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Mesoscopic simulations at the physics-chemistry-biology interface
Rev. Mod. Phys. 91, 025004 – Published 28 May, 2019
DOI: https://doi.org/10.1103/RevModPhys.91.025004
Abstract
This review discusses the lattice Boltzmann–particle dynamics (LBPD) multiscale paradigm for the simulation of complex states of flowing matter at the interface between physics, chemistry, and biology. In particular, current large-scale LBPD simulations of biopolymer translocation across cellular membranes, molecular transport in ion channels, and amyloid aggregation in cells are described. Prospects are provided for future LBPD explorations in the direction of cellular organization, the direct simulation of full biological organelles, all the way up to physiological scales of potential relevance to future precision-medicine applications, such as the accurate description of homeostatic processes. It is argued that, with the advent of Exascale computing, the mesoscale physics approach advocated in this review may come to age in the next decade and open up new exciting perspectives for physics-based computational medicine.
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References (229)
- Abraham, F. F., J. Q. Broughton, N. Bernstein, and E. Kaxiras, 1998, “Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture,” Europhys. Lett. 44, 783.
- Adhikari, R., K. Stratford, M. E. Cates, and A. J. Wagner, 2005, “Fluctuating lattice boltzmann,” Europhys. Lett. 71, 473.
- Ahlrichs, P., and B. Dünweg, 1998, “Lattice-Boltzmann simulation of polymer-solvent systems,” Int. J. Mod. Phys. C 09, 1429–1438.
- Alfahani, F., M. Antonelli, and J. Kreft Pearce, 2015, “Separation of DNA by length in rotational flow: Lattice-Boltzmann-based simulations,” Biomicrofluidics 9, 044107.
- Alowayyed, S., D. Groen, P. V. Coveney, and A. G. Hoekstra, 2017, “Multiscale computing in the exascale era,” J. Comput. Sci. 22, 15–25.
- Anderson, C., 2008, “The end of theory: The data deluge makes the scientific method obsolete. Wired Magazine 16.07,” https://www.wired.com/2008/06/pb-theory/.
- Ansumali, S., and I. V. Karlin, 2002, “Kinetic boundary conditions in the lattice Boltzmann method,” Phys. Rev. E 66, 026311.
- Ansumali, S., I. V. Karlin, S. Arcidiacono, A. Abbas, and N. I. Prasianakis, 2007, “Hydrodynamics beyond Navier-Stokes: Exact solution to the lattice Boltzmann hierarchy,” Phys. Rev. Lett. 98, 124502.
- Artoli, A. M., A. G. Hoekstra, and P. M. A. Sloot, 2003, “Simulation of a systolic cycle in a realistic artery with the Lattice Boltzmann BGK method,” Int. J. Mod. Phys. B 17, 95–98.
- Auer, S., et al., 2008, “A generic mechanism of emergence of amyloid protofilaments from disordered oligomeric aggregates,” PLoS Comput. Biol. 4, e1000222.
- Axner, L., J. Bernsdorf, T. Zeiser, P. Lammers, J. Linxweiler, and A. G. Hoekstra, 2008, “Performance evaluation of a parallel sparse lattice Boltzmann solver,” J. Comput. Phys. 227, 4895–4911.
- Ayodele, S. G., F. Varnik, and D. Raabe, 2011, “Lattice Boltzmann study of pattern formation in reaction-diffusion systems,” Phys. Rev. E 83, 016702.
- Bekard, I. B., P. Asimakis, J. Bertolini, and D. E. Dunstan, 2011, “The effects of shear flow on protein structure and function,” Biopolymers 95, 733–745.
- Benzi, R., S. Succi, and M. Vergassola, 1992, “The lattice Boltzmann equation: Theory and applications,” Phys. Rep. 222, 145–197.
- Bernaschi, M., M. Bisson, T. Endo, S. Matsuoka, and M. Fatica, 2011, “Petaflop biofluidics simulations on a two million-core system,” in 2011 International Conference for High Performance Computing, Networking, Storage and Analysis (SC) (IEEE, New York), pp. 1–12.
- Bernaschi, M., M. Bisson, M. Fatica, and S. Melchionna, 2013a, “20 petaflops simulation of proteins suspensions in crowding conditions,” in Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis (ACM, New York), p. 2.
- Bernaschi, M., M. Bisson, M. Fatica, S. Melchionna, and S. Succi, 2013b, “Petaflop hydrokinetic simulations of complex flows on massive GPU clusters,” Comput. Phys. Commun. 184, 329–341.
- Bernaschi, Massimo, Massimiliano Fatica, Simone Melchionna, Sauro Succi, and Efthimios Kaxiras, 2010, “A flexible high-performance Lattice Boltzmann GPU code for the simulations of fluid flows in complex geometries,” Concurrency and Computation: Practice and Experience (Wiley Online Library), Vol. 22, pp. 1–14.
- Bernaschi, M., S. Melchionna, S. Succi, M. Fyta, and E. Kaxiras, 2008, “Quantized current blockade and hydrodynamic correlations in biopolymer translocation through nanopores: Evidence from multiscale simulations,” Nano Lett. 8, 1115–1119.
- Bernaschi, M., S. Melchionna, S. Succi, M. Fyta, E. Kaxiras, and J, K. Sircar, 2009, “MUPHY: A parallel MUlti PHYsics/scale code for high performance bio-fluidic simulations,” Comput. Phys. Commun. 180, 1495–1502.
- Bhatnagar, P. L., E. P. Gross, and M. Krook, 1954, “A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems,” Phys. Rev. 94, 511.
- Bird, G. A., 1994, “Molecular gas dynamics and the direct simulation Monte Carlo of gas flows,” Oxford Engineering Science Series (Clarendon Press, Oxford), Vol. 508, p. 128.
- Bisson, M., M. Bernaschi, and S. Melchionna, 2011, “Parallel Molecular Dynamics with Irregular Domain Decomposition,” Commun. Comput. Phys. 10, 1071–1088.
