ZincProteome.lyx

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\begin_body

\begin_layout Chapter
Investigation of intermolecular metal-binding sites
\end_layout

\begin_layout Standard
Zn(II) ions were found to be essential for the growth of the toxic mold
 – 
\emph on
Aspergillus niger 
\emph default
in 1869, nearly one hundred years later, in 1961, it was postulated that
 zinc is essential also for humans.
 
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout
(1) Raulin J.
 Etudes cliniques sur la vegetation.
 Ann.
 Sci.
 Nat.
 Bot.
 Biol.
 Veg.
 Ser.
 1869, 11, 293– 299.
 (2) Prasad, A.
 S.
 et al.
 Syndrome of iron deficiency anemia, hepatosplenomegaly, hypogonadism, dwarfism
 and geophagia.
 Am.
 J.
 Med.
 1961, 31, 532–546.
\end_layout

\end_inset

 Almost 20 years later the first structures of proteins containing Zn(II)
 started to appear.
 It will not be an exaggeration if I say that the number of scientific questions
 is proportional to the amount of new data—with the advent of the first
 Zn(II)-containing macromolecular structures, questions about the factors
 that govern the formation of the zinc-binding sites started to appear.
 With more Zn(II)-containing structures deposited in the 
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\backslash
gls{rcsb}
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 some tendencies became clear (see 
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\begin_layout Plain Layout
\begin_inset CommandInset ref
LatexCommand labelonly
reference "sec:Zinc-Binding-Sites"
plural "false"
caps "false"
noprefix "false"

\end_inset


\end_layout

\end_inset

), however, the fact that the Zn(II) ions (and other metal ions) can be
 bound at the 
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\backslash
gls{interface}
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 of two or more macromolecules was rather ignored – one of the first reviews
 of structural knowledge of metal-binding sites in proteins appeared in
 
\begin_inset CommandInset citation
LatexCommand citebyear
key "Tainer1992"
literal "true"

\end_inset

, 
\begin_inset CommandInset citation
LatexCommand citep
key "Tainer1992"
literal "true"

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 whereas the first review regarding the binding of metals at 
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\backslash
glspl{ppi}
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 appeared in 
\begin_inset CommandInset citation
LatexCommand citebyear
key "Song2014"
literal "true"

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.
 
\begin_inset CommandInset citation
LatexCommand citep
key "Song2014"
literal "true"

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 This Chapter will focus on the methodology of how one can investigate the
 metal-binding sites at 
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\backslash
glsdescplural{ppi}
\end_layout

\end_inset

.
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\begin_layout Plain Layout
podać jakieś charakterystyki miejsc cynkowych, powiedzieć dlaczego szukanie
 miejsc białkowych na poddstawie tych charakterystyk jest głupie
\end_layout

\end_inset


\end_layout

\begin_layout Section

\emph on
In silico
\emph default
 investigation of intermolecular metal-binding sites
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\begin_layout Plain Layout
gdzieś tu powinno pojawić się
\begin_inset space \space{}
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informacje o tym, że możliwe, że coś się zmieniło wraz z typem annotacji
 zrobionej przez włochów, ale nwm.
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
The problems of 
\shape italic
in silico
\shape default
 investigation of intermolecular metal-binding sites
\end_layout

\begin_layout Standard
To date, there are no computational algorithms or other methods that are
 able to identify or classify intermolecular metal-binding based on protein
 sequence or structure.
 The problem of metal-binding sites prediction was undertaken in the past
 several times.
 Apart from the availability of such tools, which is often unacceptable
 
\begin_inset CommandInset citation
LatexCommand citep
key "Ye2022"
literal "true"

\end_inset

, the quality of the proposed classifiers is often poor.
 
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Classifier is a tool that assigns an element to a certain class.
 An algorithm that tells whether a protein is a 
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\backslash
gls{mprotein}
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\end_inset

 based on the protein attributes is a classifier.
\end_layout

\end_inset

 Usually, the authors of such algorithms present the quality and efficiency
 of their classifier in a reliable way, e.g., by showing various kinds of
 statistics like receiver operating characteristic curve in the case of
 binary classifiers, the presented tools at first glance seem to work very
 well, however, to date, the use of such tools is limited.
 For sure one cannot accuse the authors of such articles of scientific misconduc
t or ill-faith – usually, the problem lies deeper.
 The are two main problems with the classifiers: the first one is the problem
 with the initial data set, which eventually is a source for creating the
 training and the test data sets, and the second problem is the choice of
 explanatory variables.
\end_layout

\begin_layout Standard
The availability of well-annotated (due to manual curation) protein sequence
 data is quite good.
 The primary source of such information is scientific articles.
 A publication that treats whether a protein binds metal or not has a number
 of methods that show and describe this binding.
 Such publication does not need to include information about the structure
 of the protein, this information is not necessary to prove the interaction
 of the metal with the protein.
 Typically, this type of data can be aggregated in 
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\backslash
gls{UniProt}
\end_layout

\end_inset

, where metal-interacting residues are often assigned based on similarity
 and sequence.
 The problem with this type of data is the sparsity of annotations – not
 every known 
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gls{mprotein}
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 is annotated in 
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gls{UniProt}
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 to interact with metal.
 This leads to the attempts to create one's own data set, which in turn
 involves the use of the other type of input – the structural data deposited
 in the 
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gls{rcsb}
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, however, the metal-binding sites in the 
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gls{rcsb}
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\end_inset

 are not annotated to be a true physiological or adventitious metal-binding
 sites.
 This, in turn, leads to the use of simple algorithms that sort 
\begin_inset Quotes eld
\end_inset

true
\begin_inset Quotes erd
\end_inset

 from 
\begin_inset Quotes eld
\end_inset

false
\begin_inset Quotes erd
\end_inset

 metal-binding sites in the data set based on simple rules, i.e., the distance
 between the metal and 
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, the number of 
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, type of 
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, etc., however, this approach is far from being accurate.
\end_layout

\begin_layout Standard
The problem with the selection of explanatory variables is most acute with
 classifiers that are based on the sequence.
 Whereas structural-based classifiers may involve the abundance of meaningful
 variables for the classifier (e.g., hydrophobicity, a charge of the amino
 acids, geometry, position in space, etc.), the effort of prediction of a
 metal-binding site based solely on the sequence might be similar to the
 prediction of the sales on stock exchange based using only stock shares
 name.
 Nevertheless, in some specific cases, where there is an existing pattern
 in the sequence it is possible to build sensitive and specific classifiers,
 e.g., the prediction of zinc fingers based on sequence is possible due to
 the existence of well-defined input data and the existence of patterns
 in the sequences 
\begin_inset CommandInset citation
LatexCommand citep
key "Sathyaseelan2023"
literal "true"

\end_inset

.
\end_layout

\begin_layout Standard
The above problems with the prediction of metal-binding sites are the same
 for intermolecular metal-binding sites, as well, moreover, the fact of
 two or more interacting macromolecules increases the complexity of the
 problem.
 So how to search for metals bound at 
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\backslash
glspl{ppi}
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\end_inset

 if there are no viable 
\begin_inset Note Note
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nwm czy tu dobrze viiable
\end_layout

\end_inset

 
\emph on
in silico
\emph default
 tools? The question is addressed below in 
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\begin_inset CommandInset ref
LatexCommand labelonly
reference "subsec:Obtaining-knowledge-about-InterMBS"
plural "false"
caps "false"
noprefix "false"

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\end_layout

\end_inset

.
\end_layout

\begin_layout Subsection
Obtaining knowledge about intermolecular metal-binding sites
\begin_inset CommandInset label
LatexCommand label
name "subsec:Obtaining-knowledge-about-InterMBS"

