Atlas of Science

Tag: stochastic

  • Complexity of malaria dynamics under climate change

    Complexity of malaria dynamics under climate change

    The transmission of malaria is highly variable and depends on a range of climatic and anthropogenic factors. For more than two decades, there has been a growing concern and hot debate over the impact of global warming on this deadly mosquito-borne disease. It is now widely recognized that while malaria risk could be limited by economic growth, changes in climate suitability in poor regions remain a significant challenge for malaria control.

    Life cycles of Anopheles mosquitoes and Plasmodium parasites. Atlas of Science
    Fig. 1. Life cycles of Anopheles mosquitoes and Plasmodium parasites. Female mosquitoes seek humans and animals for their blood feeding required for egg production. Plasmodium is transmitted into hosts through the saliva by an infectious carrier mosquito during its blood feeding. The parasites then advance through several stages and can multiply inside the host before being transmitted to other mosquitoes through their blood meals. Inside the mosquito, Plasmodium continues developing with a degree-day air temperature dependence until the mosquito becomes infectious to humans. The parasite life cycle is completed when these parasites are injected to another human by this mosquito, perpetuating transmission. For oviposition, gravid females randomly search for larval habitats and deposit eggs. The eggs then advance to larval and pupal stages before emerging as adult mosquitoes. After emergence, female mosquitoes mate once with males during their entire life for producing eggs. Climate change as manifested through elevated atmospheric CO2, higher temperature, and altered precipitation magnitude induce vegetation acclimation through change in energy and hydrologic fluxes. Changing landscape may even affect local weather more acutely than long-term climate change. Along with socioeconomic activities, these processes have potential impacts on malaria transmission [Credit: Phong V. V. Le and Praveen Kumar]
    The ecology of malaria is markedly complex, involving two different replication cycles of the Plasmodium parasite alternating in human hosts and Anopheles vectors (Fig. 1). These cycles are often controlled by fluctuations dominated by the random nature of population events and the space-time variability of environmental conditions. While 3/4 of the mosquitoes’ life stages are aquatic, the life cycle of Plasmodium inside the mosquitoes, that are ectothermic or cold-blooded insects, is air-temperature dependent. So, it is very likely that ecohydrological shifts in response to global warming will have a significant impact on the dynamics of malaria.

    We investigated the complexity and ecological aspects of climate change’s impacts on malaria transmission. Specifically, we analyzed modification in (i) the sporogonic cycle of Plasmodium induced by air temperature increase, and (ii) the life cycle of Anopheles vector triggered by changes in natural breeding habitat arising from the altered moisture dynamics. We developed a stochastic modeling approach to capture uncertainty and the interaction between malaria dynamics and the life cycles of both vectors and parasites. Our model consists of two stochastic time-continuous, space- discrete models: one for vector dispersal that represents the entomological life cycles of female Anopheles, and a second for malaria dynamics that simulates the circulation of the Plasmodium pathogen between host and vector populations. We also coupled this framework with a sophisticated ecohydrologic model to incorporate climate-driven hydrologic and ecologic processes as factors that determine mosquito population and malaria transmission dynamics. Our study was performed in a coastal area in Kenya.

    This research revealed for the first time the complicated role of vegetation acclimation under climate change on malaria and indicated an indirect but often ignored impact of air temperature increase on malaria transmission through reduction in breeding habitats and vector density. Particularly, we showed that elevated atmospheric CO2 concentration increases the habitat availability for mosquito reproduction, which leads to higher density of vectors and an increase in malaria incidence. Unlike the elevated CO2 condition, the increase of air temperature has two distinct effects on malaria dynamics. First, higher air temperature shortens the life cycles of Anopheles and Plasmodium. Second, it also reduces soil moisture, thus decreasing the habitat availability for the vector. Our findings shed light on better understanding the linkage between climate change and the infection dynamics of malaria.