- Bobylev, A. V., 1982, “The Chapman-Enskog and Grad methods for solving the Boltzmann equation,” Akad. Nauk SSSR Dokl. 262, 71–75.
- Boltzmann, Ludwig, 2012, Lectures on gas theory (Courier Corporation, North Chelmsford, MA).
- Boon, J. P., D. Dab, K. Raymond, and L. Anna, 1996, “Lattice gas automata for reactive systems,” Phys. Rep. 273, 55–147.
- Boon, J. P., and S. Yip, 1991, Molecular hydrodynamics (Courier Corporation, North Chelmsford, MA).
- Boyd, J., J. M. Buick, and S. Green, 2007, “Analysis of the Casson and Carreau-Yasuda non-Newtonian blood models in steady and oscillatory flows using the lattice Boltzmann method,” Phys. Fluids 19, 093103.
- Bryngelson, J. D., J. N. Onuchic, N. D. Socci, and P. G. Wolynes, 1995, “Funnels, pathways, and the energy landscape of protein folding: A synthesis,” Proteins: Structure, Function, and Bioinformatics (Wiley Online Library), Vol. 21, pp. 167–195.
- Buckner, R. L., et al., 2005, “Molecular, structural, and functional characterization of Alzheimer’s disease: Evidence for a relationship between default activity, amyloid, and memory,” J. Neurosci. 25, 7709–7717.
- Buick, J. M., J. A. Cosgrove, S. J. Tonge, M. W. Collins, A. J. Mulholland, and B. A. Steves, 2003, “The Lattice Boltzmann equation for modelling arterial flows: Review and application,” Biomed. Pharmacother. 56, 345–346.
- Caiazzo, A., et al., 2009, “Towards a complex automata multiscale model of in-stent restenosis,” in International Conference on Computational Science (Springer, New York), pp. 705–714.
- Capuani, F., I. Pagonabarraga, and D. Frenkel, 2004, “Discrete solution of the electrokinetic equations,” J. Chem. Phys. 121, 973–986.
- Cercignani, C., and A. S. Berman, 1976, “Theory and application of the Boltzmann equation,” J. Appl. Mech. 43, 521.
- Chebaro, Y., S. Pasquali, and P. Derreumaux, 2012, “The Coarse-Grained OPEP Force Field for Non-Amyloid and Amyloid Proteins,” J. Phys. Chem. B 116, 8741–8752.
- Chen, H., O. Filippova, J. Hoch, K. Molvig, R. Shock, C. Teixeira, and R. Zhang, 2006, “Grid refinement in lattice Boltzmann methods based on volumetric formulation,” Physica A (Amsterdam) 362, 158–167.
- Chen, H., S. Kandasamy, S. Orszag, R. Shock, S. Succi, and V. Yakhot, 2003, “Extended Boltzmann kinetic equation for turbulent flows,” Science 301, 633–636.
- Chen, S., D. Martinez, and R. Mei, 1996, “On boundary conditions in lattice Boltzmann methods,” Phys. Fluids 8, 2527–2536.
- Chen, Y.-L., H. Ma, M. D. Graham, and J. J. De Pablo, 2007, “Modeling DNA in confinement: A comparison between the Brownian dynamics and lattice Boltzmann method,” Macromolecules 40, 5978–5984.
- Chinappi, M., C. M. Casciola, F. Cecconi, U. M. B. Marconi, and S. Melchionna, 2014, “Modulation of current through a nanopore induced by a charged globule: Implications for DNA-docking,” Europhys. Lett. 108, 46002.
- Chiricotto, M., S. Melchionna, P. Derreumaux, and F. Sterpone, 2016, “Hydrodynamic effects on -amyloid (16–22) peptide aggregation,” J. Chem. Phys. 145, 035102.
- Chiricotto, M., F. Sterpone, P. Derreumaux, and S. Melchionna, 2016, “Multiscale simulation of molecular processes in cellular environments,” Phil. Trans. R. Soc. A 374, 20160225.
- Chiricotto, M., T. T. Tran, P. H. Nguyen, S. Melchionna, F. Sterpone, and P. Derreumaux, 2017, “Coarse-grained and All-atom Simulations towards the Early and Late Steps of Amyloid Fibril Formation,” Isr. J. Chem. 57, 564–573.
- Chopard, B., and M. Droz, 1998, Cellular automata (Springer, New York).
- Chopard, B., R. Ouared, and D. A. Rüfenacht, 2006, “A lattice Boltzmann simulation of clotting in stented aneursysms and comparison with velocity or shear rate reductions,” Math. Comput. Simul. 72, 108–112.
- Cuda C Programming Guide, 2019, https://docs.nvidia.com/cuda/cuda-c-programming-guide.
- Clausen, J. R., D. A. Reasor, and C. K. Aidun, 2010, “Parallel performance of a lattice-Boltzmann/finite element cellular blood flow solver on the IBM Blue Gene/P architecture,” Comput. Phys. Commun. 181, 1013–1020.
- Courant, R., K. Friedrichs, and H. Lewy, 1928, “Über die partiellen Differenzengleichungen der mathematischen Physik,” Math. Ann. 100, 32–74.
- Coveney, P. V., J. P. Boon, and S. Succi, 2016, Bridging the gaps at the physics–chemistry–biology interface (The Royal Society, London).
- Coveney, P. V., E. R. Dougherty, and R. R. Highfield, 2016, “Big data need big theory too,” Phil. Trans. R. Soc. A 374, 20160153.
- Cruz-León, S., A. Vázquez-Mayagoitia, S. Melchionna, N. Schwierz, and M. Fyta, 2018, “A Coarse-Grained Double-Stranded RNA Model from Quantum-Mechanical Calculations,” J. Phys. Chem. B 122, 7915–7928.
- Datar, A. V., M. Fyta, U. M. B. Marconi, and S. Melchionna, 2017, “Electrokinetic Lattice Boltzmann solver coupled to Molecular Dynamics: Application to polymer translocation,” Langmuir 33, 11635–11645.
