Rugged Landscape Research Articles

Cover-Encodings of Fitness Landscapes

The traditional way of tackling discrete optimization problems is by using local search on suitably defined cost or fitness landscapes. Such approaches are however limited by the slowing down that occurs when the local minima that are a feature of the typically rugged landscapes encountered arrest the progress of the search process. Another way of tackling optimization problems is by the use of heuristic approximations to estimate a global cost minimum. Here, we present a combination of these two approaches by using cover-encoding maps which map processes from a larger search space to subsets of the original search space. The key idea is to construct cover-encoding maps with the help of suitable heuristics that single out near-optimal solutions and result in landscapes on the larger search space that no longer exhibit trapping local minima. We present cover-encoding maps for the problems of the traveling salesman, number partitioning, maximum matching and maximum clique; the practical feasibility of our method is demonstrated by simulations of adaptive walks on the corresponding encoded landscapes which find the global minima for these problems.

Quantum algorithm for energy matching in hard optimization problems

We consider the ability of local quantum dynamics to solve the energy matching problem: given an instance of a classical optimization problem and a low energy state, find another macroscopically distinct low energy state. Energy matching is difficult in rugged optimization landscapes, as the given state provides little information about the distant topography. Here we show that the introduction of quantum dynamics can provide a speed-up over local classical algorithms in a large class of hard optimization problems. The essential intuition is that tunneling allows the system to explore the optimization landscape while approximately conserving the classical energy, even in the presence of large barriers. In particular, we study energy matching in the random p-spin model of spin glass theory. Using perturbation theory and numerical exact diagonalization, we show that introducing a transverse field leads to three sharp dynamical phases, only one of which solves the matching problem: (1) a small-field trapped phase, in which tunneling is too weak for the system to escape the vicinity of the initial state; (2) a large-field excited phase, in which the field excites the system into high energy states, effectively forgetting the initial low energy; and (3) the intermediate tunneling phase, in which the system succeeds at energy matching. We find that in the tunneling phase, the time required to find distant states scales exponentially with system size but is nevertheless exponentially faster than simple classical Monte Carlo.

Structures of two aptamers with differing ligand specificity reveal ruggedness in the functional landscape of RNA.

Two classes of riboswitches related to the ykkC guanidine-I riboswitch bind phosphoribosyl pyrophosphate (PRPP) and guanosine tetraphosphate (ppGpp). Here we report the co-crystal structure of the PRPP aptamer and its ligand. We also report the structure of the G96A point mutant that prefers ppGpp over PRPP with a dramatic 40,000-fold switch in specificity. The ends of the aptamer form a helix that is not present in the guanidine aptamer and is involved in the expression platform. In the mutant, the base of ppGpp replaces G96 in three-dimensional space. This disrupts the S-turn, which is a primary structural feature of the ykkC RNA motif. These dramatic differences in ligand specificity are achieved with minimal mutations. ykkC aptamers are therefore a prime example of an RNA fold with a rugged fitness landscape. The ease with which the ykkC aptamer acquires new specificity represents a striking case of evolvability in RNA.

Kinetics of pattern formation in symmetric diblock copolymer melts.

In equilibrium, copolymers self-assemble into spatially modulated phases with long-range order. When the system is quenched far below the order-disorder transition temperature, however, such an idealized, defect-free structure is difficult to obtain in experiments and simulations, instead a fingerprint-like structure forms. The relaxation toward long-range order is very protracted because it involves numerous thermally activated processes, and the rugged free-energy landscape has been likened to that of glass-forming systems. Using large-scale particle-based simulations of high-aspect-ratio, quasi-two-dimensional systems with periodic boundary condition, we study the kinetics of structure formation in symmetric, lamella-forming diblock copolymers after a quench from the disordered state. We characterize the ordering process by the correlation length of the lamellar structure and its Euler characteristic and observe that the growth of the correlation length and the rate of change of the Euler characteristic significantly slow down in the range of incompatibilities, 15 ≤ χN ≤ 20, studied. The increase of the time scale of ordering is, however, gradual. The density fields of snapshots of the particle-based simulations are used as starting values for self-consistent field theory (SCFT) calculations. The latter converge to the local, metastable minimum of the free-energy basin. This combination of particle-based simulations and SCFT calculations allows us to relate an instantaneous configuration of the particle-based model to a corresponding metastable free-energy minimum of SCFT-the inherent morphology-and we typically observe that a change of a free-energy basin is associated with a change of the Euler characteristic of the particle-based morphology, i.e., changes of free-energy basins are correlated to changes of the domain topology. Subsequently, we employ the string method in conjunction with SCFT to study the minimum free-energy paths (MFEPs) of changes of the domain topology. Since the time scales of relaxing toward the inherent morphology within a free-energy basin and jumps between free-energy basins are not well separated, the MFEP may overestimate the barriers encountered in the course of ordering.

