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2.
Nanomaterials (Basel) ; 13(23)2023 Dec 04.
Artigo em Inglês | MEDLINE | ID: mdl-38063771

RESUMO

The challenge of continuous CaCO3 particle synthesis is addressed using microfluidic technology. A custom microfluidic chip was used to synthesize CaCO3 nanoparticles in vaterite form. Our focus revolved around exploring one-phase and two-phase synthesis methods tailored for the crystallization of these nanoparticles. The combination of scanning electron microscopy, X-ray diffraction, dynamic light scattering, and small-angle scattering allowed for an evaluation of the synthesis efficiency, including the particle size distribution, morphology, and polymorph composition. The results demonstrated the superior performance of the two-phase system when precipitation occurred inside emulsion microreactors, providing improved size control compared with the one-phase approach. We also discussed insights into particle size changes during the transition from one-phase to two-phase synthesis. The ability to obtain CaCO3 nanoparticles in the desired polymorph form (∼50 nm in size, 86-99% vaterite phase) with the possibility of scaling up the synthesis will open up opportunities for various industrial applications of the developed two-phase microfluidic method.

3.
Biomolecules ; 13(12)2023 12 12.
Artigo em Inglês | MEDLINE | ID: mdl-38136647

RESUMO

Currently, there is great interest in the development of highly sensitive bioanalytical systems for diagnosing diseases at an early stage, when pathological biomarkers are present in biological fluids at low concentrations and there are no clinical manifestations. A promising direction is the use of molecular detectors-highly sensitive devices that detect signals from single biomacromolecules. A typical detector in this class is the atomic force microscope (AFM). The high sensitivity of an AFM-based bioanalysis system is determined by the size of the sensing element of an atomic force microscope-the cantilever-the radius of the curvature of which is comparable to that of a biomolecule. Biospecific molecular probe-target interactions are used to ensure detection system specificity. Antibodies, aptamers, synthetic antibodies, and peptides can be used as molecular probes. This study has demonstrated the possibility of using aptamers as molecular probes for AFM-based detection of the ovarian cancer biomarker CA125. Antigen detection in a nanomolar solution was carried out using AFM chips with immobilized aptamers, commercially available or synthesized based on sequences from open sources. Both aptamer types can be used for antigen detection, but the availability of sequence information enables additional modeling of the aptamer structure with allowance for modifications necessary for immobilization of the aptamer on an AFM chip surface. Information on the structure and oligomeric composition of aptamers in the solution was acquired by combining small-angle X-ray scattering and molecular modeling. Modeling enabled pre-selection, before the experimental stage, of aptamers for use as surface-immobilized molecular probes.


Assuntos
Aptâmeros de Nucleotídeos , Microscopia de Força Atômica , Aptâmeros de Nucleotídeos/química , Sondas Moleculares , Modelos Moleculares
4.
Biophys J ; 122(15): 3078-3088, 2023 08 08.
Artigo em Inglês | MEDLINE | ID: mdl-37340636

RESUMO

A critical quality attribute for liquid formulations is the absence of visible particles. Such particles may form upon polysorbate hydrolysis resulting in release of free fatty acids into solution followed by precipitation. Strategies to avoid this effect are of major interest for the pharmaceutical industry. In this context, we investigated the structural organization of polysorbate micelles alone and upon addition of the fatty acid myristic acid (MA) by small-angle x-ray scattering. Two complementary approaches using a model of polydisperse core-shell ellipsoidal micelles and an ensemble of quasiatomistic micelle structures gave consistent results well describing the experimental data. The small-angle x-ray scattering data reveal polydisperse mixtures of ellipsoidal micelles containing about 22-35 molecules per micelle. The addition of MA at concentrations up to 100 µg/mL reveals only marginal effects on the scattering data. At the same time, addition of high amounts of MA (>500 µg/mL) increases the average sizes of the micelles indicating that MA penetrates into the surfactant micelles. These results together with molecular modeling shed light on the polysorbate contribution to fatty acid solubilization preventing or delaying fatty acid particle formation.