- De Rosis, A., 2014, “Analysis of blood flow in deformable vessels via a lattice Boltzmann approach,” Int. J. Mod. Phys. C 25, 1350107.
- Descovich, X., G. Pontrelli, S. Melchionna, S. Succi, and S. Wassertheurer, 2013, “Modeling fluid flows in distensible tubes for applications in hemodynamics,” Int. J. Mod. Phys. C 24, 1350030.
- d’Humières, D., 1992, “Generalized Lattice Boltzmann Equations, Rarefied Gas Dynamics: Theory and Simulations,” Prog. Astronaut. Aeronaut. 159, 450–458.
- Di Ilio, G., D. Chiappini, S. Ubertini, G. Bella, and S. Succi, 2017, “Hybrid lattice Boltzmann method on overlapping grids,” Phys. Rev. E 95, 013309.
- Dimarco, G., R. Loubére, J. Narski, and T. Rey, 2018, “An efficient numerical method for solving the Boltzmann equation in multidimensions,” J. Comput. Phys. 353, 46–81.
- Doyle, D. A., J. M. Cabral, R. A. Pfuetzner, A. Kuo, J. M. Gulbis, S. L. Cohen, B. T. Chait, and R. MacKinnon, 1998, “The structure of the potassium channel: Molecular basis of conduction and selectivity,” Science 280, 69–77.
- Dunstan, D. E., P. Hamilton-Brown, P. Asimakis, W. Ducker, and J. Bertolini, 2009, “Shear flow promotes fibrilization,” Protein Engineering, Design & Selection 22, 741–746.
- Dünweg, B., and A. J. Ladd, 2009, “Lattice Boltzmann simulations of soft matter systems,” in Advanced Computer Simulation Approaches for Soft Matter Sciences III (Springer, New York), pp. 89–166.
- Dünweg, B., U. D. Schiller, and A. J. Ladd, 2007, “Statistical mechanics of the fluctuating lattice Boltzmann equation,” Phys. Rev. E 76, 036704.
- Dupin, M. M., I. Halliday, and C. M. Care, 2003, “Multi-component lattice Boltzmann equation for mesoscale blood flow,” J. Phys. A 36, 8517.
- Dupin, M. M., I. Halliday, and C. M. Care, 2006, “A multi-component lattice Boltzmann scheme: Towards the mesoscale simulation of blood flow,” Medical engineering & physics 28, 13–18.
- Dupin, M. M., I. Halliday, C. M. Care, and L. L. Munn, 2008, “Lattice Boltzmann modelling of blood cell dynamics,” Int. J. Comput. Fluid Dyn. 22, 481–492.
- Dupuis, A., and B. Chopard, 1999, “Lattice gas: An efficient and reusable parallel library based on a graph partitioning technique,” in International Conference on High-Performance Computing and Networking (Springer, New York), pp. 319–328.
- Eitel, G., R. K. Freitas, A. Lintermann, M. Meinke, and W. Schröder, 2010, “Numerical simulation of nasal cavity flow based on a lattice-boltzmann method,” in New Results in Numerical and Experimental Fluid Mechanics VII (Springer, New York), pp. 513–520.
- Ellis, R. J., 2001, “Macromolecular crowding: Obvious but underappreciated,” Trends Biochem. Sci. 26, 597–604.
- Falcucci, G., et al., 2016, “Mapping reactive flow patterns in monolithic nanoporous catalysts,” Microfluid. Nanofluid. 20, 105.
- Fang, H., Z. Wang, Z. Lin, and M. Liu, 2002, “Lattice Boltzmann method for simulating the viscous flow in large distensible blood vessels,” Phys. Rev. E 65, 051925.
- Fedosov, D. A., B. Caswell, and G. E. Karniadakis, 2010, “A multiscale red blood cell model with accurate mechanics, rheology, and dynamics,” Biophys. J. 98, 2215–2225.
- Feichtinger, C., S. Donath, H. Köstler, J. Götz, and U. Rüde, 2011, “WaLBerla: HPC software design for computational engineering simulations,” J. Comput. Sci. 2, 105–112.
- Feig, M., I. Yu, P.-h. Wang, G. Nawrocki, and Y. Sugita, 2017, “Crowding in Cellular Environments at an Atomistic Level from Computer Simulations,” J. Phys. Chem. B 121, 8009.
- Fenner, J. W., et al., 2008, “The EuroPhysiome, STEP and a roadmap for the virtual physiological human,” Phil. Trans. R. Soc. A 366, 2979–2999.
- Fersht, A., 2017, Structure and mechanism in protein science: A Guide to enzyme catalysis and protein folding (World Scientific, Singapore), Vol. 9.
- Frauenfelder, H., S. G. Sligar, and P. G. Wolynes, 1991, “The energy landscapes and motions of proteins,” Science 254, 1598–1603.
- Freitas, R. K., and W. Schröder, 2008, “Numerical investigation of the three-dimensional flow in a human lung model,” J. Biomech. 41, 2446–2457.
- Fyta, M., S. Melchionna, E. Kaxiras, and S. Succi, 2008, “Multiscale simulation of nanobiological flows,” Comput. Sci. Eng. 10, 10.
- Fyta, M., S. Melchionna, and S. Succi, 2011, “Translocation of biomolecules through solid-state nanopores: Theory meets experiments,” J. Polym. Sci., Part B: Polym. Phys. 49, 985–1011.
- Fyta, M., S. Melchionna, S. Succi, and E. Kaxiras, 2008, “Hydrodynamic correlations in the translocation of a biopolymer through a nanopore: Theory and multiscale simulations,” Phys. Rev. E 78, 036704.
- Fyta, M. G., S. Melchionna, E. Kaxiras, and S. Succi, 2006, “Multiscale coupling of molecular dynamics and hydrodynamics: Application to DNA translocation through a nanopore,” Multiscale Modeling & Simulation 5, 1156–1173.
- Gan, Y., A. Xu, G. Zhang, and S. Succi, 2015, “Discrete Boltzmann modeling of multiphase flows: Hydrodynamic and thermodynamic non-equilibrium effects,” Soft Matter 11, 5336–5345.