    Phong V. V. Le 1,2, Praveen Kumar 1
    1Department of Civil and Environmental Engineering, University of Illinois, Urbana, IL, USA
    2Faculty of Hydrology Meteorology and Oceanography, Vietnam National University, Hanoi, Vietnam

    Publications

    Predicting the direct and indirect impacts of climate change on malaria in coastal Kenya.
    Le PVV, Kumar P, Ruiz MO, Mbogo C, Muturi EJ
    PLoS One. 2019 Feb 6

    Stochastic lattice-based modelling of malaria dynamics.
    Le PVV, Kumar P, Ruiz MO
    Malar J. 2018 Jul 5

  • Phenotype as agent, not product of reproductive success

    Phenotype as agent, not product of reproductive success

    The phenotype of an organism is the aggregate of its physical traits. It is the net result of the merging of parental gene pools, and in Darwinian evolutionary terms its ‘fitness’ is considered a measure of evolutionary success. However, with the emergence of Lamarckian epigenetic inheritance from the environment, phenotype takes on a very different character, actively interacting with the environment to retrieve information from the environment in order to optimize the acquisition of epigenetic ‘marks’ that modify DNA transcription. That process occurs in the germ cells (egg and sperm) during meiosis, where there is sorting of such marks. The marks are further sorted during embryogenesis and during the life cycle based on homeostatic principles. This mechanism integrates the organism and its environmental niche based on principles of cellular evolution.

    Fig. 1. Darwinian vs Lamarckian Inheritance. The two mechanisms of evolution are displayed. On the left is Darwinian Inheritance, on the right is Lamarckian Inheritance. Note that Darwinian Inheritance is the result of the merging of parental gene pools during reproduction. In contrast to that, Lamarckian Inheritance involves the acquisition of epigenetic ‘marks’ from the environmental niche over the course of the organism’s life cycle, reproduction actively acting to sort the epigenetic marks during meiosis and embryogenesis based on homeostasis. The latter is a much more robust adaptational mechanism that accommodates novelty, whereas the former does not.

    This way of understanding the generation of phenotype is consistent with the concept of Niche Construction. When cells respond to environmental stresses through epigenetic inheritance, evolution is understood as much more dynamic and interactive with its surroundings than by means of the filtering mechanisms of Darwinian evolution. Moreover, the phenotype as agent concept reflects the process of evolution as a self-organizing, self-referential mechanism that originates within the unicellular domain, and always remains contingent on it. Seen in this light, the phenotype becomes a directed product of cellular activities in response to its environment, rather than a mere result of random forces.

    Most importantly, the effects of epigenetic inheritance on the cell within its physiologic constraints are subject to hypothesis testing and falsification, whereas Darwinian evolution is not. Natural Selection is still relevant, but not as the primary mechanism of evolution. With this consideration of phenotype as agent, every aspect of the life cycle can be viewed as derivative of cellular needs and imperatives that determine the timing and expression of each life cycle stage. Of these, arguably the endocrine system has primacy, bearing in mind that the endocrine system itself is its own cellular composite of epigenetic marks and their differential activation, ever-dependent upon environmental stresses.

    According to the Darwinian narrative, the phenotype is the net result of differential survival and reproductive success. However, we now know that there is direct inheritance from the environment. So it can be argued that epigenetic mechanisms are a primary means for organisms to evolve in reciprocation to environmental stresses, exemplified by niche construction. As a result of this new perspective on epigenetic inheritance, the iterative return of eukaryotic multicellular organisms to their unicellular form becomes the primary stage for resolving differences between the organism and its environment. Therefore, a renewed evolutionary narrative centered on the primacy of epigenetic inheritance within deeply rooted cellular mechanisms can be considered. Under such conditions, cellular imperatives determine the course of evolution rather than random mutation and selection. Phenotype becomes a means through which organisms explore the outward environment and its stresses. Those impacts are then revisited by the eukaryotic unicell, enabling the reiterative extension of phenotype into its environment to experience subsequent environmental impacts in service to its next set of adjustments. It is this internally consistent reciprocation that shapes the phenotype. When considered as a whole, this new concept is a novel testable and refutable path to further progress in evolutionary theory and biomedicine.