Dynamic and Structural Modeling of the Specificity in Protein-DNA Interactions Guided by Binding Assay and Structure Data.

How transcription factors (TFs) recognize their DNA sequences is often investigated complementarily by high-throughput protein binding assays and by structural biology experiments. The former quantifies the specificity of TF binding sites for numerous DNA sequences, often represented as the position-weight-matrix (PWM). The latter provides mechanistic insights into the interactions via the protein-DNA complex structures. However, these two types of data are not readily integrated. Here, we propose and test a new modeling method that incorporates the PWM with complex structure data. On the basis of pretuned coarse-grained models for proteins and DNAs, we model the specific protein-DNA interactions, PWMcos, in terms of an orientation-dependent potential function, which enables us to perform molecular dynamics simulations at unprecedentedly large scales. We show that the PWMcos model reproduces subtle specificity in the protein-DNA recognition. During the target search in genomic sequences, TF moves on highly rugged landscapes and occasionally flips on DNA depending on the sequence. The TATA-binding protein exhibits two remarkably distinct binding modes, of which frequencies differ between TATA-containing and TATA-less promoters. The PWMcos is general and can be applied to any protein-DNA interactions given their PWMs and complex structure data are available.

Trajectory reweighting for non-equilibrium steady states

Modern methods for sampling rugged landscapes in state space mainly rely on knowledge of the relative probabilities of microstates, which is given by the Boltzmann factor for equilibrium systems. In principle, trajectory reweighting provides an elegant way to extend these algorithms to non-equilibrium systems, by numerically calculating the relative weights that can be directly substituted for the Boltzmann factor. We show that trajectory reweighting has many commonalities with Rosenbluth sampling for chain macromolecules, including practical problems which stem from the fact that both are iterated importance sampling schemes: for long trajectories the distribution of trajectory weights becomes very broad and trajectories carrying high weights are infrequently sampled, yet long trajectories are unavoidable in rugged landscapes. For probing the probability landscapes of genetic switches and similar systems, these issues preclude the straightforward use of trajectory reweighting. The analogy to Rosenbluth sampling suggests though that path-ensemble methods such as PERM (pruned-enriched Rosenbluth method) could provide a way forward.

A non-equilibrium approach to allosteric communication.

While the theory of protein folding is well developed, including concepts such as rugged energy landscape, folding funnel, etc., the same degree of understanding has not been reached for the description of the dynamics of allosteric transitions in proteins. This is not only due to the small size of the structural change upon ligand binding to an allosteric site, but also due to challenges in designing experiments that directly observe such an allosteric transition. On the basis of recent pump-probe-type experiments (Buchli et al. 2013 Proc. Natl Acad. Sci. USA110, 11 725-11 730. (doi:10.1073/pnas.1306323110)) and non-equilibrium molecular dynamics simulations (Buchenberg et al. 2017 Proc. Natl Acad. Sci. USA114, E6804-E6811. (doi:10.1073/pnas.1707694114)) studying an photoswitchable PDZ2 domain as model for an allosteric transition, we outline in this perspective how such a description of allosteric communication might look. That is, calculating the dynamical content of both experiment and simulation (which agree remarkably well with each other), we find that allosteric communication shares some properties with downhill folding, except that it is an 'order-order' transition. Discussing the multiscale and hierarchical features of the dynamics, the validity of linear response theory as well as the meaning of 'allosteric pathways', we conclude that non-equilibrium experiments and simulations are a promising way to study dynamical aspects of allostery.This article is part of a discussion meeting issue 'Allostery and molecular machines'.

Anchoring and adjusting amidst humans: Ranging behavior of Persian leopards along the Iran-Turkmenistan borderland.

Understanding the space use and movement ecology of apex predators, particularly in mosaic landscapes encompassing different land-uses, is fundamental for formulating effective conservation policy. The top extant big cat in the Middle East and the Caucasus, the Persian leopard Panthera pardus saxicolor, has disappeared from most of its historic range. Its spatial ecology in the areas where it remains is almost unknown. Between September 2014 and May 2017, we collared and monitored six adult leopards (5 males and 1 female) using GPS-satellite Iridium transmitters in Tandoureh National Park (355 km2) along the Iran-Turkmenistan borderland. Using auto-correlated Kernel density estimation based on a continuous-time stochastic process for relocation data, we estimated a mean home range of 103.4 ± SE 51.8 km2 for resident males which is larger than has been observed in other studies of Asian leopards. Most predation events occurred in core areas, averaging 32.4 ± SE 12.7 km2. Although neighboring leopards showed high spatiotemporal overlap, their hunting areas were largely exclusive. Five out of six of leopards spent some time outside the national park, among human communities. Our study suggests that a national park can play an ‘anchoring’ role for individuals of an apex predator that spend some time in the surrounding human-dominated landscapes. Therefore, we envisage that instead of emphasizing either land sharing or land sparing, a combined approach can secure the viability of resilient large carnivores that are able to coexist with humans in the rugged montane landscapes of west and central Asia.