- Goldberg, D. E., and J. H. Holland, 1988, “Genetic algorithms and machine learning,” Mach. Learn. 3, 95–99.
- Grad, H., 1949, “On the kinetic theory of rarefied gases,” Commun. Pure Appl. Math. 2, 331–407.
- Groen, D., J. Hetherington, H. B. Carver, R. W. Nash, M. O. Bernabeu, and P. V. Coveney, 2013, “Analysing and modelling the performance of the HemeLB lattice-Boltzmann simulation environment,” J. Comput. Sci. 4, 412–422.
- Gunstensen, A. K., D. H. Rothman, S. Zaleski, and G. Zanetti, 1991, “Lattice Boltzmann model of immiscible fluids,” Phys. Rev. A 43, 4320.
- Guvench, O., and A. D. MacKerell, 2008, “Comparison of protein force fields for molecular dynamics simulations,” Molecular modeling of proteins (Springer, New York), pp. 63–88.
- Hammack, A., Y.-L. Chen, and J. K. Pearce, 2011, “Role of dissolved salts in thermophoresis of DNA: Lattice-Boltzmann-based simulations,” Phys. Rev. E 83, 031915.
- Hansen, J.-P., and I. R. McDonald, 1990, Theory of simple liquids (Elsevier, New York).
- Harrison, S. E., J. Bernsdorf, D. R. Hose, and P. V. Lawford, 2008, “A lattice Boltzmann framework for simulation of thrombogenesis,” Prog. Comput. Fluid Dyn. 8, 121–128.
- Harrison, S. E., S. M. Smith, J. Bernsdorf, D. R. Hose, and P. V. Lawford, 2007, “Application and validation of the lattice Boltzmann method for modelling flow-related clotting,” J. Biomech. 40, 3023–3028.
- Hénon, M., 1987, “Viscosity of a lattice gas,” Complex Syst. 1, 762–790.
- Heuveline, V., and J. Latt, 2007, “The OpenLB project: An open source and object oriented implementation of lattice Boltzmann methods,” Int. J. Mod. Phys. C 18, 627–634.
- Hickey, O. A., C. Holm, and J. Smiatek, 2014, “Lattice-Boltzmann simulations of the electrophoretic stretching of polyelectrolytes: The importance of hydrodynamic interactions,” J. Chem. Phys. 140, 164904.
- Higuera, F. J., S. Succi, and R. Benzi, 1989, “Lattice gas dynamics with enhanced collisions,” Europhys. Lett. 9, 345.
- Hille, B., et al., 2001, Ion channels of excitable membranes (Sinauer Sunderland, MA), Vol. 507.
- Hirabayashi, M., M. Ohta, D. A. Rüfenacht, and B. Chopard, 2004, “A lattice Boltzmann study of blood flow in stented aneurism,” Future Generation Computer Systems (Elsevier, New York), Vol. 20, pp. 925–934.
- Hoekstra, A. G., J. van’t Hoff, A. M. M. Artoli, and P. M. Sloot, 2003, “Lattice BGK simulations of unsteady flow in a 2D elastic tube,” in International Conference on Computational Science (Springer, New York), pp. 997–1006.
- Horbach, J., and S. Succi, 2006, “Lattice Boltzmann versus molecular dynamics simulation of nanoscale hydrodynamic flows,” Phys. Rev. Lett. 96, 224503.
- Hosni, Hykel, and Angelo Vulpiani, 2018, “Forecasting in light of big data,” Philosophy & Technology (Springer, New York), Vol. 31, pp. 557–569.
- Hsu, C. W., M. Fyta, G. Lakatos, S. Melchionna, and E. Kaxiras, 2012, “Ab initio determination of coarse-grained interactions in double-stranded DNA,” J. Chem. Phys. 137, 105102.
- Hua-Bing, L., J. Li, and Q. Bing, 2008, “Deformation of two-dimensional nonuniform-membrane red blood cells simulated by a lattice Boltzmann model,” Chin. Phys. Lett. 25, 4042.
- Janoschek, F., F. Toschi, and J. Harting, 2010, “Simplified particulate model for coarse-grained hemodynamics simulations,” Phys. Rev. E 82, 056710.
- Junk, M., A. Klar, and L.-S. Luo, 2005, “Asymptotic analysis of the lattice Boltzmann equation,” J. Comput. Phys. 210, 676–704.
- Kamerlin, S. C., S. Vicatos, A. Dryga, and A. Warshel, 2011, “Coarse-Grained (Multiscale) Simulations in Studies of Biophysical and Chemical Systems,” Annu. Rev. Phys. Chem. 62, 41–64.
- Karlin, I. V., A. Ferrante, and H. C. Öttinger, 1999, “Perfect entropy functions of the lattice Boltzmann method,” Europhys. Lett. 47, 182.
- Karlin, I. V., A. N. Gorban, S. Succi, and V. Boffi, 1998, “Maximum entropy principle for lattice kinetic equations,” Phys. Rev. Lett. 81, 6.
- Karpatne, A., W. Watkins, J. Read, and V. Kumar, 2017, “Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling,” arXiv:1710.11431.
- Keller, S. R., and R. Skalak, 1982, “Motion of a tank-treading ellipsoidal particle in a shear flow,” J. Fluid Mech. 120, 27–47.
- Ketsdever, A., and H. Struchtrup, 2016, “30th International Symposium on Rarefied Gas Dynamics: RGD 30 1786,” (IOP Publishing, Bristol, UK).
- Knowles, T. P. J., M. Vendruscolo, and C. M. Dobson, 2015, “The physical basis of protein misfolding disorders,” Phys. Today 68, No. 3, 36.
- Krause, M. J., 2010, “Fluid flow simulation and optimisation with lattice Boltzmann methods on high performance computers: Application to the human respiratory system,” Ph.D. thesis (Karlsruhe Institute of Technology).
