The pace of evolution across fitness valleys

How fast does a population evolve from one fitness peak to another? We study the dynamics of evolving, asexually reproducing populations in which a certain number of mutations jointly confer a fitness advantage. We consider the time until a population has evolved from one fitness peak to another one with a higher fitness. The order of mutations can either be fixed or random. If the order of mutations is fixed, then the population follows a metaphorical ridge, a single path. If the order of mutations is arbitrary, then there are many ways to evolve to the higher fitness state. We address the time required for fixation in such scenarios and study how it is affected by the order of mutations, the population size, the fitness values and the mutation rate

A case report on ruptured interstitial ectopic pregnancy: diagnostic dilemma

The ectopic pregnancy occurs when implantation of the blastocyst takes place in a site other than the endometrium of the uterine cavity. Interstitial ectopic pregnancies are gestations that implant within the proximal, intramural portion of the fallopian tubes with high vascularity. Ectopic pregnancy in the interstitial part of the fallopian tubes can be life-threatening considering the thin myometrial tissue surrounding the gestational sac and high vascularization which may result in catastrophic haemorrhage when interstitium is ruptured. Being a hazardous type of ectopic pregnancy, it becomes extremely important to diagnose and manage it. This condition presents a challenge for clinical as well as radiological diagnosis. Generally, a case of interstitial ectopic pregnancy has typical radiological features distinguishing it from other ectopic. The ultrasonographic finding of interstitial line has better sensitivity (80%) and specificity (98%) than eccentric gestational sac location (sensitivity, 40%; specificity, 88%) and myometrial thinning (sensitivity, 40%; specificity, 93%) for the diagnosis of interstitial ectopic pregnancy. Ultrasound is the mainstay of diagnosis, but magnetic resonance imaging can be helpful in unusual or complicated cases. Interstitial ectopic pregnancy rupturing into the leaves of broad ligament and creating a tamponade effect to alter the clinical presentation is a rare event which presents as a diagnostic challenge. Here authors present a case of ruptured interstitial ectopic pregnancy confined to the leaves of broad ligament, with atypical presentation and radiological features which led to difficulty in diagnosing the interstitial ectopic pregnancy. After laparoscopic confirmation of ruptured interstitial ectopic pregnancy, the patient was managed successfully by laparoscopic cornual resection

The Covid-19 pandemic: basic insights from basic mathematical models

Mathematical models for the spread of infectious diseases have a long history. From the start of the Covid-19 pandemic, there was a huge public interest in applying such models, since they help to understand general features of epidemic spread and support the assessment of possible mitigation measures – and their later relaxation. We describe and discuss some well-established mathematical models for epidemic spread, starting from the susceptible-infected-recovered (SIR) model and branching processes and discussing insights from network-based models. During the Covid-19 pandemic, such classical models have also been extended to include many additional aspects that affect epidemic spread, such as mobility patterns or testing possibilities. However, such complex models are increasingly difficult to assess from the outside. In a situation where their predictions can directly affect the lives of millions of people, this can become a severe problem. We argue that simple mathematical models have huge merits and can explain many of the key features of more complex models, such as the importance of heterogeneity in disease transmission. For example, basic models allow inferring whether super-spreading, where very few infected individuals cause the vast majority of secondary cases, should be the rule or the exception – with wide-ranging consequences for the possible success of mitigation measures. In addition, these basic models are simple enough to be understood and implemented without expert knowledge in theoretical epidemiology or computer science. Thus, they offer a level of transparency that can be important for a society to accept mitigation measures

Ecological Drivers of Community Cohesion

From protocellular to societal, networks of living systems are complex and multiscale. Discerning the factors that facilitate assembly of these intricate interdependencies using pairwise interactions can be nearly impossible. To facilitate a greater understanding, we developed a mathematical and computational model based on a synthetic four-strain Saccharomyces cerevisiae interdependent system. Specifically, we aimed to provide a greater understanding of how ecological factors influence community dynamics. By leveraging transiently structured ecologies, we were able to drive community cohesion. We show how ecological interventions could reverse or slow the extinction rate of a cohesive community. An interconnected system first needs to persist long enough to be a subject of natural selection. Our emulation of Darwin’s “warm little ponds” with an ecology governed by transient compartmentalization provided the necessary persistence. Our results reveal utility across scales of organization, stressing the importance of cyclic processes in major evolutionary transitions, engineering of synthetic microbial consortia, and conservation biology.journal articl

