Yue Shi

Pengyu Ren

Michael Schnieders

Jean-Philip Piquemal

Polarizable Force Fields for Biomolecular Modeling

Keywords:

 or use "machine learning methods" 33 also exist, but incur higher computational costs. Discussions of the advantages and disadvantages of each model and their applications will be presented in the following sections.

Compared to fixed charge models, the polarizable models are still in a relatively early stage. Only in the past decade or so has there been a systematic effort to develop general polarizable force fields for molecular modeling. A number of reviews have been published to discuss various aspects of polarizable force fields and their development. 9, 34- 40 Here, we focus on the recent development and applications of different polarizable force fields. We begin with a brief introduction to the basic principles and formulae underlying alternative models. Next, the recent progress of several well-developed polarizable force fields is reviewed. Finally, applications of polarizable models to a range of molecular systems, including water and other small molecules, ion solvation, peptides, proteins and lipid systems are presented.

Modeling Polarization Effects

1.1.

Introduction

Molecular mechanics based modeling has been widely used in the study of chemical and biological systems. The classical potential energy functions and their parameters are referred to as force fields. Empirical force fields for biomolecules emerged in the early 1970's, [START_REF] Warshel | Theoretical Studies of Enzymic Reactions -Dielectric, Electrostatic and Steric Stabilization of Carbonium-Ion in Reaction of Lysozyme[END_REF] followed by the first molecular dynamics simulations of the bovine pancreatic trypsin inhibitors (BPTI). [START_REF] Mccammon | Dynamics of Folded Proteins[END_REF][START_REF] Spackman | The Use of the Promolecular Charge Density to Approximate the Penetration Contribution to Intermolecular Electrostatic Energies[END_REF][START_REF] Nachtigallova | Assigning the Nh Stretches of the Guanine Tautomers Using Adiabatic Separation: CCSD(T) Benchmark Calculations[END_REF] Over the past 30 years, a great number of empirical molecular mechanics force fields, including AMBER, [START_REF] Cornell | A 2nd Generation Force-Field for the Simulation of Proteins, Nucleic-Acids, and Organic-Molecules[END_REF] CHARMM, [START_REF] Mackerell | All-Atom Empirical Potential for Molecular Modeling and Dynamics Studies of Proteins[END_REF] GROMOS, [START_REF] Valdes | Benchmark Database on Isolated Small Peptides Containing an Aromatic Side Chain: Comparison between Wave Function and Density Functional Theory Methods and Empirical Force Field[END_REF] OPLS, [START_REF] Jorgensen | Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids[END_REF] and many others, have been developed. These force fields share similar functional forms, including valence interactions represented by harmonic oscillators, point dispersionrepulsion for van der Waals (vdW) interactions, and an electrostatic contribution based on fixed atomic partial charges. This generation of molecular mechanics force fields has been widely used in the study of molecular structures, dynamics, interactions, design and engineering. We refer interested readers to some recent reviews for detailed discussions. [START_REF] Ponder | Force Fields for Protein Simulations[END_REF][START_REF] Rezac | Quantum Chemical Benchmark Energy and Geometry Database for Molecular Clusters and Complex Molecular Systems (Www.Begdb.Com): A Users Manual and Examples[END_REF] Although the fixed charge force fields enjoyed great success in many areas, there remains much room for improvement. In fixed charge based electrostatic models, the atomic partial charges are meant to be "pre-polarized" for condensed phases in an averaged fashion, typically achieved by the fortuitous overestimation of electrostatic charges by low-level ab initio quantum mechanics. Such models thus lack the ability to describe the variation in electrostatics due to many-body polarization effects, which have been shown to be a significant component of intermolecular forces. [START_REF] Rezac | Quantum Chemical Benchmark Energy and Geometry Database for Molecular Clusters and Complex Molecular Systems (Www.Begdb.Com): A Users Manual and Examples[END_REF][START_REF] Rezac | S66: A Well-Balanced Database of Benchmark Interaction Energies Relevant to Biomolecular Structures[END_REF][START_REF] Berka | Representative Amino Acid Side Chain Interactions in Proteins. A Comparison of Highly Accurate Correlated Ab Initio Quantum Chemical and Empirical Potential Procedures[END_REF] With the rapid growth of computational resources, there has been increasing effort to explicitly incorporate manybody induction into molecular mechanics to improve the accuracy of molecular modeling.

To describe electrostatic interactions involving polarization, we consider a system consisting of a collection of charge distribution sites located at lone-pair positions, atomic centers and/or molecular centers, depending on the resolution of the model. The total charge distribution at site i is the sum of permanent and induced charge [1] where M represents the charge distribution. This distribution can be a simple point charge, a point multipole expansion with charge, dipole, quadrupole and/or higher order moments, or a continuous charge distribution. While the principles described below are not limited to any particular representation of charge distribution, we will use point multipoles for convenience.

The electrostatic interaction energy between two charge sites i and j is given by [2] where T is the interaction operator and is a function of the distance between i and j. In the case of point charge interactions, T is simply 1/r. The work (positive energy) needed to polarize a charge distribution also has a quadratic dependence on the induced charge distribution: [3] where α is the polarizability of site i that includes all orders of polarizability including dipole polarizability. [START_REF] Applequist | An Atom Dipole Interaction Model for Molecular Polarizability. Application to Polyatomic Molecules and Determination of Atom Polarizabilities[END_REF] Although α is generally treated as an isotropic quantity, as in the quantum mechanical calculations. [START_REF] Le Sueur | Practical Schemes for Distributed Polarizabilities[END_REF][START_REF] Garmer | Transferability of Molecular Distributed Polarizabilities from a Simple Localized Orbital Based Method[END_REF] The total electrostatic energy is [4] The values of the induced moments minimize the total energy, by satisfying [5] As a result [6] Equation [6] can be solved iteratively to obtain the induced dipoles. The self-consistent calculation is computationally expensive; however it can be accelerated with predictors and non-stationary iterative methods. [START_REF] Wang | Fast Evaluation of Polarizable Forces[END_REF]

Substituting

from Eq [5] into Eq [6], the final electrostatic energy becomes [7] where the first term is the permanent electrostatic energy and the second term is the polarization energy.

Classic Drude Oscillators

In the Drude oscillator model, the polarization effect is described by a point charge (the Drude oscillator) attached to each non-hydrogen atom via a harmonic spring. The point charge can move relative to the attachment site in response to the electrostatic environment. The electrostatic energy is the sum of the pairwise interactions between atomic charges and the partial charge of the Drude particles , [8] where N D and N are the number of Drude particles and non-hydrogen atoms, q D and q C are the charges on the Drude particle and its parent atom, respectively, r D and r C are their respective positions, and k D is the force constant of the harmonic spring between the Drude oscillator and its parent atom. The last term in Equation [8] accounts for the cost of polarizing the Drude particles.

The atomic polarizability (α) is a function of both the partial charge on the Drude particle and the force constant of the spring [9] Both the induced-dipole and Drude oscillator approaches benefit from short-range Thole damping to avoid a polarization catastrophe and to produce an anisotropic molecular polarization response. 45

Fluctuating Charges

The formalism of the fluctuating charge model is based on the charge equilibration (CHEQ) method, [START_REF] Truchon | Accurate Molecular Polarizabilities Based on Continuum Electrostatics[END_REF] in which the chemical potential is equilibrated via the redistribution of charge density. The charge-dependent energy for a system of M molecules containing N i atoms per molecule is expressed as (10) where Q i is the partial charge on atomic site i. The χ describes the atomic electronegativity controlling the directionality of electron flow, and J is the atomic hardness that represents the resistance to electron flow to or from the atom. These parameters are optimized to reproduce molecular dipoles and the molecular polarization response. The charge degrees of freedom are typically propagated via an extended Lagrangian formulation: 47 [11] where the first two terms represent the nuclear and charge kinetic energies, the third term is the potential energy, and the fourth term is the molecular charge neutrality constraint enforced on each molecule i via a Lagrange multiplier λ i . The extended Lagrangian approach can also be applied to the induced dipole and Drude oscillator models described earlier. While the extended Lagrangian seems to be more efficient than the iterative method, fictitious masses and smaller time-steps are required to minimize the coupling between the polarization and atomic degrees of freedom, which can never be completely eliminated. [START_REF] Wang | Fast Evaluation of Polarizable Forces[END_REF] A few general force fields have been developed based on these formulas to explicitly treat the polarization effect. We now discuss development highlights for some of the representative force fields.

Recent Developments

AMOEBA

The AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) force field, developed by Ponder, Ren and co-workers, [START_REF] Ren | Polarizable Atomic Multipole Water Model for Molecular Mechanics Simulation[END_REF][START_REF] Ren | Consistent Treatment of Inter-and Intramolecular Polarization in Molecular Mechanics Calculations[END_REF][START_REF] Ponder | Current Status of the AMOEBA Polarizable Force Field[END_REF] utilizes atomic multipoles to represent permanent electrostatics and induced atomic dipoles for many-body polarization. The valence interactions include bond, angle, torsion and out-of-plane contributions using typical molecular mechanics functional forms. The van der Waals interaction is described by a buffered-14-7 function. The atomic multipole moments consist of charge, dipole and quadrupole moments, which are derived from ab initio quantum mechanical calculations using procedures such as Stone's Distributed Multipole Analysis (DMA). [START_REF] Stone | Distributed Multipole Analysis, or How to Describe a Molecular Charge Distribution[END_REF][START_REF] Stone | Distributed Multipole Analysis: Methods and Applications[END_REF][START_REF] Stone | Distributed Multipole Analysis: Stability for Large Basis Sets[END_REF] The higher order moments make possible anisotropic representations of the electrostatic potential outside atoms and molecules. The polarization effect is explicitly taken into account via atomic dipole induction. The combination of permanent atomic multipoles and induced dipoles enables AMOEBA to capture electrostatic interactions in both gas and condensed phase accurately. The vdW parameters of AMOEBA are optimized simultaneously against both ab initio gas-phase data and condensed-phase experimental properties.

In the past decade, AMOEBA has been applied to the study of water, [START_REF] Ren | Polarizable Atomic Multipole Water Model for Molecular Mechanics Simulation[END_REF] monovalent and divalent ions, [START_REF] Grossfield | Ion Solvation Thermodynamics from Simulation with a Polarizable Force Field[END_REF][START_REF] Jiao | Simulation of Ca 2+ and Mg 2+ Solvation Using Polarizable Atomic Multipole Potential[END_REF][START_REF] Wu | Polarizable Molecular Dynamics Simulation of Zn(II) in Water Using the AMOEBA Force Field[END_REF] small molecules, [START_REF] Ren | Polarizable Atomic Multipole-Based Molecular Mechanics for Organic Molecules[END_REF][START_REF] Shi | Multipole Electrostatics in Hydration Free Energy Calculations[END_REF] peptides [START_REF] Ren | Consistent Treatment of Inter-and Intramolecular Polarization in Molecular Mechanics Calculations[END_REF][START_REF] Jiang | Assessing the Performance of Popular Quantum Mechanics and Molecular Mechanics Methods and Revealing the Sequence-Dependent Energetic Features Using 100 Tetrapeptide Models[END_REF] and proteins. [START_REF] Jiao | Calculation of Protein-Ligand Binding Free Energy by Using a Polarizable Potential[END_REF][START_REF] Zhang | Modeling Structural Coordination and Ligand Binding in Zinc Proteins with a Polarizable Potential[END_REF][START_REF] Shi | Probing the Effect of Conformational Constraint on Phosphorylated Ligand Binding to an SH2 Domain Using Polarizable Force Field Simulations[END_REF] AMOEBA demonstrated that a polarizable force field is able to perform well in both gas and solution phases with a single set of parameters. In addition, AMOEBA is the first general-purpose polarizable force field utilized in molecular dynamics simulations of protein-ligand binding and calculation of absolute and relative binding free energies. [START_REF] Zhang | Modeling Structural Coordination and Ligand Binding in Zinc Proteins with a Polarizable Potential[END_REF][START_REF] Shi | Probing the Effect of Conformational Constraint on Phosphorylated Ligand Binding to an SH2 Domain Using Polarizable Force Field Simulations[END_REF][START_REF] Jiang | Free Energy Perturbation Hamiltonian Replica-Exchange Molecular Dynamics (FEP/H-REMD) for Absolute Ligand Binding Free Energy Calculations[END_REF][START_REF] Jiao | Trypsin-Ligand Binding Free Energies from Explicit and Implicit Solvent Simulations with Polarizable Potential[END_REF][START_REF] Shi | Trypsin-Ligand Binding Free Energy Calculation with AMOEBA[END_REF] The computed binding free energies between trypsin and benzamidine derivatives suggests significant non-additive electrostatic interactions as the ligand desolvates from water and enters the protein pocket (see Section 4.4 for further discussion). AMOEBA has recently been extended to biomolecular X-ray crystallography refinement [START_REF] Schnieders | Polarizable Atomic Multipole X-Ray Refinement: Particle Mesh Ewald Electrostatics for Macromolecular Crystals[END_REF][START_REF] Schnieders | Polarizable Atomic Multipole X-Ray Refinement: Application to Peptide Crystals[END_REF] , and consistently successful prediction of the structure, thermodynamic stability and solubility of organic crystals 65 are encouraging.