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\begin_layout Standard
As in the case of information about the interaction of the metal with the
 protein, here also publications may also be the primary source of information
 about metal-binding on 
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\backslash
gls{ppi}
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.
 However, the lack of recognition of inter-protein metal ion binding has
 partly contributed to the fact that even if a publication is accompanied
 by the deposition of a structure in the 
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\backslash
gls{rcsb}
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, the fact of inter-protein metal ion binding is not necessarily commented
 on in the publication in any way.
 An additional problem with extracting knowledge directly from publications
 is the fact that the search for this type of information can be time-consuming.
 There may be problems with the availability of the article (not every article
 is published as an open access article), and the fact that there is no
 tool that aggregates the articles based on the information on whether the
 described protein within the article has an inter-protein metal-binding
 site, makes this approach unreasonable.
 Nevertheless, it is not out of the question that this type of information
 aggregation will change (not necessarily regarding the 
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) with the increasing number of open access articles published each year
 and the development of technologies related to natural language processing.
\end_layout

\begin_layout Standard
To date, the best source of information on proteins that bind metal ions
 in an intermolecular manner are structural databases like 
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gls{rcsb}
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.
 Since 
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gls{rcsb}
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 contains all deposited structures (whether they contain metal or not) searching
 for information on metal-binding sites in 
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\backslash
gls{rcsb}
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 is not necessarily an easy task.
 For this reason, various secondary databases have been created that rely
 on the information contained in the 
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gls{rcsb}
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.
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\begin_layout Standard
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MESPEUS
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 was one of the first databases to include information on zinc sites, MESPEUS
 allowed filtering of data based on metal, 
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\backslash
gls{Lg}
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 type, and resolution, unfortunately, MESPEUS is now no longer available
 
\begin_inset CommandInset citation
LatexCommand citep
key "Hsin2008,Harding2014"
literal "true"

\end_inset

.
 
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ZifBASE
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 is an even more specific database – it is dedicated only to zinc fingers,
 plus it contains far more information than just structural information
 – it contains sequence information, potential DNA interaction sequences,
 and more.
 However, as of today, despite the existence of the site, ZifBASE appears
 to be severely broken or non-functional at all, search and other functions
 do not work, additionally, it is not known how often the database is updated
 or whether longer updated 
\begin_inset CommandInset citation
LatexCommand citep
key "Jayakanthan2009"
literal "true"

\end_inset

.
 
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\begin_layout Standard
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MetalPDB
\end_layout

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\end_layout

\end_inset

 is the best-known derivative database based on 
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\backslash
gls{rcsb}
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 regarding metal ions.
 MetalPDB has more advanced features compared to a simple database like
 MESPEUS, it has, for example, the ability to search for binding sites by
 geometric likeness.
 The big advantage of MetalPDB is the use of the 
\begin_inset Quotes eld
\end_inset

Minimal Functional Site
\begin_inset Quotes erd
\end_inset

 concept which allows the implementation of the above function.
 The disadvantage of MetalPDB is that MetalPDB is based on 
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glspl{asunit}
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, not 
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glspl{bassembly}
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.
 This approach to building a database is incorrect because some of the binding
 sites (and especially the intermolecular binding) can only be seen after
 the symmetry operations are applied and the 
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\backslash
gls{bassembly}
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 is created.
 Like the rest of these tools, MetalPDB does not allow searching for inter-prote
in binding sites of metal ions.
 MetalPDB despite the fact that it is possible to automate this type of
 tool seems to be rarely updated, as of February 13, 2023, MetalPDB gives
 an update date as of April 5, 2022, which does not seem to be true.
 No metal-containing structures, but published close to the supposed MetalPDB
 update date are present in the database – for example, the structures 
\begin_inset CommandInset href
LatexCommand href
name "7V8G"
target "https://www.rcsb.org/structure/7V8G"
literal "false"

\end_inset

 (published March 30, 2022) or 
\begin_inset CommandInset href
LatexCommand href
name "7TIH"
target "https://www.rcsb.org/structure/7TIH"
literal "false"

\end_inset

 (published March 30, 2022) despite the fact that it is strewn with metals
 is also absent.
 The fact that derivative databases do not have all the records that are
 present in the primary database is understandable – for various reasons,
 over the years 
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gls{pdb}
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 files have all sorts of errors, inaccuracies, or format incompatibilities
 that cause problems in processing, nevertheless, the number of missing
 files in MetalPDB is puzzling 
\begin_inset CommandInset citation
LatexCommand citep
key "Andreini2013,Putignano2018"
literal "true"

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.
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\begin_layout Standard
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\begin_layout Plain Layout
ZincBind
\end_layout

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\end_inset

 is one of the newest databases, which includes information on 
\begin_inset Quotes eld
\end_inset

physiological
\begin_inset Quotes erd
\end_inset

 binding sites for Zn(II) ions, however,  it does not have information on
 intermolecular zinc-binding.
 Physiological sites in ZincBind are understood to be those with at least
 two binding residues and at least three binding atoms, additionally, ZincBind
 overcomes the biggest issues of MetalPDB: ZincBind is automatically updated,
 presented structures are already in the 
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, and most of all the 
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 of ZincBind is freely available under the MIT License 
\begin_inset CommandInset citation
LatexCommand citep
key "Ireland2019"
literal "true"

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.
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The 
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 availability makes the science more transparent.
\end_layout

\end_inset

 
\end_layout

\begin_layout Standard
Using various types of databases, it is possible, after applying certain
 logic, to select 
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\backslash
gls{pdb}
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 files that have metal ions at the interface of two macromolecules.
\begin_inset Foot
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\begin_layout Plain Layout
This does not automatically mean that these sites will be physiologically
 relevant.
 
\end_layout

\end_inset

 However, this type of manipulation may require some programming expertise
 to avoid the tedious manual review of hundreds or thousands of structures.
 To make this search possible for scientists without programming knowledge
 to find intermolecular metal-binding sites in proteins, I have decided
 to create a publicly available database – InterMetalDB
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https://intermetaldb.biotech.uni.wroc.pl/
\end_layout

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\end_layout

\end_inset

(
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\begin_layout Plain Layout
\begin_inset CommandInset ref
LatexCommand labelonly
reference "chap:InterMetalDB"
plural "false"
caps "false"
noprefix "false"

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\end_layout

\end_inset

).
\end_layout

\begin_layout Subsection
How one does build a database?
\end_layout

\begin_layout Standard
The first step in building a database is data acquisition.
 In the case of creating a primary database, data should be obtained directly
 from a suitable source.
 For scientific databases, the source of such data is often publications.
 For example, the NIST46
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https://www.nist.gov/srd/nist46
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\end_layout

\end_inset

 database of affinity constants for chelator complexes with metals was built
 by searching and evaluating data from publications.
 In the case of 
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\backslash
gls{rcsb}
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\end_inset

, the situation is somewhat different nowadays – journals now often require
 the structure to be deposited prior to the article acceptation or release.
 This is a very smart approach, for several reasons – it reduces the workload
 on the 
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\backslash
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 side, and guarantees that virtually every publication presenting a new
 structure will simultaneously deposit the structure in the 
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gls{rcsb}
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.
 However, this does not mean that every structure described by humankind
 will be available in the 
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.
 In 2023, private companies still do not publish macromolecular structures
 in the 
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, while structures deposited in the 
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 contribute to the development of new drugs by public entities 
\begin_inset CommandInset citation
LatexCommand citep
key "Westbrook2019"
literal "true"

\end_inset

.
 