REFOLDING OF HOMOPOLYMER UNDER QUENCHED FORCE

Recently single molecule force spectroscopy has become an useful tool to study protein, DNA and RNA. However, very little attention was paid to homopolymer which plays an important role in many domains of science. In this paper we make the first attempt to decipher the free energy landscape of homopolymer using the external force as reaction coordinate. The impact of the quenched force on the free energy landscape was studied using simplified coarse-grain Go model. Similar to protein, we have obtained a clear switch from the thermal regime to force-driven regime. The distance between the denatured state and transition state in the temperature-driven regime is smaller than in the force-driven one. Having a rugged free energy landscape without a pronounced funnel the homopolymer folding is much slower than that of protein making study of homopolymer very time consuming.

Rugged Landscape: Complexity, Evolution and Self-Adaptation

Problem complexity is described well through the landscape ruggedness. The rugged landscaped are better explored for near optimum solution through evolutionary computing methods. Automatic adaptation of the method to the ruggedness of the landscape is addressed through self-adaptive features of the method. This paper concerns with the detailed analysis of the self-adaptation in evolutionary computing methods to solve complex problems. In this paper two evolutionary self-adapting methods are described. The potentialities of these methods are verified on five rugged landscapes.

Variation in Ecosystem Service Values in an Agroforestry Dominated Landscape in Ethiopia: Implications for Land Use and Conservation Policy

Human pressure on a rugged and fragile landscape can cause land use/cover changes that significantly alter the provision of ecosystem services. Estimating the multiple services, particularly those obtained from agroforestry systems, is seldom attempted. A combined approach of geospatial technology, cross-sectional field investigations, and economic valuation of natural capital was used to develop an ecosystem service valuation (ESV) model to estimate changes in ESV between 1986 and 2015 in southern Ethiopia. Over 120 values were sourced, mainly from an ecosystem service valuation database and allied sources, to establish value coefficients via benefit transfer method. Our 1848 km2 study landscape, with eight land use categories, yielded an annual total ESV of $129 × 106 in 1986 and $147 × 106 in 2015, a 14.2% ($18.3 million) increase in three decades, showing its relative resilience. Yet we observed losses of natural vegetation classes whose area and/or value coefficients were too small to offset their increased value from expanding agroforestry and wetland/marshes, which have the largest cover share and highest economic value, respectively. Appreciating the unique features of agroforests, we strongly recommend that their economic value is studied as a separate ecosystem for further valuation accuracy improvement.

An Exploration of Discerning Search

This paper argues that great strategies come from individuals or organizations that engage in “discerning search.” A discerning searcher has heightened taste, sensitivity, and judgment as to how individual elements of a strategy contribute to overall organizational fitness. This paper draws on Kauffman’s (1993) [ Kauffman S (1993) The Origins of Order: Self-Organization and Selection in Evolution (Oxford University Press, New York).] NK model to compare the fitness impact of local and discerning search. The more rugged the fitness landscape, the more that discerning search outperforms local search. Organizations capable of performing discerning search in rugged landscapes are able to overcome what are generally regarded as inevitable trade-offs between organizational exploration and exploitation. Implications for modularization and organizational design are briefly discussed.

Repeated Diversification of Ecomorphs in Hawaiian Stick Spiders

Insular adaptive radiations in which repeated bouts of diversification lead to phenotypically similar setsof taxa serve to highlight predictability in the evolutionary process [1]. However, examples of such replicated events are rare. Cross-clade comparisons of adaptive radiations are much needed to determine whether similar ecological opportunities can lead to the same outcomes. Here, we report a heretofore uncovered adaptive radiation of Hawaiian stick spiders (Theridiidae, Ariamnes) in which different species exhibit a set of discrete ecomorphs associated with different microhabitats. The three primary ecomorphs (gold, dark, and matte white) generally co-occur in native forest habitats. Phylogenetic reconstruction mapped onto the well-known chronosequence of the Hawaiian Islands shows both that this lineage colonized the islands only once and relatively recently (2-3 mya, when Kauai and Oahu were the only high islands in the archipelago) and that the distinct ecomorphs evolved independently multipletimes following colonization of new islands. This parallel evolution of ecomorphs matches that of "spiny-leg" long-jawed spiders (Tetragnathidae, Tetragnatha), also in Hawaii [2]. Both lineages are free living, and both have related lineages in the Hawaiian Islands that show quite different patterns of diversification with no evidence of deterministic evolution. We argue that repeated evolution of ecomorphs results from a rugged adaptive landscape, with the few peaks associated with camouflage forthese free-living taxa against the markedly low diversity of predators on isolated islands. These features, coupled with a limited genetic toolbox and reduced dispersal between islands, appear to be common to situations of repeated evolution of ecomorphs.