AMOEBA has been implemented in several widely used software packages including TINKER, [START_REF] Ponder | Tinker: Software Tools for Molecular Design Washington University[END_REF] OpenMM, [START_REF] Friedrichs | Accelerating Molecular Dynamic Simulation on Graphics Processing Units[END_REF] Amber, [START_REF] Case | The AMBER Biomolecular Simulation Programs[END_REF] and Force Field X. [START_REF] Schnieders | Force Field X Open Source, Platform Independent Modules for Molecular Biophsyics Simulations[END_REF] The AMOEBA polarizable force field was first implemented within the FORTRAN-based TINKER software package [START_REF] Ponder | Tinker: Software Tools for Molecular Design[END_REF] using Particle Mesh Ewald (PME) for long-range electrostatics. Implementation of the polarizable-multipole Poisson-Boltzmann, [START_REF] Schnieders | Polarizable Atomic Multipole Solutes in a Poisson-Boltzmann Continuum[END_REF] which depends on the Adaptive Poisson-Boltzmann Solver (APBS), [START_REF] Baker | Electrostatics of Nanosystems: Application to Microtubules and the Ribosome[END_REF] and generalized Kirkwood 73 continuum electrostatics models also exist in TINKER, which is now being parallelized using OpenMP. The algorithms in TINKER are also available from within CHARMM using the MSCALE interface. [START_REF] Brooks | CHARMM: The Biomolecular Simulation Program[END_REF][START_REF] Woodcock | MSCALE: A General Utility for Multiscale Modeling[END_REF] Alternative FORTRAN implementations of AMOEBA using PME are available in the Sander and PMEMD molecular dynamics engines of AMBER, [START_REF] Case | The AMBER Biomolecular Simulation Programs[END_REF] with the latter parallelized using MPI. The PME treatment of AMOEBA electrostatics has recently been extended within the Java Runtime Environment (JRE) program Force Field X by incorporating explicit support for crystal space group symmetry, [START_REF] Schnieders | Polarizable Atomic Multipole X-Ray Refinement: Particle Mesh Ewald Electrostatics for Macromolecular Crystals[END_REF] parallelizing for heterogeneous computer hardware environments [START_REF] Schnieders | Polarizable Atomic Multipole X-Ray Refinement: Particle Mesh Ewald Electrostatics for Macromolecular Crystals[END_REF] and supporting advanced free energy methods such as the Orthogonal Space Random Walk (OSRW) strategy. [START_REF] Schnieders | The Structure, Thermodynamics and Solubility of Organic Crystals from Simulation with a Polarizable Force Field[END_REF][START_REF] Zheng | Random Walk in Orthogonal Space to Achieve Efficient Free-Energy Simulation of Complex Systems[END_REF] These advancements are critical for applications such as AMOEBA-assisted biomolecular X-ray refinement, [START_REF] Schnieders | Polarizable Atomic Multipole X-Ray Refinement: Particle Mesh Ewald Electrostatics for Macromolecular Crystals[END_REF][START_REF] Fenn | Polarizable Atomic Multipole X-Ray Refinement: Weighting Schemes for Macromolecular Diffraction[END_REF] efficient computation of protein-ligand binding affinity, [START_REF] Jiao | Calculation of Protein-Ligand Binding Free Energy by Using a Polarizable Potential[END_REF][START_REF] Jiao | Trypsin-Ligand Binding Free Energies from Explicit and Implicit Solvent Simulations with Polarizable Potential[END_REF] and prediction of the structure, stability and solubility of organic crystals. [START_REF] Schnieders | The Structure, Thermodynamics and Solubility of Organic Crystals from Simulation with a Polarizable Force Field[END_REF] Finally, the OpenMM software is working toward a general implementation of AMOEBA using the CUDA GPU programming language. 78

SIBFA

The SIBFA (Sum of Interactions Between Fragments Ab initio computed) force field for small molecules and flexible proteins, developed by Gresh, Piquemal et. al, [START_REF] Gresh | Theoretical Studies of Molecular Conformation -Derivation of an Additive Procedure for the Computation of Intramolecular Interaction Energies -Comparison with ab Initio SCF Computations[END_REF][START_REF] Gresh | Energetics of Zn 2+ Binding to a Series of Biologically Relevant Ligands -A Molecular Mechanics Investigation Grounded on Ab-Initio Self-Consistent-Field Supermolecular Computations[END_REF][START_REF] Piquemal | Inclusion of the Ligand Field Contribution in a Polarizable Molecular Mechanics: SIBFA-LF[END_REF][START_REF] Piquemal | Toward a Separate Reproduction of the Contributions to the Hartree-Fock and DFT Intermolecular Interaction Energies by Polarizable Molecular Mechanics with the SIBFA Potential[END_REF][START_REF] Gresh | Anisotropic, Polarizable Molecular Mechanics Studies of Inter-and Intramolecular Interactions and Ligand-Macromolecule Complexes. A Bottom-up Strategy[END_REF] is one of the most sophisticated polarizable force fields because it incorporates polarization, electrostatic penetration [START_REF] Piquemal | Improved Formulas for the Calculation of the Electrostatic Contribution to the Intermolecular Interaction[END_REF] and charge-transfer effects. [START_REF] Gresh | Intermolecular Interactions -Elaboration on an Additive Procedure Including an Explicit Charge-Transfer Contribution[END_REF] The polarization is treated with an induced dipole model, in which the distributed anisotropic polarizability tensors [START_REF] Garmer | Transferability of Molecular Distributed Polarizabilities from a Simple Localized Orbital Based Method[END_REF] SIBFA has been validated on a wide range of molecular systems from water clusters [START_REF] Gresh | Inter-and Intramolecular Interactions. Inception and Refinements of the SIBFA, Molecular Mechanics (SMM) Procedure, A Separable, Polarizable Methodology Grounded on Ab Initio SCF/MP2 Computations. Examples of Applications to Molecular Recognition Problems[END_REF] to large complexes like metalloenzymes encompassing Zn(II). [START_REF] Antony | Complexes of Thiomandelate and Captopril Mercaptocarboxylate Inhibitors to Metallo-Beta-Lactamase by Polarizable Molecular Mechanics. Validation on Model Binding Sites by Quantum Chemistry[END_REF][START_REF] Roux | Binding of 5-Phospho-D-Arabinonohydroxamate and 5-Phospho-D-Arabinonate Inhibitors to Zinc Phosphomannose Isomerase from Candida Albicans Studied by Polarizable Molecular Mechanics and Quantum Mechanics[END_REF][START_REF] Jenkins | Specificity of Acylf Transfer from 2-Mercaptobenzamide Thioesters to the HIV-1 Nucleocapsid Protein[END_REF][START_REF] Foret | Synthesis and Evaluation of Non-Hydrolyzable D-Mannose 6-Phosphate Surrogates Reveal 6-Deoxy-6-Dicarboxymethyl-D-Mannose as a New Strong Inhibitor of Phosphomannose Isomerases[END_REF][START_REF] Gresh | Analysis of the Interactions Taking Place in the Recognition Site of a Bimetallic Mg(II)-Zn(II) Enzyme, Isopentenyl Diphosphate Isomerase. A Parallel Quantum-Chemical and Polarizable Molecular Mechanics Study[END_REF][START_REF] Roux | The Reaction Mechanism of Type I Phosphomannose Isomerases: New Information from Inhibition and Polarizable Molecular Mechanics Studies[END_REF] It has been used to investigate molecular recognition problems including the binding of nucleic acids to metal ions, [START_REF] Ledecq | Modeling of Copper(II) Complexes with the SIBFA Polarizable Molecular Mechanics Procedure. Application to a New Class of HIV-1 Protease Inhibitors[END_REF][START_REF] Marjolin | Toward Accurate Solvation Dynamics of Lanthanides and Actinides in Water Using Polarizable Force Fields: From Gas-Phase Energetics to Hydration Free Energies[END_REF][START_REF] Rogalewicz | Interaction of Neutral and Zwitterionic Glycine with Zn 2+ in Gas Phase: ab Initio and SIBFA Molecular Mechanics Calculations[END_REF] the prediction of oligopeptide conformations, [START_REF] Gresh | Inter-and Intramolecular Interactions. Inception and Refinements of the SIBFA, Molecular Mechanics (SMM) Procedure, A Separable, Polarizable Methodology Grounded on Ab Initio SCF/MP2 Computations. Examples of Applications to Molecular Recognition Problems[END_REF][START_REF] Gresh | Conformational Properties of a Model Alanyl Dipeptide and of Alanine-Derived Oligopeptides: Effects of Solvation in Water and in Organic Solvents -A Combined SIBFA/Continuum Reaction Field, ab Initio Self-Consistent Field, and Density Functional Theory Investigation[END_REF] and for ligand-protein binding. [START_REF] Graf | Structure and Dynamics of the Homologous Series of Alanine Peptides: A Joint Molecular Dynamics/NMR Study[END_REF] Most of the SIBFA calculations reproduced closely the quantum chemistry results, including both the interaction energy and the decomposed energy terms. At the same time, electrostatic parameters are demonstrated to be transferable between similar molecules.

,A Gaussian based electrostatic model (GEM) has been explored as an alternative to distributed point multipole electrostatic representation. [START_REF] Cisneros | Design of Next Generation Force Fields from ab Initio Computations: Beyond Point Charges Electrostatics[END_REF] GEM computes the molecular interaction energies using an approach similar to SIBFA but replacing distributed multipoles by electron densities. [START_REF] Piquemal | Towards a Force Field Based on Density Fitting[END_REF] GEM better captures the short-range effects on intermolecular interaction energies, and it naturally includes the penetration effect.

