On non-trivial hyperbolic sets and their bifurcations in families of diffeomorphisms of a two-dimensional torus.

We propose a simple model-two-parameter family of diffeomorphisms of a two-dimensional torus. Combining analytical and numerical methods, we find regions in the parameter plane such that each diffeomorphism of the family is hyperbolic and describe the structure of the corresponding hyperbolic sets. We also study bifurcations on the boundaries of these regions, which lead to the change of hyperbolicity type (from Anosov diffeomorphisms to DA-diffeomorphisms).

Attractor-repeller collision and the heterodimensional dynamics.

We study the heterodimensional dynamics in a simple map on a three-dimensional torus. This map consists of a two-dimensional driving Anosov map and a one-dimensional driven Möbius map, and demonstrates the collision of a chaotic attractor with a chaotic repeller if parameters are varied. We explore this collision by following tangent bifurcations of the periodic orbits and establish a regime where periodic orbits with different numbers of unstable directions coexist in a chaotic set. For this situation, we construct a heterodimensional cycle connecting these periodic orbits. Furthermore, we discuss properties of the rotation number and of the nontrivial Lyapunov exponent at the collision and in the heterodimensional regime.

Nonspecific Amyloid Aggregation of Chicken Smooth-Muscle Titin: In Vitro Investigations.

A giant multidomain protein of striated and smooth vertebrate muscles, titin, consists of tandems of immunoglobulin (Ig)- and fibronectin type III (FnIII)-like domains representing ß-sandwiches, as well as of disordered segments. Chicken smooth muscles express several titin isoforms of ~500-1500 kDa. Using various structural-analysis methods, we investigated in vitro nonspecific amyloid aggregation of the high-molecular-weight isoform of chicken smooth-muscle titin (SMTHMW, ~1500 kDa). As confirmed by X-ray diffraction analysis, under near-physiological conditions, the protein formed amorphous amyloid aggregates with a quaternary cross-ß structure within a relatively short time (~60 min). As shown by circular dichroism and Fourier-transform infrared spectroscopy, the quaternary cross-ß structure-unlike other amyloidogenic proteins-formed without changes in the SMTHMW secondary structure. SMTHMW aggregates partially disaggregated upon increasing the ionic strength above the physiological level. Based on the data obtained, it is not the complete protein but its particular domains/segments that are likely involved in the formation of intermolecular interactions during SMTHMW amyloid aggregation. The discovered properties of titin position this protein as an object of interest for studying amyloid aggregation in vitro and expanding our views of the fundamentals of amyloidogenesis.

On the origin of chaotic attractors with two zero Lyapunov exponents in a system of five biharmonically coupled phase oscillators.

We study chaotic dynamics in a system of four differential equations describing the interaction of five identical phase oscillators coupled via biharmonic function. We show that this system exhibits strange spiral attractors (Shilnikov attractors) with two zero (indistinguishable from zero in numerics) Lyapunov exponents in a wide region of the parameter space. We explain this phenomenon by means of bifurcation analysis of a three-dimensional Poincaré map for the system under consideration. We show that chaotic dynamics develop here near a codimension three bifurcation, when a periodic orbit (fixed point of the Poincaré map) has the triplet of multipliers ( 1 , 1 , 1 ). As it is known, the flow normal form for such bifurcation is the well-known three-dimensional Arneodó-Coullet-Spiegel-Tresser (ACST) system, which exhibits spiral attractors. According to this, we conclude that the additional zero Lyapunov exponent for orbits in the observed attractors appears due to the fact that the corresponding three-dimensional Poincaré map is very close to the time-shift map of the ACST-system.

Conjoined Lorenz twins-a new pseudohyperbolic attractor in three-dimensional maps and flows.

We describe new types of Lorenz-like attractors for three-dimensional flows and maps with symmetries. We give an example of a three-dimensional system of differential equations, which is centrally symmetric and mirror symmetric. We show that the system has a Lorenz-like attractor, which contains three saddle equilibrium states and consists of two mirror-symmetric components that are adjacent at the symmetry plane. We also found a discrete-time analog of this "conjoined-twins" attractor in a cubic three-dimensional Hénon map with a central symmetry. We show numerically that both attractors are pseudohyperbolic, which guarantees that each orbit of the attractor has a positive maximal Lyapunov exponent, and this property is preserved under small perturbations. We also describe bifurcation scenarios for the emergence of the attractors in one-parameter families of three-dimensional flows and maps possessing the symmetries.