Assuntos
Ácidos Graxos não Esterificados , Micelas , Polissorbatos , Espalhamento a Baixo Ângulo , Polissorbatos/química , Ácidos Graxos não Esterificados/química , Ácido Mirístico/química , Composição de Medicamentos
5.
Mol Ther Nucleic Acids ; 32: 267-288, 2023 Jun 13.
Artigo em Inglês | MEDLINE | ID: mdl-37090419

RESUMO

Here, we present DNA aptamers capable of specific binding to glial tumor cells in vitro, ex vivo, and in vivo for visualization diagnostics of central nervous system tumors. We selected the aptamers binding specifically to the postoperative human glial primary tumors and not to the healthy brain cells and meningioma, using a modified process of systematic evolution of ligands by exponential enrichment to cells; sequenced and analyzed ssDNA pools using bioinformatic tools and identified the best aptamers by their binding abilities; determined three-dimensional structures of lead aptamers (Gli-55 and Gli-233) with small-angle X-ray scattering and molecular modeling; isolated and identified molecular target proteins of the aptamers by mass spectrometry; the potential binding sites of Gli-233 to the target protein and the role of post-translational modifications were verified by molecular dynamics simulations. The anti-glioma aptamers Gli-233 and Gli-55 were used to detect circulating tumor cells in liquid biopsies. These aptamers were used for in situ, ex vivo tissue staining, histopathological analyses, and fluorescence-guided tumor and PET/CT tumor visualization in mice with xenotransplanted human astrocytoma. The aptamers did not show in vivo toxicity in the preclinical animal study. This study demonstrates the potential applications of aptamers for precise diagnostics and fluorescence-guided surgery of brain tumors.

6.
J Biol Chem ; 299(4): 104585, 2023 04.
Artigo em Inglês | MEDLINE | ID: mdl-36889586

RESUMO

Emfourin (M4in) is a protein metalloprotease inhibitor recently discovered in the bacterium Serratia proteamaculans and the prototype of a new family of protein protease inhibitors with an unknown mechanism of action. Protealysin-like proteases (PLPs) of the thermolysin family are natural targets of emfourin-like inhibitors widespread in bacteria and known in archaea. The available data indicate the involvement of PLPs in interbacterial interaction as well as bacterial interaction with other organisms and likely in pathogenesis. Arguably, emfourin-like inhibitors participate in the regulation of bacterial pathogenesis by controlling PLP activity. Here, we determined the 3D structure of M4in using solution NMR spectroscopy. The obtained structure demonstrated no significant similarity to known protein structures. This structure was used to model the M4in-enzyme complex and the complex model was verified by small-angle X-ray scattering. Based on the model analysis, we propose a molecular mechanism for the inhibitor, which was confirmed by site-directed mutagenesis. We show that two spatially close flexible loop regions are critical for the inhibitor-protease interaction. One region includes aspartic acid forming a coordination bond with catalytic Zn2+ of the enzyme and the second region carries hydrophobic amino acids interacting with protease substrate binding sites. Such an active site structure corresponds to the noncanonical inhibition mechanism. This is the first demonstration of such a mechanism for protein inhibitors of thermolysin family metalloproteases, which puts forward M4in as a new basis for the development of antibacterial agents relying on selective inhibition of prominent factors of bacterial pathogenesis belonging to this family.


Assuntos
Proteínas de Bactérias , Metaloproteases , Termolisina/metabolismo , Proteínas de Bactérias/metabolismo , Metaloproteases/genética , Espectroscopia de Ressonância Magnética , Peptídeo Hidrolases
7.
Protein Sci ; 32(2): e4563, 2023 02.
Artigo em Inglês | MEDLINE | ID: mdl-36605018

RESUMO

Nerve growth factor (NGF), the prototypical neurotrophic factor, is involved in the maintenance and growth of specific neuronal populations, whereas its precursor, proNGF, is involved in neuronal apoptosis. Binding of NGF or proNGF to TrkA, p75NTR , and VP10p receptors triggers complex intracellular signaling pathways that can be modulated by endogenous small-molecule ligands. Here, we show by isothermal titration calorimetry and NMR that ATP binds to the intrinsically disordered pro-peptide of proNGF with a micromolar dissociation constant. We demonstrate that Mg2+ , known to play a physiological role in neurons, modulates the ATP/proNGF interaction. An integrative structural biophysics analysis by small angle X-ray scattering and hydrogen-deuterium exchange mass spectrometry unveils that ATP binding induces a conformational rearrangement of the flexible pro-peptide domain of proNGF. This suggests that ATP may act as an allosteric modulator of the overall proNGF conformation, whose likely distinct biological activity may ultimately affect its physiological homeostasis.


