Entropic Path Sampling: Computational Protocol to Evaluate Entropic Profile along a Reaction Path

Fleeting intermediates constitute dynamically-stepwise mechanisms. They have been characterized in molecular dynamics trajectories, but whether these intermediates form a free energy minimum to become entropic intermediate remains elusively defined. We developed a computational protocol known as entropic path sampling to evaluate the entropic variation of reacting species along a reaction path based on an ensemble of trajectories. Using cyclopentadiene dimerization as a model reaction, we observed a shallow entropic trap (–T∆S = –0.8 kcal/mol) along the reaction path which originates from an enhanced conformational flexibility as the reacting species enter into a flat energy region. As the reacting species further approach product formation, unfavorable entropic restriction fails to offset the potential energy drop, resulting in no free energy minimum along the post-TS pathway. Our results show that cyclopentadiene dimerization involves an entropic trap that leads to dynamic intermediates with elongated lifetime, but the reaction does not involve entropic intermediates.

The 2-D Cluster Variation Method: Topography Illustrations and Their Enthalpy Parameter Correlations

One of the biggest challenges in characterizing 2-D image topographies is finding a low-dimensional parameter set that can succinctly describe, not so much image patterns themselves, but the nature of these patterns. The 2-D cluster variation method (CVM), introduced by Kikuchi in 1951, can characterize very local image pattern distributions using configuration variables, identifying nearest-neighbor, next-nearest-neighbor, and triplet configurations. Using the 2-D CVM, we can characterize 2-D topographies using just two parameters; the activation enthalpy (ε0) and the interaction enthalpy (ε1). Two different initial topographies (“scale-free-like” and “extreme rich club-like”) were each computationally brought to a CVM free energy minimum, for the case where the activation enthalpy was zero and different values were used for the interaction enthalpy. The results are: (1) the computational configuration variable results differ significantly from the analytically-predicted values well before ε1 approaches the known divergence as ε1→0.881, (2) the range of potentially useful parameter values, favoring clustering of like-with-like units, is limited to the region where ε0<3 and ε1<0.25, and (3) the topographies in the systems that are brought to a free energy minimum show interesting visual features, such as extended “spider legs” connecting previously unconnected “islands,” and as well as evolution of “peninsulas” in what were previously solid masses.

Electrostatic Interactions with Choline and Phosphate Groups Regulate Cisplatin Permeation through a Dioleoylphosphocholine Bilayer

The investigation of the intermolecular interactions between platinum-based anticancer drugs and lipid bilayers is of special relevance to unveil the mechanisms involved in different steps of the mode of action of these drugs. We have simulated the permeation of cisplatin through a model membrane composed of 1,2-dioleoyl-sn-glycero-3-phosphocholine lipids by means of umbrella sampling classical molecular dynamics simulations. The initial physisorption of cisplatin in the polar region of the membrane is controlled, in a first moment, by long-range electrostatic interactions with the choline groups, which trap the drug in a shallow free-energy minimum. Then, cisplatin is driven to a deeper free-energy minimum by long-range electrostatic interactions with the phosphate groups. From this minimum to the middle of the bilayer the electrostatic repulsion between cisplatin and the choline groups partially cancels out the electrostatic attraction between cisplatin and the phosphate groups, inducing a general drop of the total interaction with the polar heads. In addition, the attractive interactions with the non-polar tails, which are dominated by van der Waals contributions, gain significance. The large energy barrier found when going from the global minimum to the middle of the membrane indicates that the non-electrostatic interactions between the drug and the non-polar tails are badly reproduced by the fixed point-charge force field used here, and that the introduction of polarization effects are likely necessary.

Electrostatic Interactions with Choline and Phosphate Groups Regulate Cisplatin Permeation through a Dioleoylphosphocholine Bilayer

The investigation of the intermolecular interactions between platinum-based anticancer drugs and lipid bilayers is of special relevance to unveil the mechanisms involved in different steps of the mode of action of these drugs. We have simulated the permeation of cisplatin through a model membrane composed of 1,2-dioleoyl-sn-glycero-3-phosphocholine lipids by means of umbrella sampling classical molecular dynamics simulations. The initial physisorption of cisplatin in the polar region of the membrane is controlled, in a first moment, by long-range electrostatic interactions with the choline groups, which trap the drug in a shallow free-energy minimum. Then, cisplatin is driven to a deeper free-energy minimum by long-range electrostatic interactions with the phosphate groups. From this minimum to the middle of the bilayer the electrostatic repulsion between cisplatin and the choline groups partially cancels out the electrostatic attraction between cisplatin and the phosphate groups, inducing a general drop of the total interaction with the polar heads. In addition, the attractive interactions with the non-polar tails, which are dominated by van der Waals contributions, gain significance. The large energy barrier found when going from the global minimum to the middle of the membrane indicates that the non-electrostatic interactions between the drug and the non-polar tails are badly reproduced by the fixed point-charge force field used here, and that the introduction of polarization effects are likely necessary.

Axioms of mathe- matical immunology

Current wisdom describes the immune system as a defense against microbial pathogens. It is claimed that the virgin immune system has a capacity to produce antibodies against the entire antigenic universe. We assume, by contrast, that the responding capacity of the immune system is limited. Thus it cannot stand in readiness to deal with a practi- cally endless diversity and abundance of microbes. Axioms and theorems are suggested for a mathematician audience delineating how the immune system could use its limited resources economically. It is suggested that the task of the immune system is twofold: (i) It sustains homeostasis to preserve the genome by constant surveillance of the intracellular antigenic milieu. This is achieved by standardization of the T cell repertoire through a positive selection. The driving force of positive selection is immune cell survival. T cells must constantly seek contact with complementary MHC structures to survive. Such contact is based on molecular complementarity between immune cell receptors and MHC/self-peptide complexes. At the highest level of complementarity a local free energy minimum is achieved, thus a homeostatic system is created. Homeostatic interactions happen at intermediate afinity and are reversible. Alteration in the presented peptides typically decreases complementarity. That pushes the system away from the free energy minimum, which activates T cells. Complementarity is restored when cytotoxic T cells destroy altered (mutated/infected) host cells. (ii) B cells carry out an immune response to foreign proteins what requires a change in the genome. B cells raised under the antigenic in uence of the normal intestinal micro o- ra, self-proteins and alimentary antigens must go through a hypermutation process to be able to produce specific antibodies. It has a certain probability that hypermutation will successfully change the genome in some clones to switch from low afinity IgM antibody production to high afinity IgG production. Interactions (typically antibody antigen reac- tions) in an immune response happen at high afinity and are irreversible. High afinity clones will be selected, stimulated and enriched by the invading microbes. A complete account of the course of an infectious disease must also include a descrip- tion of the ecology of the immune response. It is therefore suggested that during prolonged interaction between host and infectious organism, carried on across many generations, the adaptive antibody population may facilitate the evolution of the natural antibody reper- toire, in accordance with the Baldwin effect in the evolution of instinct (see Appendix 6).