Diffusive intracellular interactions: On the role of protein net charge and functional adaptation.

A striking feature of nucleic acids and lipid membranes is that they all carry net negative charge and so is true for the majority of intracellular proteins. It is suggested that the role of this negative charge is to assure a basal intermolecular repulsion that keeps the cytosolic content suitably 'fluid' for function. We focus in this review on the experimental, theoretical and genetic findings which serve to underpin this idea and the new questions they raise. Unlike the situation in test tubes, any functional protein-protein interaction in the cytosol is subject to competition from the densely crowded background, i.e. surrounding stickiness. At the nonspecific limit of this stickiness is the 'random' protein-protein association, maintaining profuse populations of transient and constantly interconverting complexes at physiological protein concentrations. The phenomenon is readily quantified in studies of the protein rotational diffusion, showing that the more net negatively charged a protein is the less it is retarded by clustering. It is further evident that this dynamic protein-protein interplay is under evolutionary control and finely tuned across organisms to maintain optimal physicochemical conditions for the cellular processes. The emerging picture is then that specific cellular function relies on close competition between numerous weak and strong interactions, and where all parts of the protein surfaces are involved. The outstanding challenge is now to decipher the very basics of this many-body system: how the detailed patterns of charged, polar and hydrophobic side chains not only control protein-protein interactions at close- and long-range but also the collective properties of the cellular interior as a whole.

Vesicles Balance Osmotic Stress with Bending Energy That Can Be Released to Form Daughter Vesicles.

The bending energy of the lipid membrane is central to biological processes involving vesicles, such as endocytosis and exocytosis. To illustrate the role of bending energy in these processes, we study the response of single-component giant unilamellar vesicles (GUVs) subjected to external osmotic stress by glucose addition. For osmotic pressures exceeding 0.15 atm, an abrupt shape change from spherical to prolate occurs, showing that the osmotic pressure is balanced by the free energy of membrane bending. After equilibration, the external glucose solution was exchanged for pure water, yielding rapid formation of monodisperse daughter vesicles inside the GUVs through an endocytosis-like process. Our theoretical analysis shows that this process requires significant free energies stored in the deformed membrane to be kinetically allowed. The results indicate that bending energies stored in GUVs are much higher than previously implicated, with potential consequences for vesicle fusion/fission and the osmotic regulation in living cells.

On the osmotic pressure of cells.

The chemical potential of water () provides an essential thermodynamic characterization of the environment of living organisms, and it is of equal significance as the temperature. For cells, is conventionally expressed in terms of the osmotic pressure (πosm). We have previously suggested that the main contribution to the intracellular πosm of the bacterium E. coli is from soluble negatively-charged proteins and their counter-ions. Here, we expand on this analysis by examining how evolutionary divergent cell types cope with the challenge of maintaining πosm within viable values. Complex organisms, like mammals, maintain constant internal πosm ≈ 0.285 osmol, matching that of 0.154 M NaCl. For bacteria it appears that optimal growth conditions are found for similar or slightly higher πosm (0.25-0.4 osmol), despite that they represent a much earlier stage in evolution. We argue that this value reflects a general adaptation for optimising metabolic function under crowded intracellular conditions. Environmental πosm that differ from this optimum require therefore special measures, as exemplified with gram-positive and gram-negative bacteria. To handle such situations, their membrane encapsulations allow for a compensating turgor pressure that can take both positive and negative values, where positive pressures allow increased frequency of metabolic events through increased intracellular protein concentrations. A remarkable exception to the rule of 0.25-0.4 osmol, is found for halophilic archaea with internal πosm ≈ 15 osmol. The internal organization of these archaea differs in that they utilize a repulsive electrostatic mechanism operating only in the ionic-liquid regime to avoid aggregation, and that they stand out from other organisms by having no turgor pressure.

Thermal fluctuations and osmotic stability of lipid vesicles.

