Five challenges in evolution and infectious diseases.

Evolution is a key aspect of the biology of many pathogens, driving processes ranging from immune escape to changes in virulence. Because evolution is inherently subject to feedbacks, and because pathogen evolution plays out at scales ranging from within-host to between-host and beyond, evolutionary questions provide special challenges to the modelling community. In this article, we provide an overview of five challenges in modelling the evolution of pathogens and their hosts, and point to areas for development, focussing in particular on the issue of linking theory and data.

A generalized functional response for predators that switch between multiple prey species.

We develop a theory for the food intake of a predator that can switch between multiple prey species. The theory addresses empirical observations of prey switching and is based on the behavioural assumption that a predator tends to continue feeding on prey that are similar to the prey it has consumed last, in terms of, e.g., their morphology, defences, location, habitat choice, or behaviour. From a predator's dietary history and the assumed similarity relationship among prey species, we derive a general closed-form multi-species functional response for describing predators switching between multiple prey species. Our theory includes the Holling type II functional response as a special case and makes consistent predictions when populations of equivalent prey are aggregated or split. An analysis of the derived functional response enables us to highlight the following five main findings. (1) Prey switching leads to an approximate power-law relationship between ratios of prey abundance and prey intake, consistent with experimental data. (2) In agreement with empirical observations, the theory predicts an upper limit of 2 for the exponent of such power laws. (3) Our theory predicts deviations from power-law switching at very low and very high prey-abundance ratios. (4) The theory can predict the diet composition of a predator feeding on multiple prey species from diet observations for predators feeding only on pairs of prey species. (5) Predators foraging on more prey species will show less pronounced prey switching than predators foraging on fewer prey species, thus providing a natural explanation for the known difficulties of observing prey switching in the field.

Wrist denervation in isolation: a prospective outcome study with patient selection by wrist blockade.

Surgical wrist denervation involves division of the anterior and posterior interosseous nerves and articular branches of the superficial radial nerve. In this outcome study, 37 patients were individually assessed and deemed suitable for denervation surgery due to appreciable symptom resolution following a local anesthetic wrist block. At a mean of 18 months following denervation surgery, median activity pain scores had decreased by 60% (p < 0.001) from initial assessment levels, and more than three quarters (30/37) of patients reported continued improvement in their activity pain (p < 0.001). More than two thirds of patients had a satisfaction VAS of greater than 50, with less postoperative resting pain and a greater reduction in postoperative activity pain as the important predictors of patient satisfaction. Thirty-one out of the 37 patients had not represented to our department for revision wrist surgery by a mean of 10.3 years follow-up. We have found this procedure useful in ameliorating symptoms for some patients who would conventionally have required partial or total wrist fusions with greater residual functional limitation.

Endemic disease, awareness, and local behavioural response.

The spread of a contagious disease is often accompanied by a rise in awareness of those in the social vicinity of infected individuals, and a subsequent change in behaviour. Such reactions can manifest themselves in lower susceptibility as people try to prevent themselves from catching the disease, but also in lower infectivity because of self-imposed quarantine or better hygiene, shorter durations of infectiousness or longer immunity. We here focus on the scenario of an endemic disease of which members of the population can be either aware or unaware, and consider a broad set of possible reactions. We quantify the impact on the endemicity of a disease in a well-mixed population under the variation of different disease parameters as a consequence of growing awareness in the population. Applying a pair-closure scheme allows us to analyse the effect of local correlations if aware individuals tend to occur near infected cases, and to link this to the amount of overlap between the networks underlying the spread of awareness and disease, respectively. Lastly, we study the consequences on the dynamics when the pathogen and awareness spread at different velocities.

Evolutionary consequences of a search image.

Many predators are able to become better at spotting cryptic prey by recognising specific clues, but by concentrating on one prey type they will become worse at spotting other prey types. This phenomenon is known as the formation of a search image for a certain prey by a predator and is related to apostatic selection. Here, we study the evolution of a search image in the predator by formulating and analysing a mathematical model. The predator forages for two prey types and is able to form an independent search image for both prey. The results show that the evolutionary dynamics can be divided into two parts: a fast and a slow part. At first selection pressure will be strong towards a stable ratio of prey, which is the same as the ratio found for the unbeatable prey choice for predators with a Holling type II functional response. Following this, the slow dynamics will keep this ratio constant independent of the trait values, but the predator will slowly evolve towards a stronger search image and ultimately become a specialist predator or slowly evolve towards generalist with a weak search image. In conclusion, the formation of a search image causes the predator to control the prey densities such that the ratio of available prey is kept constant by the predator.

