Dynamic Effects in Nucleation of Receptor Clusters

Nucleation theory has been widely applied for the interpretation of critical phenomena in nonequilibrium systems. Ligand-induced receptor clustering is a critical step of cellular activation. Receptor clusters on the cell surface are treated from the nucleation theory point of view. The authors propose that the redistribution of energy over the degrees of freedom is crucial for forming each new bond in the growing cluster. The expression for a kinetic barrier for new bond formation in a cluster was obtained. The shape of critical receptor clusters seems to be very important for the clustering on the cell surface. The von Neumann entropy of the graph of bonds is used to determine the influence of the cluster shape on the kinetic barrier. Numerical studies were carried out to assess the dependence of the barrier on the size of the cluster. The asymptotic expression, reflecting the conditions necessary for the formation of receptor clusters, was obtained. Several dynamic effects were found. A slight increase of the ligand mass has been shown to significantly accelerate the nucleation of receptor clusters. The possible meaning of the obtained results for medical applications is discussed.

[1]  S. Franceschelli,et al.  Morphogenesis, Structural Stability and Epigenetic Landscape , 2011 .

[2]  Omer Dushek,et al.  Mathematical Modelling of T Cell Activation , 2021 .

[3]  F. Gantmacher.  Lectures in Analytical Mechanics , 1975 .

[4]  Mathias Kluge,et al.  Theory Of Phase Transitions Rigorous Results , 2016 .

[5]  D. Nardo.  Toll-like receptors: Activation, signalling and transcriptional modulation. , 2015 .

[6]  Jason Yi,et al.  TCR microclusters form spatially segregated domains and sequentially assemble in calcium-dependent kinetic steps , 2019, Nature Communications.

[7]  P. W. Janes,et al.  Architecture of Eph receptor clusters , 2010, Proceedings of the National Academy of Sciences.

[8]  A. Neishtadt.  The separation of motions in systems with rapidly rotating phase , 1984 .

[9]  D. Fletcher,et al.  Cell–cell interfaces as specialized compartments directing cell function , 2020, Nature Reviews Molecular Cell Biology.

[10]  Waddington Ch,et al.  The epigenotype. 1942. , 2012 .

[11]  G. Guria,et al.  Stability Analysis of the PI3K–Akt–mTOR Signaling Pathway , 2020, Biophysics.

[12]  S. Kunapuli,et al.  C-type lectin like receptor 2 (CLEC-2) signals independently of lipid raft microdomains in platelets. , 2015, Biochemical pharmacology.

[13]  T. K. Radhakrishnan,et al.  A Review of Classical and Nonclassical Nucleation Theories , 2016 .

[14]  J. Cochran,et al.  The relationship of MHC-peptide binding and T cell activation probed using chemically defined MHC class II oligomers. , 2000, Immunity.

[15]  H. Eyring.  The Activated Complex in Chemical Reactions , 1935 .

[16]  D. De Nardo,et al.  Toll-like receptors: Activation, signalling and transcriptional modulation. , 2015, Cytokine.

[17]  A. Kolmogorov,et al.  The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[18]  S. Kuznetsov,et al.  Dynamics of coupled generators of quasiperiodic oscillations: Different types of synchronization and other phenomena , 2019, Physica D: Nonlinear Phenomena.

[19]  Matthias Dehmer,et al.  Entropy and the Complexity of Graphs Revisited , 2012, Entropy.

[20]  V. Tybulewicz,et al.  CD19 is essential for B cell activation by promoting B cell receptor–antigen microcluster formation in response to membrane-bound ligand , 2008, Nature Immunology.

[21]  E. Jones,et al.  Cell guidance ligands, receptors and complexes – orchestrating signalling in time and space , 2019, Current opinion in structural biology.

[22]  S. Davis,et al.  Membrane Ultrastructure and T Cell Activation , 2018, Front. Immunol..

[23]  D. M. Pushin,et al.  Platelet activation via dynamic conformational changes of von Willebrand factor under shear , 2020, PloS one.

[24]  I. Prigogine.  Chemical Kinetics and Dynamics , 2003, Annals of the New York Academy of Sciences.

[25]  J. Groves,et al.  T-cell triggering thresholds are modulated by the number of antigen within individual T-cell receptor clusters , 2011, Proceedings of the National Academy of Sciences.

[26]  R. Schneppenheim,et al.  Update on von Willebrand factor multimers: focus on high-molecular-weight multimers and their role in hemostasis , 2014, Blood coagulation & fibrinolysis : an international journal in haemostasis and thrombosis.

[27]  B. Chirikov,et al.  Statistical Properties of a Nonlinear String , 1966 .

[28]  S. Khakoo,et al.  Spatial Clustering of Receptors and Signaling Molecules Regulates NK Cell Response to Peptide Repertoire Changes , 2019, Front. Immunol..

[29]  R. Thom.  Stabilité structurelle et morphogenèse , 1974 .

[30]  E. A. Moelwyn-Hughes.  A short course of physical chemistry , 1966 .

[31]  Arnauld Sergé,et al.  Signalling complexes and clusters: functional advantages and methodological hurdles , 2010, Journal of Cell Science.

[32]  Alexander S. Abyzov,et al.  Crystallization of Supercooled Liquids: Self-Consistency Correction of the Steady-State Nucleation Rate , 2020, Entropy.