Biological membranes constantly change their shape in response to external stimuli, and understanding the remodeling and stability of vesicles in heterogeneous environments is therefore of fundamental importance for a range of cellular processes. One crucial question is how vesicles respond to external osmotic stresses, imposed by differences in solute concentrations between the vesicle interior and exterior. Previous analyses of the membrane bending energy have predicted that micron-sized giant unilamellar vesicles (GUVs) should become globally deformed already for nanomolar concentration differences, in contrast to experimental findings that find deformations at much higher osmotic stresses. In this article, we analyze the mechanical stability of a spherical vesicle exposed to an external osmotic pressure in a statistical-mechanical model, including the effect of thermally excited membrane bending modes. We find that the inclusion of thermal fluctuations of the vesicle shape changes renders the vesicle deformation continuous, in contrast to the abrupt transition in the athermal picture. Crucially, however, the predicted critical pressure associated with global vesicle deformation remains the same as when thermal fluctuations are neglected, approximately six orders of magnitude smaller than the typical collapse pressure recently observed experimentally for GUVs. We conclude by discussing possible sources of this persisting dissonance between theory and experiments.

Derivation of the Derjaguin approximation for the case of inhomogeneous solvents.

The Derjaguin approximation (DA) relates the force between curved surfaces to the interaction free energy between parallel planes. It is typically derived by considering the direct interaction between the bodies involved, thus treating the effect of an intervening solvent implicitly by a rescaling of the corresponding Hamaker constant. Here, we provide a generalization of DA to the case of a molecular medium between the bodies, as is the case in most applications. The derivation is based on an explicit statistical-mechanical treatment of the contribution to the interaction force from a molecular solvent using a general expression for intermolecular and molecule-surface interactions. Starting from an exact expression for the force, DA is arrived at by a series of well-defined approximations. Our results show that DA remains valid in a molecular solvent as long as (i) the surface-molecule interactions are of a much shorter range than the radius R of the sphere and (ii) the density correlation length in the solvent is smaller than R. We then extend our analysis to the case where a phase transition occurs between the surfaces, which cannot easily be covered using a statistical-mechanical formalism due to the discontinuous change in the density of the medium. Instead, using a continuum thermodynamic description, we show that this phase transformation induces an attractive force between the bodies and that the force between curved surfaces can be related to the free energy in the corresponding planar case, in accordance with DA.

Colloidal stability of the living cell.

Cellular function is generally depicted at the level of functional pathways and detailed structural mechanisms, based on the identification of specific protein-protein interactions. For an individual protein searching for its partner, however, the perspective is quite different: The functional task is challenged by a dense crowd of nonpartners obstructing the way. Adding to the challenge, there is little information about how to navigate the search, since the encountered surrounding is composed of protein surfaces that are predominantly "nonconserved" or, at least, highly variable across organisms. In this study, we demonstrate from a colloidal standpoint that such a blindfolded intracellular search is indeed favored and has more fundamental impact on the cellular organization than previously anticipated. Basically, the unique polyion composition of cellular systems renders the electrostatic interactions different from those in physiological buffer, leading to a situation where the protein net-charge density balances the attractive dispersion force and surface heterogeneity at close range. Inspection of naturally occurring proteomes and in-cell NMR data show further that the "nonconserved" protein surfaces are by no means passive but chemically biased to varying degree of net-negative repulsion across organisms. Finally, this electrostatic control explains how protein crowding is spontaneously maintained at a constant level through the intracellular osmotic pressure and leads to the prediction that the "extreme" in halophilic adaptation is not the ionic-liquid conditions per se but the evolutionary barrier of crossing its physicochemical boundaries.

Electrostatic interactions in concentrated colloidal dispersions.

An explicit expression, free from adjustable parameters, is derived for the effective pair interaction between charged colloidal spheres at high concentration in a medium containing an electrolyte. This is accomplished by first considering the electrostatic interaction between two infinite charged plates placed in a stack of identical plates. These act as a reservoir defining the chemical potentials of solvent and electrolyte ions in a way that depends on the plate separation in the stack. The results for the planar case are then applied to a suspension of identical charged spheres. Also for this case the concentration defines the properties of a reservoir quantitatively affecting the particle-particle interaction. At short range this interaction can be determined using the Derjaguin approximation relating the interaction for the planar system to the inter-particle force. In the opposite limit the effective potential around the most probable separation is derived assuming pair-wise additive interactions from nearest neighbors. For very concentrated systems the Derjaguin approximation can be used. For a more dilute system an effective local potential is derived based on solutions of the Poisson-Boltzmann equation in the cell model.

Attractive ion-ion correlation forces and the dielectric approximation.