Calculations on a few simple systems like water clusters [START_REF] Piquemal | Towards a Force Field Based on Density Fitting[END_REF] have demonstrated GEM's capability to reproduce quantum chemistry results. Furthermore, implementating PME for GEM in a PBC showed reasonable computational efficiency thanks to the use of Hermite Gaussian functions. 100 Therefore, replacing SIBFA's distributed multipoles with the GEM continuous electrostatic model will be a future direction of methodology development. [START_REF] Cisneros | Design of Next Generation Force Fields from ab Initio Computations: Beyond Point Charges Electrostatics[END_REF]

NEMO

NEMO (Non-Empirical Molecular Orbital) is a polarizable potential developed by Karlström and co-workers. [101][102][103] The NEMO potential energy function is composed of electrostatics, induction, dispersion and repulsion terms. The induction component is modeled using induced point-dipole moments with recent addition of induced pointquadrupole moments. [START_REF] Holt | Inclusion of the Quadrupole Moment When Describing Polarization. The Effect of the Dipole-Quadrupole Polarizability[END_REF] The electrostatics, previously represented by atomic charges and dipoles, has also been extended to include atomic quadrupole moments leading to notable improvement on formaldehyde. The atomic multipole moments are now obtained from ab initio calculation using a LoProp procedure. 104 The LoProp is claimed to provide atomic multipoles and atomic polarizabilities that are less sensitive to basis sets than are other methods such as Distributed Multipole Analysis (DMA). Also, NEMO is the only force field that explores the possibility of including interactions between permanent multipoles and higher-order induced multipoles involving higher-order hyperpolarizabilities. [START_REF] Holt | Inclusion of the Quadrupole Moment When Describing Polarization. The Effect of the Dipole-Quadrupole Polarizability[END_REF] NEMO has demonstrated its ability to describe accurately both inter and intramolecular interactions in small systems, including: glycine dipeptide conformation profiles, 105 ionwater droplets, 106 and urea transition from nonplanar to planar conformation in water. 107 Its applicability to biomacromolecules is not yet known.

CHARMM-Drude

In addition to the induced dipole model, the classical Drude oscillator model is another popular approach for modeling polarization effects. [START_REF] Rick | Potentials and Algorithms for Incorporating Polarizability in Computer Simulations[END_REF]108 Roux, MacKerell and their colleagues have been developing a polarizable CHARMM force field based on this approach. [START_REF] Lamoureux | A Polarizable Model of Water for Molecular Dynamics Simulations of Biomolecules[END_REF][START_REF] Lamoureux | A Simple Polarizable Model of Water Based on Classical Drude Oscillators[END_REF]109,117 Unlike the induced dipole model, which treats the polarization response using point dipoles, the Drude model represents the polarizable centers by a pair of point charges. A point partial charge is tethered via a harmonic spring for each nonhydrogen atom. This point charge (the Drude oscillator) can react to the electrostatic environment and cause the displacement of the local electron density. The atomic polarizability depends on both the Drude particle charge and the harmonic force constant.

In MD simulations, the extended Lagrangian is used to evaluate the polarization response, by allowing the Drude particles to move dynamically and experience nonzero forces.

Small fictitious masses are assigned to each Drude particle and independent low temperature thermostats are applied to the Drude particle degrees of freedom. 118 In case of energy minimization, self-consistent iteration will be required to solve for the polarization.

Determining electrostatic parameters for the Drude oscillator is not as straightforward as for induced dipole models. Masses assigned to the Drude particles are chosen empirically.

The values for atomic charges and polarizabilities requires a series of calculations of perturbed ESP maps. This force field has been parameterized for water [START_REF] Lamoureux | A Polarizable Model of Water for Molecular Dynamics Simulations of Biomolecules[END_REF][START_REF] Lamoureux | A Simple Polarizable Model of Water Based on Classical Drude Oscillators[END_REF] , and for a series of organic molecules including: alkanes, 110 alcohols, 111 aromatics, 112 ethers, 113,114 amides, 109 sulfurs, 115 and ions. 119,120 An attempt has also been made to combine the Drude-based polarizable force field with quantum mechanics in QM/MM methods. 121 It was noted that pair-specific vdW parameters are needed to obtain accurate hydration free energies of small molecules using the polarizable force field. This is likely due to the problematic combining rules used to compute the vdW interactions between unlike atoms.

The Drude model has been implemented in CHARMM [START_REF] Brooks | CHARMM: The Biomolecular Simulation Program[END_REF]122 and in the NAMD package, 123 in which the computational cost is about 1.2 to 1.8 times greater than that of fixed-charge CHARMM. 124

CHARMM-FQ

The fluctuating charge model (FQ), also known as charge equilibration or electronegativity equalization model, is an empirical approach for calculating charge distributions in molecules. In this formalism, the partial charge on each atom is allowed to change to adapt to different electrostatic environments. The variable partial charges are computed by minimizing the electrostatic energy for a given molecular geometry.

Compared with the induced dipole and Drude models, the fluctuating charge models are minimally parameterized and easier to implement because the polarizability is induced without introducing new interactions beyond the point charges. Either extended Lagrangian or self-consistent iteration can be used to compute the fluctuating charges in MD simulations, with similar advantages and disadvantages as discussed above.

The CHARMM-FQ force field, 125,126 developed by Patel, Brooks, and their coworkers, has been parameterized for small molecules, [START_REF] Patel | CHARMM Fluctuating Charge Force Field for Proteins: I Parameterization and Application to Bulk Organic Liquid Simulations[END_REF] proteins, [START_REF] Patel | CHARMM Fluctuating Charge Force Field for Proteins: I Parameterization and Application to Bulk Organic Liquid Simulations[END_REF]127 lipids, lipid bilayers, 113,128 and carbohydrates. 125 The force field has been applied to investigate liquid-vapor interfaces in addition to biophysical studies. 129 There are some known limitations for fluctuating charge models, however, such models allow artificial charge transfer between widely separated atoms but that can be controlled with additional constraints. Also the intramolecular charge-flow is limited by the chemical connectivity. It is thus difficult to capture the out-of-plane polarization in molecules such as aromatic benzenes with additional charge sites. The CHARMM-FQ force field has been implemented in the CHARMM software package. 74

X-Pol

Gao and coworkers proposed the X-Pol framework by combining the fragment-based electronic structure theory with a molecular mechanical force field. [START_REF] Song | Explicit Polarization (X-Pol) Potential Using Ab Initio Molecular Orbital Theory and Density Functional Theory[END_REF][START_REF] Xie | X-Pol Potential: An Electronic Structure-Based Force Field for Molecular Dynamics Simulation of a Solvated Protein in Water[END_REF]130 Unlike the traditional force fields, X-Pol does not require bond stretching, angle, and torsion terms because they are represented explicitly by quantum mechanics. The polarization and charge transfer between fragments are also evaluated quantum mechanically. 130 Furthermore, X-Pol can be used to model chemical reactions.

In X-Pol, large molecular systems are divided into small fragments. Electrostatic interactions within the fragments are treated using the electronic structure theory. The electrostatic interactions between fragments are described by the combined quantum mechanical and molecular mechanical (QM/MM) approach. Also, a vdW term is added to the interfragment interaction as a consequence of omitting electron correlation and exchange repulsion. A double self-consistent-field (DSCF) procedure is used to converge the total electronic energy of the system as well as the energy within the fragments (this includes the mutual polarization effect).

The X-Pol potential has been applied to MD simulations of liquid water, 131 liquid hydrogen fluoride, 132 and covalently bonded fragments. 133,134 This model was recently used in a molecular dynamics simulation of a solvated protein. 135 As expected the computational efficiency of the X-Pol is in between that of a simple classical force field and a full ab initio method. The solvated trypsin required 62.6 h to run a 5 ps simulation on a single 1.5 GHz IBM Power4 processor. A parallel version of X-Pol is being developed.

PFF

Kaminski et al. developed a polarizable protein force field (PFF) based on ab initio quantum theory. 136,137 The electrostatic interaction is modeled with induced dipoles and permanent point charges. With the exception of a dispersion parameter, all other parameters, including the electrostatic charges and polarizabilities, are obtained by fitting to quantum chemical binding energy calculations for homodimers. The dispersion parameters are later refined by fitting to the experimental densities of organic liquids. [START_REF] Kaminski | Development of a Polarizable Force Field for Proteins Via Ab Initio Quantum Chemistry: First Generation Model and Gas Phase Tests[END_REF] Gas-phase many-body effects, as well as conformational energies, are well reproduced, 137 and MD simulations for real proteins are reasonably accurate at modest computational costs. [START_REF] Kaminski | Development of a Polarizable Force Field for Proteins Via Ab Initio Quantum Chemistry: First Generation Model and Gas Phase Tests[END_REF]138 To reduce the computational cost, a POSSIM (Polarizable Simulations with Second-order Interaction Model) force field was later proposed, in which the calculation of induced dipoles stops after one iteration. 139,140 The computational efficiency can be improved by almost an order of magnitude by using this formalism. Because the analytical gradients (forces) are unavailable, a Monte-Carlo technique is used in condensed-phase simulations.

POSSIM has been validated on selected small model systems, showing good agreement with ab initio quantum mechanical and experimental data. Parameters for alanine and protein backbone have been reported. 141 Polarizable force fields for non-biological systems also exist. A many-body polarizable force field by Smith and coworkers was developed and applied to the simulations of ion conduction in polyethylene oxide (PEO). [142][143][144] Cummings and coworkers developed an interesting Gaussian charge polarizable force field for ions and in polyethylene oxide (PEO). [145][146][147] A polarizable force field for ionic liquids was also reported to provide accurate thermodynamics and transport properties. 148 PROL, 155 Dang-Chang 156 and others. These models all adopted the induced dipole framework to treat polarization, typically using a single polarizable site on water. TTM models [157][158][159][160] and the AMOEBA water model 15 utilize an interactive, distributed atomic polarizability with Thole's damping scheme [START_REF] Thole | Molecular Polarizabilities Calculated with a Modified Dipole Interaction[END_REF] to treat electrostatics and polarization. The Drude Oscillator-based water models include SWM4-DP, [START_REF] Lamoureux | A Simple Polarizable Model of Water Based on Classical Drude Oscillators[END_REF] and SWM4-NDP, [START_REF] Lamoureux | A Polarizable Model of Water for Molecular Dynamics Simulations of Biomolecules[END_REF] as well as the Charge-On-Spring (COS) model, 161 and its improved variation. 162 The third group includes the SPC-FQ and TIP4P-FQ 163 An advantage of a polarizable water model over most non-polarizable models is the ability to describe the structure and energetics of water in both gas and condensed phases.

Applications

Water dimer interaction energies, the geometry of water clusters and the heat of vaporization of neat water can be reproduced well by most polarizable models. Some highly parameterized nonpolarizable force fields such as TIP5P, TIP4P-EW and TIP4P/2005 actually perform as well or better than some polarizable force fields over a range of liquid properties, including the density-temperature profile, radial distribution function, and diffusion coefficient. However, for water molecules experiencing significant changes in environment, e.g., from bulk water to the vicinity of ions or nonpolar molecules, only the polarizable models can capture the change of water dipole, structure and energetics. 168 Polarization water models are being extended and applied to other phases as well as to the interface between different phases. Rick et al recently incorporated charge transfer into their polarizable water model that was then used to study ice/water coexistence properties and properties of the ice Ih phase. 169 The POL3 water model [START_REF] Caldwell | Structure and Properties of Neat Liquids Using Nonadditive Molecular Dynamics: Water, Methanol, and N-Methylacetamide[END_REF]170 was used to

Ion Solvation

Ions are an important component in many chemical and biological systems. Nearly half of all proteins contain metal ions, and they play essential roles in many fundamental biological functions. Some metal ions are critical for both protein structure and function.

In enzymes, ions can bind and orient the substrates through electrostatic interactions at the active sites, thus controlling catalytic reaction. Divalent ions are vital in nucleic acid structures. Modeling ion-water and ion-biomolecule interactions accurately is very important.

Due to the high electron density and small sizes of ions, the non-polarizable models fail to capture the structural details adequately and do not or to reproduce the atomic dipole of water around the ions. [172][173][174][175][176] Several studies of ion solvation have been reported using different polarizable models 51-53, 116, 120, 177-187 with analyses focused on solvation structures, charge distribution, and binding energies. Noted that no straightforward experimental measurement of hydration free energy data exist because the macroscopic system must be neutral. Different assumptions are used to decompose the experimental hydration free energy into single ion contributions. The hydration free energy of some monovalent ions such as Na + and K + from different sources can vary by as much as 10 kcal/mol. It is more reliable to compare the hydration free energy of the whole salt and the relative energy between cations or anions.

