Добавил:
Sekretar
kiopkiopkiop18@yandex.ru
t.me/Prokururor I Вовсе не секретарь, но почту проверяю
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5440_Библиотеки_им_академика_М_И_Перельмана.pdf
Screening
Biophysical and biochemical methods
Fragment library Fragment hits
S
O
N
N
N
H
NH
2
H
2
N
3D-structure of the
fragment/protein complex
Modeling the binding mode
X-ray, NMR, docking
Fragment to
lead optimization
Figure 10.1 The FBDD process, exemplified on vemurafenib. The fragment 7-azaindole is a nonselective kinase inhibitor, and vemurafenib is a potent
inhibitor of oncogenic B-RAF kinase activity. Source: Jacquemard and Kellenberger (2019)/with permission of Taylor & Francis.
224
Another important step is the identification of possible interaction sites in the protein. Several
computational methods have been developed for this task, using the topology of the macromole-
cule to identify pockets, such as CASTp (Tian et al. 2018) or by comparing the protein with others
of the same ancestor by homology, such as SiteComp (Lin, Yoo and Sanchez, 2012). Further sites
and resources are mentioned in our previous work [13].
CASTp uses the mathematical methodologies of Delaunay triangulation, alpha shape, and dis-
crete flow [14–16], finding pockets (empty hollows in the protein structure that give access to sol-
vent molecules, using a spherical probe of radius 1.4 Å), and cavities (empty spaces inside the
structure with no access to the solvent). The CASTp method employs a triangulation algorithm
using the centers of each atom situated on the walls of a concavity and their corresponding Van der
Waals radii.
The following step is to make the connections among fragments and sites, which can be done
through several strategies: fragment evolution, fragment linking, fragment self-assembly, and frag-
ment optimization [17].
In fragment evolution, an initial fragment is optimized by adding functionality to bind to adjacent
regions of the active site, as illustrated by Figure 10.2a: fragment 1 binds to the receptor at one site,
and a new fragment grows into a second pocket. Fragment linking is done when two (or more) frag-
ments, which bind to proximal parts of the active site, are joined together to give a larger,
Table 10.1 Some common structure databases.
Protein Databank, PDB Protein database, containing more than 130,000 structures. http://www.
rcsb.org
The Nucleic Acid
Knowledgebase, NAKB
DNA and RNA database. www.nakb.org
Structural Classification
of Proteins, SCOP 2
A database that lists proteins according to their structural and evolutionary
similarities. https://scop.mrc-lmb.cam.ac.uk
ModBase A database similar to SCOUP, which allows comparison between primary
protein structures. http://modbase.compbio.ucsf.edu
ChemDB Database of small molecules, containing different physicochemical data.
http://cdb.ics.uci.edu
Cambridge Structural
Database, CSD
One of the leading repositories of small-molecule crystallographic
structures. http://www.ccdc.cam.ac.uk/products/csd
Uppsala Electron Density
Server
Very complete database with crystallographic information on PDB
structures. http://eds.bmc.uu.se/eds
Crystallography Open
Database
Database of crystallographic structures of numerous organic, inorganic,
organometallic, mineral, and biopolymer substances. http://www.
crystallography.net
Table 10.2 Required and desired features of drug orally bioavailable.
Required features
Molecular weight ≤300 Da
Number of hydrogen-bond donors
≤3
Number of hydrogen-bond acceptors ≤3
Desired features Number of rotatable bonds ≤3
Polar surface area (PSA)
≤60
225
higher-affinity-binding molecule. In Figure 10.2b, fragment 1 binds to the receptor at one site, frag-
ment 2 to the receptor at an adjacent site, and they as linked each other. Fragment self-assembly
occurs when complementary functional groups are built up around the protein target in order to
reach the most complimentary one (Figure 10.2c). With fragment optimization, fragment
approaches are used to optimize drug-like properties of a lead other than just binding affinity
(Figure 10.2d).
It is important to warrant a wide spread of fragments in the study, a condition that can be related
to molecular diversity, a measure of the variability in a set of molecules, based on statistical and
chemometric techniques. One common way to measure molecular diversity is to use a similarity
measure. A similarity measure is a function that takes two molecules as input and returns a value
that indicates how similar they are. There are many different similarity measures available, but
some of the most common include the Tanimoto coefficient and the Dice and Jaccard coeffi-
cient [18]. Once a similarity measure has been chosen, it can be used to calculate the diversity of a
set of molecules. The diversity of a set of molecules is typically defined as the average similarity
between all pairs of molecules in the set.