We analyze the classical problem of the interaction between two charged surfaces separated by a solution containing neutralizing counter-ions. The focus is on obtaining a description where the solvent is treated explicitly rather than through a dielectric approximation as is conventionally done. We summarize the results of three papers where we have used a Stockmayer fluid model in Monte Carlo simulations. It is shown that the attractive ion-ion correlation mechanism is also operating when the solvent is described explicitly. There appears an oscillatory component to the force, but when this is accounted for, there is a semi-quantitative agreement between the continuum model and the model with explicit solvent. The properties of the continuum model can be reached in a molecular system by making the solvent molecules much smaller than the ions. It is demonstrated that having an explicit solvent model makes the analysis of force mechanisms more delicate due to the interplay between several different microscopic contributions to the force. Finally, it is argued that the agreement between the forces calculated using the continuum and the explicit solvent models, respectively, has as its basis the circumstance that the force between the surfaces is mainly caused by long-range ion-ion interactions, for which the dielectric approximation is most adequate. This argument applies equally well to an aqueous system as to the Stockmayer fluid.

Microemulsions of Record Low Amphiphile Concentrations Are Affected by the Ambient Gravitational Field.

It is shown that the ternary system heavy water-heptane-hexadecyl hexaethylene oxide (C16E6) has a stable bicontinuous microemulsion phase down to an exceptionally low concentration at the balanced temperature of 26.8 °C. It is further demonstrated that the ambient gravitational field has an influence on the observed phase equilibria for typical sample sizes (∼1 cm). Direct measurements using a nuclear magnetic resonance imaging technique demonstrate that sample compositions vary with the height in the vials. It is furthermore found that some samples show four phases at equilibrium in apparent violation of Gibbs' phase rule. It is pointed out that Gibbs' phase rule strictly applies only when effects of gravity are negligible. A further consequence of the ambient gravitational field is that, for the system studied, the microemulsion one-phase samples are not observed, when using standard size vials, that is, sample heights on the order of a centimeter. Quantitative determinations of concentration profiles can be used to determine parameters of the free-energy density for the system.

Thermodynamics of protein destabilization in live cells.

Although protein folding and stability have been well explored under simplified conditions in vitro, it is yet unclear how these basic self-organization events are modulated by the crowded interior of live cells. To find out, we use here in-cell NMR to follow at atomic resolution the thermal unfolding of a ß-barrel protein inside mammalian and bacterial cells. Challenging the view from in vitro crowding effects, we find that the cells destabilize the protein at 37 °C but with a conspicuous twist: While the melting temperature goes down the cold unfolding moves into the physiological regime, coupled to an augmented heat-capacity change. The effect seems induced by transient, sequence-specific, interactions with the cellular components, acting preferentially on the unfolded ensemble. This points to a model where the in vivo influence on protein behavior is case specific, determined by the individual protein's interplay with the functionally optimized "interaction landscape" of the cellular interior.

The dynamic association processes leading from a silica precursor to a mesoporous SBA-15 material.

During the last two decades, the synthesis of silica with an ordered mesoporous structure has been thoroughly explored. The basis of the synthesis is to let silica monomers polymerize in the presence of an amphiphilic template component. In the first studies, cationic surfactants were used as structure inducer. Later it was shown that pluronic copolymers also could have the role. One advantage with the pluronics copolymers is that they allow for a wider variation in the radius of pores in the resulting silica material. Another advantage lies in the higher stability resulting from the thicker walls between the pores. Mesoporous silica has a very high area to volume ratio, and the ordered structure ensures surface homogeneity. There are a number of applications of this type of material. It can be used as support for catalysts, as templates to produces other mesoporous inorganic materials, or in controlled release applications. The synthesis of mesoporous silica is, from a practical point of view, simple, but there are significant possibilities to vary synthesis conditions with a concomitant effect on the properties of the resulting material. It is clear that the structural properties on the nanometer scale are determined by the self-assembly properties of the amphiphile, and this knowledge has been used to optimize pore geometry and pore size. To have a practical functional material it is desirable to also control the structure on a micrometer scale and larger. In practice, one has largely taken an empirical approach in optimizing reaction conditions, paying less attention to underlying chemical and physicochemical mechanisms that lead from starting conditions to the final product. In this Account, we present our systematic studies of the processes involved not only in the formation of the mesoporous structure as such, but also of the formation of structures on the micrometer scale. The main point is to show how the ongoing silica polymerization triggers a sequence of structural changes through the action of colloidal interactions. Our approach is to use a multitude of experimental methods to characterize the time evolution of the same highly reproducible synthesis process. It is the silica polymerization reactions that set the time scale, and the block copolymer self-assembly responds to the progress of the polymerization through a basically hydrophobic interaction between silica and ethylene oxide units. The progression of the silica polymerization leads to an increased hydrophobicity triggering an aggregation process resulting in the formation of silica-copolymer composite particles of increasing size. The particle growth occurs in a stepwise way caused by intricate shifts between colloidal stability and instability. By tuning reaction conditions one can have an end product of hexagonal prism composite particles with single crystal 2D hexagonal order.