The AMOEBA polarizable force field has been used to model a number of anions and cations, including Na + , K + , Mg ++ , Ca ++ , Zn ++ , Cl -, Br -, and I -. [START_REF] Grossfield | Ion Solvation Thermodynamics from Simulation with a Polarizable Force Field[END_REF][START_REF] Jiao | Simulation of Ca 2+ and Mg 2+ Solvation Using Polarizable Atomic Multipole Potential[END_REF][START_REF] Wu | Polarizable Molecular Dynamics Simulation of Zn(II) in Water Using the AMOEBA Force Field[END_REF]188 Parameters for these ions, including the vdW parameters and polarization damping coefficients (for divalent ions only), were obtained by fitting to the ab initio QM interaction energy profiles of ionwater pairs. Molecular dynamics simulations were then performed to evaluate the ioncluster solvation enthalpies and solvation free energies. [START_REF] Grossfield | Ion Solvation Thermodynamics from Simulation with a Polarizable Force Field[END_REF][START_REF] Jiao | Simulation of Ca 2+ and Mg 2+ Solvation Using Polarizable Atomic Multipole Potential[END_REF][START_REF] Wu | Polarizable Molecular Dynamics Simulation of Zn(II) in Water Using the AMOEBA Force Field[END_REF]188 The excellent agreement between calculated and experimental hydration free energy, often within 1%, demonstrate that polarizable force fields are transferable between phases. Ab initio energy decomposition using, e.g., the Constrained Space Orbital Variations (CSOV) method, [START_REF] Piquemal | Towards a Force Field Based on Density Fitting[END_REF]189 have also been applied to examine the polarization component of the ion-water interaction energy and to guide the force field parameterization. [START_REF] Wu | Polarizable Molecular Dynamics Simulation of Zn(II) in Water Using the AMOEBA Force Field[END_REF]190 More recently, the AMOEBA force field was used to model the hydration of high valent Th(IV) [START_REF] Marjolin | Toward Accurate Solvation Dynamics of Lanthanides and Actinides in Water Using Polarizable Force Fields: From Gas-Phase Energetics to Hydration Free Energies[END_REF] and studies on open-shell actinides are underway.

The SIBFA model was used to examine Pb(II), 191 lanthanides (La(III) and Lu(III)) and actinides (Th(IV)) in water. [START_REF] Marjolin | Toward Accurate Solvation Dynamics of Lanthanides and Actinides in Water Using Polarizable Force Fields: From Gas-Phase Energetics to Hydration Free Energies[END_REF] SIBFA-predicted interaction energies generally matched well with the ab initio results, including the energy decompositions. Lamoureux and Roux developed the CHARMM polarizable force field for alkali and halide ions based on the Drude Oscillator. 177 Hydration free energies, calculated via thermodynamic integration, 192 showed an encouraging agreement with experiment.

Small Molecules

Small molecules are building blocks of biomolecules and serve as substrates and inhibitors. Abundant experimental measurements on various physical and chemical properties exist for common organic molecules which in turn are used in the parameterization of the force fields. Polarizable and non-polarizable force fields can usually produce reasonable estimations of physical properties of neat liquids. [193][194][195][196] Extensive studies using polarizable force fields, covering major functional group, including alkanes, alcohols, aldehydes, ketones, ethers, acids, aromatic compounds, amines, amides, and some halogen compounds have been reported. 28, 36, 55, 110, 112, 126, 197- 199 Calculations of structure, dipole moment, heterodimer binding energy, liquid diffusion constant, density, heat of vaporization, and hydration free energy are usually performed to assess the quality of force field parameters.

The electrostatic multipole parameters in AMOEBA were derived using the DMA procedure. They can be further optimized to the electrostatic potentials of chosen ab initio theory and basis sets. The AMOEBA valence parameters were derived from ab initio data such as molecular geometries and vibrational frequencies of the gas-phase monomer. The vdW parameters are estimated from gas-phase cluster calculations, and subsequently refined in liquid simulations using experimental data (e.g., densities and heats of vaporization). The torsional parameters the last obtained during the parameterization scheme are derived by fitting to ab initio QM conformational energy

profiles. An automated protocol (PolType) that can generate AMOEBA parameters for small molecules is under development. 200 Because force field parameterization is a tedious process, such an automated tool is convenient and reduces the likelihood of human error.

The CHARMM-Drude force field developers devoted much of their efforts on organic compounds. Their parameterization scheme starts from an initial guess of charge (based on the CHARMM22 force field), and invokes changes at some lone pair sites. Those parameters are then fit to a series of "perturbed" ESP maps. The vdW parameters are then optimized to match neat liquid properties as is done many other force fields. 115 Overall, a systematic improvement over the CHARMM22 additive force field has been observed for both gas-phase and condensed-phase properties. These studies on small molecules lay the groundwork for developing a Drude-based polarizable force field for proteins and nucleic acids.

Proteins

One of the goals for polarizable force fields is to model accurately protein structures, dynamics, and interactions. Proteins are a ubiquitous class of biopolymers whose functionalities depend on the details of their 3D structures, which, in turn, are largely determined by their amino acid sequences. Fixed-charge force fields for proteins, like AMBER, CHARMM, and OPLS-AA, have been developed and for years subjected to various tests and validations. The development of polarizable protein force fields is still in its infancy. Although the importance of including polarization effects was recognized long ago, polarizable protein force fields emerged only in the past decade. [START_REF] Ponder | Force Fields for Protein Simulations[END_REF][START_REF] Wang | Strike a Balance: Optimization of Backbone Torsion Parameters of AMBER Polarizable Force Field for Simulations of[END_REF][START_REF] Patel | CHARMM Fluctuating Charge Force Field for Proteins: I Parameterization and Application to Bulk Organic Liquid Simulations[END_REF][START_REF] Patel | CHARMM Fluctuating Charge Force Field for Proteins: II -Protein/Solvent Properties from Molecular Dynamics Simulations Using a Nonadditive Electrostatic Model[END_REF][START_REF] Ponder | Current Status of the AMOEBA Polarizable Force Field[END_REF]138,[201][202][203][204][205] The use of polarizable electrostatics in protein simulations dates back to 1976, 1 when Warshel and Levitt simulated lysozyme via single point calculations. Kaminski et al. reported in 2002 an ab initio polarizable protein force field (PFF) based on inducible dipoles and point charges. [START_REF] Kaminski | Development of a Polarizable Force Field for Proteins Via Ab Initio Quantum Chemistry: First Generation Model and Gas Phase Tests[END_REF]137 Simulations on bovine pancreatic trypsin inhibitor using PDFF showed a satisfactory root mean square displacement (RMSD) compared to the experimental crystal structure and polarization was found to affect the solvation dynamics. 138 The fluctuating-charge based ABEEM/MM force field was used to examine protein systems like trypsin inhibitors 206 and the heme prosthetic group. 207 The SIBFA force field has been used to study the interaction between focal adhesion kinase (FAK)

and five pyrrolopyrimidine inhibitors. 208 The energy balances accounting for the solvation/desolvation effects calculated by SIBFA agree with experimental ordering.

Water networks in the binding pocket were shown to be critical in terms of binding affinity. Moreover, the polarization contribution was considered as an indispensable component during the molecular recognition. In comparison, the continuum reaction field procedure fails to reproduce these properties. In addition kinases, the SIBFA protein force field has been used to study a variety of metalloproteins encompassing cations such as Cu + , Zn ++ , Ca ++ or Mg ++ , as well as enabling inhibition studies. [START_REF] Gresh | Analysis of the Interactions Taking Place in the Recognition Site of a Bimetallic Mg(II)-Zn(II) Enzyme, Isopentenyl Diphosphate Isomerase. A Parallel Quantum-Chemical and Polarizable Molecular Mechanics Study[END_REF][209][210][211] Future molecular dynamics simulations should extend the applicability of SIBFA to proteinligand binding.

Ren and coworkers have been systematically developing the AMOEBA protein force field, and using it to study to several protein systems to understand protein-ligand binding. [START_REF] Jiao | Calculation of Protein-Ligand Binding Free Energy by Using a Polarizable Potential[END_REF][START_REF] Zhang | Modeling Structural Coordination and Ligand Binding in Zinc Proteins with a Polarizable Potential[END_REF][START_REF] Shi | Probing the Effect of Conformational Constraint on Phosphorylated Ligand Binding to an SH2 Domain Using Polarizable Force Field Simulations[END_REF][START_REF] Jiao | Trypsin-Ligand Binding Free Energies from Explicit and Implicit Solvent Simulations with Polarizable Potential[END_REF] More recently an X-Pol force field for proteins has been developed and demonstrated in a simulation of solvated trypsin. [START_REF] Xie | X-Pol Potential: An Electronic Structure-Based Force Field for Molecular Dynamics Simulation of a Solvated Protein in Water[END_REF] The first attempt to compute the protein-ligand binding free energy using a polarizable force field was made on the trypsin-benzamidine systems using AMOEBA. [START_REF] Jiao | Calculation of Protein-Ligand Binding Free Energy by Using a Polarizable Potential[END_REF][START_REF] Jiao | Trypsin-Ligand Binding Free Energies from Explicit and Implicit Solvent Simulations with Polarizable Potential[END_REF][START_REF] Shi | Trypsin-Ligand Binding Free Energy Calculation with AMOEBA[END_REF] The absolute binding free energy of benzamidine to trypsin, and the relative binding free energies for a series of benzamidine analogs, were computed using a rigorous alchemical transformation. AMOEBA was successful in evaluating the binding free energies accurately with an average error well within 1.0 kcal/mol. A similar study on trypsin, thrombin and urokinase was reported using another ab initio QM-based polarizable force field. 212 A thermodynamic integration scheme was used to compute the relative binding free energies, which were in excellent agreement with experimental data (root mean squre error (RMSE)=1.0 kcal/mol).

AMOEBA was later used to examine an "entropic paradox" associated with ligand preorganization discovered in a previous study of conformationally constrained phosphorylated-peptide analogs that bind to the SH2 domain of the growth receptor binding protein 2 (Grb2). [START_REF] Shi | Probing the Effect of Conformational Constraint on Phosphorylated Ligand Binding to an SH2 Domain Using Polarizable Force Field Simulations[END_REF] The paradox refers to the unusual trend in which the binding of unconstrained peptides (assumed to lose more entropy upon binding) is actually more favorable entropically than are the constrained counterparts. AMOEBA correctly reproduced the experimental trend and at the same time repeated a mechanism in which the unconstrained peptide ligands were "locked" by intramolecular nonbonded interactions. The simulations uncovered a crucial caveat that had not been previously acknowledged regarding the general design principle of ligand preorganization, which is presumed by many to have a favorable effect on binding entropy.

More recently, Zhang et al. demonstrated the ability of AMOEBA in dealing with systems with a metal ion. [START_REF] Zhang | Modeling Structural Coordination and Ligand Binding in Zinc Proteins with a Polarizable Potential[END_REF] Those authors studied the Zinc-containing matrix metalloproteinases (MMPs) in a complex with an inhibitor where the coordination of Zn ++ was with organic compounds and protein side chains. Polarization was found to play a key role in Zn ++ coordination geometry in MMP. In addition, the relative binding free energies of selected inhibitors binding with MMP13 were found to be in excellent agreement with experimental results. As with the previous trypsin study, it was found that binding affinities are likely to be overestimated when the polarization between ligands and environments is ignored.

Having a more rigorous physical model for treating polarization, the ability to model protein-ligand interactions has been improved significantly. Systems involving highly charged species, like metal ions, can now be treated with confidence. This in turn, provides tremendous opportunities for investifating important proteins for drug discovery and for protein engineering.