    John S. Torday, William B. Miller
    Evolutionary Medicine Program
    University of California- Los Angeles, CA, USA

     

    Publication

    Phenotype as Agent for Epigenetic Inheritance.
    Torday JS, Miller WB
    Biology (Basel). 2016 Jul 8

  • Combining discrete and continuous for a clever multiscale modelling

    Combining discrete and continuous for a clever multiscale modelling

    There is rarely a process in physical, biological or chemical sciences that spans a single time or length scale. Computational methods must be chosen accordingly when modeling such processes. For instance, ab initio quantum-mechanical calculations or molecular dynamics simulations, although highly reliable, are computationally inefficient for large-scale systems or long-lasting processes. One way to proceed in such cases is to develop multiscale approaches. Multiscale means that methods applicable at different scales are combined into a single computational framework. Typically this is done by using high resolution simulations on short length and time scales, to calculate quantities that are needed as input parameters for lower resolution models, applicable on longer time and length scales. This is known as the bottom-up approach. In the top-down approach, in contrast, the observed properties of a system on a high level are used to deduce the mechanisms or parameters for a lower lever model.

    Discrete-continuous model and the comparison with the all-discrete and fully continuous approaches, in which all molecular species in a system are treated as discrete particles or described by continuous fields, respectively

    An alternative is to combine two or more approaches on equal footing. A scientifically sound example is the enzyme kinetics. Enzymes are large proteins that catalyse many important reactions in living organism and are ubiquitously used in biotechnological applications. The metabolites, ie the reactants that these proteins catalyze, are typically much smaller and move faster than the enzymes. Additionally, in a typical living cell or a catalytic reactor, there is abundance of reactants but only relatively few enzymes present. Thus, it must be possible to describe the behaviour of reactants by continuous fields, representing their densities in space and time, and to use discrete particles to represent the enzymes. The enzymes will then change the values of these fields locally where they reside, similarly as it happens in nature.

    What are the advantages of such an approach? The figure on the right shows that at a low concentration of enzymes, the discrete-continuous method agrees with the all-discrete, stochastic simulations of the same system, but both approaches differ qualitatively from a fully continuous model, in which both enzymes and reactants are described by continuous fields. This effect is long known in the literature and means that continuous models are inappropriate when the number of molecules is low.

    Now, while it is unphysical to describe enzymes by continuous fields at low enzyme concentrations, it might be possible to treat all molecules as discrete particles, as the figure demonstrates. However, at high concentrations of metabolites the methods developed so far become inefficient because computational cost increases at best linearly with the number of molecules in a system. The advantage of the discrete-continuous method is that we pay nearly the same price, independently of the density of metabolites.

    Stochastic systems contain random elements, and their behaviour can therefore be predicted only with certain probability. This is unlike deterministic systems whose behaviours are absolutely destined. Examples of stochastic systems are numerous and include practically all processes in living organisms, business economies and market behaviour, social systems, etc. It is frequently the case that there is more than one source of stochasticity (randomness) in a system, and it becomes increasingly important, in particular for understanding living systems, to separate different sources of stochasticity. The discrete-continuous method can help do this job. When appropriate, a system can be divided into stochastic and deterministic subsystems, where the latter results merely from averaging of the originally stochastic subsystem. For instance, the enzyme-metabolite system is stochastic in nature, where the stochasticity is in particular due to diffusive (or random, Brownian) motion of both enzymes and metabolites. By averaging out the stochastic degrees of freedom of metabolites, we end up with a deterministic continuous model that is naturally coupled with the enzyme subsystem, as described above. The stochastic behaviour due to enzymes alone can now be studied more conveniently (see the figure and note much stronger stochastic fluctuations by the all-discrete, stochastic approach). Inverse is also possible when needed, provided of course the concentration of enzymes is appreciable. This approach can be applied to other systems as well.