Another common way to measure molecular diversity is to use a diversity index, a function that
takes a set of molecules as input and returns a value that indicates the diversity of the set. There
1
(a)
(c)
(b)
(d)
1 1
11
1
1
2 2
2 2
3
Figure 10.2 (a) Fragment evolution.
(b) Fragment linking. (c) Fragment
self-assembly. (d) Fragment
optimization. Source: Ress et al. [17]/
with permission of Springer Nature.
226
are many different diversity indices available, but some of the most common include the Shannon
index [19] and the Simpson index [20]. The choice of similarity measure or diversity index will
depend on the specific application. For example, if the goal is to identify the most diverse mole-
cules in a set, then a similarity measure or diversity index that is sensitive to small differences
between molecules would be a good choice.
In addition to statistical and chemometric techniques, there are also a number of other methods
that can be used to measure molecular diversity. These methods include machine learning, AI, and
bioinformatics. Machine learning is a branch of AI that allows computers to learn from data.
Machine learning algorithms can be used to develop models that predict the properties of mole-
cules, such as their biological activity or their toxicity. These models can then be used to identify
molecules that are likely to be diverse. Bioinformatics algorithms can also be used to identify mol-
ecules that are likely to be diverse by comparing them to other molecules in a database.
The prediction of fragments must be supported by experimental techniques that are capable of
monitoring ligand–receptor interactions, such as nuclear magnetic resonance, surface plasmon
resonance, and X-ray crystallography.
The most common is the use of nuclear magnetic resonance, through which changes in the
chemical environments of the protein’s active site are monitored with the insertion of the ligand.
The most used NMR techniques for this purpose are relaxation edited 1D NMR, water–ligand
observed via gradient spectroscopy (WaterLOGSY), and saturation transfer difference (STD) spec-
troscopy [21]. In relaxation-edited 1D NMR, ligand binding to a macromolecule is accompanied by
shortened relaxation properties of the complex relative to the free ligand, and longitudinal relaxa-
tion or transverse relaxation filter is applied to the pulse sequence. Fragments that bind to the
target exhibit a loss in signal intensity in the NMR spectrum, relative to fragments that do not [22].
NMR gradient spectroscopy (WaterLOGSY) makes use of the interactions between the target and
the ligand that are mediated by water molecules, which cause a change in the profile of the relaxa-
tion times related to the interactions between ligand and water in the bound state or in the free
state [23]. The cross-relaxation rate of dipole–dipole interaction between water and ligand is positive
for free ligand and negative for bound ligands nearby water molecules associated with the protein.
The saturation-transfer difference NMR (STD-NMR) technique is based on the nuclear
Overhauser effect (NOE) and is used for measuring through-space distances. The protein target is
irradiated by a radiofrequency field specific for the protein nuclei and removes their magnetic
polarization. The fast exchange between the free and protein-bound form causes a saturation
transfer through the protein to the bound ligand and that saturation is carried on to the free ligand,
where it is detected (Angulo, Enríquez-Navas and Nieto, 2010). A magnetization saturation of the
target takes place, which by its turn is transferred to the bound ligand, and not to the free one. A
“difference spectrum” is then obtained by subtracting the spectrum obtained with the
magnetization-saturated target from the spectrum obtained with the nonirradiated target.
X-ray crystallography is another method to validate fragment generation. Obtaining crystallo-
graphic structures of macromolecules represented an important progress in the development of
new drugs. X-ray structure databases have become popular, providing information at an increasing
level of accuracy, such as the Brookhaven Protein Database, PDB [24]. Crystals can be obtained by
using the cocrystallization method (the ligand is added to the mixture before crystal formation
starts) or the soaking technique (the ligand is added directly to a mixture with pre-existing crystals).
Congreve et al. [25] explain how dynamic combinatorial chemistry (DCC) allows specific mem-
bers of a combinatorial library to be selected and amplified with the use of a template. The reaction
connecting the building blocks is reversible and an interchange between the different members of
the dynamic combinatorial library takes place [26]. The authors report an approach in which
10.3 FBDD Strategies 227
ligands are observed directly by X-ray crystallography from their electron-density maps from crys-
tals exposed to a dynamic combinatorial library mixture.
