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This article reviews the state of the art of the studies on charge regulation (CR) effects in flexible weak polyelectrolytes (FWPE). The characteristic of FWPE is the strong coupling of ionization and conformational degrees of freedom. After introducing the necessary fundamental concepts, some unconventional aspects of the the physical chemistry of FWPE are discussed. These aspects are: (i) the extension of statistical mechanics techniques to include ionization equilibria and, in particular, the use of the recently proposed Site Binding-Rotational Isomeric State (SBRIS) model, which allows the calculation of ionization and conformational properties on the same foot; (ii) the recent progresses in the inclusion of proton equilibria in computer simulations; (iii) the possibility of mechanically induced CR in the stretching of FWPE; (iv) the non-trivial adsorption of FWPE on ionized surfaces with the same charge sign as the PE (the so-called 'wrong side' of the isoelectric point); (v) the influence of macromolecular crowding on CR.

[eng] I have carried out this thesis in the Biophysical Chemistry of Macromolecules and Colloids research group of the University of Barcelona. In the recent years, the research group have made significant contributions to the study of the conformational, binding, diffusion and reactivity properties of weak polyelectrolytes and biopolymers. On the one hand, the group has contributed to the design and development of the Site Binding Rotational Isomeric State (SBRIS) model for weak polyelectrolytes. They have also successfully used the SBRIS model to reproduce the complex experimental titration curves of polyethylenimine. On the other hand, the research group has done significant contributions in the study of biopolymer diffusion and reactivity in crowded media. They tracked the diffusion of α-chymiotrypsin in solutions crowded by different- sized dextran macromolecules. They rationalized the experimental results comparing them with on-lattice Monte Carlo (MC) simulations, observing a qualitative agreement between both sets of data. The present thesis follows the efforts of the research group in the development of theoretical and computational models for weak polyelectrolytes and biopolymers. I investigate different theoretical aspects of the conformational, ionization, elastic and diffusive properties of weak polyelectrolytes and biopolymers using theoretical and computational simulation techniques. The thesis includes six original peer-reviewed publications, which are distributed in six different chapters. Moreover, a complete description of the fundamental concepts and methodologies relevant for the thesis is also given. On the one hand, I focus in the complex interplay of the ionization and conformational degrees of freedom of weak polyelectrolytes using the recently developed Site Binding Rotational Isomeric State (SBRIS) model. A new analytical technique, the Local Effective Interaction Parameters (LEIP) method, is presented to solve the SBRIS model including long range intramolecular electrostatic interactions. The model is validated against constant pH Monte Carlo (MC) simulations. The SBRIS model is used to study the elastic response of a model weak polyelectrolyte. A new force regime is found for which (i) the force-extension curves are significantly dependent on the pH and the ionic strength values (ii) the polyelectrolyte charge is modified by the stretching force. The effect of charge fluctuation in the conformational and stretching properties of weak polyelectrolytes is studied comparing the results obtained with SGCMC simulation with those obtained with MC simulation with the same charge but keeping it constant. The conformational and elastic properties of the polyelectrolyte are observed to be significantly affected by the presence of charge regulation. On the other hand, I study the diffusive and ionization properties of biopolymers in solution with a high concentration of macromolecules. These conditions, known as macromolecular crowding, are characteristic of biological media where up to the 40% of the volume is occupied by macromolecules. The diffusion of two globular proteins, α-chymiotrypsin and streptavidin, is analysed in different crowding conditions with Brownian Dynamics simulations. A new coarse grained model is proposed, named as Chain Entanglement Softened Potential (CESP), which is found to reproduce quantitatively the experimental data. I have investigated the effect of macromolecular crowding in the binding and conformational properties of two Intrinsically Disordered Proteins (IDPs), histatin-5 and β-amyloid 42, which are modelled using a bead and spring model. The crowders are modelled using the CESP model mimicking Bovin Serum Albumin (BSA). The investigation is motivated by the hypothesis that, in the same way that the conformational and ionization degrees of freedom are coupled in weak polyelectrolytes, the macromolecular crowding should also cause a charge regulation in IDPs whose flexible structure is similar to those of weak polyelectrolytes. Two possible mechanisms through by macromolecular crowding can alter the IDP ionization are proposed: (i) the increase in the effective ionic strength (same ions in a reduced volume) and (ii) the IDP compaction due to macromolecular crowding. The IDPs global charge is found to exhibit significant variations when neutral and charged crowders are added to the system, due to the increase in the effective ionic strength., [cat] Els polímers són omnipresents a la nostra vida diària, presents en múltiples aplicacions industrials i involucrats en processos biològics essencials. Per exemple, l’ADN, les proteïnes i els sucres poden ser considerats polímers, normalment denominats biopolímers. Aquells polímers amb un gran nombre de grups carregats són coneguts com a polielectròlits i freqüentment classificats en termes de la seva ionització com a forts (completament ionizats) o febles (parcialment ionizats). En aquesta tesi, investigo diferents aspectes teòrics de les propietats conformacionals, elàstiques, difusives i d'ionització de polielectròlits febles i biopolímers. Per un costat, em centro en la complexa interació entre els graus de llibertat d'ionització i conformacionals dels polielectròlits febles utilitzant el model Site Binding Rotational Isomeric State (SBRIS), desenvolupat recentment. S’introdueix una nova tècnica analítica, el mètode Local Effective Interaction Parameters (LEIP), per resoldre el model SBRIS incloent les interaccions electroestàtiques intramoleculars de llarg abast. El model es valida comparant els resultats amb la solució obtinguda per simulacions Monte Carlo a pH constant. El model SBRIS s’utilitza per estudiar la resposta elàstica d’un polielectròlit model. Es troba un nou règim de força en el que (i) les corbes força-extensió són significativament dependents del valor del pH i la força iònica (ii) la càrrega del polielectròlit es modificada per la acció de la força d’estirament. S’observa que les propietats conformacionals i elàstiques del polielectròlit es veuen significativament i moderadament afectades per la presència de fluctuacions en la càrrega, respectivament. Per l’altre costat, avaluo les propietats difusives i d'ionització de biopolímers en solució amb una elevada concentració de macromolecules. Aquestes condicions, conegudes com crowding macromolecular, son característiques dels medis biologics on fins el 40% del volum es ocupat per macromolecules. S’analitza la difusió de dues proteïnes globulars, α-chimiotripsina i estreptavidina, en diferents condicions de crowding macromolecular amb simulacions de Dinàmica Browniana. Es proposa un nou model de gra gruixut, anomenat Chain Entanglement Softened Potential (CESP), el qual es trobat que reprodueix quantitativament les dades experimentals. S’ha investigat l’efecte del \emph{crowding} macromolecular en les propietats conformacionals i de protonació de dues proteïnes intrínsecament desordenades (IDPs), histidina