Interferon-ß Activity Is Affected by S100B Protein.

Interferon-ß (IFN-ß) is a pleiotropic cytokine secreted in response to various pathological conditions and is clinically used for therapy of multiple sclerosis. Its application for treatment of cancer, infections and pulmonary diseases is limited by incomplete understanding of regulatory mechanisms of its functioning. Recently, we reported that IFN-ß activity is affected by interactions with S100A1, S100A4, S100A6, and S100P proteins, which are members of the S100 protein family of multifunctional Ca2+-binding proteins possessing cytokine-like activities (Int J Mol Sci. 2020;21(24):9473). Here we show that IFN-ß interacts with one more representative of the S100 protein family, the S100B protein, involved in numerous oncological and neurological diseases. The use of chemical crosslinking, intrinsic fluorescence, and surface plasmon resonance spectroscopy revealed IFN-ß binding to Ca2+-loaded dimeric and monomeric forms of the S100B protein. Calcium depletion blocks the S100B-IFN-ß interaction. S100B monomerization increases its affinity to IFN-ß by 2.7 orders of magnitude (equilibrium dissociation constant of the complex reaches 47 pM). Crystal violet assay demonstrated that combined application of IFN-ß and S100B (5-25 nM) eliminates their inhibitory effects on MCF-7 cell viability. Bioinformatics analysis showed that the direct modulation of IFN-ß activity by the S100B protein described here could be relevant to progression of multiple oncological and neurological diseases.

Calcium-Bound S100P Protein Is a Promiscuous Binding Partner of the Four-Helical Cytokines.

S100 proteins are multifunctional calcium-binding proteins of vertebrates that act intracellularly, extracellularly, or both, and are engaged in the progression of many socially significant diseases. Their extracellular action is typically mediated by the recognition of specific receptor proteins. Recent studies indicate the ability of some S100 proteins to affect cytokine signaling through direct interaction with cytokines. S100P was shown to be the S100 protein most actively involved in interactions with some four-helical cytokines. To assess the selectivity of the S100P protein binding to four-helical cytokines, we have probed the interaction of Ca2+-bound recombinant human S100P with a panel of 32 four-helical human cytokines covering all structural families of this fold, using surface plasmon resonance spectroscopy. A total of 22 cytokines from all families of four-helical cytokines are S100P binders with the equilibrium dissociation constants, Kd, ranging from 1 nM to 3 µM (below the Kd value for the S100P complex with the V domain of its conventional receptor, receptor for advanced glycation end products, RAGE). Molecular docking and mutagenesis studies revealed the presence in the S100P molecule of a cytokine-binding site, which overlaps with the RAGE-binding site. Since S100 binding to four-helical cytokines inhibits their signaling in some cases, the revealed ability of the S100P protein to interact with ca. 71% of the four-helical cytokines indicates that S100P may serve as a poorly selective inhibitor of their action.

Ibuprofen Favors Binding of Amyloid-ß Peptide to Its Depot, Serum Albumin.

The deposition of amyloid-ß peptide (Aß) in the brain is a critical event in the progression of Alzheimer's disease (AD). This Aß deposition could be prevented by directed enhancement of Aß binding to its natural depot, human serum albumin (HSA). Previously, we revealed that specific endogenous ligands of HSA improve its affinity to monomeric Aß. We show here that an exogenous HSA ligand, ibuprofen (IBU), exerts the analogous effect. Plasmon resonance spectroscopy data evidence that a therapeutic IBU level increases HSA affinity to monomeric Aß40/Aß42 by a factor of 3-5. Using thioflavin T fluorescence assay and transmission electron microcopy, we show that IBU favors the suppression of Aß40 fibrillation by HSA. Molecular docking data indicate partial overlap between the IBU/Aß40-binding sites of HSA. The revealed enhancement of the HSA-Aß interaction by IBU and the strengthened inhibition of Aß fibrillation by HSA in the presence of IBU could contribute to the neuroprotective effects of the latter, previously observed in mouse and human studies of AD.

