The envelope spike of HIV-1 employs a ‘glycan shield’ to protect itself from antibody-mediated neutralization. Paradoxically, however, potent broadly neutralizing antibodies (bnAbs) have been isolated which target this shield. The unusually high glycan density on the gp120 subunit limits processing during biosynthesis, leaving a region of under-processed oligomannose-type structures which is a primary target of these bnAbs. Here we investigate the contribution of individual glycosylation sites to formation of this so-called intrinsic mannose patch. Deletion of individual sites has a limited effect on the overall size of the intrinsic mannose patch but leads to changes in the processing of neighboring glycans. These structural changes are largely tolerated by a panel of glycan-dependent bnAbs targeting these regions, indicating a degree of plasticity in their recognition. These results support the intrinsic mannose patch as a stable target for vaccine design.

BackgroundWe aimed to create a theoretical tool to model the effect of three haemostatic agents containing fibrinogen (therapeutic plasma, cryoprecipitate, and fibrinogen concentrate) on the patient's plasma fibrinogen level.MethodsA mathematical model was developed step-wise. The relationship between the amount of haemostatic agent and plasma fibrinogen level was plotted for each agent. A fibrinogen concentration simulator (FCSamount) was developed, where the amount of haemostatic agent was calculated from patient characteristics, agent characteristics, and target plasma fibrinogen level. Refinements were introduced so that (i) FCSamount would account for in vivo fibrinogen recovery, (ii) circulatory volume would not increase ad infinitum with increasing amounts, and (iii) red blood cells would be included in the simulation if haematocrit decreased below a certain level. A second FCS (FCSlevel) was created to calculate fibrinogen levels resulting from specified amounts of haemostatic agents.ResultsFibrinogen concentration in haemostatic agents has a critical impact on their ability to increase patients' fibrinogen levels. If the target plasma fibrinogen level approaches the concentration of the fibrinogen source, the required amounts increase exponentially; it is impossible to achieve a target above the concentration of the fibrinogen source.ConclusionsWe successfully developed two theoretical tools answering the questions: ‘How much therapeutic plasma, cryoprecipitate, or fibrinogen concentrate would be needed to achieve a specified target fibrinogen level?’ and ‘What would be the resultant fibrinogen level for a specified amount of haemostatic agent?’ The current tools are not intended for clinical application, but they are potentially useful for educational purposes.

Determining accurate capital requirements is a central activity across the life insurance industry. This is computationally challenging and often involves the acceptance of proxy errors that directly impact capital requirements. Within simulation-based capital models, where proxies are being used, capital estimates are approximations that contain both statistical and proxy errors. Here, we show how basic error analysis combined with targeted exact computation can entirely eliminate proxy errors from the capital estimate. Consideration of the possible ordering of losses, combined with knowledge of their error bounds, identifies an important subset of scenarios. When these scenarios are calculated exactly, the resulting capital estimate can be made devoid of proxy errors. Advances in the handling of proxy errors improve the accuracy of capital requirements.

A combination of Galerkin's method and linking theory with monotonicity in the calculus of variations is used to study Hamiltonian systems in which the kinetic-energy functional is a (not necessarily definite) quadratic form and the potential-energy functional may be bounded. The existence of non-constant brake periodic orbits for almost all prescribed energies is established. An example of a Hamiltonian system which satisfies our hypotheses but has no non-constant brake periodic orbits with energy in an uncountable set of measure zero is given. Additional hypotheses, sufficient to ensure the existence of non-constant brake periodic orbits of all energies, are found. (2000): 37J45 Mathematics Subject Classification