The Influence of Topography and Fracking on Cellular Network Availability in Underserved Areas of Pennsylvania

This study was originally inspired by several acquaintances of the author who are residents of North-Central Pennsylvania. These correspondents informed the author that their region has many large gaps in consumer cellular telephone coverage, with even fairly sizable towns being neglected; this is a long-known fact based on the region’s sparse population. But the local people are also aware that cellular connectivity can be found in remote backwoods areas at high elevations, often less than one mile outside of an unserved town. Meanwhile, there is a certain amount of discontent in the region as the rapidly-growing natural gas development industry (known colloquially as “fracking”) enjoys cellular network connectivity at its well sites and compressor stations, which also can be tantalizingly close to a town that has no coverage at all. Field research by the author revealed that the poorly-distributed cellular network coverage of North-Central Pennsylvania, in which communities have long been neglected while a relatively new industry is able to connect to its own benefit, is caused by the topography of the region and is also a manifestation of longstanding challenges arising from a thinly-distributed population and shortage of traditional transportation infrastructure. Specifically, inhabited towns are often in steep river valleys in which the rugged landscape blocks line-of-sight propagation of cellular signals, while that same landscape has thwarted transportation to areas that could be utilized for strategically-placed antennas. On the other hand, nearby uninhabited areas at higher elevations have coverage that until recently has benefited nobody, thanks to line-of-sight coverage from network towers at similar elevations a considerable distance away. The region also faces a less-specific challenge shared by other sparsely-populated places: the consumer cellular industry’s longstanding lack of interest in building more infrastructure in areas deemed to be unprofitable. This study finds that the natural gas industry has built infrastructure in previously inaccessible areas that had been beyond the reach or interest of telecommunications firms, and there is now much less reason for those firms to conclude that such areas are inaccessible. The paper starts with an analysis of the challenging geography of North-Central Pennsylvania and how this has shaped cellular network coverage in the region. This is followed by an analysis of land usage in the region by the natural gas industry, and that industry’s use of extant high-elevation connectivity for its own communications, often tantalizingly close to unserved communities at lower elevations. The paper concludes with recommendations for more efficient land usage by both the telecommunications and natural gas industries in ways that can enable the expansion of consumer cellular networks into presently unserved areas, with suggestions for interpreting existing Pennsylvania land use regulations to justify shared use of cleared lands and access roads that have already been approved for fracking, and which could also be a benefit for telecommunications.

Conflict between heterozygote advantage and hybrid incompatibility in haplodiploids (and sex chromosomes).

In many diploid species, the sex chromosomes play a special role in mediating reproductive isolation. In haplodiploids, where females are diploid and males haploid, the whole genome behaves similarly to the X/Zchromosomes of diploids. Therefore, haplodiploid systems can serve as a model for the role of sex chromosomes in speciation and hybridization. A previously described population of Finnish Formica wood ants displays genome-wide signs of ploidally and sexually antagonistic selection resulting from hybridization. Here, hybrid females have increased survivorship but hybrid males are inviable. To understand how the unusual hybrid population may be maintained, we developed a mathematical model with hybrid incompatibility, female heterozygote advantage, recombination and assortative mating. The rugged fitness landscape resulting from the co-occurrence of heterozygote advantage and hybrid incompatibility results in a sexual conflict in haplodiploids, which is caused by the ploidy difference. Thus, whereas heterozygote advantage always promotes long-term polymorphism in diploids, we find various outcomes in haplodiploids in which the population stabilizes either in favour of males, females or via maximizing the number of introgressed individuals. We discuss these outcomes with respect to the potential long-term fate of the Finnish wood ant population and provide approximations for the extension of the model to multiple incompatibilities. Moreover, we highlight the general implications of our results for speciation and hybridization in haplodiploids versus diploids and how the described fitness relationships could contribute to the outstanding role of sex chromosomes as hotspots of sexual antagonism and genes involved in speciation.