The undulation force; theoretical results versus experimental demonstrations.

In 1978 Wolfgang Helfrich published a paper (Helfrich W. Z Naturforsch 1978; 33a:305) where he introduced the notion of an undulation force between bilayers. This is caused by thermal excitations of the bending modes being restricted by the presence of neighboring layers. Although there is now a consensus on the qualitative picture put forward by Helfrich there is still a debate concerning the quantitative aspects. We discuss in particular the distance dependence of the interaction and also the value of the numerical coefficient of the force law derived by Helfrich.

Scattering and diffraction described using the momentum representation.

We present a unified analysis of the scattering and diffraction of neutrons and photons using momentum representation in a full quantum description. The scattering event is consistently seen as a transfer of momentum between the target and the probing particles. For an elastic scattering process the observed scattering pattern primarily provides information on the momentum distribution for the particles in the target that cause the scattering. Structural information then follows from the Fourier transform relation between momentum and positional state functions. This description is common to the scattering of neutrons, X-ray photons and photons of light. In the quantum description of the interaction between light and the electrons of the target the scattering of X-rays is dominated by the first order contribution from the vector potential squared. The interaction with the electron is local and there is a close analogy, evident from the explicit quantitative expressions, with the neutron scattering case where the nucleus-neutron interaction is fully local from a molecular perspective. For light scattering, on the other hand, the dominant contribution to the scattering comes from a second order term linear in the vector potential. Thus the scattering of light involves correlations between electrons at different positions giving a conceptual explanation of the qualitative difference between the scattering of high and low energy photons. However, at energies close to resonance conditions the scattering of high energy photons is also affected by the second order term which results in a so called anomalous X-ray scattering/diffraction. It is also shown that using the momentum representation the phenomenon of diffraction is a direct consequence of the fact that for a system with periodic symmetry like a crystal the momentum distribution is quantized, which follows from Bloch's theorem. The momentum transfer to a probing particle is then also quantized resulting in a discrete diffraction pattern.

Björn Lindman: fifty years in science and technology.

Björn Lindman has for fifty years had an active role in science and technology. His main contributions are briefly described. In the science part particular emphasis is put on his studies of ion binding, of amphiliphilc self-association, of molecular diffusion in solution and of polymer-surfactant systems. Furthermore we describe his role in introducing scientific areas, his role in scientific collaborations and his contributions to scientific organizations. The text is concluded by some personal reflections by the author.

Lipid phase behaviour under steady state conditions.

At the interface between two regions, for example the air-liquid interface of a lipid solution, there can arise non-equilibrium situations. The water chemical potential corresponding to the ambient RH will, in general, not match the water chemical potential of the solution, and the gradients in chemical potential cause diffusional flows. If the bulk water chemical potential is close to a phase transition, there is the possibility of forming an interfacial phase with structures qualitatively different from those found in the bulk. Based on a previous analysis of this phenomenon in two component systems (C. Aberg, E. Sparr, K. J. Edler and H. Wennerström, Langmuir, 2009, 25, 12177), we here analyse the henomenon for three-component systems. The relevant transport equations are erived, and explicit results are given for some limiting cases. Then the formalism s applied conceptually to four different aqueous lipid systems, which in addition to water and a phospholipid contain (i) octyl glucoside, (ii) urea, (iii) heavy water, and (iv) sodium cholate as the third component. These four cases are chosen to illustrate (i) a method to use a micelle former to transport lipid to the interface where a multi-lamellar structure can form; (ii) to use a co-solvent to inhibit the formation of a gel phase at the interface; (iii) a method to form pure phospholipid multi-lamellar structures at the interface; (iv) a method to form a sequence of phases in the interfacial region. These four cases all have the character of theoretically based conjectures and it remains to investigate experimentally whether or not the conditions can be realized in practice.

The Stern-Gerlach experiment and the effects of spin relaxation.