- Krüger, T., M. Gross, D. Raabe, and F. Varnik, 2013, “Crossover from tumbling to tank-treading-like motion in dense simulated suspensions of red blood cells,” Soft Matter 9, 9008–9015.
- Krüger, T., D. Holmes, and P. V. Coveney, 2014, “Deformability-based red blood cell separation in deterministic lateral displacement devices—A simulation study,” Biomicrofluidics 8, 054114.
- Krüger, T., H. Kusumaatmaja, A. Kuzmin, O. Shardt, G. Silva, and E. M. Viggen, 2017, The Lattice Boltzmann Method: Principles and Practice (Springer, New York).
- Ladd, A. J. C., 1993, “Short-time motion of colloidal particles: Numerical simulation via a fluctuating lattice-Boltzmann equation,” Phys. Rev. Lett. 70, 1339.
- Ladd, A. J. C., 1994a, “Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation,” J. Fluid Mech. 271, 285–309.
- Ladd, A. J. C., 1994b, “Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results,” J. Fluid Mech. 271, 311–339.
- Lagrava, D., O. Malaspinas, J. Latt, and B. Chopard, 2012, “Advances in multi-domain lattice Boltzmann grid refinement,” J. Comput. Phys. 231, 4808–4822.
- Latt, J., and B. Chopard, 2006, “Lattice Boltzmann method with regularized pre-collision distribution functions,” Math. Comput. Simul. 72, 165–168.
- Leclaire, S., A. Parmigiani, O. Malaspinas, B. Chopard, and J. Latt, 2017, “Generalized three-dimensional lattice Boltzmann color-gradient method for immiscible two-phase pore-scale imbibition and drainage in porous media,” Phys. Rev. E 95, 033306.
- Ledesma-Aguilar, R., T. Sakaue, and J. M. Yeomans, 2012, “Easier sieving through narrower pores: Fluctuations and barrier crossing in flow-driven polymer translocation,” Soft Matter 8, 4306–4309.
- Lee, T., and C.-L. Lin, 2005, “A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio,” J. Comput. Phys. 206, 16–47.
- Levitt, M., and A. Warshel, 1975, “Computer simulation of protein folding,” Nature (London) 253, 694.
- Li, Z., and C. Kleinstreuer, 2011, “Airflow analysis in the alveolar region using the lattice-Boltzmann method,” Med. Biol. Eng. Comput. 49, 441–451.
- Lindorff-Larsen, K., P. Maragakis, S. Piana, M. P. Eastwood, R. O. Dror, and D. E. Shaw, 2012, “Systematic validation of protein force fields against experimental data,” PLoS One 7, e32131.
- Lintermann, A., M. Meinke, and W. Schröder, 2011, “Investigations of human nasal cavity flows based on a Lattice-Boltzmann method,” in High Performance Computing on Vector Systems 2011 (Springer, New York), pp. 143–158.
- Liu, Y., L. Moevius, X. Xu, T. Qian, J. M. Yeomans, and Z. Wang, 2014, “Pancake bouncing on superhydrophobic surfaces,” Nat. Phys. 10, 515–519.
- Luo, L.-S., 2004, “Comment on Discrete Boltzmann equation for microfluidics,” Phys. Rev. Lett. 92, 139401.
- MacMeccan, R. M., J. R. Clausen, G. P. Neitzel, and C. K. Aidun, 2009, “Simulating deformable particle suspensions using a coupled lattice-Boltzmann and finite-element method,” J. Fluid Mech. 618, 13–39.
- Marconi, U. M. B., and S. Melchionna, 2009, “Kinetic theory of correlated fluids: From dynamic density functional to Lattice Boltzmann methods,” J. Chem. Phys. 131, 014105.
- Marconi, U. M. B., and S. Melchionna, 2011a, “Dynamics of fluid mixtures in nanospaces,” J. Chem. Phys. 134, 064118.
- Marconi, U. M. B., and S. Melchionna, 2011b, “Multicomponent diffusion in nanosystems,” J. Chem. Phys. 135, 044104.
- Marconi, U. M. B., and S. Melchionna, 2012, “Charge transport in nanochannels: A molecular theory,” Langmuir 28, 13727–13740.
- Marconi, U. M. B., S. Melchionna, and I. Pagonabarraga, 2013, “Effective electrodiffusion equation for non-uniform nanochannels,” J. Chem. Phys. 138, 244107.
- Masliyah, J. H., and S. Bhattacharjee, 2006, Electrokinetic and colloid transport phenomena (John Wiley & Sons, New York).
- Matyka, M., Z. Koza, and Ł. Mirosław, 2013, “Wall orientation and shear stress in the lattice Boltzmann model,” Comput. Fluids 73, 115–123.
- Maxwell, J. C., 1878, “On Stresses in Rarefied Gases Arising from Inequalities of Temperature.,” Proc. R. Soc. London 27, 304–308.
- Mazzeo, M. D., and P. V. Coveney, 2008, “HemeLB: A high performance parallel lattice-Boltzmann code for large scale fluid flow in complex geometries,” Comput. Phys. Commun. 178, 894–914.
- McWhirter, J. L., H. Noguchi, and G. Gompper, 2009, “Flow-induced clustering and alignment of vesicles and red blood cells in microcapillaries,” Proc. Natl. Acad. Sci. U.S.A. 106, 6039–6043.
- Melchionna, S., 2011, “A Model for Red Blood Cells in Simulations of Large-scale Blood Flows,” Macromol. Theory Simul. 20, 548–561.
- Melchionna, S., and U. M. B. Marconi, 2008, “Lattice Boltzmann method for inhomogeneous fluids,” Europhys. Lett. 81, 34001.
- Melchionna, S., M. Bernaschi, M. Fyta, E. Kaxiras, and S. Succi, 2009, “Quantized biopolymer translocation through nanopores: Departure from simple scaling,” Phys. Rev. E 79, 030901.