Specific S100 Proteins Bind Tumor Necrosis Factor and Inhibit Its Activity.

Tumor necrosis factor (TNF) inhibitors (anti-TNFs) represent a cornerstone of the treatment of various immune-mediated inflammatory diseases and are among the most commercially successful therapeutic agents. Knowledge of TNF binding partners is critical for identification of the factors able to affect clinical efficacy of the anti-TNFs. Here, we report that among eighteen representatives of the multifunctional S100 protein family, only S100A11, S100A12 and S100A13 interact with the soluble form of TNF (sTNF) in vitro. The lowest equilibrium dissociation constants (Kd) for the complexes with monomeric sTNF determined using surface plasmon resonance spectroscopy range from 2 nM to 28 nM. The apparent Kd values for the complexes of multimeric sTNF with S100A11/A12 estimated from fluorimetric titrations are 0.1-0.3 µM. S100A12/A13 suppress the cytotoxic activity of sTNF against Huh-7 cells, as evidenced by the MTT assay. Structural modeling indicates that the sTNF-S100 interactions may interfere with the sTNF recognition by the therapeutic anti-TNFs. Bioinformatics analysis reveals dysregulation of TNF and S100A11/A12/A13 in numerous disorders. Overall, we have shown a novel potential regulatory role of the extracellular forms of specific S100 proteins that may affect the efficacy of anti-TNF treatment in various diseases.

The genetic basis of phage susceptibility, cross-resistance and host-range in Salmonella.

Though bacteriophages (phages) are known to play a crucial role in bacterial fitness and virulence, our knowledge about the genetic basis of their interaction, cross-resistance and host-range is sparse. Here, we employed genome-wide screens in Salmonella enterica serovar Typhimurium to discover host determinants involved in resistance to eleven diverse lytic phages including four new phages isolated from a therapeutic phage cocktail. We uncovered 301 diverse host factors essential in phage infection, many of which are shared between multiple phages demonstrating potential cross-resistance mechanisms. We validate many of these novel findings and uncover the intricate interplay between RpoS, the virulence-associated general stress response sigma factor and RpoN, the nitrogen starvation sigma factor in phage cross-resistance. Finally, the infectivity pattern of eleven phages across a panel of 23 genome sequenced Salmonella strains indicates that additional constraints and interactions beyond the host factors uncovered here define the phage host range.

On bifurcations of Lorenz attractors in the Lyubimov-Zaks model.

We provide numerical evidence for the existence of the Lorenz and the Rovella (contracting Lorenz) attractors in the generalization of the Lorenz model proposed by Lyubimov and Zaks. The Lorenz attractor is robustly chaotic (pseudohyperbolic) in contrast to the Rovella attractor, which is only measure-persistent (it exists for a set of parameter values, which is nowhere dense but has a positive Lebesgue measure). It is well known that in this model, for certain values of parameters, there exists a homoclinic butterfly (a pair of homoclinic loops) to the symmetric saddle equilibrium, which is neutral, i.e., its eigenvalues λ2<λ1<0<γ are such that the saddle index ν=-λ1/γ is equal to ∼1. The birth of the Lorenz attractor at this codimension-two bifurcation is established by means of numerical verification of the Shilnikov criterion. For the birth of the Rovella attractor, we propose a new criterion, which is also verified numerically.

On discrete Lorenz-like attractors.

We study geometrical and dynamical properties of the so-called discrete Lorenz-like attractors. We show that such robustly chaotic (pseudohyperbolic) attractors can appear as a result of universal bifurcation scenarios, for which we give a phenomenological description and demonstrate certain examples of their implementation in one-parameter families of three-dimensional Hénon-like maps. We pay special attention to such scenarios that can lead to period-2 Lorenz-like attractors. These attractors have very interesting dynamical properties and we show that their crises can lead, in turn, to the emergence of discrete Lorenz shape attractors of new types.