Assuntos
Fator de Crescimento Neural , Neurônios , Fator de Crescimento Neural/química , Fator de Crescimento Neural/metabolismo , Domínios Proteicos , Neurônios/metabolismo , Trifosfato de Adenosina
8.
Micromachines (Basel) ; 15(1)2023 Dec 21.
Artigo em Inglês | MEDLINE | ID: mdl-38276844

RESUMO

The development of advanced methods for the synthesis of nano- and microparticles in the field of biomedicine is of high interest due to a range of reasons. The current synthesis methods may have limitations in terms of efficiency, scalability, and uniformity of the particles. Here, we investigate the synthesis of submicron calcium carbonate using a microfluidic chip with a T-shaped oil supply for droplet-based synthesis to facilitate control over the formation of submicron calcium carbonate particles. The design of the chip allowed for the precise manipulation of reaction parameters, resulting in improved porosity while maintaining an efficient synthesis rate. The pore size distribution within calcium carbonate particles was estimated via small-angle X-ray scattering. This study showed that the high porosity and reduced size of the particles facilitated the higher loading of a model peptide: 16 vs. 9 mass.% for the particles synthesized in a microfluidic device and in bulk, correspondingly. The biosafety of the developed particles in the concentration range of 0.08-0.8 mg per plate was established by the results of the cytotoxicity study using mouse fibroblasts. This innovative approach of microfluidically assisted synthesis provides a promising avenue for future research in the field of particle synthesis and drug delivery systems.

9.
Biomedicines ; 10(10)2022 Sep 21.
Artigo em Inglês | MEDLINE | ID: mdl-36289609

RESUMO

Chaperonins, a family of molecular chaperones, assist protein folding in all domains of life. They are classified into two groups: bacterial variants and those present in endosymbiotic organelles of eukaryotes belong to group I, while group II includes chaperonins from the cytosol of archaea and eukaryotes. Recently, chaperonins of a prospective new group were discovered in giant bacteriophages; however, structures have been determined for only two of them. Here, using cryo-EM, we resolved a structure of a new chaperonin encoded by gene 228 of phage AR9 B. subtilis. This structure has similarities and differences with members of both groups, as well as with other known phage chaperonins, which further proves their diversity.

10.
Int J Mol Sci ; 23(12)2022 Jun 13.
Artigo em Inglês | MEDLINE | ID: mdl-35743044

RESUMO

The human genetic variant BDNF (V66M) represents the first example of neurotrophin family member that has been linked to psychiatric disorders. In order to elucidate structural differences that account for the effects in cognitive function, this hproBDNF polymorph was expressed, refolded, purified, and compared directly to the WT variant for the first time for differences in their 3D structures by DSF, limited proteolysis, FT-IR, and SAXS measurements in solution. Our complementary studies revealed a deep impact of V66M polymorphism on hproBDNF conformations in solution. Although the mean conformation in solution appears to be more compact in the V66M variant, overall, we demonstrated a large increase in flexibility in solution upon V66M mutation. Thus, considering that plasticity in IDR is crucial for protein function, the observed alterations may be related to the functional alterations in hproBDNF binding to its receptors p75NTR, sortilin, HAP1, and SorCS2. These effects can provoke altered intracellular neuronal trafficking and/or affect proBDNF physiological functions, leading to many brain-associated diseases and conditions such as cognitive impairment and anxiety. The structural alterations highlighted in the present study may pave the way to the development of drug discovery strategies to provide greater therapeutic responses and of novel pharmacologic strategy in human populations with this common polymorphism, ultimately guiding personalized medicine for neuropsychiatric disorders.


Assuntos
Fator Neurotrófico Derivado do Encéfalo/genética , Transtornos Mentais , Precursores de Proteínas , Fator Neurotrófico Derivado do Encéfalo/metabolismo , Humanos , Transtornos Mentais/genética , Precursores de Proteínas/genética , Precursores de Proteínas/metabolismo , Espalhamento a Baixo Ângulo , Espectroscopia de Infravermelho com Transformada de Fourier , Difração de Raios X
11.
Protein Sci ; 31(1): 269-282, 2022 01.
Artigo em Inglês | MEDLINE | ID: mdl-34767272