\end_layout

\begin_layout Standard
In the case of the derivative databases, the first step o acquiring a data
 set is to query a primary database.
 If 
\begin_inset ERT
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\backslash
gls{api}
\end_layout

\end_inset

 is available the acquisition is usually trivial, as it requires only the
 application of the proper querying logic.
 If the database does not provide the 
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\backslash
gls{api}
\end_layout

\end_inset

 one still can obtain the information – manually or by constructing a web
 crawler 
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status collapsed

\begin_layout Plain Layout
A web crawler is a program that scans the Internet.
 The main purpose of web crawlers is to collect data for various purposes,
 such as search engine indexing, data mining, and content monitoring.
\end_layout

\end_inset

 provided the database has an online version.
\end_layout

\begin_layout Standard
If the data was not filtered in the previous step the next step is the data
 selection, annotation, organization, and storage.
 The goal of this step is to ensure that the data is accurate and consistent.
 This step is particularly important in scientific research, where data
 is often complex, and diverse and requires long-term preservation.
 This can be done manually, by computer programs or scripts, or by a combination
 of these approaches.
 In case of the curation of the macromolecular data, it is important to
 take into account various information that accompanies the structure: the
 sequence of the macromolecules in the 
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gls{pdb}
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 files, the coordinates in the file, gene source organism, the expression
 mechanism, ways of structure acquisition, etc.
 An important issue with the data aggregated in the 
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\backslash
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 is the fact of the redundancy
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In the case of the 
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 redundancy is understood as the existence of many similar macromolecular
 structures, i.e., two 
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\backslash
gls{pdb}
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\end_inset

 files of the same protein can be almost identical, however, one file may
 have a better resolution.
\end_layout

\end_inset

 of structural files, which should be taken into account during the construction
 of the derivative database.
 This redundancy is dealt with usually by clustering based on the sequence.
\end_layout

\begin_layout Standard
During the data organization it is important to design a proper logic of
 the database – how the records of the databases are connected together
 within the database.
 For example macromolecular structure may contain multiple metal-binding
 sites, this simple and hardly revealing fact implies several questions,
 e.g.,: how the records of the metal-binding sites should be connected with
 the records of the structures?; how to choose a representative metal-binding
 site from a structure, or maybe are there multiple representative metal-binding
 sites?.
 If the answers to those and other questions are known it is possible to
 implement the logic behind the database.
\end_layout

\begin_layout Standard
The final step of the data curation is the data presentation and sharing,
 in the age of the Internet it is normal to present the curated data over
 the Internet as a hosted web application that allows for the querying,
 and viewing the aggregated results.
 This step largely relies on the previous step and the logic behind the
 database, if the database has poorly done bindings the querying of the
 database for the end user will be cumbersome.
 
\end_layout

\begin_layout Subsubsection
Use of programming and markup languages in the creation and presentation
 of databases
\end_layout

\begin_layout Standard
Programming languages play an important role in the creation of modern databases.
 There are several programming languages that are commonly used for creating
 the back-end
\begin_inset Marginal
status open

\begin_layout Plain Layout
The back-end is understood as everything that is invisible to the end user.
 It contains all the application logic, bindings, etc.
\end_layout

\end_inset

 databases including 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{sql}
\end_layout

\end_inset

, 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{python}
\end_layout

\end_inset

, 
\family typewriter
Java
\family default
, and others.
\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Gls{sql}
\end_layout

\end_inset

 is the most widely used language for managing and querying relational databases.
 It is used to create, modify, and delete database objects, such as tables,
 views, and indexes.
 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Gls{sql}
\end_layout

\end_inset

 is also used to insert, update, and retrieve data from tables.
\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Gls{python}
\end_layout

\end_inset

 is a popular general-purpose programming language that is widely used for
 data processing and analysis.
 A variety of libraries allow for easy object manipulation in 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{python}
\end_layout

\end_inset

, which allows for managing and building the logic in the database.
 For example, 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{django}
\end_layout

\end_inset

 is a popular web framework that is built on 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{python}
\end_layout

\end_inset

 and is often used for creating web applications that are operating on databases.
 The use of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{django}
\end_layout

\end_inset

 allows working with databases using high-level abstractions instead of
 writing raw 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{sql}
\end_layout

\end_inset

 queries.
 With 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{django}
\end_layout

\end_inset

, it is possible to define the logic and models of the database tables as
 regular 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{python}
\end_layout

\end_inset

 classes.
 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Gls{django}
\end_layout

\end_inset

 provides a convenient 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{api}
\end_layout

\end_inset

 for querying the database allowing it to retrieve and manipulate the data
 with 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{python}
\end_layout

\end_inset

 objects and methods, which allows finally for a presentation as a front-end.
 
\begin_inset Marginal
status open

\begin_layout Plain Layout
Front-end is everything that the end-user is able to see – user interface;
 buttons, images, etc.
 
\end_layout

\end_inset

 
\end_layout

\begin_layout Standard
The front-end of the web application is usually built with 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{html}
\end_layout

\end_inset

, the website is stylized using Cascading Style Sheets, and the interactivity
 is added using JavaScript (e.g., the ability to view the protein structure).
\end_layout

\begin_layout Subsubsection
Clustering
\end_layout

\begin_layout Standard
The part of data curation is the clustering of the primary data.
 One of the most common ways of dealing with redundancy in the protein structure
s is the use of a sequence clustering algorithm.
 This can be done by several programs, however,  in the InterMetalDB (
\begin_inset Flex CT - auto cross-reference
status open

\begin_layout Plain Layout
\begin_inset CommandInset ref
LatexCommand labelonly
reference "chap:InterMetalDB"
plural "false"
caps "false"
noprefix "false"

\end_inset


\end_layout

\end_inset

) I have decided to utilize CD-HIT 
\begin_inset CommandInset citation
LatexCommand citep
key "Li2006,Fu2012"
literal "true"

\end_inset

.
 Similar algorithms and programs may be used, e.g., BLAST 
\begin_inset CommandInset citation
LatexCommand citep
key "Camacho2009"
literal "true"

\end_inset

 or mmseqs2 
\begin_inset CommandInset citation
LatexCommand citep
key "Mirdita2019,Mirdita2021"
literal "true"

\end_inset

.
 To cluster 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{pdb}
\end_layout

\end_inset

 files one typically follows several steps:
\end_layout

\begin_layout Enumerate
Convert the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{pdb}
\end_layout

\end_inset

 files into a FASTA format (a text file extending 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{ascii}
\end_layout

\end_inset

).
\end_layout

\begin_layout Enumerate
Use CD-HIT to cluster the protein sequences at a desired sequence identity
 threshold.
\end_layout

\begin_layout Enumerate
Map the clustered sequences back to the original 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{pdb}
\end_layout

\end_inset

 structures.
\end_layout

\begin_layout Enumerate
Remove redundant structures in each cluster and select a representative
 structure for each cluster.
 This step can be performed by choosing as a representative a structure
 with the best resolution or newest structure.
\end_layout

\begin_layout Standard
The resulting output is a set of non-redundant (or with diminished redundancy)
 representative structures for each cluster.
 Depending on the clustering threshold it may be required to cluster the
 structures based on another factor, e.g., based on the structure.
\end_layout

\begin_layout Standard

\emph on
\begin_inset Note Note
status open

\begin_layout Plain Layout

\emph on
w tym rozdziale info o tym, że ze struktury nie można nic mówić o stopniu
 utlenienia
\end_layout

\end_inset


\end_layout

\begin_layout Section

\emph on
Ex silico 
\emph default
investigation of intermolecular metal-binding sites
\end_layout

\begin_layout Standard
What if one already have some preliminary information (for example, obtained
 through database research, 
\begin_inset Flex CT - auto cross-reference
status open

\begin_layout Plain Layout
\begin_inset CommandInset ref
LatexCommand labelonly
reference "subsec:Obtaining-knowledge-about-InterMBS"
plural "false"
caps "false"
noprefix "false"

\end_inset


\end_layout

\end_inset

) or hunch about the intermolecular metal-binding at 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{ppi}
\end_layout

\end_inset

? With preliminary knowledge (or suspicion) of intermolecular metal binding,
 one can proceed with
\emph on
 ex silico 
\emph default
testing, where
\emph on
 ex silico 
\emph default
I will understand as all experiments performed without the use of a computer
 as the main working tool.
 In general, verification of intermolecular metal-binding is not significantly
 different from the study of metal–protein interaction, although there are
 existent some important differences that should be taken into account during
 the design of the experiment.
\end_layout

\begin_layout Subsection
Proteomic tools for the detection of metal-involved protein-protein interfaces
\end_layout

\begin_layout Standard
At the outset, it is worth noting that the issues addressed below concern
 both intermolecular metal ion binding and metal-induced 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glspl{ppi}
\end_layout

\end_inset

 formation.
 The verdict, which process is dealt of 
\begin_inset Note Note
status open

\begin_layout Plain Layout
nwm czy zdanie dobre
\end_layout

\end_inset

may require a more thorough investigation, for example, the involvement
 of structural and biophysical methods (see bellow).
 To my knowledge no 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glspl{hts}
\end_layout