An interesting case of young onset diabetes mellitus

A 24 years old female, was admitted with symptoms of urinary tract infection. She was married and had bad obstetric history. She was known diabetic for 16 years of age and was on regular treatment with injection human insulin mixtard since the time of diagnosis, but had no episode of diabetic ketosis/ ketoacidosis. She had a positive family history of diabetes. She was further evaluated and was found to have normal C peptide levels and islet cell antibodies were found to be negative. Hence, the possibility of MODY (monogenic diabetes) was considered. Her genetic testing could not be done due to financial constraints. But a trial of sulfonylureas was given along with reduction in the dose of insulin to which she responded well and is presently well controlled

A case of SLE with pancreatitis

Systemic lupus erythematosus (SLE) is a chronic, autoimmune inflammatory disease characterized by the presence of autoantibodies, immune complex formation, and multiple organ system involvement. Gastrointestinal manifestations are common in SLE patients, but acute pancreatitis is rare. Here we present a case of a 23 yrs. old male who came to the medicine OPD with the chief complaints of pain in abdomen, swelling all over the body since, 8 days and multiple joint pain for 1 and half months. On examination he was febrile pallor present with anasarca, periorbital edema with heliotrope around both eyes. Dry and xerotic ski over the face, butterfly rash present. Blood investigations, USG and CECT suggestive of acute panceatitis. Patient was treated in ICU for pancreatitis. Patient was found to be hypothyroid and treated with thyroid supplements. ANA BLOT was suggestive of SLE. Renal biopsy showed diffuse proliferative lupus nephritis. Hence our patient had pancreatitis possibly due to SLE induced hypertriglyceridemia.

Synthetic Symbiosis under Environmental Disturbances

By virtue of complex ecologies, the behavior of mutualisms is challenging to study and nearly impossible to predict. However, laboratory engineered mutualistic systems facilitate a better understanding of their bare essentials. On the basis of an abstract theoretical model and a modifiable experimental yeast system, we explore the environmental limits of self-organized cooperation based on the production and use of specific metabolites. We develop and test the assumptions and stability of the theoretical model by leveraging the simplicity of an artificial yeast system as a simple model of mutualism. We examine how one-off, recurring, and permanent changes to an ecological niche affect a cooperative interaction and change the population composition of an engineered mutualistic system. Moreover, we explore how the cellular burden of cooperating influences the stability of mutualism and how environmental changes shape this stability. Our results highlight the fragility of mutualisms and suggest interventions, including those that rely on the use of synthetic biology.IMPORTANCE The power of synthetic biology is immense. Will it, however, be able to withstand the environmental pressures once released in the wild. As new technologies aim to do precisely the same, we use a much simpler model to test mathematically the effect of a changing environment on a synthetic biological system. We assume that the system is successful if it maintains proportions close to what we observe in the laboratory. Extreme deviations from the expected equilibrium are possible as the environment changes. Our study provides the conditions and the designer specifications which may need to be incorporated in the synthetic systems if we want such "ecoblocs" to survive in the wild

Evolutionary games in the multiverse

Evolutionary game dynamics of two players with two strategies has been studied in great detail. These games have been used to model many biologically relevant scenarios, ranging from social dilemmas in mammals to microbial diversity. Some of these games may in fact take place between a number of individuals and not just between two. Here, we address one-shot games with multiple players. As long as we have only two strategies, many results from two player games can be generalized to multiple players. For games with multiple players and more than two strategies, we show that statements derived for pairwise interactions do no longer hold. For two player games with any number of strategies there can be at most one isolated internal equilibrium. For any number of players $\boldsymbol{d}$ with any number of strategies n, there can be at most (d-1)^(n-1) isolated internal equilibria. Multiplayer games show a great dynamical complexity that cannot be captured based on pairwise interactions. Our results hold for any game and can easily be applied for specific cases, e.g. public goods games or multiplayer stag hunts

Stochastic slowdown in evolutionary processes

We examine birth--death processes with state dependent transition probabilities and at least one absorbing boundary. In evolution, this describes selection acting on two different types in a finite population where reproductive events occur successively. If the two types have equal fitness the system performs a random walk. If one type has a fitness advantage it is favored by selection, which introduces a bias (asymmetry) in the transition probabilities. How long does it take until advantageous mutants have invaded and taken over? Surprisingly, we find that the average time of such a process can increase, even if the mutant type always has a fitness advantage. We discuss this finding for the Moran process and develop a simplified model which allows a more intuitive understanding. We show that this effect can occur for weak but non--vanishing bias (selection) in the state dependent transition rates and infer the scaling with system size. We also address the Wright-Fisher model commonly used in population genetics, which shows that this stochastic slowdown is not restricted to birth-death processes.Comment: 8 pages, 3 figures, accepted for publicatio