Shilnikov attractors in three-dimensional orientation-reversing maps.

A Shilnikov homoclinic attractor of a three-dimensional diffeomorphism contains a saddle-focus fixed point with a two-dimensional unstable invariant manifold and homoclinic orbits to this saddle-focus. The orientation-reversing property of the diffeomorphism implies a symmetry between two branches of the one-dimensional stable manifold. This symmetry leads to a significant difference between Shilnikov attractors in the orientation-reversing and orientation-preserving cases. We consider the three-dimensional Mirá map x¯=y,y¯=z, and z¯=Bx+Cy+Az-y2 with the negative Jacobian (B<0) as a basic model demonstrating various types of Shilnikov attractors. We show that depending on values of parameters A,B, and C, such attractors can be of three possible types: hyperchaotic (with two positive and one negative Lyapunov exponent), flow-like (with one positive, one very close to zero, and one negative Lyapunov exponent), and strongly dissipative (with one positive and two negative Lyapunov exponents). We study scenarios of the formation of such attractors in one-parameter families.

Mutual singularities of overlapping attractor and repeller.

We apply the concepts of relative dimensions and mutual singularities to characterize the fractal properties of overlapping attractor and repeller in chaotic dynamical systems. We consider one analytically solvable example (a generalized baker's map); two other examples, the Anosov-Möbius and the Chirikov-Möbius maps, which possess fractal attractor and repeller on a two-dimensional torus, are explored numerically. We demonstrate that although for these maps the stable and unstable directions are not orthogonal to each other, the relative Rényi and Kullback-Leibler dimensions as well as the mutual singularity spectra for the attractor and repeller can be well approximated under orthogonality assumption of two fractals.

Serotonin Promotes Serum Albumin Interaction with the Monomeric Amyloid ß Peptide.

Prevention of amyloid ß peptide (Aß) deposition via facilitation of Aß binding to its natural depot, human serum albumin (HSA), is a promising approach to preclude Alzheimer's disease (AD) onset and progression. Previously, we demonstrated the ability of natural HSA ligands, fatty acids, to improve the affinity of this protein to monomeric Aß by a factor of 3 (BBRC, 510(2), 248-253). Using plasmon resonance spectroscopy, we show here that another HSA ligand related to AD pathogenesis, serotonin (SRO), increases the affinity of the Aß monomer to HSA by a factor of 7/17 for Aß40/Aß42, respectively. Meanwhile, the structurally homologous SRO precursor, tryptophan (TRP), does not affect HSA's affinity to monomeric Aß, despite slowdown of the association and dissociation processes. Crosslinking with glutaraldehyde and dynamic light scattering experiments reveal that, compared with the TRP-induced effects, SRO binding causes more marked changes in the quaternary structure of HSA. Furthermore, molecular docking reveals distinct structural differences between SRO/TRP complexes with HSA. The disintegration of the serotonergic system during AD pathogenesis may contribute to Aß release from HSA in the central nervous system due to impairment of the SRO-mediated Aß trapping by HSA.

Disulfide Dimerization of Neuronal Calcium Sensor-1: Implications for Zinc and Redox Signaling.

Neuronal calcium sensor-1 (NCS-1) is a four-EF-hand ubiquitous signaling protein modulating neuronal function and survival, which participates in neurodegeneration and carcinogenesis. NCS-1 recognizes specific sites on cellular membranes and regulates numerous targets, including G-protein coupled receptors and their kinases (GRKs). Here, with the use of cellular models and various biophysical and computational techniques, we demonstrate that NCS-1 is a redox-sensitive protein, which responds to oxidizing conditions by the formation of disulfide dimer (dNCS-1), involving its single, highly conservative cysteine C38. The dimer content is unaffected by the elevation of intracellular calcium levels but increases to 10-30% at high free zinc concentrations (characteristic of oxidative stress), which is accompanied by accumulation of the protein in punctual clusters in the perinuclear area. The formation of dNCS-1 represents a specific Zn2+-promoted process, requiring proper folding of the protein and occurring at redox potential values approaching apoptotic levels. The dimer binds Ca2+ only in one EF-hand per monomer, thereby representing a unique state, with decreased α-helicity and thermal stability, increased surface hydrophobicity, and markedly improved inhibitory activity against GRK1 due to 20-fold higher affinity towards the enzyme. Furthermore, dNCS-1 can coordinate zinc and, according to molecular modeling, has an asymmetrical structure and increased conformational flexibility of the subunits, which may underlie their enhanced target-binding properties. In HEK293 cells, dNCS-1 can be reduced by the thioredoxin system, otherwise accumulating as protein aggregates, which are degraded by the proteasome. Interestingly, NCS-1 silencing diminishes the susceptibility of Y79 cancer cells to oxidative stress-induced apoptosis, suggesting that NCS-1 may mediate redox-regulated pathways governing cell death/survival in response to oxidative conditions.