\end_inset

, to detect complexes with an intermolecularly bound metal ion, have been
 performed so far, thus leaving the landscape of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glspl{mppi}
\end_layout

\end_inset

 hidden in the fog 
\begin_inset Note Note
status open

\begin_layout Plain Layout
(https://febs.onlinelibrary.wiley.com/doi/full/10.1111/j.1742-4658.2011.08061.x#b28)
 to dzieswłożyć
\end_layout

\end_inset

—for this reason, considerations in this Subsection are purely theoretical.
\end_layout

\begin_layout Standard
State of art proteomic technologies already may give some information about
 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glspl{mppi}
\end_layout

\end_inset

, however, the detection of such interactions by those methods requires
 to take into experimental framework some important ideas regarding the
 complexes stabilities (see 
\begin_inset Flex CT - auto cross-reference
status open

\begin_layout Plain Layout
\begin_inset CommandInset ref
LatexCommand labelonly
reference "subsec:Equilibria"
plural "false"
caps "false"
noprefix "false"

\end_inset


\end_layout

\end_inset

).
 One of the most important issues to take care for is the availability of
 the free metal (e.g., 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{freezn}
\end_layout

\end_inset

) in the experiment.
 The care should be taken to supply used buffers with an appropriate metal,
 preferably in an controlled manner (
\begin_inset Flex CT - auto cross-reference
status open

\begin_layout Plain Layout
\begin_inset CommandInset ref
LatexCommand labelonly
reference "subsec:Equilibria"
plural "false"
caps "false"
noprefix "false"

\end_inset


\end_layout

\end_inset

).
 Unfortunately the most of the modern proteomic technologies are not suitable
 for the investigation of transient (or weak) interactions, mostly due to
 the washing steps aimed at removal of nonspecific interactions.
 Furthermore, the subsequent detection of interaction partners with 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{MS}
\end_layout

\end_inset

 techniques efficiently removes metals due to the low pH during sample preparati
on, thus additionally to the control experiments, experiments that stabilize
 the complexes (e.g, by crosslinking) should be prepared.
\end_layout

\begin_layout Subsubsection
Mass spectrometry
\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Glsfirst{MS}
\end_layout

\end_inset

 is the gold standard method that is utilized in proteomics.
 Using 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{MS}
\end_layout

\end_inset

 it is possible to tell what is the mass of the measured protein, or the
 fragments of the protein – peptides.
 Seemingly this information is of low value to the researcher, however,
 the the number of articles published each year proves different – with
 known protein mass it is possible to identify modifications of the protein.
 Tandem 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{MS}
\end_layout

\end_inset

 and/or enzymatic fragmentation can give information about identity of the
 protein (provided the genome of the investigated organism is known).
 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Glsdesc{MS}
\end_layout

\end_inset

 combined with crosslinking and computational modeling can provide information
 about protein topology or even the structure 
\begin_inset CommandInset citation
LatexCommand citep
key "Petrotchenko2022"
literal "true"

\end_inset

.
 So it is not without reason why 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{MS}
\end_layout

\end_inset

 techniques are used so often in proteomics, including the investigation
 of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glspl{ppi}
\end_layout

\end_inset

.
 Unfortunately the investigation of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glspl{mppi}
\end_layout

\end_inset

 with 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{MS}
\end_layout

\end_inset

 is not straightforward, as the sample prepared for the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{MS}
\end_layout

\end_inset

 usually have different pH than the physiological, and combined with protein
 fragmentation (enzymatic or in tandem 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{MS}
\end_layout

\end_inset

), and harsh ionization causes loosing of the bound metal ion.
 Combining regular 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{MS}
\end_layout

\end_inset

 with native 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{MS}
\end_layout

\end_inset

 can partly facilitate the detection of metal, however, native 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{MS}
\end_layout

\end_inset

 comes with its own limitations.
\end_layout

\begin_layout Subsubsection
Affinity chromatography
\end_layout

\begin_layout Standard
The identification of novel 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glspl{mppi}
\end_layout

\end_inset

 can be realized by means of affinity purification methods – based on the
 selective interaction between a 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Lg}
\end_layout

\end_inset

 and a target proteins of peptides followed by identification using a coupled
 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{MS}
\end_layout

\end_inset

.
\begin_inset Foot
status open

\begin_layout Plain Layout
Note that sample preparation and ionization in 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{MS}
\end_layout

\end_inset

 usually leads to loss of the metal.
\end_layout

\end_inset

 From various affinity purification techniques two techniques stand out:
 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{OSETA}
\end_layout

\end_inset

 and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{TAP}
\end_layout

\end_inset

.
 Both techniques rely on recombinant fusion proteins with affinity labels.
 The affinity labels used in those methods are used to pull-down
\begin_inset Note Note
status open

\begin_layout Plain Layout
nie wiem czy nie jest to żargon
\end_layout

\end_inset

 the recombinant protein in complex with the interaction partner.
 The binding and washing steps determine the composition of eluted sample
 so during the experiment care should be taken to perform those steps in
 the buffers containing metal ions of interest, preferably in a controlled
 manner.
 The control experiments should be made that are conducted in metal of interest
 free environment.
 
\end_layout

\begin_layout Standard
Additionally improvements, mostly due to the use of crosslinking (which
 can be made 
\emph on
in vivo
\emph default
) in those techniques have been made to detect transient binding.
 The crosslinking allows for use of more rigorous washing steps, however,
 at cost of loosing bound metal ions.
\end_layout

\begin_layout Standard
Unfortunately this approach seems unsuitable for homomeric interactions.
 
\begin_inset Note Note
status open

\begin_layout Plain Layout
moze coś tu jeszcze?
\end_layout

\end_inset

 
\end_layout

\begin_layout Subsubsection
Label transfer
\end_layout

\begin_layout Standard
In label transfer, the protein of interest is tagged with a reagent that
 after the crosslinking reaction is able to transfer the label to an interacting
 partner.
 The first step of the label transfer is the crosslinking of the complex
 composed of tagged protein of interest with an interaction partner, this
 is done usually using the photoreactive mechanism.
 The label transfer can be performed by another type of chemistry,
\begin_inset Note Note
status open

\begin_layout Plain Layout
nwm jak to napisać
\end_layout

\end_inset

 e.g., by reducing the disulfide bond in the label.
 The transferred label can be used in affinity purification and detection.
 The obtained sample can be analyzed by downstream methods like Western
 Blot or 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{MS}
\end_layout

\end_inset

 
\begin_inset CommandInset citation
LatexCommand citep
key "Liu2007"
literal "true"

\end_inset

.
 Potentially this system could be used to detect 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glspl{mppi}
\end_layout

\end_inset

 by performing crosslinking in the presence of metal of interest and comparison
 with a control crosslinking in metal-free buffers.
 The proteins that are found in the experiment with metal, but are missing
 from the control, the metal-free experiment could interact with the protein
 of interest due to the presence of particular metal.
\end_layout

\begin_layout Subsubsection
Crosslinking
\end_layout

\begin_layout Standard
Crosslinking can assist or be a part of the above-mentioned methods.
 The development of reactive groups that allow 
\emph on
in vivo
\emph default
 crosslinking certainly can facilitate the discovery of new 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glspl{mppi}
\end_layout

\end_inset

, even those that are transient.
 The cell environment contains the physiological concentrations of free
 metals, thus providing the ideal environment for the metal-protein interaction.
 The crosslinking 
\emph on
in vivo
\emph default
 can be performed using cell-permeable chemicals or using genetically encoded
 noncanonical amino acids containing the reactive crosslinking groups.
 The crosslinked proteins can be detected using 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{MS}
\end_layout

\end_inset

.
 
