berridge, PLC
Application Number : 8/302,749

Use of .alpha.-hydroxy acids and poly-.alpha.-hydroxy acids as spacer between a therapeutically and/or diagnostically active compound and a soluble macromolecular carrier in pharmaceutical compositions having site-specific delivery. In one embodiment glycolic acid, L-lactic acid or tetra-L-lactic acid is used as spacer between a non-steroidal anti-inflammatory substance and a carrier of low molecular protein (LMWP).


Summary: Voro3D is an original easy-to-use tool, which provides a brand new point of view on protein structures through the three-dimensional (3D) Voronoi tessellations. To construct the Voronoi cells associated with each amino acid by a number of different tessellation methods, Voro3D uses a protein structure file in the PDB format as an input. After calculation, different structural properties of interest like secondary structures assignment, environment accessibility and exact contact matrices can be derived without any geometrical cut-off. Voro3D provides also a visualization of these tessellations superimposed on the associated protein structure, from which it is possible to model a polygonal protein surface using a model solvent or to quantify, for instance, the contact areas between a protein and a ligand.



VoroCNN: Deep convolutional neural network built on 3D Voronoi tessellation of protein structures


1Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble, France.
2Moscow Institute of Physics and Technology, 141701 Dolgoprudniy, Russia.
3Institute of Biotechnology Life Sciences Center Vilnius University, Saule ̇tekio 7, Vilnius, LT 10257, Lithuania.

Protein structure prediction and protein structure analysis are very important problems in structural biology and bioinformatics. They have recently been subject to revolution thanks to multiple developments in several fields, most notably deep learning (1–3). Indeed, as the recent Critical Assessment of protein Structure Prediction (CASP) community-wide challenge has demonstrated, nowadays we are able to accurately predict protein structures even if they possess novel folds (4– 8).


Super-resolution microscopy (PALM, STORM etc.) provides a plethora of fluorescent signals in dense cellular environments which can be difficult to interpret. Here we describe ClusterViSu, a method for image reconstruction, visualization and quantification of labelled protein clusters, based on Voronoi tessellation of the individual fluorescence events. The general applicability of this clustering approach for the segmentation of super-resolution microscopy data, including for co-localization, is illustrated on a series of important biological objects such as chromatin complexes, RNA polymerase, nuclear pore complexes and microtubules. (my emphasis)


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A new milestoning procedure using Voronoi tessellations is proposed. In the new procedure, the edges of Voronoi cells are used as milestones, and the necessary kinetic information about the transitions between the milestones is calculated by running molecular dynamics (MD) simulations restricted to these cells. Like the traditional milestoning technique, the new procedure offers a reduced description of the original dynamics and permits to efficiently compute the various quantities necessary in this description. However, unlike traditional milestoning, the new procedure does not require to reinitialize trajectories from the milestones, and thereby it avoids the approximation made in traditional milestoning that the distribution for reinitialization is the equilibrium one. In this paper we concentrate on Markovian milestoning, which we show to be valid under suitable assumptions, and we explain how to estimate the rate matrix of transitions between the milestones from data collected from the MD trajectories in the Voronoi cells. The rate matrix can then be used to compute mean first passage times between milestones and reaction rates. The procedure is first illustrated on test-case examples in two dimensions and then applied to study the kinetics of protein insertion into a lipid bilayer by means of a coarse-grained model. (my emphasis)

When liquid water is deeply supercooled below its melting point, it separates into two liquid phases, one is low-density liquid and another is high density liquid.

This is the first visual evidence by molecular dynamics simulation that water can separate spontaneously and make two segments.

Thin green lines are edges of the Voronoi polyhedra. Blue and red spheres are water molecules having larger and smaller Voronoi volume than a designated volume threshold.

Temperature is 300K before the time origin and then it is suddenly cooled down to the specified temperature. Molecular dynamics simulations are performed by Dr. Takuma Yagasaki.

To cite this: Yagasaki, T., Matsumoto, M. & Tanaka, H. Spontaneous liquid-liquid phase separation of water. Phys. Rev. E 89, 020301 (2014). doi:10.1103/PhysRevE.89.020301

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I am working on this information @Stephers . It is not easy though, but very stimulating to my mind. Thanks you so much for leading the way. It is amazing how you can pin point where to find this information from academia and share it with us here on this forum. Still not understanding exactly how it is delivered into various fields of society. AI, Structural engineering, biometric, visual arts, agitech for instance. Combined with Nano technology the possibilities seem endless. I am going to pass this information on to my nephew, who is in a math masters program at the University of Victoria. He working towards a PhD. He may further help me get a grasp of voronoi patterns that is getting much attention and research in acidemia.

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Follow the money! It is always interesting to see where the cancer businesses go with the voronoi concept.

@Stephers is there the possibility that acidemia has hyped the miracle of the voronoi concept up to sell yet another Big Pharma drug to society.
Using acidemia experts as their pitchmen. BTW acidemia in the field of biochemistry is funded and owned by Big Pharma.
Will it work, who knows that is not the point. The point is to sell another drug to society using scientific research done by the experts getting paid by them. Empire is notorious for using acidemia to pump their make believe stories. Climate change for instance. Not saying voronoi patterns can not be used effectively in some fields, but we need to be on guard for voronoi to be hyped up to sell something. Information warfare is for sure coming directly from the modern day priests in the church of acidemia.