Thermal shift assay is a technique that supervises the changes undergone by a protein when it
interacts with another molecule by measuring its denaturation temperature. Protein stability
depends on factors like pH, ionic strength of the medium, presence of cofactors, and mutations.
Correlated experimental parameters that are related to structural stability and that are sensitive to a
temperature gradient, such as differential scanning fluorimetry, can be used to measure the ligand–
macromolecule interaction [27]. The fluorescence of a protein solution depends on a temperature
gradient, and the addition of fluorescence dye exhibits a low fluorescence signal in a polar environ-
ment and a high signal in a nonpolar environment [28]. The interaction of the protein with the
ligand causes exposure of polar regions previously solvated by water molecules that are dispersed
with the entry of the ligand, at the same time that it unbalances the distribution of nonpolar zones.
Isothermal titration calorimetry is a technique that allows the measuring of thermodynamic
parameters such as enthalpy changes and Gibbs free energy, which by its turn allows for the calcu-
lation of the binding affinity [29], as well as stoichiometry in one single experiment [30]. The main
advantage of this method is the discrimination it allows between enthalpic and entropic contribu-
tions to the binding.
Finally, mass spectrometry (MS) is a technique widely used in the structural determination of
organic compounds. MS provides advantages over their counterpart techniques for allowing
weak binding detection due to its high sensitivity. Besides, few sample amount is required, no
modifications or labeling of the protein target is needed, and a direct visualization of all species
in solution alongside the binding process is feasible [31, 32]. The use of milder ionization tech-
niques, such as nondenaturing electro-spray-ionization (ESI), is always more interesting because
it preserves the structural integrity of the protein: ligand complex. An example of this applica-
tion is described by Liu and Quinn [33]: 643 natural products (NPs) fragment-sized library with
low molecular weight were screened against 62 potential protein targets for malaria, which led
to 96 low molecular NPs capable of binding and 79 fragments that could inhibit the growth of
malaria parasites in vitro. Another worth-citing case is the discovery of a benzimidazole moiety
with high affinity to a 29-mer RNA model, identified from a 180,000-fragment library using
MS-based screening methods [34].
10.3 FBDD Strategies
FBDD studies can follow several strategies and approaches, which will depend on the available
information and the level of refinement of the results that are desired. We can mention the follow-
ing strategies: Build-up Core FBDD, HTS Complimentary, and Chemical Biology Exploration of
Biological Targets. We will briefly discuss the scope of each one.
The strategy known as Build-up Core FBDD, which has applications in drug design, consists
of the construction of new ligand candidates (hits) to determine targets from pure fragments.
Several tools that use this path can be mentioned, the most well-known being CAVEAT [35],
which employs a vector algorithm. This strategy uses molecular docking to build new candi-
dates around the interaction site. To avoid a prohibitive number of solutions for the calculation,
the pharmacophore structure is used as a guide. The choice of the docking scoring function is
also important, which might include: binding energy, free energy, or interaction energies.
Modern force fields group their scoring functions in force field, empirical, and knowledge-
based (Guedes et al. 2014).
228
Another common approach is to combine FBDD with HTS. Just as large libraries of whole com-
pounds are screened in HTS against a target, using scoring parameters such as ligand efficiency
(LE, calculated from the interaction free energy), libraries of fragments can also be screened [36].
Searching for viable interaction sites in libraries of targets is also a widely used strategy, such as
in the multiple solvent crystal structures method, which uses solvent molecules as bridges between
the site and the ligands (Allen et al. 1996), or when guiding properties such as druggability are used
to select the fragments that best fit the sites.
10.4 Case Studies
NPs are a rich source of biologically active compounds. They have been used for centuries in tradi-
tional medicine to treat a variety of diseases. In recent years, there has been a growing interest in the
development of NP-inspired compounds as new drugs [12]. NPs are often complex molecules with
a variety of functional groups. This complexity can make it difficult to synthesize them in the labo-
ratory. However, there are a number of methods that can be used to synthesize NPs or their analogs.
These methods include chemical synthesis, enzymatic synthesis, and combinatorial chemistry.
Once an NP-inspired compound has been synthesized, it must be tested for its biological activity.