\end_layout

\begin_layout Subsection
Equilibria of metal-protein complexes
\begin_inset CommandInset label
LatexCommand label
name "subsec:Equilibria"

\end_inset


\begin_inset Note Note
status open

\begin_layout Plain Layout
coś jeszcze o pH
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Biophysical tools that are suitable for the investigation of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glspl{mppi}
\end_layout

\end_inset

 generally answer the question 
\begin_inset Quotes eld
\end_inset

How strong is the interaction?
\begin_inset Quotes erd
\end_inset

.
 The answer to the question can be expressed as a value, namely 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset

 ( or 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Kd}
\end_layout

\end_inset

).
 This thermodynamic property of a metal–protein system is a key element,
 that allows one to understand the interaction in a biological systems.
 So how to obtain those values and how are they defined? To simplify the
 discussion presented below I will focus only on the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glsfirst{Ka}
\end_layout

\end_inset

, which is sufficient to obtain the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Kd}
\end_layout

\end_inset

 value as it is defined as 
\begin_inset Formula $K_{\text{d}}=\frac{1}{K_{\text{a}}}$
\end_inset

.
 As the reader reads through the following somewhat lengthy introduction,
 it should become clear to the reader that, along with choosing the right
 experiment, the right models must be chosen to describe metal binding—each
 case may require a slightly different approach.
\end_layout

\begin_layout Standard
For reaction:
\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{equation}
\end_layout

\begin_layout Plain Layout


\backslash
label{eq:equilibrium}
\end_layout

\begin_layout Plain Layout


\backslash
ce{A_x + B_y <=>[${k_
\backslash
text{on}}$][${k_
\backslash
text{off}}$] A_xB_y}
\end_layout

\begin_layout Plain Layout


\backslash
end{equation}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
in which theoretical particles A and B form the complex 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
ce{A_xB_y}
\end_layout

\end_inset

 the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset

 is defined as:
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
K_{\text{a}}=\frac{[A_{x}B_{y}]}{[A]^{x}\cdot[B]^{y}}=\frac{k_{\text{on}}}{k_{\text{off}}}\label{eq:Ka_definition}
\end{equation}

\end_inset

,where 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glslink{kon}{
\backslash
textit{k}
\backslash
textsubscript{on}}
\end_layout

\end_inset

 is the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glsdesc{kon}
\end_layout

\end_inset

 and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glslink{koff}{
\backslash
textit{k}
\backslash
textsubscript{off}}
\end_layout

\end_inset

 is the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glsdesc{koff}
\end_layout

\end_inset

.
 All the equilibria reactions that concern the interaction of metal ions
 with proteins are happening in water, thus one should define a new constant—
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Kex}
\end_layout

\end_inset

:
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
K_{\text{ex}}=\frac{[\text{MeL}]\cdot[\text{H}_{2}\text{O}]^{x}}{[\text{M\text{e}_{\text{aq}}}]\cdot[\text{L}]}=K_{\text{a}}[\text{H}_{2}\text{O}]^{x}
\end{equation}

\end_inset

,where 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gshort{Me}
\end_layout

\end_inset

 is a metal ion and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gshort{L}
\end_layout

\end_inset

 is a 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Lg}
\end_layout

\end_inset

.
 Note that in reaction:
\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{equation}
\end_layout

\begin_layout Plain Layout


\backslash
label{eq:equilibrium}
\end_layout

\begin_layout Plain Layout


\backslash
ce{Me_{aq} + L <=> ML + x H2O}
\end_layout

\begin_layout Plain Layout


\backslash
end{equation}
\end_layout

\end_inset

the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
ce{[H2O]}
\end_layout

\end_inset

 does not change due to the fact that in most systems 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
ce{Me}$<<$
\backslash
ce{[H2O]}
\end_layout

\end_inset

, the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Kex}
\end_layout

\end_inset

 does not change making the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset

 constant.
 Due to this fact in biochemistry, 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset

 is usually defined as in 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Ka_definition"
plural "false"
caps "false"
noprefix "false"

\end_inset

.
 Following this logic, 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset

 for the process
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{equation}
\end_layout

\begin_layout Plain Layout


\backslash
label{eq:ML}
\end_layout

\begin_layout Plain Layout


\backslash
ce{Me + L <=> MeL}
\end_layout

\begin_layout Plain Layout


\backslash
end{equation}
\end_layout

\end_inset

is defined as:
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
K_{\text{a}}=\frac{[\text{MeL}]}{[\text{Me}]\cdot[\text{L}]}\label{eq:KaML}
\end{equation}

\end_inset

So the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset

 for the homodimeric 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
ce{MeL2}
\end_layout

\end_inset

 complex, which formation is defined by:
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{equation}
\end_layout

\begin_layout Plain Layout


\backslash
label{eq:ML2}
\end_layout

\begin_layout Plain Layout


\backslash
ce{Me + 2L <=> MeL2}
\end_layout

\begin_layout Plain Layout


\backslash
end{equation}
\end_layout

\end_inset

is defined as:
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
K_{\text{a}}=\frac{[\text{MeL}_{2}]}{[\text{Me}]\cdot[\text{L}]^{2}}\label{eq:Ka_ML2}
\end{equation}

\end_inset

In case of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
ce{MeL^1L^2}
\end_layout

\end_inset

, (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gshort{L}
\end_layout

\end_inset


\begin_inset script superscript

\begin_layout Plain Layout
1
\end_layout

\end_inset

 and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gshort{L}
\end_layout

\end_inset


\begin_inset script superscript

\begin_layout Plain Layout
2
\end_layout

\end_inset

 are two different types of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glspl{Lg}
\end_layout

\end_inset

) which forming is described by equation 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
ref{eq:ML1L2}
\end_layout

\end_inset

 the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset

 assume the same unit as 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset

 defined in equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Ka_ML2"
plural "false"
caps "false"
noprefix "false"

\end_inset

, however, have different form (equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Ka_ML1L2"
plural "false"
caps "false"
noprefix "false"

\end_inset

).
\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{equation}
\end_layout

\begin_layout Plain Layout


\backslash
label{eq:ML1L2}
\end_layout

\begin_layout Plain Layout


\backslash
ce{Me + L^1 + L^2 <=> MeL^1L^2}
\end_layout

\begin_layout Plain Layout


\backslash
end{equation}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
K_{\text{a}}=\frac{[\text{Me}\text{L}^{1}\text{L}^{2}]}{[\text{Me}]\cdot[\text{L}^{1}]\cdot[\text{L}^{2}]}\label{eq:Ka_ML1L2}
\end{equation}

\end_inset

Note that with more interacting partners the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset

 definition, thus as well as the unit, will change.
 This should be taken into consideration when comparing complexes of various
 stoichiometries.
 Depending on the system the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset

 can be determined with direct titration of the metal to the protein or
 competition experiments.
 
\end_layout

\begin_layout Subsubsection
Direct titration experiments
\end_layout

\begin_layout Standard
In direct titrations, the only competing 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Lg}
\end_layout

\end_inset

 for the metal is only water.
 Thus in the case of the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
ce{MeL}
\end_layout

\end_inset

 complex, equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:KaML"
plural "false"
caps "false"
noprefix "false"

\end_inset

 defines the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset

.
 In such conditions the total concentration of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Me}
\end_layout

\end_inset

 is equal to the sum of protein-bound 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Me}
\end_layout

\end_inset

 and free 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Me}
\end_layout

\end_inset

, thus:
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
\frac{[\text{MeL}]}{[\text{Me]_{\text{t}}}}=\frac{1}{1+\frac{1}{K_{\text{a}}\cdot[\text{L}]}}\label{eq:MeL/Me_t ratio}
\end{equation}

\end_inset

, where 
\begin_inset Formula $[\text{Me]_{\text{t}}}$
\end_inset

 is total 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Me}
\end_layout

\end_inset

 concentration.
 So in situations where 
\begin_inset Formula $\frac{1}{K_{\text{a}}}>>[L]$
\end_inset

 the ratio of 
\begin_inset Formula $\frac{[\text{MeL}]}{[\text{Me]_{\text{t}}}}\rightarrow0$
\end_inset

, which means that the affinity is too low to be observable (or nonexistent)
 during the titration, the similar situation is observed when 
\begin_inset Formula $\frac{1}{K_{\text{a}}}<<[L]$
\end_inset

, in such case 
\begin_inset Formula $\frac{[\text{MeL}]}{[\text{Me]_{\text{t}}}}\rightarrow1$
\end_inset

, which means that the affinity is to high to be observable.
 This behavior of the system can be modified by precise choice of the concentrat
ions of the reagents.
 However the manipulation with reagent's concentrations is possible in some
 range: solubility of the reagents in case of weak-binding, and the detection
 limit in case of tight-binding.
\end_layout