- Melchionna, S., M. Bernaschi, S. Succi, E. Kaxiras, F. J. Rybicki, D. Mitsouras, A. U. Coskun, and C. L. Feldman, 2010, “Hydrokinetic approach to large-scale cardiovascular blood flow,” Comput. Phys. Commun. 181, 462–472.
- Melchionna, S., M. G. Fyta, E. Kaxiras, and S. Succi, 2007, “Exploring DNA translocation through a nanopore via a multiscale Lattice-Boltzmann molecular-dynamics methodology,” Int. J. Mod. Phys. C 18, 685–692.
- Melchionna, S., and U. M. B. Marconi, 2011, “Electro-osmotic flows under nanoconfinement: A self-consistent approach,” Europhys. Lett. 95, 44002.
- Melchionna, S., S. Succi, and J.-P. Hansen, 2006, “Simulation of single-file ion transport with the lattice Fokker-Planck equation,” Phys. Rev. E 73, 017701.
- Mendoza, M., B. M. Boghosian, H. J. Herrmann, and S. Succi, 2010, “Derivation of the lattice Boltzmann model for relativistic hydrodynamics,” Phys. Rev. D 82, 105008.
- Mendoza, M., S. Succi, and H. J. Herrmann, 2014, “Kinetic formulation of the Kohn-Sham equations for ab initio electronic structure calculations,” Phys. Rev. Lett. 113, 096402.
- Meng, J., and Y. Zhang, 2011, “Gauss-Hermite quadratures and accuracy of lattice Boltzmann models for nonequilibrium gas flows,” Phys. Rev. E 83, 036704.
- Miki, T., X. Wang, T. Aoki, Y. Imai, T. Ishikawa, K. Takase, and T. Yamaguchi, 2012, “Patient-specific modelling of pulmonary airflow using GPU cluster for the application in medical practice,” Comput. Methods Biomech. Biomed. Eng. 15, 771–778.
- Miocchi, P., P. Derreumaux, F. Sterpone, and S. Melchionna, 2019, “Mesoscale biosimulations within a unified framework: From proteins to plasmids,” Mol. Simul., 1–12.
- Montessori, A., G. Falcucci, P. Prestininzi, M. La Rocca, and S. Succi, 2014, “Regularized lattice Bhatnagar-Gross-Krook model for two-and three-dimensional cavity flow simulations,” Phys. Rev. E 89, 053317.
- Montessori, A., P. Prestininzi, M. La Rocca, and S. Succi, 2017, “Entropic lattice pseudo-potentials for multiphase flow simulations at high Weber and Reynolds numbers,” Phys. Fluids 29, 092103.
- Montessori, A., and G. Falcucci, 2018, Lattice Boltzmann Modeling of Complex Flows for Engineering Applications (Morgan & Claypool Publishers, San Rafael, CA).
- Montessori, A., M. Lauricella, M. La Rocca, S. Succi, E. Stolovicki, R. Ziblat, and D. Weitz, 2018, “Regularized lattice Boltzmann multicomponent models for low capillary and Reynolds microfluidics flows,” Comput. Fluids 167, 33–39.
- Montessori, A., M. Lauricella, and S. Succi, 2018, “Mesoscale modelling of soft flowing crystals,” arXiv:1807.05415.
- Montessori, A., M. Lauricella, S. Succi, E. Stolovicki, and D. Weitz, 2018, “Elucidating the mechanism of step emulsification,” Phys. Rev. Fluids 3, 072202.
- Moroni, D., B. Rotenberg, J.-P. Hansen, S. Succi, and S. Melchionna, 2006, “Solving the Fokker-Planck kinetic equation on a lattice,” Phys. Rev. E 73, 066707.
- Munn, L. L., and M. M. Dupin, 2008, “Blood cell interactions and segregation in flow,” Ann. Biomed. Eng. 36, 534–544.
- Nasica-Labouze, Jessica, et al., 2015, “Amyloid -protein and Alzheimer’s Disease: When Computer Simulations Complement Experimental Studies,” Chem. Rev. 115, 3518.
- Nie, X., X. Shan, and H. Chen, 2008, “Thermal lattice Boltzmann model for gases with internal degrees of freedom,” Phys. Rev. E 77, 035701.
- Noble, D., 2008, The music of life: Biology beyond genes (Oxford University Press, New York).
- Noble, D., 2016, Dance to the Tune of Life: Biological Relativity (Cambridge University Press, Cambridge, England).
- Noguchi, H., and G. Gompper, 2005, “Shape transitions of fluid vesicles and red blood cells in capillary flows,” Proc. Natl. Acad. Sci. U.S.A. 102, 14159–14164.
- Noid, W. G., J.-W. Chu, G. S. Ayton, V. Krishna, S. Izvekov, G. A. Voth, A. Das, and H. C. Andersen, 2008, “The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models,” J. Chem. Phys. 128, 244114.
- Omori, T., Y. Imai, K. Kikuchi, T. Ishikawa, and T. Yamaguchi, 2015, “Hemodynamics in the microcirculation and in microfluidics,” Ann. Biomed. Eng. 43, 238–257.
- Ouared, R., and B. Chopard, 2005, “Lattice Boltzmann simulations of blood flow: Non-Newtonian rheology and clotting processes,” J. Stat. Phys. 121, 209–221.
- Ouared, R., B. Chopard, B. Stahl, D. A. Rüfenacht, H. Yilmaz, and G. Courbebaisse, 2008, “Thrombosis modeling in intracranial aneurysms: A lattice Boltzmann numerical algorithm,” Comput. Phys. Commun. 179, 128–131.
- Papoian, G. A., J. Ulander, M. P. Eastwood, Z. Luthey-Schulten, and P. G. Wolynes, 2004, “Water in protein structure prediction,” Proc. Natl. Acad. Sci. U.S.A. 101, 3352–3357.
- Patronis, A., R. A. Richardson, S. Schmieschek, B. J. Wylie, R. W. Nash, and P. V. Coveney, 2018, “Modelling Patient-Specific Magnetic Drug Targeting within the Intracranial Vasculature,” Front. Physiol. 9, 331.