This can be done in a variety of ways, including in vitro assays, animal studies, and clinical trials.
In vitro assays can be used to test the compound’s activity against a variety of targets, such as
enzymes, receptors, and DNA. Animal studies can be used to assess the compound’s toxicity and
its potential for therapeutic efficacy. Clinical trials are conducted in humans to determine the com-
pound’s safety and efficacy in treating a specific disease.
A number of NP-inspired compounds have been shown to have biological activity. Some of these
compounds have been approved for use as drugs, while others are in clinical development [37].
Examples of NP-inspired drugs include paclitaxel, a chemotherapy drug used to treat cancer; arte-
misinin, an antimalarial drug; and rapamycin, an immunosuppressant drug used to prevent organ
rejection.
The development of NP-inspired compounds is a promising area of research. These compounds
have the potential to provide new treatments for a variety of diseases [38]. However, the develop-
ment of new drugs is a long and expensive process. It can take many years and millions of dollars
to bring a new drug to market. Despite the challenges, the development of NP-inspired compounds
is an important area of research. These compounds have the potential to provide new treatments
for a variety of diseases and improve the lives of millions of people.
An interesting application of FBDD is in the design of compounds inspired by NPs [39]. Due to their
diversity and complexity, their biological action is accompanied by side effects associated with the abil-
ity to bind to different biological receptors. The growth in the number of NP databases signals the
importance of this information source for the development of new treatments for diseases (Table 10.3).
An application of the use of FBDD/HTS in drug design is the study described by Vu et al. [32],
which collected 650 compounds from various fragment libraries (Figure 10.3), following as a crite-
rion the permitted ranges of physicochemical properties (compare Table 10.2):
● Molecular weight ≤250 Da
● Octanol–water partition coefficient <4
● Hydrogen bond donors ≤4
● Hydrogen bond acceptors ≤5
● Rotatable bonds ≤6
● Percent polar surface area <45.
10.4 Case Studies 229
These fragments were tested against 62 molecular targets associated with malaria. About 100 NP-
like fragments were identified, able to interact with 32 of the molecular targets. About 80% of these
compounds proved effective against Plasmodium falciparum.
One can also mention the search for drugs to fight COVID-19, alongside immunological
treatments. FDA-approved drugs obtained from theoretical calculations, such as remdesivir,
saquinavir, and darunavir, and some flavone and coumarin derivatives as potential inhibitors of
human SARS-CoV2 main protease [40]. Shaffer [41] mentions some drugs being tested against
SARS-Cov2, like chloroquine, lopinavir, nafamostat, hydroxychloroquine, ritonavir, camostat,
corticosteroids, and sarilumab. Inhibitors for the main protease in SARS-CoV2 using FBDD
have been described [42], from a fragment database derived from Auto Core Fragment in silico
Screening (ACFIS) 2.0 web server [43] followed by docking against the enzyme using PyRx [44]
and AutoDock [45], and ADMET [46] and molecular dynamics studies [47]. ADMET properties
followed total polar surface area [48], water solubility, lipophilicity (log P), skin permea-
tion [49], and synthetic criteria.
Table 10.3 Some NP databases.
ANPDB
African Natural
Products Database
https://african-compounds.org/anpdb
AfroMalariaDB
African Antimalarial Natural Products Library
https://african-compounds.org/about/afromalariadb
BIOFACQUIM
A Mexican Compound Database of Natural Products
https://www.difacquim.com/d-tools
COCONUT
Natural Products Online
https://coconut.naturalproducts.net
NANPDB
North American Natural Product Database
http://african-compounds.org/nanpdb
NPATLAS
The Natural Products Atlas
https://www.npatlas.org
NPASS Natural Product Activity and Species Source Database
https://bidd.group/NPASS
NuBBE Nuclei of Bioassays, Biosynthesis and Ecophysiology of Natural Products
https://nubbe.iq.unesp.br/portal/nubbe-search.html
SANCDB
South African Natural Compounds Database
https://sancdb.rubi.ru.ac.za
StreptomeDB
Database of compounds isolated from Streptomyces spp.