\begin_layout Subsubsection
Competition titration experiments
\begin_inset CommandInset label
LatexCommand label
name "subsec:Competition-titration-experiment"

\end_inset


\end_layout

\begin_layout Standard
In situations of tight binding (i.e.,
\begin_inset Formula $\frac{1}{K_{\text{a}}}<<[L]\Rightarrow\frac{[\text{MeL}]}{[\text{Me]_{\text{t}}}}\rightarrow1$
\end_inset

, according to equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:MeL/Me_t ratio"
plural "false"
caps "false"
noprefix "false"

\end_inset

) the metals in direct titration are bound to the protein in a manner that
 prevents the direct detection of free metal (in case of metals that can
 be observed directly, e.g.
 Fe(II) by 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{uvvis}
\end_layout

\end_inset

 spectroscopy.
 To determine the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset

 of such metal-protein complexes the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Lg}
\end_layout

\end_inset

 has to compete for the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Me}
\end_layout

\end_inset

 (equation 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
ref{eq:competition}
\end_layout

\end_inset

) with another compound (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{C}
\end_layout

\end_inset

) of which 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset


\begin_inset script superscript

\begin_layout Plain Layout
MeC
\end_layout

\end_inset

 is known.
\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{equation}
\end_layout

\begin_layout Plain Layout


\backslash
label{eq:competition}
\end_layout

\begin_layout Plain Layout


\backslash
ce{MeL + C <=> MeC + L}
\end_layout

\begin_layout Plain Layout


\backslash
end{equation}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
With known 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset


\begin_inset script superscript

\begin_layout Plain Layout
MeL
\end_layout

\end_inset

 and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset


\begin_inset script superscript

\begin_layout Plain Layout
MeC
\end_layout

\end_inset

 it is possible to define 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Kex}
\end_layout

\end_inset

 (equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Kex_competition"
plural "false"
caps "false"
noprefix "false"

\end_inset

).
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
K_{\text{ex}}=\frac{[\text{MeL}]\cdot[\text{C}]}{[\text{MeC}]\cdot[\text{L}]}=\frac{K_{\text{a}}^{\text{MeL}}}{K_{\text{a}}^{\text{MeC}}}\label{eq:Kex_competition}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
With defined 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Kex}
\end_layout

\end_inset

 and known 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset


\begin_inset script superscript

\begin_layout Plain Layout
MeC
\end_layout

\end_inset

 it is possible to determine the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset


\begin_inset script superscript

\begin_layout Plain Layout
MeL
\end_layout

\end_inset

 provided that at least one of the components can be measured at equilibrium
 or can give a measurable signal (e.g., heat change, fluorescence, etc.).
 The shortly described titration experiment can be designed to determine
 affinities of complexes with higher stoichiometries (i.e.
 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Me}
\end_layout

\end_inset


\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{L}
\end_layout

\end_inset


\begin_inset script subscript

\begin_layout Plain Layout
2
\end_layout

\end_inset

, 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Me}
\end_layout

\end_inset


\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{L}
\end_layout

\end_inset


\begin_inset script subscript

\begin_layout Plain Layout
3
\end_layout

\end_inset

, etc.), as well as using the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glsdescplural{C}
\end_layout

\end_inset

 with higher stoichiometries, so long as the affinities of the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glsdescplural{C}
\end_layout

\end_inset

 are known, and in range of the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset


\begin_inset script superscript

\begin_layout Plain Layout
MeL
\end_layout

\end_inset

.
 Of course in practice it is better to use 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glsdescplural{C}
\end_layout

\end_inset

 with 1:1 stoichiometry when possible.
 The use of competition titration sometimes is called a metal-ion buffer,
 due to the fact that a 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glsdesc{C}
\end_layout

\end_inset

 provides a controlled source of free metal ions analogously to the pH buffers.
\end_layout

\begin_layout Subsection
Structural methods for the characterization of metal-involved protein-protein
 interfaces
\end_layout

\begin_layout Standard
The detailed description of structural methods that are used for the characteriz
ation of the proteins, metal-proteins complexes, and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glspl{mppi}
\end_layout

\end_inset

 is far beyond the scope of this thesis – more comprehensive and elaborate
 resources are available.
 Structures of proteins and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glspl{mprotein}
\end_layout

\end_inset

 can be acquired by X-ray crystallography, 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{cryoem}
\end_layout

\end_inset

, 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{nmr}
\end_layout

\end_inset

 spectroscopy, and other, less frequently used techniques.
 Due to the fact that during my PhD project, I have utilized some more `exotic`
 structural methods they are worth mentioning.
 At the outset, it is worth noting that the methods used by me during the
 PhD project do not give the precise coordinates of each atom in the protein,
 contrary to the above-mentioned structural methods.
 
\end_layout

\begin_layout Subsubsection
Small-angle X-ray scattering
\end_layout

\begin_layout Standard
Similarly, like 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{nmr}
\end_layout

\end_inset

 spectroscopy or X-ray crystallography 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{saxs}
\end_layout

\end_inset

 results may be written into a 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{pdb}
\end_layout

\end_inset

 file.
 This technique provides information about the overall shape and size distributi
on of a protein.
 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Gls{saxs}
\end_layout

\end_inset

 is particularly useful for studying large proteins.
 The biggest advantage over the X-ray crystallography and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{nmr}
\end_layout

\end_inset

 spectroscopy is the fact that 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{saxs}
\end_layout

\end_inset

 can be applied to flexible proteins.
 The combination of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{saxs}
\end_layout

\end_inset

 with other biophysical techniques allows for the understanding of the shape
 and dynamics of the protein.
 Although 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{saxs}
\end_layout

\end_inset

 itself is blind to metal ions it can be a helpful tool for the description
 of protein dynamics 
\begin_inset CommandInset citation
LatexCommand citep
key "Padjasek2022"
literal "true"

\end_inset

 (or its lack—
\begin_inset Flex CT - auto cross-reference
status open

\begin_layout Plain Layout
\begin_inset CommandInset ref
LatexCommand labelonly
reference "chap:hRad50"
plural "false"
caps "false"
noprefix "false"

\end_inset


\end_layout

\end_inset

, 
\begin_inset CommandInset citation
LatexCommand citep
key "Tran2022"
literal "true"

\end_inset

) induced by metal ion complexation.
\end_layout

\begin_layout Subsubsection
Extended X-ray absorption fine structure and X-ray absorption near-edge
 structure
\end_layout

\begin_layout Standard
X-ray absorption spectroscopy is a technique used to study the electronic
 structure of elements and their local coordination environment in various
 materials, also in 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glspl{mprotein}
\end_layout

\end_inset

.
 X-ray absorption spectroscopy encompasses two techniques 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{exafs}
\end_layout

\end_inset

 and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{xanes}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Gls{exafs}
\end_layout

\end_inset

 involves the measurement of the intensity of X-rays scattered at large
 angles from a target atom.
 The scattered X-rays are collected and analyzed to determine the average
 distance and coordination number of the neighboring atoms surrounding the
 target atom.
 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{exafs}
\end_layout

\end_inset

 provides information about the local coordination environment of the target
 atom and can be used to study the bonding environment of target atoms in
 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glspl{mprotein}
\end_layout

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Gls{xanes}
\end_layout

\end_inset

, on the other hand, involves the measurement of the absorption of X-rays
 near the absorption edge of the target atom.
 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Gls{xanes}
\end_layout

\end_inset

 provides information about the oxidation state and coordination geometry
 of the target atom by analyzing the fine structure in the X-ray absorption
 spectra near the absorption edge.
 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Gls{xanes}
\end_layout

\end_inset

 can be used to determine the oxidation state of metal ions in 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glspl{mprotein}
\end_layout

\end_inset

, which can provide valuable information about their function and reactivity.
\end_layout

\begin_layout Standard
Both 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Gls{exafs}
\end_layout

\end_inset

 and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Gls{xanes}
\end_layout

\end_inset

 have been widely used in the study of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glspl{mprotein}
\end_layout