    Although methods similar to the discrete-continuous model have been previously used by other researchers, the approach undertaken by Kondrat et al. has the advantage of being more rigorously established, and has therefore the potential to be extended and adjusted to a large variety of systems. The method can also be naturally placed within the bottom-up or top-down frameworks. For instance, the diffusion and reaction properties of enzymes and metabolites can be obtained from Brownian or molecular dynamics simulations and transition path sampling simulations, respectively, or by using other techniques. In this way the method can become an efficient and reliable computational framework for studying physical, chemical, biological and other problems.

     

    Publication

    Discrete-continuous reaction-diffusion model with mobile point-like sources and sinks.
    Kondrat S, Zimmermann O, Wiechert W, von Lieres E
    Eur Phys J E Soft Matter. 2016 Jan

  • More from less

    Ice melts and that is easy to see. But supposed you cut the ice cube in half and in quarters, and so on until there was only one water molecule left? What does it mean to melt one molecule? Remarkably, it is possible to query individual molecules!  We can measure biological receptors and ion channels (since the 70s), quantum microscopic objects (since the 80s), and molecular engines (since the 90s). Individual molecules can be detected and measured with a variety of tools including spectroscopy and mechanical and electrical probes. Looking at single molecules provides the most detailed view you can get of their life cycle, but it suffers from the fact that life at that resolution is complicated by the random motion of the molecules and the whole environment. Regardless of the type of molecules, their motion is dictated by the temperature, which is equivalent to the average kinetic energy. So studying single molecules is a bit like dissembling a conversation from the background noise of a cocktail party. We can do it, but we make mistakes, and the same is true when studying single molecules. So how can we separate the life cycle of individual molecules from the noise of their neighbors? Software is the key.

    We calculate the probability that a given movement of a molecule or change in current or brightness might have come from the molecule under study, and how often it might be an accident of measuring noise. We try to find the parameters of the molecule under study that best separates its behavior from that of the surrounding noise. As one might imagine, you can never do this without making some mistakes; there is no perfect analysis that tells you what you pet molecule is doing.

    There are a variety of tricks we have developed to reduce the errors, but despite the aura of statistics, underneath all the computation is a subjective statement of what is important. The easiest tool to limit errors is the of bandwidth. Just like the tone control on an audio amplifier, we can filter out the high frequency hissing caused by the random motion of small objects and rumbling caused by passing trucks. The penalty is that you also erase events generated by the object under study. This is a universal problem in experimental science: you make subjective choices between the amount of noise you want and the accuracy of the data.

    Another software tool is to guess roughly what you think the object is doing, and based on that guess minimize the probability of making a mistake. The software calculates the probability that the observed behavior viewed came from our choice of model, and then we tweak the properties of the guess to get the best probability. But what is the best guess? If you have a collection of possible guesses, you can reasonably ask which of the guesses is more likely. But there will always be an infinite number of possible guesses and this is where the scientist meets the data head on. The scientist chooses the most friendly version, the one that has a probability better than most and the fewest parameters, and then which decides which feels best;  the heartland of real science!

    Needless to say, all this trial and error approach is too much work for pencil and paper, but thanks to the development of computers we ask them to do the work (with thanks to the gamers that promoted high speed video processors). Creating algorithms and writing programs to execute them has its own noise level. There is no perfect solution. But there are good alternatives, many of which are available for free on the web. The price is right!

    Ophir Flomenbom and Frederick Sachs

     

    Publication

    How to get more from less: Comments on “Extracting physics of life at the molecular level: A review of single-molecule data analyses” by W. Colomb and S.K. Sarkar.
    Sachs F, Flomenbom O.
    Phys Life Rev. 2015 Jun