http://132.230.102.198 : 8000/streptomedb/
TCM-ID Traditional Chinese Medicine Information Database
https://bidd.group/TCMID
TIPdb Database of Taiwan indigenous plants
https://cwtung.kmu.edu.tw/tipdb
YaTCM
Yet another Traditional Chinese Medicine database
https://github.com/jianping-grp/yatcm
230
10.5 Conclusion and Future Perspectives
In our previous work on FBDD [13], we listed several computational strategies employed in HTS
and that serve well the purposes of FBDD studies, such as dynamic combinatorial chemistry (DCC)
and de novo drug design approach. Dynamic combinatorial chemistry (DCC) serves as a
O
O
O
O
(a) (b) (c)
N
N
HN
OH
HO
HO
OH
Cl
Cl
OH
OH
OH
Br
Br
Br
OH
HN
O
O
O
O
O
O
N
N
N
N
O
O
O
O
O
O
O
O
S
O
O
O
O
O
O
O
O
O
O
O
O
S
O
S
S
N
N
N
+
N
H
N
H
N
HN
HN
Figure 10.3 Examples of fragment hit scaffolds present among antimalarial HTS hits. (a) Fragment scaffold. (b)
Original fragment. (c) Antimalarial HTS hit molecule. Source: Vu et al. [32]/American Chemical Society/CC BY 4.0.
231
compelling method for crafting targeted ligand libraries for macromolecular targets. Its efficacy
lies in the reversible reactions of building blocks, leading to a stable thermodynamic equilibrium.
An extension, termed target-directed DCC (tdDCC), identifies potent ligands for relevant pharma-
cological targets.
A natural progression from FBDD involves its integration with three-dimensional quantitative
structure–activity relationships (3D QSAR). Unlike classic QSAR, which statistically correlates
physicochemical properties with biological activity, 3D QSAR evaluates electronic and steric
energy values, generating three-dimensional maps indicating favorable interaction sites. In the
1990s and 2000s, the de novo drug design approach using the LeapFrog (LF) program gained popu-
larity, available in the Sybyl package. LF facilitates molecular evolution or electronic screening
with three alternative modes: OPTIMIZE enhances existing leads, DREAM proposes new mole-
cules for binding, and GUIDE supports interactive design. Binding energy calculation involves
steric and electrostatic enthalpies, cavity desolvation energy, and ligand desolvation energy.
Addressing the rationality of druggability and molecular shape, a concept explored by Bemis and
Murcko in the 1990s, presents a challenge open to investigation. Although their work focused on
2D fragment topological features, limited graph portraits appear promising for potential drug
development. This concept proves valuable in constructing fragment libraries with topological
constraints.
The success of FBDD hinges on advancing computational capabilities and disease-specific frag-
ment library availability. The COVID-19 pandemic has spurred new demands, especially in drug
repurposing and toxicity studies. Despite challenges, this field offers a cost-effective avenue for
synthesizing novel chemical entities, contrasting with traditional pharmaceutical combinatorial
screening.
The development of novel drugs is a complex and intricate process that plays a crucial role in
modern healthcare. As researchers strive to address various diseases, they encounter numerous
challenges in drug planning and design. De novo drug design (DNDD) and FBDD are prominent
methods in this endeavor. DNDD involves the construction of entirely new molecular entities. The
complexity of designing molecules with desired pharmacological properties while ensuring safety
and efficacy poses a significant challenge [50]. Computational tools play a crucial role in de novo
design, but the accurate prediction of a molecule’s biological activity and safety remains challeng-
ing. The reliance on computational models introduces uncertainties that need to be carefully
addressed [51]. Synthesizing novel compounds is a costly and time-consuming process. Ensuring
the chemical feasibility of designed molecules and their synthesis on a practical scale poses a sub-
stantial challenge [52]. Verifying the predicted biological activity of DNDD designed molecules
experimentally is a critical step. Challenges arise in obtaining accurate and reliable data that can
validate the effectiveness of the designed compounds [51]. The success of FBDD, by its turn, heav-
ily relies on the quality and diversity of the fragment libraries used. Ensuring that the fragments
cover a broad chemical space and possess drug-like properties is a persistent challenge [53].
Integrating fragments into a lead compound with high binding affinity is a delicate task. Achieving
optimal interactions while maintaining drug-like properties can be challenging and requires care-
ful optimization [54]. Identifying hits from fragment screening is just the initial step. Expanding
these hits into viable lead compounds and linking fragments to form a cohesive, effective drug
candidate presents a considerable challenge [53]. FBDD often deals with structurally complex mol-
ecules. Elucidating the three-dimensional structures of these compounds and their interactions
with biological targets can be challenging using traditional methods [54].