- Pelliccioni, O., M. Cerrolaza, and M. Herrera, 2007, “Lattice Boltzmann dynamic simulation of a mechanical heart valve device,” Math. Comput. Simul. 75, 1–14.
- Peskin, C. S., 2002, “The immersed boundary method,” Acta Numer. 11, 479–517.
- Ponce Dawson, S., S. Chen, and G. D. Doolen, 1993, “Lattice Boltzmann computations for reaction-diffusion equations,” J. Chem. Phys. 98, 1514–1523.
- Ponder, J. W., and D. A. Case, 2003, “Force fields for protein simulations,” Adv. Protein Chem. 66, 27–85.
- Pontrelli, G., I. Halliday, S. Melchionna, T. J. Spencer, and S. Succi, 2012, “The Lattice Boltzmann Method and Multiscale Hemodynamics: Recent Advances and Perspectives,” IFAC Proceedings Volumes (Elsevier, New York), Vol. 45, pp. 30–39.
- Pontrelli, G., I. Halliday, S. Melchionna, T. J. Spencer, and S. Succi, 2014, “Lattice Boltzmann method as a computational framework for multiscale haemodynamics,” Mathematical and Computer Modelling of Dynamical Systems 20, 470–490.
- Pontrelli, G., I. Halliday, T. J. Spencer, C. S. König, and M. W. Collins, 2015, “Modelling the glycocalyx–endothelium–erythrocyte interaction in the microcirculation: A computational study,” Comput. Methods Biomech. Biomed. Eng. 18, 351–361.
- Praprotnik, M., L. D. Site, and K. Kremer, 2008, “Multiscale simulation of soft matter: From scale bridging to adaptive resolution,” Annu. Rev. Phys. Chem. 59, 545–571.
- Prigogine, I., 2017, Non-equilibrium statistical mechanics (Courier Dover Publications, New York).
- Purcell, E. M., 1977, “Life at low Reynolds number,” Am. J. Phys. 45, 3–11.
- Qian, Y. H., D. d’Humières, and P. Lallemand, 1992, “Lattice BGK models for Navier-Stokes equation,” Europhys. Lett. 17, 479.
- Raissi, M., and G. E. Karniadakis, 2018, “Hidden physics models: Machine learning of nonlinear partial differential equations,” J. Comput. Phys. 357, 125–141.
- Reasor, D. A., J. R. Clausen, and C. K. Aidun, 2012, “Coupling the lattice-Boltzmann and spectrin-link methods for the direct numerical simulation of cellular blood flow,” Int. J. Numer. Methods Fluids 68, 767–781.
- Reboux, S., F. Capuani, N. González-Segredo, and D. Frenkel, 2006, “Lattice-Boltzmann simulations of ionic current modulation by DNA translocation,” J. Chem. Theory Comput. 2, 495–503.
- Rivet, J.-P., and J. P. Boon, 2005, Lattice gas hydrodynamics (Cambridge University Press, Cambridge, England), Vol. 11.
- Rossinelli, D., et al., 2015, “The in-silico lab-on-a-chip: Petascale and high-throughput simulations of microfluidics at cell resolution,” in Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (ACM, New York), p. 2.
- Rybicki, Frank J., et al., 2009, “Prediction of coronary artery plaque progression and potential rupture from 320-detector row prospectively ECG-gated single heart beat CT angiography: Lattice Boltzmann evaluation of endothelial shear stress,” Int. J. Cardiovascular Imaging 25, 289–299.
- Sbragaglia, M., H. Chen, X. Shan, and S. Succi, 2009, “Continuum free-energy formulation for a class of lattice Boltzmann multiphase models,” Europhys. Lett. 86, 24005.
- Schulz, M., M. Krafczyk, J. Tölke, and E. Rank, 2002, “Parallelization strategies and efficiency of CFD computations in complex geometries using Lattice Boltzmann methods on high-performance computers,” High performance scientific and engineering computing (Springer, New York), Vol. 21, pp. 115–122.
- Sega, M., M. Sbragaglia, S. S. Kantorovich, and A. O. Ivanov, 2013, “Mesoscale structures at complex fluid–fluid interfaces: A novel lattice Boltzmann/molecular dynamics coupling,” Soft Matter 9, 10092–10107.
- Shan, X., and H. Chen, 1993, “Lattice Boltzmann model for simulating flows with multiple phases and components,” Phys. Rev. E 47, 1815.
- Shan, X., and H. Chen, 1994, “Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation,” Phys. Rev. E 49, 2941.
- Shan, X., X.-F. Yuan, and H. Chen, 2006, “Kinetic theory representation of hydrodynamics: A way beyond the Navier–Stokes equation,” J. Fluid Mech. 550, 413–441.
- Shaw, D. E., et al., 2014, “Anton 2: Raising the Bar for Performance and Programmability in a Special-Purpose Molecular Dynamics Supercomputer,” in SC14: International Conference for High Performance Computing, Networking, Storage and Analysis (ACM, New York), pp. 41–53.
- Shaw, D. E., et al., 2008, “Anton, a special-purpose machine for molecular dynamics simulation,” Commun. ACM 51, 91–97.
- Shi, X., G. Lin, J. Zou, and D. A. Fedosov, 2013, “A lattice Boltzmann fictitious domain method for modeling red blood cell deformation and multiple-cell hydrodynamic interactions in flow,” Int. J. Numer. Methods Fluids 72, 895–911.
- Sofonea, V., A. Lamura, G. Gonnella, and A. Cristea, 2004, “Finite-difference lattice Boltzmann model with flux limiters for liquid-vapor systems,” Phys. Rev. E 70, 046702.
- Sterpone, F., et al., 2014, “The OPEP protein model: From single molecules, amyloid formation, crowding and hydrodynamics to DNA/RNA systems,” Chem. Soc. Rev. 43, 4871–4893.
- Storm, A. J., C. Storm, J. Chen, H. Zandbergen, J.-F. Joanny, and C. Dekker, 2005, “Fast DNA translocation through a solid-state nanopore,” Nano Lett. 5, 1193–1197.