Merger of a Hénon-like attractor with a Hénon-like repeller in a model of vortex dynamics.

We study the phenomenon of a collision of a Hénon-like attractor with a Hénon-like repeller leading to the emergence of mixed dynamics in the model describing the motion of two point vortices in a shear flow perturbed by an acoustic wave. The mixed dynamics is a recently discovered type of chaotic behavior for which a chaotic attractor of the system intersects with a chaotic repeller. In all known systems with mixed dynamics, the difference between the numerically obtained attractor and repeller is small. Unlike these systems, the model under consideration demonstrates another type of mixed dynamics that we call "strongly dissipative." In this case, a strange attractor and a strange repeller have a nonempty intersection but are very different from each other, and this difference does not appear to decrease with increasing computation time.

Kantorovich-Rubinstein-Wasserstein distance between overlapping attractor and repeller.

We consider several examples of dynamical systems demonstrating overlapping attractor and repeller. These systems are constructed via introducing controllable dissipation to prototypic models with chaotic dynamics (Anosov cat map, Chirikov standard map, and incompressible three-dimensional flow of the ABC-type on a three-torus) and ergodic non-chaotic behavior (skew-shift map). We employ the Kantorovich-Rubinstein-Wasserstein distance to characterize the difference between the attractor and the repeller, in dependence on the dissipation level.

Homoclinic chaos in the Rössler model.

We study the origin of homoclinic chaos in the classical 3D model proposed by Rössler in 1976. Of our particular interest are the convoluted bifurcations of the Shilnikov saddle-foci and how their synergy determines the global bifurcation unfolding of the model, along with transformations of its chaotic attractors. We apply two computational methods proposed, one based on interval maps and a symbolic approach specifically tailored to this model, to scrutinize homoclinic bifurcations, as well as to detect the regions of structurally stable and chaotic dynamics in the parameter space of the Rössler model.

Interferon Beta Activity Is Modulated via Binding of Specific S100 Proteins.

Interferon-ß (IFN-ß) is a pleiotropic cytokine used for therapy of multiple sclerosis, which is also effective in suppression of viral and bacterial infections and cancer. Recently, we reported a highly specific interaction between IFN-ß and S100P lowering IFN-ß cytotoxicity to cancer cells (Int J Biol Macromol. 2020; 143: 633-639). S100P is a member of large family of multifunctional Ca2+-binding proteins with cytokine-like activities. To probe selectivity of IFN-ß-S100 interaction with respect to S100 proteins, we used surface plasmon resonance spectroscopy, chemical crosslinking, and crystal violet assay. Among the thirteen S100 proteins studied S100A1, S100A4, and S100A6 proteins exhibit strictly Ca2+-dependent binding to IFN-ß with equilibrium dissociation constants, Kd, of 0.04-1.5 µM for their Ca2+-bound homodimeric forms. Calcium depletion abolishes the S100-IFN-ß interactions. Monomerization of S100A1/A4/A6 decreases Kd values down to 0.11-1.0 nM. Interferon-α is unable of binding to the S100 proteins studied. S100A1/A4 proteins inhibit IFN-ß-induced suppression of MCF-7 cells viability. The revealed direct influence of specific S100 proteins on IFN-ß activity uncovers a novel regulatory role of particular S100 proteins, and opens up novel approaches to enhancement of therapeutic efficacy of IFN-ß.