The classical Stern-Gerlach experiment is analyzed with an emphasis on the spin dynamics. The central question asked is whether there occurs a relaxation of the spin angular momentum during the time the particle passes through the Stern-Gerlach magnet. We examine in particular the transverse relaxation, involving angular momentum exchange between the spin of the particles and the spins of the magnet. A method is presented describing relaxation effects at an individual particle level. This leads to a stochastic equation of motion for the spins. This is coupled to a classical equation of motion for the particle translation. The experimental situation is then modeled through simulations of individual trajectories using two sets of parameter choices and three different sets of initial conditions. The two main conclusions are: (A) if the coupling between the magnet and the spin is solely described by the Zeeman interaction with the average magnetic field the simulations show a clear disagreement with the experimental observation of Stern and Gerlach. (B) If one, on the other hand, also allows for a T(2) relaxation time shorter than the passage time one can obtain a practically quantitative agreement with the experimental observations. These conclusions are at variance with the standard textbook explanation of the Stern-Gerlach experiment.

The transition from a molecular to a continuum solvent in electrical double layers showing ion-ion correlation effects.

We analyze, using Monte Carlo simulations, how a dielectric medium, modeled as a Stockmayer fluid, modulates the force between two similarly charged surfaces. A major objective is to provide a basis for understanding the strengths and weaknesses of the primitive model. The system studied has uniformly charged walls separated by counterions and solvent, where the latter is kept at constant chemical potential as the separation between the walls is varied. For two different types of Stockmayer fluids, one with a "low" (ε(r) ≃ 4.4) and one with a "high" (ε(r) ≃ 20) relative dielectric permittivity, the size of the solvent molecules is varied systematically. As the size of the solvent molecules becomes smaller one approaches the continuum limit, where the primitive model should give an increasingly more accurate representation. We find that having an explicit description of the solvent gives rise to an oscillatory component in the force between the surfaces. The wavelength of the oscillations reflects the diameter of the solvent molecules. The smaller the solvent molecules the smaller are the amplitudes of the oscillations. On integrating the force curves to yield interaction free energies the oscillatory features become less apparent. For the smallest solvent size studied the interaction curves show clear similarities with those obtained from the primitive model. The qualitative effect of the dielectric screening is recovered. It is found that the deviations from the mean field description also appear for the molecular solvent. All this suggests that there are no major deviations due to the neglect of many-body contributions in the solvent-averaged potential of the primitive model. This also holds for the incompressibility assumption implicitly applied when using the primitive model.

An exact calculation of the van der Waals interaction between two spheres of classical dipolar fluid.

An exact treatment of the van der Waals interaction between two spherical dielectric bodies possessing purely classical degrees of freedom is presented. The spheres are described by multipole expansions of their fluctuating charge distributions, and the correlation between the fluctuations are taken into account using classical electrostatics and statistical mechanics. The presented approach avoids both the assumption of pairwise additivity of Hamaker theory and the implicit linear response assumption of Lifshitz theory. The resulting equations are solved numerically for D/a ≥ 0.01, where a is the radius of the spheres and D is their minimum separation, for a system with ε = 80, and the results are compared to the analytical Hamaker formula with a Hamaker constant calculated from Lifshitz theory.

A theoretical study of diffusional transport over the alveolar surfactant layer.

In this communication, we analyse the passage of oxygen and carbon dioxide over the respiratory membrane. The lung surfactant membrane at the alveolar interface can have a very special arrangement, which affects the diffusional transport. We present a theoretical model for the diffusion of small molecules in membranes with a complex structure, and we specifically compare a membrane composed of a tubular bilayer network with a membrane consisting of a stack of bilayers. Oxygen and carbon dioxide differ in terms of their solubility in the aqueous and the lipid regions of the membrane, and we show that this difference clearly influences their transport properties in the different membrane structures. During normal respiration, the rate-limiting step for carbon dioxide transport is in the gas phase of the different compartments in the lung. For oxygen, on the other hand, the rate is limited by the transport between alveoli and the capillary blood vessels, including the lung surfactant membrane. In a membrane with a structure of a continuous tubular lipid network, oxygen transport is facilitated to a significant extent compared with the structure of aligned lipid bilayers. The model calculations in the present study show that transport of oxygen through the tubular structure is indeed ca 30 per cent faster than transport through a membrane composed of stacked bilayers. The tubular network will also facilitate the transport of apolar substances between the gas phase and the blood. Important examples are ethanol and other volatile liquids that can leave the blood through the lungs, and gaseous anaesthetics or volatile solvents that are inhaled. This exemplifies a new physiological role of a tubular lipid network in the lung surfactant membrane.