How population dynamics shape the functional response in a one-predator-two-prey system.

The type III functional response has historically been associated with switching predators; when there is a choice of prey the predator favors the more abundant prey type. Although this functional response has been found in experiments where both prey densities are manipulated, in real world studies the type II functional response is more commonly found. In modeling, the type III functional response is often used in systems where the second prey type is, implicitly, assumed to be constant. Here we define a functional response that takes into account both prey densities. This causes the functional response to show both type II and type III behavior, dependent on the interaction between the two prey densities. If we take into account population dynamics, we find a type II functional response in most cases, because predation regulates the relative prey densities. This explains why type III functional responses are found in experiments where both prey densities are manipulated, but type II functional responses occur when the feedback of population dynamics on the functional response is important. Furthermore, the results show that switching can have a stabilizing or destabilizing effect and can even lead to predator extinction.

[Plasma concentration of endothelin-1 after myocutaneous latissimus dorsi-transplantation -- role in reperfusion injury]. / Plasmakonzentrationen von Endothelin-1 nach myokutaner Latissimus dorsi-Transplantation -- Bedeutung für den Reperfusionsschaden.

The success of a free flap transplantation is based on a sufficient microanastomosis which meets the following requirements: a pedicle placed without kinking or twisting, a good drainage, a well defined recipient vessel and integrity of the endothelium. The aim of this study was to determine whether operation-related ischaemia through flap transplantation and tourniquet induces an increase of Endothelin-1 plasma levels as one cause of vasospasm during microvascular procedures. We focused our attention in particular on the reperfusion period which is often limited to an irreversible perfusion failure of microcirculation due to free radicals, interleukin and Endothelin-1. Twenty-one patients with tissue injury of the lower leg were included in our study, fourteen underwent a latissimus dorsi muscle transplantation with a combined ischaemia, seven patients had a tourniquet ischaemia for tumour resection, debridement and local flap transfer. The duration of ischaemia varied due to the course of operation. The withdrawal of venous blood via central vein catheter, flap vein and wound bed followed a fixed time table pre- and post-reperfusion (T1: preoperative day via cubital vein, T2: 6th postoperative day, T3: 5 min, T4: 10 min, T5: 15 min, T6: 1 h post-declamping and after tourniquet ischaemia via central vein catheter and T7: within 5 min from the flap vein immediate after recharging the flap). The vessel anastomosis determined the withdrawal from the local wound bed. ET-1 in venous blood samples were measured with ELISA. The duration of ischaemia in the tourniquet group ranged from 22 min up to 210 min with a mean of 76.58 min and in the latissimus group from 87 min up to 203 min with a mean of 139.21 min. The mean ET-1 plasma concentration measured systemically before operation in the 21 patients was 0.51 +/- 0.08 pg/ml (Mean +/- SD). This result corresponds with data published in literature. The locally measured plasma levels of ET-1 after tourniquet and flap ischaemia were increased with 0.34 up to 3.90 pg/ml (0.95 +/- 0.79 pg/ml [Mean +/- SD]) for the tourniquet group and with 0.34 up to 14.87 pg/ml (1.85 +/- 3.64 pg/ml [Mean +/- SD]) for the latissimus group. This is an increase compared to systemically measured values as 0.75 +/- 0.06 pg/ml (Mean +/- SD) for the tourniquet group and 0.58 +/- 0.21 pg/ml (Mean +/- SD) for the latissimus group. We conclude that Endothelin-1 is increased locally in the early reperfusion period after free latissimus dorsi-transplantation.

[The use of regional anesthesia in orthopedics]. / Regionalanästhesie in der Orthopädie.

Regional anesthesia has its place in the perioperative pain management of orthopedic patients. A reduction in postoperative mortality and morbidity with regional anesthesia is acknowledged for subsets of patient populations. Single shot and continuous applications are techniques for providing regional analgesia. Continuous infusion of local anesthetics with catheter techniques provides for uninterrupted postoperative analgesia. The combination of regional and general anesthesia reduces the consumption of systemic anesthetics. The side effects of opioid therapy are thereby reduced. The inhibition of intraoperative stress reaction, especially with epidural anesthesia, helps to prevent or lower unwanted metabolic changes. Patient contentment with analgesic quality differs with the technique with which the regional anesthesia is applied (PDA, PCEA, IVRA, peripheral block, i.a. injection), and the medication (LA, opioid) used.