[33]  ヤクルト本社.  Cell Signalling , 1998, The Journal of physiology.

[34]  S. Alberti.  Phase separation in biology , 2017, Current Biology.

[35]  J. Schmelzer,et al.  Curvature-Dependent Surface Tension and Nucleation Theory , 1996 .

[36]  Nicolas L. Fawzi,et al.  Protein Phase Separation: A New Phase in Cell Biology. , 2018, Trends in cell biology.

[37]  Jianhong Ou,et al.  Control of osteoblast regeneration by a train of Erk activity waves , 2020, Nature.

[38]  M. Volmer,et al.  Keimbildung in übersättigten Gebilden , 1926 .

[39]  Catherine J. Wu,et al.  Investigation of Antigen-Specific T-Cell Receptor Clusters in Human Cancers , 2019, Clinical Cancer Research.

[40]  K. Zlobina,et al.  Platelet activation risk index as a prognostic thrombosis indicator , 2016, Scientific Reports.

[41]  R. Becker,et al.  Kinetische Behandlung der Keimbildung in übersättigten Dämpfen , 1935 .

[42]  C. Hoogenraad,et al.  Probing cytoskeletal modulation of passive and active intracellular dynamics using nanobody-functionalized quantum dots , 2016, Nature Communications.

[43]  J. Zimmerberg,et al.  "Entropic traps" in the kinetics of phase separation in multicomponent membranes stabilize nanodomains. , 2006, Biophysical journal.

[44]  A. Gadisseur,et al.  Improving diagnosis of von Willebrand disease: Reference ranges for von Willebrand factor multimer distribution , 2020, Research and practice in thrombosis and haemostasis.

[45]  Rajat Varma,et al.  Actin and agonist MHC–peptide complex–dependent T cell receptor microclusters as scaffolds for signaling , 2005, The Journal of experimental medicine.

[46]  SARS-CoV-2 Epitopes Are Recognized by a Public and Diverse Repertoire of Human T Cell Receptors , 2020, Immunity.

[47]  W. Ebeling.  Stochastic Processes in Physics and Chemistry , 1995 .

[48]  F. Takens,et al.  On the nature of turbulence , 1971 .

[49]  Nicole C. Fay,et al.  Mapping the stochastic sequence of individual ligand-receptor binding events to cellular activation: T cells act on the rare events , 2019, Science Signaling.

[50]  Tapesh Santra,et al.  Reconstructing static and dynamic models of signaling pathways using Modular Response Analysis , 2018, Current Opinion in Systems Biology.

[51]  A. Dhar.  Heat transport in low-dimensional systems , 2008, 0808.3256.

[52]  S. Herminghaus,et al.  Wetting: Statics and dynamics , 1997 .

[53]  I. Prigogine.  Time, Structure, and Fluctuations , 1978, Science.

[54]  E. E. Nikitin,et al.  Theory of Slow Atomic Collisions , 1984 .

[55]  P. Jurkiewicz,et al.  Membrane Lipid Nanodomains. , 2018, Chemical reviews.

[56]  A. Iwasaki,et al.  Toll-like receptor control of the adaptive immune responses , 2004, Nature Immunology.

[57]  Andrea Torsello,et al.  On the von Neumann entropy of graphs , 2018, J. Complex Networks.

[58]  N. Vavilov,et al.  The law of homologous series in variation , 1922, Journal of Genetics.

[59]  J. Schmelzer,et al.  Kinetics of formation of a phase with an arbitrary stoichiometric composition in a multicomponent solid solution. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[60]  Polina S. Landa,et al.  Stochastic and Chaotic Oscillations , 1992 .

[61]  Kenneth F. Kelton,et al.  Nucleation in condensed matter : applications in materials and biology , 2010 .

[62]  N. N. Bogolyubov,et al.  Problems of a Dynamical Theory in Statistical Physics , 1959 .

[63]  J. Schmelzer.  Nucleation Theory and Applications: SCHMELZER:NUCLEATION O-BK , 2005 .

[64]  A. Majda,et al.  Nonlinear Laplacian spectral analysis for time series with intermittency and low-frequency variability , 2012, Proceedings of the National Academy of Sciences.

[65]  K. Gaus,et al.  An intermolecular FRET sensor detects the dynamics of T cell receptor clustering , 2017, Nature Communications.

[66]  Lushnikov Aa,et al.  Gelation in coagulating systems , 2006 .

[67]  B. Chirikov.  A universal instability of many-dimensional oscillator systems , 1979 .

[68]  G. Bianconi,et al.  Shannon and von Neumann entropy of random networks with heterogeneous expected degree. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[69]  Joao Antonio Pereira,et al.  Linked: The new science of networks , 2002 .

[70]  Katharina Gaus,et al.  Functional role of T-cell receptor nanoclusters in signal initiation and antigen discrimination , 2016, Proceedings of the National Academy of Sciences.

[71]  G. Guria,et al.  The Role of Heterogeneous Nucleation in the Activation of Blood Cells , 2020, Physics of the Solid State.

[72]  G. Gaud,et al.  Regulatory mechanisms in T cell receptor signalling , 2018, Nature Reviews Immunology.