The classical Rotational Isomeric State (RIS) model, originally proposed by Flory, has been used to rationalize a wide range of physicochemical properties of neutral polymers. However, many weak polyelectrolytes of interest are able to regulate their charge depending on the conformational state of the bonds. Recently, it has been shown that the RIS model can be coupled with the Site Binding (SB) model, for which the ionizable sites can adopt two states: protonated or deprotonated. The resulting combined scheme, the SBRIS model, allows for analyzing ionization and conformational equilibria on the same foot. In the present work, this approach is extended to include pH-dependent electrostatic Long-Range (LR) interactions, ubiquitous in weak polyelectrolytes at moderate and low ionic strengths. With this aim, the original LR interactions are taken into account by defining effective Short-Range (SR) and pH-dependent parameters, such as effective microscopic protonation constants and rotational bond energies. The new parameters are systematically calculated using variational methods. The machinery of statistical mechanics for SR interactions, including the powerful and fast transfer matrix methods, can then be applied. The resulting technique, which we will refer to as the Local Effective Interaction Parameters (LEIP) method, is illustrated with a minimal model of a flexible linear polyelectrolyte containing only one type of rotating bond. LEIP reproduces very well the pH dependence of the degree of protonation and bond probabilities obtained by semi-grand canonical Monte Carlo simulations, where LR interactions are explicitly taken into account. The reduction in the computational time in several orders of magnitude suggests that the LEIP technique could be useful in a range of areas involving linear weak polyelectrolytes, allowing direct fitting of the relevant physical parameters to the experimental quantities.

The classical Rotational Isomeric State (RIS) model, originally proposed by Flory, has been used to rationalize a wide range of physicochemical properties of neutral polymers. However, many weak polyelectrolytes of interest are able to regulate their charge depending on the conformational state of the bonds. Recently, it has been shown that the RIS model can be coupled with the Site Binding (SB) model, for which the ionizable sites can adopt two states: protonated or deprotonated. The resulting combined scheme, the SBRIS model, allows for analyzing ionization and conformational equilibria on the same foot. In the present work, this approach is extended to include pH-dependent electrostatic Long-Range (LR) interactions, ubiquitous in weak polyelectrolytes at moderate and low ionic strengths. With this aim, the original LR interactions are taken into account by defining effective Short-Range (SR) and pH-dependent parameters, such as effective microscopic protonation constants and rotational bond energies. The new parameters are systematically calculated using variational methods. The machinery of statistical mechanics for SR interactions, including the powerful and fast transfer matrix methods, can then be applied. The resulting technique, which we will refer to as the Local Effective Interaction Parameters (LEIP) method, is illustrated with a minimal model of a flexible linear polyelectrolyte containing only one type of rotating bond. LEIP reproduces very well the pH dependence of the degree of protonation and bond probabilities obtained by semi-grand canonical Monte Carlo simulations, where LR interactions are explicitly taken into account. The reduction in the computational time in several orders of magnitude suggests that the LEIP technique could be useful in a range of areas involving linear weak polyelectrolytes, allowing direct fitting of the relevant physical parameters to the experimental quantities.

The high concentration of macromolecules (i.e., macromolecular crowding) in cellular environments leads to large quantitative effects on the dynamic and equilibrium biological properties. These effects have been experimentally studied using inert macromolecules to mimic a realistic cellular medium. In this paper, two different experimental in vitro systems of diffusing proteins which use dextran macromolecules as obstacles are computationally analyzed. A new model for dextran macromolecules based on effective radii accounting for macromolecular compression induced by crowding is proposed. The obtained results for the diffusion coefficient and the anomalous diffusion exponent exhibit good qualitative and generally good quantitative agreement with experiments. Volume fraction and hydrodynamic interactions are found to be crucial to describe the diffusion coefficient decrease in crowded media. However, no significant influence of the hydrodynamic interactions in the anomalous diffusion exponent is found. We acknowledge the financial support from: the Spanish Ministry of Science and Innovation (project CTM2012-39183 and CTM2016-78798-C2-1-P) and Generalitat de Catalunya (Grants 2014SGR1017, 2014SGR1132 and XrQTC). Sergio Madurga and Francesc Mas acknowledge the funding of the project 8SEWP-HORIZON 2020 (692146).