To overcome the challenges associated with each method individually, a hybrid approach that
integrates de novo and FBDD has gained traction [55]. By combining the strengths of designing
from scratch and utilizing fragment-based information, researchers aim to enhance the efficiency
232
and success rate of drug discovery processes. The contemporary landscape of drug planning is
marked by challenges in both de novo and FBDD. Molecular complexity, computational limita-
tions, chemical feasibility, and biological validation are hurdles in the de novo approach, while
fragment library quality, binding affinity optimization, hit expansion, and structural complexity
present challenges in FBDD. Researchers are continually working toward innovative solutions,
and the integration of these two methods offers a promising avenue for overcoming some of these
hurdles. As technology advances and our understanding of drug design deepens, the pharmaceuti-
cal industry moves closer to addressing these challenges and delivering novel therapeutics to
improve global health.
References
1 Surabhi, S. and Singh, B. (2018). Computer aided drug design: an overview. Journal of Drug
Delivery and Therapeutics 8 (5): https://doi.org/10.22270/jddt.v8i5.1894.
2 Torres, P.H.M., Sodero, A.C.R., Jofily, P., and Silva-Jr, F.P. (2019). Key topics in molecular docking
for drug design. International Journal of Molecular Sciences 20 (18): https://doi.org/10.3390/
ijms20184574.
3 Śledź, P. and Caflisch, A. (2018). Protein structure-based drug design: from docking to molecular
dynamics. Current Opinion in Structural Biology 48: https://doi.org/10.1016/j.sbi.2017.10.010.
4 Song, C.M., Lim, S.J., and Tong, J.C. (2009). Recent advances in computer-aided drug design.
Briefings in Bioinformatics 10 (5): https://doi.org/10.1093/bib/bbp023.
5 Wang, L., Ding, J., Pan, L. et al. (2019). Artificial intelligence facilitates drug design in the big data era.
In: Chemometrics and Intelligent Laboratory Systems, vol. 194. https://doi.org/10.1016/j.chemolab.
2019.103850.
6 Capdeville, R., Buchdunger, E., Zimmermann, J., and Matter, A. (2002). Glivec (ST1571, imatinib),
a rationally developed, targeted anticancer drug. Nature Reviews Drug Discovery 1 (7): https://doi.
org/10.1038/nrd839.
7 Shepard, H.M., Jin, P., Slamon, D.J. et al. (2008). Herceptin. Handbook of Experimental
Pharmacology 181: https://doi.org/10.1007/978-3-540-73259-4_9.
8 Polamreddy, P., Vishwakarma, V., Arumugam, P. et al. (2020). Discovery of hit molecules targeting
allosteric site of hepatitis C virus NS5B polymerase. Journal of Biomolecular Structure and
Dynamics 38 (5): https://doi.org/10.1080/07391102.2019.1608864.
9 Drews, J. (2000). Drug discovery: a historical perspective. Science 287: 1960–1964. https://doi. org/
10.1126/science.287.5460.1960.
10 Katsila, T., Spyroulias, G.A., Patrinos, G.P., and Matsoukas, M.T. (2016). Computational
approaches in target identification and drug discovery. Computational and Structural Biotechnology
Journal 14: 177–184. https://doi.org/10.1016/J.CSBJ.2016.04.004.
11 Schuffenhauer, A., Ruedisser, S., Marzinzik, A.L. et al. (2005). Library design for fragment based
screening. Current Topics in Medicinal Chemistry 5 (8): 751–762. https://doi.org/10.2174/15680260
54637700.
12 Vamathevan, J., Clark, D., Czodrowski, P. et al. (2019). Applications of machine learning in drug
discovery and development. Nature Reviews Drug Discovery 18 (6): 463–477. https://doi.org/
10.1038/s41573-019-0024-5.
13 Oliveira, A.M. and Rudrapal, M. (2023). Fragment-based drug design in lead discovery. In: CADD
and Informatics in Drug Discovery (ed. J.K. Org and M. Rudrapal), 174–204. Springer Singapore.
14 Edelsbrunner, H. (1995). The union of balls and its dual shape. Discrete & Computational Geometry
13 (3): 415–440. https://doi.org/10.1007/BF02574053.