Chemistry of Lipid A: At the Heart of Innate Immunity

In many Gram‐negative bacteria, lipopolysaccharide (LPS) and its lipid A moiety are pivotal for bacterial survival. Depending on its structure, lipid A carries the toxic properties of the LPS and acts as a potent elicitor of the host innate immune system via the Toll‐like receptor 4/myeloid differentiation factor 2 (TLR4/MD‐2) receptor complex. It often causes a wide variety of biological effects ranging from a remarkable enhancement of the resistance to the infection to an uncontrolled and massive immune response resulting in sepsis and septic shock. Since the bioactivity of lipid A is strongly influenced by its primary structure, a broad range of chemical syntheses of lipid A derivatives have made an enormous contribution to the characterization of lipid A bioactivity, providing novel pharmacological targets for the development of new biomedical therapies. Here, we describe and discuss the chemical aspects regarding lipid A and its role in innate immunity, from the (bio)synthesis, isolation and characterization to the molecular recognition at the atomic level.     

Formation of unexpected ions from a first‐generation polyamidoamine dendrimer by use of methanol: an artefact due to electrospray emitter corrosion?

We report the formation of unexpected ions during the analyses of a first‐generation polyamidoamine dendrimer in negative ion mode using an ion trap equipped with an electrospray ionisation source. These surprising ions corresponded to an increase of 12 m/z units over those expected. The formation of the unexpected ions was dependent on the tuning of the solution flow rate and the capillary high voltage. In addition, measurements of unusual value of the current suggested that a reaction was occurring in the corona plasma. The influence of methanol in this phenomenon was demonstrated by using CD₃OH in the sample preparation. We propose two structures to explain the observed adduct based on the results of MS² experiments and by referring to previous work dealing with 12 m/z units addition. We showed that a corona discharge caused by alterations taking place to the electrospray capillary emitter was the origin of these unexpected ions. Finally, we discuss the mechanism involved in the formation of the ions and we propose means to control such artefacts. Copyright © 2010 John Wiley & Sons, Ltd.     

Hamiltonian and Brownian systems with long-range interactions: V. Stochastic kinetic equations and theory of fluctuations

We developed a theory of fluctuations for Brownian systems with weak long-range interactions. For these systems, there exists a critical point separating a homogeneous phase from an inhomogeneous phase. Starting from the stochastic Smoluchowski equation governing the evolution of the fluctuating density field of Brownian particles, we determine the expression of the correlation function of the density fluctuations around a spatially homogeneous equilibrium distribution. In the stable regime, we find that the temporal correlation function of the Fourier components of density fluctuations decays exponentially rapidly, with the same rate as the one characterizing the damping of a perturbation governed by the deterministic mean field Smoluchowski equation (without noise). On the other hand, the amplitude of the spatial correlation function in Fourier space diverges at the critical point T=T_c (or at the instability threshold k=k_m) implying that the mean field approximation breaks down close to the critical point, and that the phase transition from the homogeneous phase to the inhomogeneous phase occurs sooner. By contrast, the correlations of the velocity fluctuations remain finite at the critical point (or at the instability threshold). We give explicit examples for the Brownian Mean Field (BMF) model and for Brownian particles interacting via the gravitational potential and via the attractive Yukawa potential. We also introduce a stochastic model of chemotaxis for bacterial populations generalizing the deterministic mean field Keller-Segel model by taking into account fluctuations and memory effects.     

Two-dimensional Brownian vortices

We introduce a stochastic model of 2D Brownian vortices associated with the canonical ensemble. The point vortices evolve through their usual mutual advection but they experience in addition a random velocity and a systematic drift generated by the system as a whole. The statistical equilibrium state of this stochastic model is the Gibbs canonical distribution. We consider a single species system and a system made of two types of vortices with positive and negative circulations. At positive temperatures, like-sign vortices repel each other (“plasma” case) and at negative temperatures, like-sign vortices attract each other (“gravity” case). We derive the stochastic equation satisfied by the exact vorticity field and the Fokker-Planck equation satisfied by the N-body distribution function. We present the BBGKY-like hierarchy of equations satisfied by the reduced distribution functions and close the hierarchy by considering an expansion of the solutions in powers of 1/N, where N is the number of vortices, in a proper thermodynamic limit. For spatially inhomogeneous systems, we derive the kinetic equations satisfied by the smooth vorticity field in a mean field approximation valid for N→+∞. For spatially homogeneous systems, we study the two-body correlation function, in a Debye-Hückel approximation valid at the order O(1/N). The results of this paper can also apply to other systems of random walkers with long-range interactions such as self-gravitating Brownian particles and bacterial populations experiencing chemotaxis. Furthermore, for positive temperatures, our study provides a kinetic derivation, from microscopic stochastic processes, of the Debye-Hückel model of electrolytes.     

Gravitational phase transitions with an exclusion constraint in position space

We discuss the statistical mechanics of a system of self-gravitating particles with anexclusion constraint in position space in a space of dimension d. Theexclusion constraint puts an upper bound on the density of the system and can stabilize itagainst gravitational collapse. We plot the caloric curves giving the temperature as afunction of the energy and investigate the nature of phase transitions as a function ofthe size of the system and of the dimension of space in both microcanonical and canonicalensembles. We consider stable and metastable states and emphasize the importance of thelatter for systems with long-range interactions. For d ≤ 2, there is nophase transition. For d > 2, phase transitions can take place betweena “gaseous” phase unaffected by the exclusion constraint and a “condensed” phase dominatedby this constraint. The condensed configurations have a core-halo structure made of a“rocky core” surrounded by an “atmosphere”, similar to a giant gaseous planet. For largesystems there exist microcanonical and canonical first order phase transitions. Forintermediate systems, only canonical first order phase transitions are present. For smallsystems there is no phase transition at all. As a result, the phase diagram exhibits twocritical points, one in each ensemble. There also exist a region of negative specificheats and a situation of ensemble inequivalence for sufficiently large systems. We showthat a statistical equilibrium state exists for any values of energy and temperature inany dimension of space. This differs from the case of the self-gravitating Fermi gas forwhich there is no statistical equilibrium state at low energies and low temperatures whend ≥ 4. By a proper interpretation of the parameters, our results haveapplication for the chemotaxis of bacterial populations in biology described by ageneralized Keller-Segel model including an exclusion constraint in position space. Theyalso describe colloids at a fluid interface driven by attractive capillary interactionswhen there is an excluded volume around the particles. Connexions with two-dimensionalturbulence are also mentioned.     

Critical mass of bacterial populations and critical temperature of self-gravitating Brownian particles in two dimensions

We show that the critical mass M_c=8π of bacterial populations in two dimensions in the chemotactic problem is the counterpart of the critical temperature T_c=GMm/4k_B of self-gravitating Brownian particles in two-dimensional gravity. We obtain these critical values by using the Virial theorem or by considering stationary solutions of the Keller-Segel model and Smoluchowski-Poisson system. We also consider the case of one-dimensional systems and develop the connection with the Burgers equation. Finally, we discuss the evolution of the system as a function of M or T in bounded and unbounded domains in dimensions d=1, 2 and 3 and show the specificities of each dimension. This paper aims to point out the numerous analogies between bacterial populations, self-gravitating Brownian particles and, occasionally, two-dimensional vortices.