Lipids

With the rapid development of computational resources, simulations of large systems like lipid bilayers with membrane proteins is feasible. 126, 213 Patel and coworkers have been developing a polarizable force field for biomembranes to study the structure and dynamics of ion channel systems. [START_REF] Patel | Exploring Ion Permeation Energetics in Gramicidin A Using Polarizable Charge Equilibration Force Fields[END_REF]113,128,214 Simulations of solvated DMPC (dimyristoyl phosphatidylcholine) and dipalmitoylphosphatidylcholine (DPPC) bilayers were reported. 113,214 The distribution of the membrane components along the lipid bilayer is similar to that from a fixed charge model. The water dipole moment was found to increase from about 1.9 Debye in the middle of the membrane plane to the average bulk value of 2.5~2.6 Debye. The lipid surface computed with the polarizable force field was not improved from those of non-polarizable ones however. In addition, ion permeation in a gramicidin A channel embedded in a DMPC bilayer was investigated. 113 Davis and

Patel concluded that including the electronic polarization lowered the ion permeation free energy barrier significantly, from 12 kcal/mol to 6 kcal/mol.

Continuum Solvents for Polarizable Biomolecular Solutes

A continuum solvent replaces explicit atomic details with a bulk, mean-field response. It is possible to demonstrate from statistical mechanics that an implicit solvent potential of mean force (PMF) exists, wihch preserves exactly the solute thermodynamic properties obtained from explicit solvent. 215 It is possible to formulate a perfect implicit solvent in principle, but in practice approximations are necessary to achieve efficiency. This remains an active area of research. 216 An implicit solvent PMF can be formulated via a thermodynamic cycle that discharges the solute in vapor, grows the uncharged (apolar) solute into a solvent and finally recharges the solute within a continuum dielectric [12] The continuum electrostatic energy, including mobile electrolytes, can be described by either the nonlinear Poisson-Boltzmann Equation (NPBE) or the simplified linearized

Poisson-Boltzmann Equation (LPBE) [13] where the coefficients are a function of position r, is the potential, is the pemittivity, is the modified Debye-Hückel screening factor, and is the solute charge density. 217,218 Implementations of a Poisson-Boltzmann continuum for many-body quantum mechanical potentials have been applied to small molecules for decades. Examples include the Polarizable Continuum Model (PCM) 219,220 , COSMO 221 and the Solvent Model series (SMx). 222 In contrast, applications of biomolecular continuum electrostatics have been limited mainly to fixed partial charge solute descriptions for reasons of computing efficiency force field availability. However, as a result of increasing computational power and the completion of the polarizable force fields for biomolecules described above, the coupling of classical many-body potentials to continuum electrostatics is now possible.

An important initial demonstration of polarizable biomolecules within a Poisson-Boltzmann continuum used the Polarizable Force Field (PFF) of Maple et al. to model protein-ligand interactions. 223 A second demonstration used the Electronic Polarization from Internal Continuum (EPIC), which accounts for intramolecular polarization using a continuum dielectric. 224,225 Finally, the polarizable multipole Poisson-Boltzmann (PMPB) model based on the AMOEBA force field demonstrated that the self-consistent reaction field (SCRF) of proteins within a continuum solvent is consonant with the ensemble average response of explicit solvent. [START_REF] Schnieders | Polarizable Atomic Multipole Solutes in a Poisson-Boltzmann Continuum[END_REF] Contrarily, end-state calculations of protein-ligand binding affinity using the PMPB model were shown to not recapitulate explicit solvent alchemical free energies to chemical accuracy. [START_REF] Jiao | Trypsin-Ligand Binding Free Energies from Explicit and Implicit Solvent Simulations with Polarizable Potential[END_REF] This motivates development of analytic continuum electrostatics (discussed next), which are fast enough to allow binding affinities to be computed using alchemical sampling, rather than merely relying on endstates. A key advantage of EPIC is that the biomolecular self-consistent field (SCF) is determined by a single numerical finite-difference (FD) solution of the PBE, unlike the aforementioned atom-centered PFF and PMPB models that require a new solution for each SCF iteration. However, a tradeoff of EPIC's efficiency gain is a reduction in model flexibility because electrostatic masking rules cannot be incorporated into the FD solver (i.e., the permanent field due to 1-2 or 1-3 interactions cannot be neglected). Although masking of short-range bonded interactions is the standard approach used by essentially all biomolecular force fields, this is not possible for an EPIC style energy model.

The first example of an analytic continuum electrostatic model for polarizable biomolecules is the generalized Kirkwood (GK) model for the AMOEBA force field. [START_REF] Schnieders | Polarizable Atomic Multipole Solutes in a Generalized Kirkwood Continuum[END_REF] The AMOEBA/GK approach has been combined with alchemical sampling to predict trypsin-ligand binding affinity with a correlation coefficient of 0.93. This is a significant improvement over the PMPB end-state approach. 226 A second example, based on the ABEEMσπ fluctuating charge force field combined with a generalized Born (GB) continuum electrostatic model, showed promising results for the computation of solvation free energies for small organic molecules and peptide fragments. Instead, phase information is derived from the Fourier transform of a model structure that is sufficiently close to the actual experimental ensemble. This is known as molecular replacement (MR). After an initial model has been built into the electron density, further refinement is based optimizating a target function of the form [14] where evaluates the agreement between measured and calculated diffraction amplitudes, restrains the model using prior knowledge of intra-and intermolecular chemical forces and weights the relative strength of the two terms. 77, 29 228 We now focus on the evolution of the prior chemical knowledge used during the Xray refinement process, and we culminate in ongoing work using polarizable force fields in combination with PME electrostatics algorithms to obtain the most accurate, informative biomolecular models possible.

The first application of molecular mechanics to macromolecular X-ray crystallography refinement (based on fixed partial charge electrostatics evaluated using a spherical cutoff)

was on influenza-virus hemagglutinin by Weis et al. in 1990. 229 This work demonstrated that electrostatics maintained chemically reasonable hydrogen-bonding, although charged surface residues were sometimes observed to form incorrect salt bridges. 229 The latter observation highlights the importance of accounting for dielectric screening arising from the heterogeneous distribution of solvent within a macromolecular crystal, by using one of the above described continuum electrostatics models. For example, the generalized Born (GB) model for fixed charge electrostatics has been described, albeit with a spherical cutoff approximation. 230 Comparing refinements with and without GB screening showed that roughly 10% of the amino acid side-chain conformations were altered, with 75% of these side-chain differences due to residues at the macromolecular surface. 230 Although these first applications of fixed charge force field electrostatics were encouraging, the use of spherical cutoffs to approximate crystal lattice sums is now known to be only conditionally convergent and therefore prone to a variety of artifacts. 231

In 1921, Ewald introduced an absolutely convergent solution to the problem of evaluating electrostatic lattice summations in crystals. He did this by separating the problem into a short-ranged real space sum and a periodic, smoothly varying, long-range sum that can be evaluated efficiently in reciprocal space. 232 This approach, now known as Ewald summation, has been described for both fixed partial charges and atomic multipoles. 233,234 More recently, the efficiency of Ewald summation was improved via the particle-mesh Ewald (PME) algorithm, wherein the reciprocal space summation leverages the fast Fourier transforms (FFT) 235 via b-Spline interpolation 236 for both fixed partial charge and atomic multipole descriptions. 237 The speed of the PME algorithm has been further improved for crystals by incorporating explicit support for space group symmetry and by parallelization for heterogeneous computer architectures. [START_REF] Schnieders | Polarizable Atomic Multipole X-Ray Refinement: Particle Mesh Ewald Electrostatics for Macromolecular Crystals[END_REF] Combining the polarizable AMOEBA force field with electrostatics evaluated using PME has been shown to improve macromolecular models from X-ray crystallography refinement in a variety of contexts. [START_REF] Schnieders | Polarizable Atomic Multipole X-Ray Refinement: Application to Peptide Crystals[END_REF][START_REF] Fenn | Polarizable Atomic Multipole X-Ray Refinement: Weighting Schemes for Macromolecular Diffraction[END_REF][238][239][240] At high resolution (~1 Å or lower), the information contained within a polarizable atomic multipole force field can be used to formulate the electron density of the scattering model ( ), in addition to contributing chemical restraints ( ). [START_REF] Schnieders | Polarizable Atomic Multipole X-Ray Refinement: Application to Peptide Crystals[END_REF]238 The importance of the prior chemical information contained in a polarizable force field is most significant when positioning parts of the model that are not discernable from the experimental electron density, as in the orientation of water hydrogen atoms 239 or secondary structure elements for mid-to-low resolution data sets (~3-4 Å). [START_REF] Schnieders | Polarizable Atomic Multipole X-Ray Refinement: Particle Mesh Ewald Electrostatics for Macromolecular Crystals[END_REF] Let use consider an example, the AMOEBA-assisted biomolecular X-ray refinement with electrostatics evaluated via PME in the program Force Field X. This program was used to re-refine nine mouse and human DNA methyltransferase 1 (Dnmt1) data sets deposited in the Protein databank (PDB). Significant improvements in model quality (presented in Prediction of thermodynamically stable crystal structures from chemical composition requires a potential energy function capable of distinguishing between large numbers of structures that are closely spaced in thermodynamic stability. 246,247 In this section, we restrict our focus to energy models that explicitly account for electronic polarization classically [START_REF] Schnieders | The Structure, Thermodynamics and Solubility of Organic Crystals from Simulation with a Polarizable Force Field[END_REF]248,249 and neglect the more expensive electronic structure methods sometimes used to (re)score favorable structures. 250 The vast majority of CSP has been limited to using intermolecular potentials that lack explicit inclusion of polarization, 249,251 although its importance has become a topic of interest [START_REF] Halgren | Polarizable Force Fields[END_REF][START_REF] Gavezzotti | Calculation of Intermolecular Interaction Energies by Direct Numerical Integration over Electron Densities. I. Electrostatic and Polarization Energies in Molecular Crystals[END_REF][START_REF] Gavezzotti | Calculation of Intermolecular Interaction Energies by Direct Numerical Integration over Electron Densities. 2. An Improved Polarization Model and the Evaluation of Dispersion and Repulsion Energies[END_REF][254] . Non-polarizable force fields, based on fixed partial charges or fixed atomic multipoles, must implicitly account for the 20% to 40% of the lattice energy attributable induction. 249 On the other hand, polarizable models such as the AMOEBA force field for organic molecules [START_REF] Ren | Polarizable Atomic Multipole-Based Molecular Mechanics for Organic Molecules[END_REF]255 based on the Thole damping scheme [START_REF] Thole | Molecular Polarizabilities Calculated with a Modified Dipole Interaction[END_REF] and the Williams-Stone-Misquitta (WSM) method 256,257 for obtaining distributed polarizabilities allow one to include polarization during CSP explicitly.

Beyond polarization, modeling the conformational flexibility and corresponding intermolecular energetics of organic molecules via sampling methods such as molecular dynamics is essential to predicting the thermodynamic properties of crystals. 258 For example, the structure, stability and solubility of n-alkylamide crystals, from acetamide through octanamide, can be predicted by an alchemical sampling method to compute the sublimation/deposition phase transition free energy. 65

Summary

Significant progress has been made in the past decade in developing general-purpose polarizable force fields. Polarizable force fields have exhibited success in disparate research areas including ion solvation, protein-ligand interactions, ion channels and lipids, macromolecular structural refinement and so on. There remain plenty of challenges ahead.

The importance of polarization still needs to be established systematically for a wide range of biological systems. While polarizable force fields in principle have better transferability than do non-polarizable force fields, they are also expected to also perform better in a broader range of systems, making parameterization a more elaborate process.

In addition to polarization, treatment of other physical effects, including high-order permanent charge distributions interactions, short-range electrostatic penetration and charge-transfer effects need further improvement to advance the overall quality of classical electrostatic models. Because computational efficiency (including the need for parallelization) has been a major barrier to the adoption of polarizable force fields, better and more efficient algorithms are also required to advance the application of polarizable force fields. A future area for advancement is to combine the polarizable force fields with fixed-charge force fields in a multiscale fashion, as is done with QM/MM. Technically this can be achieved straightforwardly but caution is needed to ensure the interactions across the two resolutions are balanced.

  scheme to model polarization. The partial charges flow from one atom to another, and the

  227

3. 7 .