RESUMO

Small-angle X-ray scattering (SAXS) is an established technique for structural analysis of biological macromolecules in solution. During the last decade, inline chromatography setups coupling SAXS with size exclusion (SEC-SAXS) or ion exchange (IEC-SAXS) have become popular in the community. These setups allow one to separate individual components in the sample and to record SAXS data from isolated fractions, which is extremely important for subsequent data interpretation, analysis, and structural modeling. However, in case of partially overlapping elution peaks, inline chromatography SAXS may still yield scattering profiles from mixtures of components. The deconvolution of these scattering data into the individual fractions is nontrivial and potentially ambiguous. We describe a cross-platform computer program, EFAMIX, for restoring the scattering and concentration profiles of the components based on the evolving factor analysis (EFA). The efficiency of the program is demonstrated in a number of simulated and experimental SEC-SAXS data sets. Sensitivity and limitations of the method are explored, and its applicability to IEC-SAXS data is discussed. EFAMIX requires minimal user intervention and is available to academic users through the program package ATSAS as from release 3.1.


Assuntos
Processamento Eletrônico de Dados , Espalhamento a Baixo Ângulo , Software , Difração de Raios X , Cromatografia
12.
Membranes (Basel) ; 11(10)2021 Oct 10.
Artigo em Inglês | MEDLINE | ID: mdl-34677538

RESUMO

Influenza A virus envelope contains lipid molecules of the host cell and three integral viral proteins: major hemagglutinin, neuraminidase, and minor M2 protein. Membrane-associated M1 matrix protein is thought to interact with the lipid bilayer and cytoplasmic domains of integral viral proteins to form infectious virus progeny. We used small-angle X-ray scattering (SAXS) and complementary techniques to analyze the interactions of different components of the viral envelope with M1 matrix protein. Small unilamellar liposomes composed of various mixtures of synthetic or "native" lipids extracted from Influenza A/Puerto Rico/8/34 (H1N1) virions as well as proteoliposomes built from the viral lipids and anchored peptides of integral viral proteins (mainly, hemagglutinin) were incubated with isolated M1 and measured using SAXS. The results imply that M1 interaction with phosphatidylserine leads to condensation of the lipid in the protein-contacting monolayer, thus resulting in formation of lipid tubules. This effect vanishes in the presence of the liquid-ordered (raft-forming) constituents (sphingomyelin and cholesterol) regardless of their proportion in the lipid bilayer. We also detected a specific role of the hemagglutinin anchoring peptides in ordering of viral lipid membrane into the raft-like one. These peptides stimulate the oligomerization of M1 on the membrane to form a viral scaffold for subsequent budding of the virion from the plasma membrane of the infected cell.

13.
Int J Biol Macromol ; 193(Pt A): 401-413, 2021 Dec 15.
Artigo em Inglês | MEDLINE | ID: mdl-34673109

RESUMO

The trimeric CCAAT-binding NF-Y is a "pioneer" Transcription Factor -TF- known to cooperate with neighboring TFs to regulate gene expression. Genome-wide analyses detected a precise stereo-alignment -10/12 bp- of CCAAT with E-box elements and corresponding colocalization of NF-Y with basic-Helix-Loop-Helix (bHLH) TFs. We dissected here NF-Y interactions with USF1 and MAX. USF1, but not MAX, cooperates in DNA binding with NF-Y. NF-Y and USF1 synergize to activate target promoters. Reconstruction of complexes by structural means shows independent DNA binding of MAX, whereas USF1 has extended contacts with NF-Y, involving the USR, a USF-specific amino acid sequence stretch required for trans-activation. The USR is an intrinsically disordered domain and adopts different conformations based on E-box-CCAAT distances. Deletion of the USR abolishes cooperative DNA binding with NF-Y. Our data indicate that the functionality of certain unstructured domains involves adapting to small variation in stereo-alignments of the multimeric TFs sites.


