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Register a new userControlling the speed and trajectory of evolution with counterdiabatic driving
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The pace and unpredictability of evolution are critically relevant in a variety of modern challenges: combating drug resistance in pathogens and cancer, understanding how species respond to environmental perturbations like climate change, and developing artificial selection approaches for agriculture. Great progress has been made in quantitative modeling of evolution using fitness landscapes, allowing a degree of prediction for future evolutionary histories. Yet fine-grained control of the speed and the distributions of these trajectories remains elusive. We propose an approach to achieve this using ideas originally developed in a completely different context: counterdiabatic driving to control the behavior of quantum states for applications like quantum computing and manipulating ultra-cold atoms. Implementing these ideas for the first time in a biological context, we show how a set of external control parameters (i.e. varying drug concentrations / types, temperature, nutrients) can guide the probability distribution of genotypes in a population along a specified path and time interval. This level of control, allowing empirical optimization of evolutionary speed and trajectories, has myriad potential applications, from enhancing adaptive therapies for diseases, to the development of thermotolerant crops in preparation for climate change, to accelerating bioengineering methods built on evolutionary models, like directed evolution of biomolecules.
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Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random walk model with long range memory for which not only the mean square displacement (MSD) can be obtained exactly in the asymptotic limit, but also the propagator. The model consists of a random walker on a lattice, which, at a constant rate, stochastically relocates at a site occupied at some earlier time. This time in the past is chosen randomly according to a memory kernel, whose temporal decay can be varied via an exponent parameter. In the weakly non-Markovian regime, memory reduces the diffusion coefficient from the bare value. When the mean backward jump in time diverges, the diffusion coefficient vanishes and a transition to an anomalous subdiffusive regime occurs. Paradoxically, at the transition, the process is an anti-correlated Levy flight. Although in the subdiffusive regime the model exhibits some features of the continuous time random walk with infinite mean waiting time, it belongs to another universality class. If memory is very long-ranged, a second transition takes place to a regime characterized by a logarithmic growth of the MSD with time. In this case the process is asymptotically Gaussian and effectively described as a scaled Brownian motion with a diffusion coefficient decaying as 1/t.
The transmission and evolution of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) are of paramount importance to the controlling and combating of coronavirus disease 2019 (COVID-19) pandemic. Currently, near 15,000 SARS-CoV-2 single mutations have been recorded, having a great ramification to the development of diagnostics, vaccines, antibody therapies, and drugs. However, little is known about SARS-CoV-2 evolutionary characteristics and general trend. In this work, we present a comprehensive genotyping analysis of existing SARS-CoV-2 mutations. We reveal that host immune response via APOBEC and ADAR gene editing gives rise to near 65% of recorded mutations. Additionally, we show that children under age five and the elderly may be at high risk from COVID-19 because of their overreacting to the viral infection. Moreover, we uncover that populations of Oceania and Africa react significantly more intensively to SARS-CoV-2 infection than those of Europe and Asia, which may explain why African Americans were shown to be at increased risk of dying from COVID-19, in addition to their high risk of getting sick from COVID-19 caused by systemic health and social inequities. Finally, our study indicates that for two viral genome sequences of the same origin, their evolution order may be determined from the ratio of mutation type C$>$T over T$>$C.
Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where a random walker intermittently revisits previously visited sites according to a reinforced rule. The emergence of frequently visited locations generates very slow diffusion, logarithmic in time, whereas the walker probability density tends to a Gaussian. This scaling form does not emerge from the Central Limit Theorem but from an unusual balance between random and long-range memory steps. In single trajectories, occupation patterns are heterogeneous and have a scale-free structure. The model exhibits good agreement with data of free-ranging capuchin monkeys.
We study simple stochastic scenarios, based on birth-and-death Markovian processes, that describe populations with Allee effect, to account for the role of demographic stochasticity. In the mean-field deterministic limit we recover well-known deterministic evolution equations widely employed in population ecology. The mean-time to extinction is in general obtained by the Wentzel-Kramers-Brillouin (WKB) approximation for populations with strong and weak Allee effects. An exact solution for the mean time to extinction can be found via a recursive equation for special cases of the stochastic dynamics. We study the conditions for the validity of the WKB solution and analyze the boundary between the weak and strong Allee effect by comparing exact solutions with numerical simulations.
A combined dynamics consisting of Brownian motion and Levy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of doing so economically of such dynamics thus poses an important problem. Here we model this dynamics by a one-dimensional fractional Fokker-Planck equation combining unbiased Brownian motion and Levy flights. By solving this equation both analytically and numerically we show that the superposition of recurrent Brownian motion and Levy flights with stable exponent $alpha<1$, by itself implying zero probability of hitting a point on a line, lead to transient motion with finite probability of hitting any point on the line. We present results for the exact dependence of the values of both the search reliability and the search efficiency on the distance between the starting and target positions as well as the choice of the scaling exponent $alpha$ of the Levy flight component.
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