Time-Resolved SAXS and Ensemble Modelling Reveal Magnesium Orchestration across an RNA Folding Landscape

RNA's unique folds and motions enable many of its newly discovered functions, yet RNA self-assembly and conformational dynamics are not well understood. Here, we use microfluidic mixing to trigger the Mg induced folding of tP5abc; a representative of the common RNA motif the three helix junction. Time-dependent conformations are measured using time-resolved small angle x-ray scattering (SAXS), and analyzed by pairing ensemble decomposition with all-atom simulations. Detailed structural ensembles, derived at crucial stages of folding, reveal distinct phases of tP5abcs journey to the native state. Many of these phases rely on the presence of Mg ions, and underscore their unique and varying role(s) in guiding RNA through a complex and rugged landscape.

Free-Energy Landscape of Amyloid-Beta Peptides

It is well known that Alzheimer's disease (AD) is correlated with the aggregation of amyloid-beta (Aβ) peptides into plaques. Due to the large size of Aβ plaques (several mm), and long incubation period (hours and days), Molecular Dynamics (MD) simulations require coarse-grained models. Our model is based on the coarse-grained model of Fawzi et al [Biophysical J. 94 (2008) 2007-2016] that represents one amino acid as a single unit. However, the new model will include an improved representation of backbone-hydrogen bonds that stabilize the β-sheet structures of plaques. The van der Waals force interactions used in the model will be based on published NMR crystal structures of Aβ segments resolved by the Eisenberg group [Nature 447 (2007) 453-457]. MD simulations observed a rugged energy landscape, with cooperative monomer state to oligomers state, as the temperature is lowered. This is followed at lower temperature, by trapped states that lead slowly to crystal structures. Transition states and trapped states are identified using a metric that includes the radius of gyration of number of backbone hydrogen bonds.

Population status and migration trends of Marco Polo argali (Ovis ammon polii) in Pakistan

Abstract Marco Polo sheep (Ovis ammon polii) occurring in the rugged mountainous landscapes of Central and South Asia, are difficult to survey and conserve due to their straggling habits in remote and inhospitable habitats. The paper presents population estimates and migration trends of Marco Polo sheep in Khunjerab, Pakistan, over 20 years (1992–2012), determined through direct count method. During this period a total of 1069 sheep visited Pakistan, with mean annual herd size of 76.35 (SD=±40.87). Sex ratio in the population skewed towards females, having male:female ratio of 0.69:1 with 43 lambs to 100 ewes. Annual population density of the immigrant populations oscillated between 0.42 and 2.13 animals/km2 (SD=±0.53). The visitation showed drastic decline over 20 years, possibly due to fencing at the Sino-Pakistan border and dietary competition with wild herbivores. Fewer lambs in summer populations is another point of concern, probably as result of predation of young cohort by avian and mammalian predators. Removing obstructions on migratory routes and reducing dietary competition with sympatric herbivores are suggested for viability of argali populations in Pakistan.

Looking for the optimal rate of recombination for evolutionary dynamics.

We consider many-site mutation-recombination models of evolution with selection. We are looking for situations where the recombination increases the mean fitness of the population, and there is an optimal recombination rate. We found two fitness landscapes supporting such nonmonotonic behavior of the mean fitness versus the recombination rate. The first case is related to the evolution near the error threshold on a neutral-network-like fitness landscape, for moderate genome lengths and large population. The more realistic case is the second one, in which we consider the evolutionary dynamics of a finite population on a rugged fitness landscape (the smooth fitness landscape plus some random contributions to the fitness). We also give the solution to the horizontal gene transfer model in the case of asymmetric mutations. To obtain nonmonotonic behavior for both mutation and recombination, we need a specially designed (ideal) fitness landscape.

Slow domain reconfiguration causes power-law kinetics in a two-state enzyme

Protein dynamics are typically captured well by rate equations that predict exponential decays for two-state reactions. Here, we describe a remarkable exception. The electron-transfer enzyme quiescin sulfhydryl oxidase (QSOX), a natural fusion of two functionally distinct domains, switches between open- and closed-domain arrangements with apparent power-law kinetics. Using single-molecule FRET experiments on time scales from nanoseconds to milliseconds, we show that the unusual open-close kinetics results from slow sampling of an ensemble of disordered domain orientations. While substrate accelerates the kinetics, thus suggesting a substrate-induced switch to an alternative free energy landscape of the enzyme, the power-law behavior is also preserved upon electron load. Our results show that the slow sampling of open conformers is caused by a variety of interdomain interactions that imply a rugged free energy landscape, thus providing a generic mechanism for dynamic disorder in multidomain enzymes.