The dual role of CD4 T helper cells in the infection dynamics of HIV and their importance for vaccination.

Given the role of the CD4 T helper cells in the development of memory CTL precursors, it seems beneficial to boost the CD4 T helper response in the context of vaccination against the human immunodeficiency virus (HIV). However, CD4 T cells are also the preferred targets of infection by HIV. Here, we address the question as to whether it is advantageous to stimulate the CD4 T helper cell response, as this will increase the pool of potential target cells of infection. To do so we formulated a mathematical model describing the interactions between virus-infected cells, susceptible cells, HIV-specific CD4 helper T cells, and CTL precursor (CTLp) and effector cells (CTLe). The effect of increased initial CD4 helper and CTLp numbers on the outcome of infection, as well as the effect on viral set point of increased CD4 T helper growth rate, CTL responsiveness and the rate at which CTLp and CTLe are produced were studied. We found that only when the virus has a low basic reproductive number does the number of CTLp and CD4 T helper cells at the moment of infection influence the outcome of infection. In this situation, high initial T helper and CTL numbers can switch the outcome from full-blown infection to virus control. However, this holds for virus with infectivity in a limited range, and current estimates of virus infectivity suggest that it is higher. In that case, only a vaccination protocol that increases CTL responsiveness, ideally in combination with the rate of production of CD4 T helper cells, may offer a solution as it can reduce the viral set point considerably. If brought under a certain level, the viral population might be unable to replicate any further. However, changing these parameters of the immune response is only beneficial when infection is controlled by CTL in the long term. When a CD4 lymphoproliferative response is mounted but the CTL response is not maintained, increasing the CD4 T helper growth rate is deleterious.

Effector cytotoxic T lymphocyte numbers induced by vaccination should exceed levels in chronic infection for protection from HIV.

Recent technological advances have revolutionised our capacity to induce cytotoxic T lymphocyte (CTL) responses with a variety of vaccine formulations and delivery systems. However, the conditions required for a CTL-inducing vaccine to provide protection from infection or disease are poorly understood, and the results of challenge experiments have not been consistent. Here we use a mathematical model to examine the requirements necessary for successful vaccination against human immunodeficiency virus (HIV) through cellular immunity. We describe the interaction between cytotoxic T cells and infected lymphocytes, capturing the essence of a persistent infection of immune cells. We conclude that to protect from infection, the cellular immune response should be boosted to levels exceeding those in chronic infection. This requires either that effector CTL exceed this threshold before infection, or that a memory CTL population is established that can yield this level of effector CTL very quickly upon infection.

The role of T cell help for anti-viral CTL responses.

Cytotoxic T lymphocyte (CTL or CD8) responses are a major branch of the immune system involved in controlling viral infections. Murine models have shown that the development of effective and sustained CD8 cell responses requires CD4 T cell help. However, the precise mechanism in which CD4 cells provide help for CD8 cell responses is still controversial. In the literature, mainly two mechanisms are discussed. According to the "classical" pathway, CD4 cells secrete cytokines, such as IL-2, which promote the responsiveness of the CD8 cells. According to the "CD4-APC-CD8" pathway, CD4 cells specifically activate antigen presenting cells (APCs), and APCs specifically interact with CD8 cells, thereby delivering help. Here, we derive kinetic models in order to describe and compare both pathways of help. We find that the two pathways might have different roles in different situations. The classical pathway is more efficient at inducing CD8 cell expansion at high virus loads, while the CD4-APC-CD8 pathway is more efficient at inducing CD8 cell proliferation at low virus loads. From this, it follows that the classical pathway might be needed in order to kick-start a CD8 cell response in the acute phase of the infection, while the CD4-APC-CD8 pathway is needed in order to ensure virus clearance when virus load is reduced by the immune system. These findings have implications for the interpretation of experimental data from virus infection in helper-deficient hosts. In particular, the models offer further suggestions for the development of treatment regimes aimed at achieving immunological control of HIV infection which has been shown to crucially depend on the availability of helper cell responses.

Host life history and the evolution of parasite virulence.