 7 Macromolecular X-ray Crystallography RefinementX-ray crystallography is the dominant experimental method for determining the 3dimensional coordinates of macromolecules. Collected diffraction data is the Fourier transform of the ensemble average electron density of the macromolecular crystal. While reciprocal space amplitudes of Bragg diffraction peaks are measured, their phases are not.

Figure 1 . 3 . 8 .

 138 Figure 1. Polarizable biomolecular X-ray refinement on two Dnmt1 data sets. The left

Table 1 )

 1 were achieved as assayed by the MolProbity 241 structure validation tool. The MolProbity score is calibrated to reflect the expected resolution of the X-ray data. After re-refinement, the average MolProbity score was reduced to 2.14, indicating a level of model improvement consistent with collecting data to 0.67 Å higher resolution. For

	example, the pose of S-adenosyl-L-homocysteine (SAH) from mouse (3PT6) and human
	(3PTA) structures differed by an RMSD of 1.6 Å before re-refinement, but only 0.9 Å
	afterwards.

Table 1 .

 1 DNA Methyltransferase 1 (Dnmt1) Models Before and After Polarizable X-Ray Refinement with the Program Force Field X.

			Protein Databank	Re-Refined with Force Field X
			Statistics	MolProbity	Statistics	MolProbity
	PDB Res. (Å) R	R free Score (%)	R	R free	Score (%)
	3AV4	2.8	0.232 0.267	2.87 68.0	0.238 0.282	2.25 95.0
	3AV5	3.3	0.188 0.264	3.09 79.0	0.216 0.275	2.44 97.0
	3AV6	3.1	0.195 0.255	2.99 81.0	0.213 0.265	2.37 97.0
	3EPZ	2.3	0.213 0.264	2.27 78.0	0.254 0.292	2.09 87.0
	3OS5	1.7	0.211 0.238	2.01 54.0	0.182 0.213	1.77 74.0
	3PT6	3.0	0.211 0.266	2.95 78.0	0.207 0.268	1.97 99.0
	3PT9	2.5	0.196 0.256	2.72 60.0	0.181 0.248	1.90 97.0
	3PTA	3.6	0.257 0.291	3.65 57.0	0.211 0.271	2.41 99.0
	3SWR	2.5	0.220 0.272	2.69 62.0	0.204 0.264	2.03 95.0
	Mean	2.7	0.214 0.264	2.80 68.6	0.212 0.264	2.14 93.3
	Mean Improvement				0.67 24.8

Acknowledgement. The authors are grateful to the support provided by Robert A. Welch Foundation (F-1691).


M Abdi Abyaneh

A Kaissoine
email: abdou.kaissoine@telecom-paristech.fr

B Huyart
email: huyart@telecom-paristech.fr

J Cousin

Multiple RF Continuous-Wave Generation Using a Single Signal Generator for Carrier Agrregation in LTE-Advanced

Keywords: frequency aggregation, CW RF signals, multi carrier, LTE-Advanced

Multiple Continuous-Wave (CW) Radio Frequency (RF) signals are used in many telecommunication applications, such as frequency aggregation in LTE-Advanced (LTE-A), intermodulation distortion measurements and …, in order to use more efficiently the frequency bands that are available. In this work a new method for generating three frequencies and more, with no a-priori condition on the frequency allocation, is elaborated in theory and practical results are presented, as well.

I. INTRODUCTION

LTE-A uses two techniques to obtain a superior data rate than its preceding technologies; Multiple-Input Multiple-Output (MIMO) and Carrier Aggregation (CA). For downlink transmission a system of up to 8x8 MIMO and for uplink transmission a system of up to 4x4 MIMO should be used depending on the user equipment [START_REF]LTE; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical channels and modulation[END_REF]. CA technique permits us to exploit up to 100MHz distributed bandwidth, using up to five carriers with a maximum of 20MHz bandwidth for each carrier , over the RF spectrum. Hence, the data rates up to 3Gbps in downlink and 1.5Gbps in uplink would be achievable.

There are three types of frequency aggregation; the first one is the contiguous intra-band frequency aggregation in which all the carriers are placed, consecutively, in one frequency band. The second type is the non-contiguous intraband frequency aggregation in which the carrier bands are not located consecutively in a single band. Finally, the third type is the inter-band frequency aggregation in which the carriers are separated in more than one frequency band [START_REF] Iwamura | Carrier aggregation framework in 3GPP LTE-advanced [WiMAX/LTE Update[END_REF].

Generating multiple carriers at unequal distances are, normally, performed using multiple signal generators which is not suitable for mobile application, since low battery consumption, cheap fabrication and light weight are important factors in mobile designs. There are several studies that have been made for multiple CW generation; in [START_REF] Lu | An oversampling-based analog multitone signal generator[END_REF]a method for generating four CW signals is elaborated with the expense of using four digital signal generators. In [START_REF] Traverso | A 14-Band Low-Complexity and High-Performance Synthesizer Architecture for MB-OFDM Communication[END_REF] 14 consecutive frequency bands are generated at multiples of 528MHz, which might be suitable, with some modifications, only for the case of intra-band CA. Also, in [START_REF] Greenstein | Phasing Multitone Signals to Minimize Peak Factors[END_REF]a method for generating coherently phased multiple tones for measuring linear responses over finite bandwidths is proposed, in which an M-tone baseband signal b(t) is created and modulated on the carrier frequency fc:

N n n n ft n A t b 1 ) 2 cos( ) (
Where N= (M-1)/2, Δf is the frequency spacing between tones and A n , α n are amplitude and phase of each tone n. Using this method one may generate non-contiguous bands by creating many tones and disabling the undesired tones but the tones are always placed at integer multiples of Δf. obviously, this method cannot be the optimum since, firstly, many tones are generated just to be turned off after, secondly, the remaining tones are integer multiples of Δf which does not give us the freedom to generate any frequency that would be desired.

In section II the mathematical procedure to generate a multitone signal with any frequency spacing is elaborated. Then, in section III the practical results supporting the theory is presented in which one 3-tone and one 4-tone signals are generated using a single signal generator and a direct application of this technique in a demodulation process is elaborated. The last part, section IV, contains the conclusion of this work.

II. M-TONE SIGNAL GENERATION METHOD

2 2 cos( )) 2 2 cos( 2 1 ( ) ( 3 2 1 2 1 3 t f f f t f f t I ) 4 2 2 sin( )) 2 2 cos( 2 1 ( ) ( 3 2 1 2 1 3 t f f f t f f t Q 4 2 3 2 1 3 f f f f c
One may develop the case with 4 tones using the same concept as:

) ) (( ) (

) 2 cos( ) ( 3
) ( 4 t f t f t Q t f t I t I k k k ) 2 sin( ) 2 sin( ) ( 3 ) 2 sin( ) ( 3
) ( 4 t f t f t Q t f t I t Q k k k 8 4 2 3 3 2 1 f f f f f k 8 4 2 3 3 2 1 4 f f f f f c
By continuing this method, any multiple-tone signal can be generated.

III. EXPERIMENTAL RESULTS

A. Signal generation:

Two practical cases were studied to generate 3-tone and 4tone signal. The in-phase and quadrature components were generated using MATLAB® and loaded to the Agilent EXG vector signal generator N5172B. The downloaded I/Q data were modulated using the I/Q modulator integrated in N5172B. The spectrums are depicted by MATLAB® using the data obtained by the Rohde & Schwarz FSIQ-40 spectrum analyzer Fig. 1(a) shows the three desired fundamentals at unequally spaced frequencies of 1.021 GHz, 1.034GHz and 1.09GHz. Also, due to nonlinearities of the mixer, that upconverts the baseband signal to RF frequency range, some intermodulation components appear which are not disturbing, since the Spurious Free Dynamic Range (SFDR) is more than 51dB, moreover, in Fig. 1(b) and(c) the 2 nd and 3 rd harmonics, generated due to mixer nonlinearities, are presented, respectively. Fig. 2(a) shows the four desired fundamentals that are generated at unequally spaced frequencies of 1.021 GHz, 1.034GHz, 1.062GHz and 1.075GHz, also, due to nonlinearities of the mixer, that up-converts the baseband signal to RF frequency range, same as the case of 3-tone signal generation, some intermodulation components appear which are not disturbing, since the SFDR is more than 52dB, moreover, in Fig. 2(b) and (c) the levels of the 2 nd and 3 rd harmonics, generated due to mixer nonlinearities, are shown, respectively.

B. 3-tone signal application

In this section, a 3-tone signal with tones at 2.8 GHz, 2.818 GHz and 2.85 GHz, is applied to the test bench depicted in fig. 3, which is a modified version of the test bench in [START_REF] Kaissoine | Demodulation of aggregated RF signal in three frequencies bands with a unique Rx chain[END_REF], as a Local Oscillator (LO) signal. The 3-tone LO signal must down-convert the 3 RF signals, with bandwidths of 67.5 KHz, at 2.8002 GHz, 2.8187 GHz and 2.8512 GHz to the baseband frequencies at 200 KHz, 700 KHz and 1200 KHz, respectively. Once the signal is down-converted, the demodulation can be proceeded as explained in [START_REF] Kaissoine | Demodulation of aggregated RF signal in three frequencies bands with a unique Rx chain[END_REF]. Fig. 4 shows the three down-converted RF signals at desired baseband frequencies of 200 KHz, 700 KHz and 1200 KHz. Also, one can observe that the channels are not disturbed by any spurious signal as it was required for the demodulation of the signals in [START_REF] Kaissoine | Demodulation of aggregated RF signal in three frequencies bands with a unique Rx chain[END_REF].

IV. CONCLUSION

A new method for generating multitone signals with any frequency spacing using a single generator was proposed in this work. The I/Q components of the multitone signal were generated and the baseband signal is modulated using a dummy carrier, which does not appear among the final tones. The experimental results for two cases of 3-tone and 4-tone signals were illustrated, moreover, an application of this technique was given as a 3-tone LO generator in an LTE-A demodulation process.

Fig. 1 .

 1 Fig. 1. (a) Fundamental frequencies of a 3-tone signal with frequencies at 1.021 GHz, 1.034GHz and 1.09GHz. (b) Weak 2 nd harmonics. (c) Weak 3 rd harmonics.

Fig. 2 .

 2 Fig. 2. (a) Fundamental frequencies of a 4-tone signal with frequencies at 1.021 GHz, 1.034GHz, 1.062GHz and 1.075GHz. (b) Weak 2 nd harmonics. (c) Weak 3 rd harmonics.

Fig. 3 .

 3 Fig. 3. Test bench for the demodulation of RF signal aggregated in frequency.

Fig. 4 .