\end_inset

 and have provided important insights into the mechanisms of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{mprotein}
\end_layout

\end_inset

 function.
 By combining these techniques with other experimental and computational
 methods, scientists have been able to gain a deeper understanding of the
 roles of metal ions in enzyme catalysis, electron transfer reactions, and
 oxidative stress.
\end_layout

\begin_layout Subsection
Biophysical tools for the characterization of metal-involved protein-protein
 interfaces
\begin_inset CommandInset label
LatexCommand label
name "subsec:Biophysical-tools-for"

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Flex CT - auto cross-reference
status open

\begin_layout Plain Layout
\begin_inset CommandInset ref
LatexCommand labelonly
reference "subsec:Equilibria"
plural "false"
caps "false"
noprefix "false"

\end_inset


\end_layout

\end_inset

 is a short introduction to the equilibria-related calculations, that are
 necessary to obtain accurate values, that can be later compared to other
 known affinities, which should give those values a biological context.
 However, to be able to calculate anything one requires data, this Subsection
 is devoted to the description of some methods that can produce the data
 for those calculations.
\end_layout

\begin_layout Subsubsection
Size Exclusion Chromatography
\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Gls{SEC}
\end_layout

\end_inset

 is one of the first liquid chromatography techniques developed to investigate
 protein–protein interactions 
\begin_inset CommandInset citation
LatexCommand citep
key "Boone2016"
literal "true"

\end_inset

.
 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Gls{SEC}
\end_layout

\end_inset

 separates the molecules based on their size (thus on the molecular weight).
 With a properly calibrated 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{SEC}
\end_layout

\end_inset

 column, it is possible to approximate the weight of the investigated protein
 or protein complex.
 Provided the change in the complexes' molecular weight is considerable
 it is possible to measure the binding.
 In the case of homodimerization, the molecular weight of the complex is
 twice as big as the monomeric protein thus making 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{SEC}
\end_layout

\end_inset

 an ideal solution for the detection.
 However, in a theoretical case of heterodimerization of a macromolecule
 with a small peptide, assuming that the binding does not induce a huge
 conformational change in the macromolecule 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{SEC}
\end_layout

\end_inset

 seems inapplicable.
 
\end_layout

\begin_layout Standard
It is possible to run directly titrated with metal samples on 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{SEC}
\end_layout

\end_inset

, however, in case of weak binding the lack of appropriate metal ions in
 the running buffers may cause the dissociation of the metal-protein complexes.
 To circumvent this inconvenience, the separation on 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{SEC}
\end_layout

\end_inset

 can be run in metal-ion buffers (
\begin_inset Flex CT - auto cross-reference
status open

\begin_layout Plain Layout
\begin_inset CommandInset ref
LatexCommand labelonly
reference "subsec:Competition-titration-experiment"
plural "false"
caps "false"
noprefix "false"

\end_inset


\end_layout

\end_inset

) that control the concentration of available metal.
 The 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset

 from the competition experiment performed with 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{SEC}
\end_layout

\end_inset

 can be calculated using the area under the peaks corresponding to the various
 protein fractions 
\begin_inset CommandInset citation
LatexCommand citep
key "Kocya2018a"
literal "true"

\end_inset

, however, it should be noted that the observed peaks are not literally
 in an equilibrium.
\end_layout

\begin_layout Standard
The detection of separated protein fractions can be performed with almost
 any flow-method, e.g.
 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{uvvis}
\end_layout

\end_inset

 spectrophotometry, 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{saxs}
\end_layout

\end_inset

, 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{mals}
\end_layout

\end_inset

.
\end_layout

\begin_layout Subsubsection
MALS
\end_layout

\begin_layout Standard
Usually 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{mals}
\end_layout

\end_inset

 is performed in conjugation with 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{SEC}
\end_layout

\end_inset

 (
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{SEC}
\end_layout

\end_inset

-
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{mals}
\end_layout

\end_inset

).
 This is due to the fact that, not every macromolecule is perfectly globular,
 and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{SEC}
\end_layout

\end_inset

 separates particles based on 
\emph on
shape
\emph default
 and hydrodynamic radius – the latter is often correlated with the molecular
 weight of the particle, however, the shape is not necessarily correlated.
 Thus the application of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{mals}
\end_layout

\end_inset

 in-line with 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{SEC}
\end_layout

\end_inset

 allows for determination of mass and size in solution, overcoming many
 inconveniences with 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{SEC}
\end_layout

\end_inset

 column calibration 
\begin_inset CommandInset citation
LatexCommand citep
key "Minton2016"
literal "true"

\end_inset

.
\end_layout

\begin_layout Subsubsection
Circular dichorism
\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Gls{cd}
\end_layout

\end_inset

 can be used in the determination of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset

 in both, direct and competition titrations.
 With 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
glsdesc{cd}
\end_layout

\end_inset

, it is possible to evaluate the secondary structure of the protein (or
 peptide) 
\begin_inset CommandInset citation
LatexCommand citep
key "Greenfield2007"
literal "true"

\end_inset

, folding and binding, provided that a change in the secondary structure
 of the protein is observed.
 The direct titration of protein with a metal ion provided tight affinities
 that can show the ratio of binding.
 For example, 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{rad}
\end_layout

\end_inset

 interaction with Zn(II) can be monitored using 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{cd}
\end_layout

\end_inset

 (
\begin_inset Flex CT - auto cross-reference
status collapsed

\begin_layout Plain Layout
\begin_inset CommandInset ref
LatexCommand labelonly
reference "chap:Galvanization-of-Protein-Protein"
plural "false"
caps "false"
noprefix "false"

\end_inset


\end_layout

\end_inset

), due to the tight binding it is possible to plot the ellipticity at the
 chosen wavelength in the Zn(II)/protein function, and observe the specific
 turning point at Zn(II)/protein=0.5, which together with the rest of the
 evidence suggests the formation of Zn(
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{rad}
\end_layout

\end_inset

)
\begin_inset script subscript

\begin_layout Plain Layout
2
\end_layout

\end_inset

complex.
 
\end_layout

\begin_layout Subsubsection
Ultraviolet-Visible spectrophotometry
\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Gls{uvvis}
\end_layout

\end_inset

 spectrophotometry is a useful tool that can be utilized as a detection
 for 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{SEC}
\end_layout

\end_inset

 separation.
 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Gls{uvvis}
\end_layout

\end_inset

 spectrophotometry is an essential method in thhe determination of a metal–prote
in stabilities.
 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Gls{uvvis}
\end_layout

\end_inset

 seems an ideal method for 'spectroscopically loud' metals.
\begin_inset Foot
status open

\begin_layout Plain Layout
Spectroscopically quiet metals have completely filled or empty 
\emph on
d
\emph default
-shell.
 So colloquially metal ions with partially filled 
\emph on
d
\emph default
-shell should be called `loud` 
\begin_inset CommandInset citation
LatexCommand citep
key "Penner-Hahn2005"
literal "true"

\end_inset

.
\end_layout

\end_inset

 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Gls{uvvis}
\end_layout

\end_inset

 observation of some 'spectroscopically quiet' metal complexes is possible
 due to the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{ct}
\end_layout

\end_inset

 phenomenon.
 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{ct}
\end_layout

\end_inset

 is a type of electron transition in which the electron from the donor is
 transitioned to the acceptor's orbital.
 In the case of thiolates and Zn(II) the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{lmct}
\end_layout

\end_inset

 transition can be observed, which shows that even in the case of `spectroscopic
ally quiet` metals 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{uvvis}
\end_layout

\end_inset

 can be applicable
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Sometimes it is not possible to observe 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{lmct}
\end_layout

\end_inset

 from the native metal coordinated by the protein of interest due to overlapping
 of the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{lmct}
\end_layout

\end_inset

 bands with the absorption bands of the protein backbone.
 In such cases one can use isostructural probes showing absorption bands
 in a different region, i.e., in case of Zn(II), Co(II) 
\begin_inset CommandInset citation
LatexCommand citep
key "Kluska2018"
literal "true"

\end_inset

 and Cd(II) 
\begin_inset CommandInset citation
LatexCommand citep
key "Freisinger2013"
literal "true"

\end_inset

 can be used as isostructural spectroscopic probes.
\end_layout

\end_inset

 
\begin_inset CommandInset citation
LatexCommand citep
key "Vasak1981"
literal "true"

\end_inset

.
 