We present a general epidemiological model of host-parasite interactions that includes various forms of superinfection. We use this model to study the effects of different host life-history traits on the evolution of parasite virulence. In particular, we analyze the effects of natural host death rate on the evolutionarily stable parasite virulence. We show that, contrary to classical predictions, an increase in the natural host death rate may select for lower parasite virulence if some form of superinfection occurs. This result is in agreement with the experimental results and the verbal argument presented by Ebert and Mangin (1997). This experiment is discussed in the light of the present model. We also point out the importance of superinfections for the effect of nonspecific immunity on the evolution of virulence. In a broader perspective, this model demonstrates that the occurrence of multiple infections may qualitatively alter classical predictions concerning the effects of various host life-history traits on the evolution of parasite virulence.

The measured level of prion infectivity varies in a predictable way according to the aggregation state of the infectious agent.

Transmissible spongiform encephalopathies are believed to be caused by an infectious form of the prion protein, designated PrP(Sc). The concentration of PrP(Sc) is often poorly correlated to the level of infectivity. Infectivity can be measured in two ways, namely endpoint titration and the incubation time assay, but patterns of infectivity vary depending on which method is used. These discrepancies can be explained by variation in the aggregation state of PrP(Sc). Both methods of measuring infectivity are modelled mathematically, and the theoretical results are in agreement with published data. It was found to be theoretically impossible to characterise prion infectivity by a multiple of a single quantity representing 'one prion', no matter how it is measured. Infectivity is instead characterised by both the number and sizes of the PrP(Sc) aggregates. Apparent discrepancies arise when these complexities are reduced to a single number.

Carrier screening for Gaucher disease in couples of mixed ethnicity.

With the advent of mutational analysis for Gaucher disease, carrier screening has been incorporated into many Jewish genetic disease screening programs. Frequencies and mutations for Gaucher disease in non-Jewish populations are less well established and the detection rate of carriers are lower. Testing is problematic for resolving residual risk in a couple of mixed ethnicity. We report the testing choices made by 20 consecutive couples of mixed ethnicity where the Ashkenazi Jewish partner was identified to be a Gaucher disease gene carrier. Carrier studies of the non-Jewish partner were elected as follows: DNA studies alone, 5 (25%); enzymatic assay, 2 (10%); both, 6 (30%); no carrier studies, 7 (35%). Of the 7 couples not electing carrier studies, one was not in a pregnancy and 6 elected prenatal diagnosis in lieu of parental testing by enzymatic analysis of amniocytes. One couple elected parental carrier studies as well as prenatal diagnosis. All couples electing prenatal Gaucher determination had amniocentesis for other indications as well (4, advanced maternal age; 4, parental anxiety). We conclude that Gaucher screening is feasible for couples of mixed ethnicity if appropriate counseling and testing are offered.

The dynamics of two diffusively coupled predator-prey populations.

I analyze the dynamics of predator and prey populations living in two patches. Within a patch the prey grow logistically and the predators have a Holling type II functional response. The two patches are coupled through predator migration. The system can be interpreted as a simple predator-prey metapopulation or as a spatially explicit predator-prey system. Asynchronous local dynamics are presumed by metapopulation theory. The main question I address is when synchronous and when asynchronous dynamics arise. Contrary to biological intuition, for very small migration rates the oscillations always synchronize. For intermediate migration rates the synchronous oscillations are unstable and I found periodic, quasi-periodic, and intermittently chaotic attractors with asynchronous dynamics. For large predator migration rates, attractors in the form of equilibria or limit cycles exist in which one of the patches contains no prey. The dynamical behavior of the system is described using bifurcation diagrams. The model shows that spatial predator-prey populations can be regulated through the interplay of local dynamics and migration.

Understanding bacteriophage therapy as a density-dependent kinetic process.

Studies of bacteriophage as therapeutic agents have had mixed and unpredictable outcomes. We argue that interpretation of these apparently paradoxical results requires appreciation of various density-dependent threshold effects. We use a mathematical model to delineate different categories of outcome, including therapy by simple inundation, by active biocontrol, and by delayed active biocontrol. Counter-intuitively, there are situations in which earlier inoculation can be less efficacious, and simultaneous inoculation with antibiotics can be detrimental. Predictions of therapeutic responses are made using formulae dependent on biologically meaningful parameters; experimental measurement of the parameters will be a prerequisite of application of the model to particular study systems. Such modelling can point to which aspects of phage biology might most fruitfully be engineered so as to enhance the viability of bacteriophage therapy.