Assuntos
DNA/metabolismo , Fatores Estimuladores Upstream/metabolismo , Regulação da Expressão Gênica , Humanos , Regiões Promotoras Genéticas , Ligação Proteica , Domínios Proteicos
14.
J Appl Crystallogr ; 54(Pt 1): 169-179, 2021 Feb 01.
Artigo em Inglês | MEDLINE | ID: mdl-33833646

RESUMO

Small-angle X-ray scattering (SAXS) is widely utilized to study soluble macromolecules, including those embedded into lipid carriers and delivery systems such as surfactant micelles, phospho-lipid vesicles and bilayered nanodiscs. To adequately describe the scattering from such systems, one needs to account for both the form factor (overall structure) and long-range-order Bragg reflections emerging from the organization of bilayers, which is a non-trivial task. Presently existing methods separate the analysis of lipid mixtures into distinct procedures using form-factor fitting and the fitting of the Bragg peak regions. This article describes a general approach for the computation and analysis of SAXS data from lipid mixtures over the entire angular range of an experiment. The approach allows one to restore the electron density of a lipid bilayer and simultaneously recover the corresponding size distribution and multilamellar organization of the vesicles. The method is implemented in a computer program, LIPMIX, and its performance is demonstrated on an aqueous solution of layered lipid vesicles undergoing an extrusion process. The approach is expected to be useful for the analysis of various types of lipid-based systems, e.g. for the characterization of interactions between target drug molecules and potential carrier/delivery systems.

15.
J Appl Crystallogr ; 54(Pt 1): 343-355, 2021 Feb 01.
Artigo em Inglês | MEDLINE | ID: mdl-33833657

RESUMO

The ATSAS software suite encompasses a number of programs for the processing, visualization, analysis and modelling of small-angle scattering data, with a focus on the data measured from biological macromolecules. Here, new developments in the ATSAS 3.0 package are described. They include IMSIM, for simulating isotropic 2D scattering patterns; IMOP, to perform operations on 2D images and masks; DATRESAMPLE, a method for variance estimation of structural invariants through parametric resampling; DATFT, which computes the pair distance distribution function by a direct Fourier transform of the scattering data; PDDFFIT, to compute the scattering data from a pair distance distribution function, allowing comparison with the experimental data; a new module in DATMW for Bayesian consensus-based concentration-independent molecular weight estimation; DATMIF, an ab initio shape analysis method that optimizes the search model directly against the scattering data; DAMEMB, an application to set up the initial search volume for multiphase modelling of membrane proteins; ELLLIP, to perform quasi-atomistic modelling of liposomes with elliptical shapes; NMATOR, which models conformational changes in nucleic acid structures through normal mode analysis in torsion angle space; DAMMIX, which reconstructs the shape of an unknown intermediate in an evolving system; and LIPMIX and BILMIX, for modelling multilamellar and asymmetric lipid vesicles, respectively. In addition, technical updates were deployed to facilitate maintainability of the package, which include porting the PRIMUS graphical interface to Qt5, updating SASpy - a PyMOL plugin to run a subset of ATSAS tools - to be both Python 2 and 3 compatible, and adding utilities to facilitate mmCIF compatibility in future ATSAS releases. All these features are implemented in ATSAS 3.0, freely available for academic users at https://www.embl-hamburg.de/biosaxs/software.html.

17.
Int J Biol Macromol ; 169: 583-596, 2021 Feb 01.
Artigo em Inglês | MEDLINE | ID: mdl-33385454

RESUMO

Protealysin is a Serratia proteamaculans metalloproteinase of the M4 peptidase family and the prototype of a large group of protealysin-like proteases (PLPs). PLPs are likely involved in bacterial interaction with plants and animals as well as in bacterial pathogenesis. We demonstrated that the PLP genes in bacteria colocalize with the genes of putative conserved proteins. In S. proteamaculans, these two genes form a bicistronic operon. The putative S. proteamaculans protein that we called emfourin (M4in) was expressed in Escherichia coli and characterized. M4in forms a complex with protealysin with a 1:1 stoichiometry and is a potent slow-binding competitive inhibitor of protealysin (Ki = 52 ± 14 pM); besides, M4in is not secreted from S. proteamaculans constitutively. A comparison of amino acid sequences of M4in and its homologs with those of known inhibitors suggests that M4in is the prototype of a new family of protein inhibitors of proteases.