 4 Fig. 4. Three clean baseband channels at 200 KHz, 700 KHz and 1200 KHz with no spurious frequency


The$ Communicative$ Dimension$ of$ Migrant$ Remittances$ and$ its$ Political$ Implications1 $ Thomas$Lacroix$ CNRS%research%fellow%at%MIGRINTER,%University%of%Poitiers%

The$ scholarship$ usually$ distinguishes$ between$ individual$ and$ groupAoriented$remittances$on$the$one$hand,$between$social$and$ economic$remittances$on$the$other.$A$communicational$approach$ to$ transnational$ engagement$ opens$ the$ possibility$ to$ unravel$ these$ categorizations$ and$ sheds$ a$ new$ light$ on$ the$ symbolic$ dimension$of$material$transfers.$This$paper$unfolds$a$conceptual$ framework$ of$ migrants'$ transnational$ engagements.$ It$ combines$ three$ elements:$ a$ concept$ of$ social$ agent$ apprehended$ in$ its$ plurality$ of$ roles$ and$ social$ embedding;$ the$ Habermas$ theory$ of$ communicative$ action$ accounting$ for$ the$ communicative$ dimension$ of$ transnational$ engagements;$ a$ concept$ of$ social$ institution$explaining$the$role$of$migrant$organizations$in$framing$ transnational$activities.$In$this$perspective,$remittances$appear$as$ a$ communicational$ act$ through$ which$ migrants$ express$ their$ identity$ of$ migrant$ embedded$ on$ a$ plurality$ of$ social$ contexts.$ Remittances,$ be$ they$ monetary,$ investments$ or$ material$ gift$ are$ ambivalent$ behaviors:$ they$ simultaneously$ are$ an$ expression$ of$ allegiance$and$of$emancipation.$This$ambivalence$of$transnational$ ties,$it$is$argued,$is$the$product$of$the$fundamental$ambivalence$of$ migration$act$itself.$

INTRODUCTION$$

Originally,$ Peggy$ Levitt$ coined$ the$ term$ "social"$ remittances$ to$ raise$ attention$ towards$the$array$of$transfers$that$were$taking$place$in$the$transnational$realm$ at$a$time$when$the$scholarship$was$almost$exclusively$focusing$on$remittances$ in$ their$ economic$ sense$ [START_REF] Levitt | Social$Remittances:$A$LocalALevel,$MigrationADriven$Form$of$ Cultural$Diffusion[END_REF].$ However,$ nowadays,$ migration$ scholars$ have

$ picked$ up$ this$ concept$ to$ draw$ a$ sharp$ distinction$ between$ economic$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $ 2$
transfers$on$the$one$hand$and$the$"rest"$on$the$other.$In$doing$so,$the$literature$ tends$to$reify$a$dubious$epistemological$line$that$separates$the$"economic"$and$ the$"social".$In$this$paper,$my$aim$is$to$cast$a$critical$eye$on$two$commonly$used$ distinctions:$ between$ social$ and$ economic$ remittances$ on$ the$ one$ hand,$ and$ between$ material$ and$ immaterial$ transfers$ on$ the$ other.$ For$ this$ purpose,$ I$ present$ a$ theoretical$ framework$ within$ which$ it$ is$ possible$ to$ think$ economic$ transfers$ as$ well$ as$ any$ other$ form$ of$ remittances,$ whether$ material$ or$ not,$ as$ symbolically$meaningful$social$constructs.$Empirically,$it$dwells$upon$a$15Ayear$ experience$ of$ research$ on$ individual$ and$ collective$ remittances$ in$ villages$ of$ North$ Africa$ (Souss$ Valley,$ Kabylia)$ and$ North$ India$ (Punjab)$ (Lacroix$ 2013;[START_REF] Lacroix | are$community[END_REF].$$$ I$ see$ remittances$ as$ communicative$ actions$ through$ which$ migrants$ express$ who$ they$ think$ they$ are$ beyond$ the$ contradictory$ nature$ of$ their$ condition$ [START_REF] Habermas | The%Theory%of%Communicative%Action%Volume%1:%Reason%and% the%Rationalization%of%Society[END_REF].$ In$ this$ paper,$ I$ want$ to$ show$ how$ ambivalence$ [START_REF] Smelser | The$Rational$and$the$Ambivalent$in$the$Social$Sciences[END_REF]$ is$ built$ into$ remittances$ (whether$ collective$ or$ individual)$ in$ particular,$ and$ into$ transnationalism$ in$ general.$ Remittances$ simultaneously$ express$ allegiance$to$the$place$of$departure$and$emancipation,$success$and$a$familiarity$ with$ modern$ lifestyle.$ Seen$ from$ the$ point$ of$ view$ of$ village$ communities$ and$ elite,$remittances$represent$both$conservative$and$subversive$forces.$In$fact,$it$is$ contended$ that$ remittances$ bear$ the$ mark$ of$ a$ double$ ambivalence,$ the$ one$ of$ the$ condition$ of$ the$ émigréAimmigré$ who$ shares$ their$ life$ between$ two$ social$ spaces,$ and$ the$ one$ of$ the$ migration$ act$ itself$ that$ is$ both$ a$ disruptive$ and$ conservative$stance.$In$this$paper,$I$will$present$different$forms$of$remittances,$ showing$how$each$of$them$expresses$this$tension$in$a$specific$way$and,$beyond,$ how$they$can$be$seen$as$a$step$toward$the$politicization$of$the$relation$between$ migrants$ and$ their$ sending$ community.$ Henceforth,$ the$ theoretical$ framework$ provides$ a$ ground$ to$ think$ of$ a$ continuum$ from$ nonApolitical$ remittances$ to$ transnational$political$engagement.$ The$first$section$briefly$presents$an$overview$of$a$structure/agency$approach$to$ immigrant$transnationalism.$The$second$section$analyses$the$implications$of$this$ theoretical$ standpoint$ for$ our$ understanding$ of$ material$ remittances.$ Finally,$ I$ raise$ some$ considerations$ about$ the$ passage$ from$ nonApolitical$ to$ political$ remittances.$

1. A$COMMUNICATIVE$APPROACH$TO$TRANSNATIONALISM This$theoretical$framework$was$initially$tailored$to$explain$the$development$of$ activities$ among$ hometown$ organizations 2 .$ It$ is$ empirically$ grounded$ in$ 15$ years$ of$ research$ on$ Moroccans,$ Algerians$ and$ Punjabis$ in$ Europe.$ The$ central$ question$ of$ this$ research$ was$ to$ understand$ why$ some$ groups$ do$ engage$ in$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 2$A$full$presentation$of$this$theoretical$model$was$published$in$a$previous$article:$(Lacroix$2014)$ $ $ 3$
collective$ practices$ of$ development$ while$ others$ do$ not.$ To$ understand$ this,$ I$ developed$ a$ structure$ and$ agency$ perspective$ that$ takes$ into$ account$ the$ plurality$of$social$contexts$in$which$migrants$are$embedded.$This$perspective$is$ threeApronged$and$relies$1)$on$the$"plural$man"$theory,$2)$Habermas'$theory$of$ communicative$ action$ and$ 3)$ a$ reformulated$ concept$ of$ social$ institution.$ Henceforth,$ I$ want$ to$ argue$ that$ any$ form$ of$ remittances$ can$ be$ conceived$ as$ communicative$acts$through$which$emigrants$express$the$multipolarity$of$their$ identity$and$the$plurality$of$the$social$milieus$in$which$they$have$been$socialized.$ Moreover,$ the$ social$ institutions$ within$ and$ across$ which$ remittances$ are$ undertaken$ (families,$ associations,$ businesses,$ etc.)$ form$ the$ communicational$ basis$that$makes$this$exchange$between$migrants$and$nonAmigrants$possible.$ Following$ Habermas'$ approach$ to$ social$ action,$ it$ is$ argued$ that$ human$ behaviors$are$communicative:$in$order$to$be$understood$and$foster$cooperation$ among$social$actors,$they$are$to$act$in$accordance$with$a$shared$understanding$ of$ the$ world,$ the$ soAcalled$ "lifeworld".$ They$ conform$ to$ the$ way$ actors$ understand$ the$ world$ and$ themselves$ in$ the$ world.$ I$ propose$ to$ enrich$ this$ approach$ by$ introducing$ the$ idea$ that$ actors$ are$ plural.$ Social$ actors$ are$ socialized$ in$ a$ plurality$ of$ social$ contexts:$ in$ the$ family,$ at$ work,$ in$ a$ given$ religious$ or$ class$ context,$ etc.$ Actors$ are$ bearer$ of$ a$ bundle$ of$ identities$ reflecting$ this$ diversity$ of$ social$ embedding,$ each$ of$ them$ associated$ with$ a$ range$ of$ roles$ and$ expectations$ that$ may,$ at$ times,$ be$ at$ odds$ with$ each$ other.$ Actors'$agency$is$to$be$understood$against$this$background:$emergence,$defined$ as$the$appearance$of$innovative$behaviors,$stems$from$the$necessity$for$actors$to$ cope$ with$ the$ contradictory$ expectations$ that$ they$ face.$ Any$ emergent$ act$ is$ polyvalent.$It$bears$the$mark$of$the$multiple$layers$of$socialization$of$those$who$ undertake$ them.$ But$ when$ the$ structural$ contradictions$ in$ which$ people$ are$ embedded$ build$ up,$ action$ becomes$ loaded$ with$ ambivalence:$ an$ emergent$ behavior$ is$ a$ way$ out$ of$ structural$ impasses,$ but$ it$ subverts$ former$ social$ equilibriums.$$ I$see$in$the$ontological$plurality$of$social$actors$the$origin$of$ambivalence.$This$ somehow$ relates$ to$ Neil$ Smelser's$ understanding$ of$ ambivalence$ as$ rooted$ in$ the$oedipal$relations$that$people$weave$with$their$parents$ (Smelser$1998,$5-6).$ This$developmental$phase$can$indeed$be$seen$as$a$founding$moment$insofar$as$it$ is$ part$ of$ the$ autonomization$ process$ of$ the$ social$ actor,$ the$ one$ that$ leads$ children$ of$ their$ parents$ to$ become$ parents$ of$ their$ children.$ It$ introduces$ children$ into$ the$ intrinsic$ unAresolvability$ of$ the$ human$ condition,$ to$ the$ necessity$AND$the$impossibility$to$be$parent$and$child,$and$later$to$endorse$the$ array$of$social$roles$that$characterize$fullAfledged$social$beings.$$ Another$ thread$ links$ this$ habermassian$ theoretical$ framework$ with$ Smelser's$ theory:$ they$ both$ can$ be$ read$ as$ critiques$ of$ interestAdriven$ rationality.$ For$ Smelser,$egoAcentered$rationality$is$hampered$by$the$ambivalent$perception$that$ we$have$of$things$and$prospects,$as$illustrated$by$one's$impossibility$to$make$a$ clearAcut$distinction$between$what$is$right$or$wrong$when$decisions$to$be$taken$ $ $ 4$ simultaneously$imply$good$and$bad$outcomes.$For$Habermas,$rationality$cannot$ solely$ be$ defined$ as$ an$ individual$ calculation$ that$ puts$ means$ and$ ends$ in$ the$ balance.$ "Instrumental$ rationality",$ as$ he$ calls$ it,$ fails$ to$ explain$ interpersonal$ and$ collective$ collaborations.$ On$ the$ contrary,$ if$ rationality$ were$ purely$ instrumental,$it$would$ultimately$be$a$centrifugal$force$impeding$groupAmaking.$ The$ German$ philosopher$ opposes$ communicative$ approach$ to$ rationality$ arguing$that$for$an$action$to$be$rational,$it$is$necessary$to$be$deemed$as$such$by$ an$ external$ observer$ on$ the$ ground$ of$ a$ common$ understanding$ of$ the$ world.$ Both$ theories$ imply$ that$ an$ act$ cannot$ be$ rational$ in$ absolute$ terms,$ and$ that$ rationality$ is$ always$ relative$ to$ a$ moral$ framework$ in$ which$ it$ is$ embedded.$ Acting$implies$for$the$actor$to$be$always$already$inscribed$into$a$collective$frame.$ Communicative$rationality$stands$upon$a$triptych:$the$actor,$observers$and$the$ world,$ as$ opposed$ to$ the$ diptych$ means/ends$ supposed$ by$ egoAcentered$ rationality.$ For$ Habermas,$ observers$ are$ not$ passive.$ If$ acting$ is$ communicational,$ observers$ are$ recipient$ of$ a$ message,$ a$ stand$ taken$ by$ the$ actor$ upon$ his$ being$ and$ the$ way$ they$ perceive$ the$ world$ beyond$ their$ multiplicity$ of$ embedding.$ A$ reciprocal$ relationship$ stands$ at$ the$ core$ of$ communicational$ action:$ on$ the$ one$ hand,$ one$ needs$ an$ external$ observer$ to$ acknowledge$ or$ question$ the$ rationality$ of$ one's$ action.$ On$ the$ other,$ through$ their$action,$people$challenge,$seek$to$transform$or$reproduce$existing$modes$of$ behaviors.$This$reciprocal$process$fosters$cooperation,$convergence$of$behaviors$ or,$on$the$contrary,$marginalizes$divergent$behaviors.$$ In$summary,$this$approach$debunks$two$impasses$of$interestAdriven$rationality:$ because$it$is$backed$upon$a$socially$(re)constructed$understanding$of$the$world,$ acting$is$possible$beyond$the$impossibility$to$discriminate$between$what$is$good$ and$what$is$bad;$because$it$needs$the$intervention$of$external$observers,$acting$ is$ never$ cut$ off$ from$ cooperation$ and$ convergence$ mechanisms.$ This$ explains$ the$ importance$ granted$ in$ this$ model$ to$ the$ collective$ dimension$ of$ decisionA making$ and$ therefore,$ the$ central$ role$ played$ by$ social$ institutions.$ As$ mentioned$above,$social$institutions$such$as$families,$enterprises$or$associations$ are$ of$ central$ importance$ in$ this$ process$ insofar$ as$ they$ produce$ a$ regime$ of$ behaviors,$ social$ roles,$ etc.,$ but$ also$ because$ they$ are$ a$ forum$ in$ which$ actors$ debate,$ negotiate$ and$ invent$ new$ forms$ of$ behaving,$ in$ accordance$ with$ their$ respective$ array$ of$ socializations.$ In$ other$ words,$ social$ institutions$ are$ the$ crucible$of$emergent$acts,$but$also$the$social$tool$through$which$they$converge$ to$ be$ adopted$ by$ a$ collective$ of$ people.$ As$ will$ be$ shown$ below,$ three$ social$ institutions$are$key$to$understand$the$communicative$dimension$of$remittances$ in$ rural$ areas:$ transnational$ families,$ hometown$ organizations$ and$ the$ village$ community.$