- Struchtrup, H., and M. Torrilhon, 2003, “Regularization of Grad’s 13 moment equations: Derivation and linear analysis,” Phys. Fluids 15, 2668–2680.
- Struchtrup, H., and M. Torrilhon, 2007, “H theorem, regularization, and boundary conditions for linearized 13 moment equations,” Phys. Rev. Lett. 99, 014502.
- Succi, S., 2001, The lattice Boltzmann equation: For fluid dynamics and beyond (Oxford University Press, New York).
- Succi, S., 2002a, “Lattice Boltzmann equation for relativistic quantum mechanics,” Phil. Trans. R. Soc. A 360, 429–436.
- Succi, S., 2002b, “Mesoscopic modeling of slip motion at fluid-solid interfaces with heterogeneous catalysis,” Phys. Rev. Lett. 89, 064502.
- Succi, S., 2018, The lattice Boltzmann equation for complex states of flowing matter (Oxford University Press, New York).
- Succi, S., G. Amati, M. Bernaschi, G. Falcucci, M. Lauricella, and A. Montessori, 2019, “Towards Exascale Lattice Boltzmann computing,” Comput. Fluids 181, 107–115.
- Succi, S., and P. V. Coveney, 2018, “Big Data: The End of the Scientific Method?,” arXiv:1807.09515.
- Succi, S., I. V. Karlin, and H. Chen, 2002, “Colloquium: Role of the H theorem in lattice Boltzmann hydrodynamic simulations,” Rev. Mod. Phys. 74, 1203.
- Succi, S., N. Moradi, A. Greiner, and S. Melchionna, 2014, “Lattice Boltzmann modeling of water-like fluids,” Front. Phys. 2, 22.
- Sui, Y., Y. T. Chew, and H. T. Low, 2007, “A lattice Boltzmann study on the large deformation of red blood cells in shear flow,” Int. J. Mod. Phys. C 18, 993–1011.
- Sui, Y., Y. T. Chew, P. Roy, Y. P. Cheng, and H. T. Low, 2008, “Dynamic motion of red blood cells in simple shear flow,” Phys. Fluids 20, 112106.
- Sun, C., C. Migliorini, and L. L. Munn, 2003, “Red blood cells initiate leukocyte rolling in postcapillary expansions: A lattice Boltzmann analysis,” Biophys. J. 85, 208–222.
- Sun, C., and L. L. Munn, 2006, “Influence of erythrocyte aggregation on leukocyte margination in postcapillary expansions: A lattice Boltzmann analysis,” Physica A (Amsterdam) 362, 191–196.
- Swift, M. R., E. Orlandini, W. R. Osborn, and J. M. Yeomans, 1996, “Lattice Boltzmann simulations of liquid-gas and binary fluid systems,” Phys. Rev. E 54, 5041.
- Takahashi, K., S. N. V. Arjunan, and M. Tomita, 2005, “Space in systems biology of signaling pathways–towards intracellular molecular crowding in silico,” FEBS Lett. 579, 1783–1788.
- Tamagawa, M., H. Kaneda, M. Hiramoto, and S. Nagahama, 2009, “Simulation of thrombus formation in shear flows using lattice Boltzmann method,” Artificial Organs 33, 604–610.
- Timr, S., S. Melchionna, P. Derreumaux, and F. Sterpone, 2019, “Multi-Scale Simulations Yield Insight into Protein Diffusion and Stability in Crowded Environments,” Biophys. J. 116, 38a.
- Tiribocchi, A., M. Lauricella, S. Melchionna, A. Montessori, and S. Succi, 2019, “Curvature dynamics and long-range effects on fluid-fluid interfaces with colloids,” Soft Matter (in press).
- Tomczak, T., and R. G. Szafran, 2017, “Sparse geometries handling in lattice-Boltzmann method implementation for graphic processors,” arXiv:1703.08015.
- Voit, E. O., 2013, “Biochemical systems theory: A review,” ISRN Biomathematics (Hindawi Publishing Corporation, London, UK), Vol. 2013.
- Wang, M., and Q. Kang, 2010, “Modeling electrokinetic flows in microchannels using coupled lattice Boltzmann methods,” J. Comput. Phys. 229, 728–744.
- Wöhrwag, M., C. Semprebon, A. M. Moqaddam, I. Karlin, and H. Kusumaatmaja, 2018, “Ternary Free-Energy Entropic Lattice Boltzmann Model with a High Density Ratio,” Phys. Rev. Lett. 120, 234501.
- Wu, J., and C. K. Aidun, 2010, “Simulating 3D deformable particle suspensions using lattice Boltzmann method with discrete external boundary force,” Int. J. Numer. Methods Fluids 62, 765–783.
- Xiong, W., and J. Zhang, 2012, “Two-dimensional lattice Boltzmann study of red blood cell motion through microvascular bifurcation: Cell deformability and suspending viscosity effects,” Biomech. Model. Mechanobiol. 11, 575–583.
- Xu, Y.-Q., F.-B. Tian, and Y.-L. Deng, 2013, “An efficient red blood cell model in the frame of IB-LBM and its application,” Int. J. Biomathematics 06, 1250061.
- Yun, B. M., L. P. Dasi, C. K. Aidun, and A. P. Yoganathan, 2014, “Computational modelling of flow through prosthetic heart valves using the entropic lattice-Boltzmann method,” J. Fluid Mech. 743, 170–201.
- Zhang, R., X. Shan, and H. Chen, 2006, “Efficient kinetic method for fluid simulation beyond the Navier-Stokes equation,” Phys. Rev. E 74, 046703.
- Zhou, H. X., G. Rivas, and A. P. Minton, 2008, “Macromolecular crowding and confinement: Biochemical, biophysical, and potential physiological consequences.,” Annu. Rev. Biophys. 37, 375–397.
- Zou, Q., and X. He, 1997, “On pressure and velocity boundary conditions for the lattice Boltzmann BGK model,” Phys. Fluids 9, 1591–1598.