Assuntos
Metaloproteases/antagonistas & inibidores , Metaloproteases/genética , Serratia/enzimologia , Serratia/genética , Sequência de Aminoácidos , Proteínas de Bactérias/antagonistas & inibidores , Proteínas de Bactérias/química , Proteínas de Bactérias/genética , Proteínas de Bactérias/farmacologia , Inibidores Enzimáticos/farmacologia , Escherichia coli/genética , Metaloproteases/química , Metaloproteases/metabolismo , Óperon/genética , Peptídeo Hidrolases/metabolismo , Serratia/metabolismo
18.
Structure ; 29(1): 70-81.e5, 2021 01 07.
Artigo em Inglês | MEDLINE | ID: mdl-33065068

RESUMO

Ataxin-3 is a deubiquitinase involved in protein quality control and other essential cellular functions. It preferentially interacts with polyubiquitin chains of four or more units attached to proteins delivered to the ubiquitin-proteasome system. Ataxin-3 is composed of an N-terminal Josephin domain and a flexible C terminus that contains two or three ubiquitin-interacting motifs (UIMs) and a polyglutamine tract, which, when expanded beyond a threshold, leads to protein aggregation and misfolding and causes spinocerebellar ataxia type 3. The high-resolution structure of the Josephin domain is available, but the structural and dynamical heterogeneity of ataxin-3 has so far hindered the structural description of the full-length protein. Here, we characterize non-expanded and expanded variants of ataxin-3 in terms of conformational ensembles adopted by the proteins in solution by jointly using experimental data from nuclear magnetic resonance and small-angle X-ray scattering with coarse-grained simulations. Our results pave the way to a molecular understanding of polyubiquitin recognition.


Assuntos
Ataxina-3/química , Doença de Machado-Joseph/genética , Dobramento de Proteína , Ataxina-3/genética , Humanos , Simulação de Dinâmica Molecular , Mutação , Peptídeos/química , Peptídeos/genética , Conformação Proteica
19.
J Mater Sci ; 55(7): 3005-3021, 2020.
Artigo em Inglês | MEDLINE | ID: mdl-32431364

RESUMO

Poly(N-vinyl pyrrolidone) (PVP)-based hydrogels with titania nanoparticles (TN) were synthesized by the sol-gel method for the first time and were characterized in different states (native, freeze-dried, air-dried to constant weight and ground to powder, or swollen to constant weight in H2O or D2O) by various methods such as wide-angle and small-angle X-ray and neutron scattering, neutron spin-echo (NSE) spectroscopy, and scanning electron microscopy. The static (static polymer-polymer correlation length (mesh size), associates of cross-links and PVP microchains) and dynamic (polymer chain relaxation rate, hydrodynamic polymer-polymer correlation length) structural elements were determined. The incorporation of titania nanoparticles into PVP hydrogel slightly increases the size of structural inhomogeneities (an increase in the static and dynamic polymer-polymer correlation length, the formation of associates of cross-links and PVP chains). Titania nanoparticles have an impact on the microstructure of the composite hydrogel and form associates with sizes from 0.5 to 2 µm attached to PVP hydrogel pore walls. The PVP and TN/PVP hydrogels show a high degree of water swelling. Moreover, the presence of titania nanoparticles in TN/PVP increases the number of water adsorption cycles compared to PVP hydrogel. The high swelling degree, bacteria-resistant and antimicrobial properties against Staphylococcus aureus allow considering NT/PVP hydrogels for medical applications as wound coatings.

20.
Acta Crystallogr A Found Adv ; 76(Pt 2): 163-171, 2020 Mar 01.
Artigo em Inglês | MEDLINE | ID: mdl-32124854

RESUMO

The theoretical framework and a joint quasi-Newton-Levenberg-Marquardt-simulated annealing (qNLMSA) algorithm are established to treat an inverse X-ray diffraction tomography (XRDT) problem for recovering the 3D displacement field function fCtpd(r - r0) = h · u(r - r0) due to a Coulomb-type point defect (Ctpd) located at a point r0 within a crystal [h is the diffraction vector and u(r - r0) is the displacement vector]. The joint qNLMSA algorithm operates in a special sequence to optimize the XRDT target function {\cal F}\{ {\cal P} \} in a χ2 sense in order to recover the function fCtpd(r - r0) [{\cal P} is the parameter vector that characterizes the 3D function fCtpd(r - r0) in the algorithm search]. A theoretical framework based on the analytical solution of the Takagi-Taupin equations in the semi-kinematical approach is elaborated. In the case of true 2D imaging patterns (2D-IPs) with low counting statistics (noise-free), the joint qNLMSA algorithm enforces the target function {\cal F} \{ {\cal P} \} to tend towards the global minimum even if the vector {\cal P} in the search is initially chosen rather a long way from the true one.

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