2.$AMBIVALENT$MIGRATION,$AMBIVALENT$TRANSNATIONALISM$

The$migration$act,$that$is$to$say$the$decision$to$leave$for$a$foreign$country$and$its$ enforcement,$ is$ to$ be$ understood$ as$ an$ emergent$ and$ communicative$ act.$ My$ $ $ 5$ research$focused$on$emigrants$coming$from$a$rural$background.$In$this$context,$ emigration$is$marked$by$three$identity$levels,$each$of$them$referring$to$a$range$ of$ expectations.$ 1)$ Migration$ is$ an$ individual$ act$ through$ which$ actors$ assert$ their$ capacity$ to$ become$ fullAfledged$ and$ autonomous$ social$ beings$ outside$ of$ the$ compound$ of$ their$ sending$ community.$ 2)$ It$ is$ a$ family$ act$ through$ which$ actors$ are$ mandated$ to$ provide$ a$ supplementary$ income.$ 3)$ And$ finally,$ it$ is$ a$ "community"$ act$ that$ participates$ in$ the$ wider$ process$ of$ reproduction$ of$ community$structures.$Migrants$are$expected$to$keep$on$pledging$allegiance$to$ the$ political$ community.$ In$ my$ caseAstudy,$ this$ primarily$ refers$ to$ the$ village's$ political$ elite,$ but$ it$ could$ be$ argued$ that$ migration$ also$ engages$ migrants$ as$ citizens$ of$ their$ sending$ nation$ and$ that$ the$ same$ expectation$ of$ allegiance$ is$ observed$between$expatriates$and$their$sending$state.$ Migrants$ simultaneously$ are$ individuals,$ family$ members$ and$ community$ members.$ Their$ departure$ is$ associated$ with$ three$ kinds$ of$ expectations:$ success,$ money$ and$ allegiance.$ But$ these$ three$ levels$ of$ meaning$ of$ the$ migration$ act$ may$ be$ at$ odds$ with$ each$ other.$ Migration$ appears$ to$ be$ at$ the$ same$ time$ an$ act$ of$ individual$ emancipation$ and$ of$ collective$ reproduction.$ In$ that$ sense,$ migration$ is$ a$ deeply$ ambivalent$ act.$ The$ problem$ is$ particularly$ sensitive$ at$ the$ community$ level:$ how$ to$ make$ sure$ that$ the$ individual$ autonomy$ and$ different$ forms$ of$ capitals$ accumulated$ by$ emigrants$ do$ not$ challenge$ political$ and$ social$ hierarchies?$ How$ to$ preserve$ the$ illusion$ of$ legitimacy$if$the$place$where$the$becoming$of$a$capable$social$being$is$possible$is$ abroad?$Seen$from$the$perspective$of$the$sending$community,$migration$is$good$ (it$can$be$reproductive$resource)$and$bad$(but$it$is$also$a$subversive$impulse)$at$ the$same$time.$ The$ ontological$ plurality$ of$ the$ social$ subject$ explains$ the$ fundamental$ ambivalence$ of$ emergent$ behaviors$ (in$ our$ case,$ the$ migration$ act)$ and$ the$ potentially$ contradictory$ set$ of$ expectations$ they$ imply.$ This$ model$ also$ explains$the$preApolitical$nature$of$migration,$as$these$tensions,$as$they$build$up,$ can$ produce$ political$ stakes$ in$ the$ public$ sphere.$ Remittances,$ it$ is$ argued,$ whether$ material$ or$ social,$ can$ be$ seen$ as$ the$ locus$ of$ politicization$ of$ the$ relationship$between$migrants$and$nonAmigrants.$$

3.$ REMITTANCES:$ A$ COMMUNICATIONAL$ MEDIUM$ BETWEEN$ MIGRANTS$ AND$NONAMIGRANTS$

The$ intrinsic$ ambivalence$ of$ the$ migration$ act$ pervades$ representations,$ ties$ and$practices.$The$representations$that$imbue$the$space$of$arrival$illustrate$this.$ The$ space$ of$ immigration$ is$ generally$ seen$ as,$ if$ not$ an$ Eldorado,$ at$ least$ as$ a$ space$where$"things$are$possible",$where$people$can$enhance$their$economic$or$ social$ capacities.$ But$ the$ immigration$ space$ is$ simultaneously$ perceived$ as$ a$ space$of$moral$corruption$and$impurity,$a$space$where$people$become$egoistic,$ infected$by$foreign$local$values$and$oblivious$of$their$kin$ [START_REF] Carling | The$Human$Dynamics$of$Migrant$Transnationalism[END_REF].$$ $ $ 6$ This$ ambivalence$ pervades$ all$ forms$ of$ material$ remittances.$ They$ all$ are$ a$ proof$of$allegiance$to$the$family$and$to$the$community$and$a$proof$of$personal$ success.$ I$ contend$ that$ different$ forms$ of$ remittances$ express$ this$ tension$ differently$ and,$ henceforth,$ that$ their$ level$ of$ politicization,$ or$ said$ differently,$ their$place$on$the$"preApolitical$to$the$overtly$political"$scale,$differs.$ Monetary$ remittances$ are$ a$ first$ instance$ of$ ambivalent$ transfer.$ The$ scholarship$ has$ amply$ documented$ the$ conspicuous$ use$ of$ migration$ monies$ made$by$both$migrants$and$beneficiaries.$But$a$strong$social$pressure$surrounds$ the$ act$ of$ remitting$ and$ those$ who$ fail$ to$ do$ so$ are$ stigmatized$ as$ selfish$ and$ oblivious$of$their$duty.$Among$West$Africans,$they$are$called$"postcard$migrants"$ because$they$only$send$postcards$to$their$family$back$home.$There$is$no$altruism$ in$the$act$of$remitting:$it$is$a$duty$that$migrants$are$expected$to$fulfill.$Arguably,$ it$is$the$least$politicized$form$of$remittances$insofar$as$it$gives$full$leeway$to$the$ recipients$to$use$it$as$they$want$to.$There$is$no$predetermined$use$of$money,$it$is$ a$pure$"potentiality"$ [START_REF] Simmel | La%Philosophie%de%L'argent[END_REF].$And$monetary$transfers$are$the$first$form$of$ transfer$undertaken$by$emigrants.$They$start$remitting$in$the$early$days$of$their$ migration,$when$they$have$the$possibility$to$do$so.$

The$ building$ of$ a$ house$ is$ the$ second$ most$ widespread$ form$ of$ remittances.$ Once$ again,$ the$ three$ levels$ of$ expectations$ are$ clearly$ legible$ in$ this$ form$ of$ investment.$Houses$primarily$benefit$the$family$living$in$the$village$and,$because$ they$are$built$in$the$place$of$origin,$they$are$a$proof$of$attachment$to$the$village$ community.$ Moreover,$ migrants'$ houses$ are$ known$ worldwide$ as$ conspicuous$ display$ of$ personal$ success$ and$ enrichment.$ But$ contrary$ to$ monetary$ remittances,$ houses$ already$ incorporate$ aspects$ imported$ from$ the$ place$ of$ settlement.$ Beyond$ their$ villageness,$ migrants$ thereby$ assert$ the$ bipolarity$ of$ their$ life$ experience$ and$ identity.$ The$ migrant's$ houses$ in$ the$ place$ of$ arrival$ and$ of$ departure$ juxtapose$ similar$ elements$ taken$ from$ their$ different$ life$ experiences:$cooking$traditional$dishes$in$modern$kitchens,$audioAvideo$devices$ in$ living$ rooms$ furnished$ with$ culturally$ marked$ furniture$ or$ ornament$ (the$ Arabic$ livingAroom$ is$ a$ case$ in$ point).$ The$ analogous$ setAup$ in$ both$ accommodations$ produces$ a$ sense$ of$ continuity$ in$ their$ spatially$ and$ socially$ disrupted$lives.$Houses$are$generally$bought$after$a$few$years$spent$abroad,$the$ time$for$migrants$to$muster$the$necessary$financial$resources.$The$house$bears$ the$symbolic$mark$of$these$years$of$contact$with$the$foreign$lands.$ Another$ form$ of$ material$ transfer$ is$ productive$ investments.$ They$ concern$ a$ smaller$proportion$of$migrants$who$have$most$of$the$time$spent$a$longer$period$ (roughly$ a$ decade)$ abroad.$ Like$ the$ house,$ it$ can$ also$ be$ seen$ as$ a$ sign$ of$ community$ belonging$ insofar$ as$ the$ project$ is$ carried$ out$ in$ the$ area$ of$ origin.$ The$ family$ may$ also$ benefit$ from$ the$ project.$ But$ productive$ investments$ are$ primarily$ geared$ towards$ private$ interests$ and$ may$ challenge$ existing$ social$ order.$ Examples$ of$ conflicts$ spurred$ by$ such$ projects$ are$ manifold.$ In$ the$ Senegal$ River$ valley,$ a$ migrant$ was$ killed$ in$ a$ fight$ opposing$ investors$ and$ a$ group$ of$ villagers$ around$ a$ project$ of$ irrigation.$ The$ project$ coordinator$ was$

$The$author$would$like$to$thank$Céline$Cantat$for$her$help$on$the$manuscript$and$Ilka$VariALavoisier$ for$her$dedication$and$energy.$Corresponding$author:$thomas.lacroix@univApoitiers.fr$or$Thomas$ Lacroix,$Migrinter,$MSHS,$5$rue$Théodore$Lefebvre,$TSA$86073$POITIERS$CEDEX$9,$France.$

$ $ 9$ customary$schools$in$their$village$of$origin$for$several$decades.$Similarly,$we$will$ not$understand$the$demonstrations$of$Sikhs$in$London$or$New$York$in$favor$of$ the$ independence$ of$ Punjab$ if$ we$ only$ look$ at$ their$ arrivalAcountryAoriented$ activism.$ The$ polyphony$ of$ transnational$ politics$ reflects$ the$ identity$ multipolarity$of$transmigrants.$