\end_layout

\begin_layout Standard
Similarly to 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{cd}
\end_layout

\end_inset

 in case of tight-affinities, it is possible to determine the binding stoichiome
try from 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{uvvis}
\end_layout

\end_inset

 titration.
 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
Gls{uvvis}
\end_layout

\end_inset

 can be used as well in competition titration studies, however, the ease
 of use of this technique will be dependent on the availability of the proper
 chelating probe 
\begin_inset CommandInset citation
LatexCommand citep
key "Kocya2015"
literal "true"

\end_inset

.
 
\end_layout

\begin_layout Subsubsection
Isothermal titration calorimetry
\end_layout

\begin_layout Standard
Virtually every chemical reaction involves heat change.
 This allows the reaction to be monitored with accurate titration calorimeters.
 Also, metal-binding can be monitored using, 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{itc}
\end_layout

\end_inset

.
 As with the aforementioned methods, competitive titration can be used,
 provided that the competitor used is well characterized thermodynamically.
 At the same time, the fact that virtually every reaction involves a change
 in heat analysis of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{itc}
\end_layout

\end_inset

 data can be somewhat problematic, that is: proton dissociation from the
 protein during binding, protonation of the buffer, association of the metal
 ion with coordinating residues, and so on.
 All these factors should be taken into account during data analysis.
 It is more than important to convert the obtained 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset


\begin_inset script superscript

\begin_layout Plain Layout
ITC
\end_layout

\end_inset

 constant into the association constants for the corresponding complex.
 
\end_layout

\begin_layout Standard
Recent data analysis advances in the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{itc}
\end_layout

\end_inset

 allow to determine the kinetic information from the experiments – this
 can be done by the analysis of each injection peak, which adds an additional
 cross-validation layer to the experiment, due to the fact that the kinetic
 constants are bound with the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset

 with the equations 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
ref{eq:equilibrium}
\end_layout

\end_inset

 and 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Ka_definition"
plural "false"
caps "false"
noprefix "false"

\end_inset

 
\begin_inset CommandInset citation
LatexCommand citep
key "Burnouf2012"
literal "true"

\end_inset

.
 
\end_layout

\begin_layout Subsubsection
Potentiometry
\end_layout

\begin_layout Standard
The use of the glass electrode in potentiometry allows for the quantitative
 determination of equation 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
ref{eq:protonation}
\end_layout

\end_inset

.
 Of course, the general equation 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
ref{eq:protonation}
\end_layout

\end_inset

 will take another form in case of different complexes with different stoichiome
try, i.e., 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Me}
\end_layout

\end_inset


\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{L}
\end_layout

\end_inset


\begin_inset script subscript

\begin_layout Plain Layout
2
\end_layout

\end_inset

, etc.
 
\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{equation}
\end_layout

\begin_layout Plain Layout


\backslash
label{eq:protonation}
\end_layout

\begin_layout Plain Layout


\backslash
ce{Me + H_x L^x+ <=> MeL + x H+}
\end_layout

\begin_layout Plain Layout


\backslash
end{equation}
\end_layout

\end_inset

Potentiometry still is the gold standard for the determination of complexes
 stabilities, however, it should be noted that all proton-related equilibria
 should be taken into account while calculating the 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset

 – this is often impossible for proteins due to large number of sidechains
 that can exchange protons.
 Moreover, proteins are sensitive to pH, in extremely acidic or basic conditions
 proteins may change structure, unfold and precipitate, thus making the
 potentiometry only suitable for shorter peptide models.
\end_layout

\begin_layout Subsubsection
Fluorescence-based techniques
\end_layout

\begin_layout Standard
Fluorescence-based techniques for determination of metal-protein complexes
 affinities can be divided into two categories:
\end_layout

\begin_layout Standard
\begin_inset Flex CT - Description Label
status open

\begin_layout Plain Layout
\begin_inset Flex CT - Spaced Low Small Caps
status open

\begin_layout Plain Layout
label-free techniques
\end_layout

\end_inset


\end_layout

\end_inset

 may rely on measurement of intrinsic protein's fluorescence, in which case
 the direct titration with metal may be applied.
 However, if the intrinsic fluorescence is lacking the label-based techniques
 may be applied, or a competition titration with a appropriate fluorescent
 probe (e.g, FluoZin-3 for Zn(II) , mag-fura-2 for Mg(II), etc.) 
\begin_inset CommandInset citation
LatexCommand citep
key "johnson2010molecular"
literal "true"

\end_inset

, 
\end_layout

\begin_layout Standard
\begin_inset Flex CT - Description Label
status open

\begin_layout Plain Layout
\begin_inset Flex CT - Spaced Low Small Caps
status open

\begin_layout Plain Layout
label-based techniques
\end_layout

\end_inset


\end_layout

\end_inset

 may use recombinant proteins of interest with fluorescent proteins to measure
 properties like fluorescence, 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{FRET}
\end_layout

\end_inset

, fluorescence anisotropy and fluorescence anisotropy decay.
 Except from the heterologous expression of recombinated proteins, proteins
 of interests may be labeled by chemical means 
\begin_inset CommandInset citation
LatexCommand citep
key "Qiao2006"
literal "true"

\end_inset

.
\end_layout

\begin_layout Standard
The biggest advantage of the use of fluorescence based techniques is the
 low protein concentration required, this if often a huge advantage for
 reasons of economy, time and workload, though care should be when envisioning
 the stabilities constants of the unlabeled proteins from the labeled counterpar
ts – the introduction of label may change the protein's conformation with
 in turn may change the affinity towards the metal.
\end_layout

\begin_layout Subsubsection
Bio-layer interferometry and surface plasmon resonance
\end_layout

\begin_layout Standard
Both 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{SPR}
\end_layout

\end_inset

 and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{BLI}
\end_layout

\end_inset

 measurement techniques provide label-free detection, due to the real-time
 monitoring and the fact that the measurement consists of both association
 and dissociation step it is possible to measure the kinetics of the interaction.
 The measurement of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{mppi}
\end_layout

\end_inset

 with the use of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{SPR}
\end_layout

\end_inset

 and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{BLI}
\end_layout

\end_inset

 implies the use of the metal ion buffers (
\begin_inset Flex CT - auto cross-reference
status open

\begin_layout Plain Layout
\begin_inset CommandInset ref
LatexCommand labelonly
reference "subsec:Competition-titration-experiment"
plural "false"
caps "false"
noprefix "false"

\end_inset


\end_layout

\end_inset

) and the loading of the protein on the surface.
 While this method may be useful for investigation of heteromeric complexes
 (i.e., 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
ce{MeL^1_xL^2_y}
\end_layout

\end_inset

 ), it seems to be non-ideal in the case of the homomeric complexes (i.e.
 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
ce{MeL_x}
\end_layout

\end_inset

), or in the case where individual components from the heterocomplex dimerize
 as a result of metal-binding (e.g.
 zinc mediated 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{lck}
\end_layout

\end_inset

 and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{cd4}
\end_layout

\end_inset

) 
\begin_inset CommandInset citation
LatexCommand citep
key "Kocya2018a"
literal "true"

\end_inset

.
 A certain limitation of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{BLI}
\end_layout

\end_inset

 and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{SPR}
\end_layout

\end_inset

 is also the fact, the lack of advanced models that can take into account
 more advanced binding stoichiometries.
 
\end_layout

\begin_layout Standard
The determination of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset

 in 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{SPR}
\end_layout

\end_inset

 and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{BLI}
\end_layout

\end_inset

 is possible by the determination of 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{kon}
\end_layout

\end_inset

 and 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{koff}
\end_layout

\end_inset

, which later can be used to calculate 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
gls{Ka}
\end_layout

\end_inset

 (see equations 
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
ref{eq:equilibrium}
\end_layout

\end_inset

 and 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Ka_definition"
plural "false"
caps "false"
noprefix "false"

\end_inset

).
\end_layout

\end_body
\end_document