Beyond the (geometric) mean: stochastic models undermine deterministic predictions of bet hedger evolution.

Bet hedging is a ubiquitous strategy for risk reduction in the face of unpredictable environmental change where a lineage lowers its variance in fitness across environments at the expense of also lowering its arithmetic mean fitness. Classically, the benefit of bet hedging has been quantified using geometric mean fitness (GMF); bet hedging is expected to evolve if and only if it has a higher GMF than the wild-type. We build upon previous research on the effect of incorporating stochasticity in phenotypic distribution, environment, and reproduction to investigate the extent to which these sources of stochasticity will impact the evolution of real-world bet hedging traits. We utilize both individual-based simulations and Markov chain numerics to demonstrate that modeling stochasticity can alter the sign of selection for the bet hedger compared to deterministic predictions. We find that bet hedging can be deleterious at small population sizes and beneficial at larger population sizes. This non-monotonic dependence of the sign of selection on population size, known as sign inversion, exists across parameter space for both conservative and diversified bet hedgers. We apply our model to published data of bet hedging strategies to show that sign inversion exists for biologically relevant parameters in two study systems: Papaver dubium, an annual poppy with variable germination phenology, and Salmonella typhimurium, a pathogenic bacteria that exhibits antibiotic persistence. Taken together, our results suggest that GMF is not enough to predict when bet hedging is adaptive.

Leveraging the genetic correlation between traits improves the detection of epistasis in genome-wide association studies.

Epistasis, commonly defined as the interaction between genetic loci, is known to play an important role in the phenotypic variation of complex traits. As a result, many statistical methods have been developed to identify genetic variants that are involved in epistasis, and nearly all of these approaches carry out this task by focusing on analyzing one trait at a time. Previous studies have shown that jointly modeling multiple phenotypes can often dramatically increase statistical power for association mapping. In this study, we present the "multivariate MArginal ePIstasis Test" (mvMAPIT)-a multioutcome generalization of a recently proposed epistatic detection method which seeks to detect marginal epistasis or the combined pairwise interaction effects between a given variant and all other variants. By searching for marginal epistatic effects, one can identify genetic variants that are involved in epistasis without the need to identify the exact partners with which the variants interact-thus, potentially alleviating much of the statistical and computational burden associated with conventional explicit search-based methods. Our proposed mvMAPIT builds upon this strategy by taking advantage of correlation structure between traits to improve the identification of variants involved in epistasis. We formulate mvMAPIT as a multivariate linear mixed model and develop a multitrait variance component estimation algorithm for efficient parameter inference and P-value computation. Together with reasonable model approximations, our proposed approach is scalable to moderately sized genome-wide association studies. With simulations, we illustrate the benefits of mvMAPIT over univariate (or single-trait) epistatic mapping strategies. We also apply mvMAPIT framework to protein sequence data from two broadly neutralizing anti-influenza antibodies and approximately 2,000 heterogeneous stock of mice from the Wellcome Trust Centre for Human Genetics. The mvMAPIT R package can be downloaded at https://github.com/lcrawlab/mvMAPIT.

Diabetes mellitus differently affects electrical membrane properties of vagal afferent neurons of rats.

To study whether diabetes mellitus (DM) would cause electrophysiological alterations in nodose ganglion (NG) neurons, we used patch clamp and intracellular recording for voltage and current clamp configuration, respectively, on cell bodies of NG from rats with DM. Intracellular microelectrodes recording, according to the waveform of the first derivative of the action potential, revealed three neuronal groups (A0 , Ainf , and Cinf ), which were differently affected. Diabetes only depolarized the resting potential of A0 (from -55 to -44 mV) and Cinf (from -49 to -45 mV) somas. In Ainf neurons, diabetes increased action potential and the after-hyperpolarization durations (from 1.9 and 18 to 2.3 and 32 ms, respectively) and reduced dV/dtdesc (from -63 to -52 V s-1 ). Diabetes reduced the action potential amplitude while increasing the after-hyperpolarization amplitude of Cinf neurons (from 83 and -14 mV to 75 and -16 mV, respectively). Using whole cell patch clamp recording, we observed that diabetes produced an increase in peak amplitude of sodium current density (from -68 to -176 pA pF-1 ) and displacement of steady-state inactivation to more negative values of transmembrane potential only in a group of neurons from diabetic animals (DB2). In the other group (DB1), diabetes did not change this parameter (-58 pA pF-1 ). This change in sodium current did not cause an increase in membrane excitability, probably explainable by the alterations in sodium current kinetics, which are also induced by diabetes. Our data demonstrate that diabetes differently affects membrane properties of different nodose neuron subpopulations, which likely have pathophysiological implications for diabetes mellitus.

Developing evolution-resistant drugs for COVID-19.

Analyzing how mutations affect the main protease of SARS-CoV-2 may help researchers develop drugs that are effective against current and future variants of the virus.

Covalent docking and molecular dynamics simulations reveal the specificity-shifting mutations Ala237Arg and Ala237Lys in TEM beta-lactamase.

The rate of modern drug discovery using experimental screening methods still lags behind the rate at which pathogens mutate, underscoring the need for fast and accurate predictive simulations of protein evolution. Multidrug-resistant bacteria evade our defenses by expressing a series of proteins, the most famous of which is the 29-kilodalton enzyme, TEM ß-lactamase. Considering these challenges, we applied a covalent docking heuristic to measure the effects of all possible alanine 237 substitutions in TEM due to this codon's importance for catalysis and effects on the binding affinities of commercially-available ß-lactam compounds. In addition to the usual mutations that reduce substrate binding due to steric hindrance, we identified two distinctive specificity-shifting TEM mutations, Ala237Arg and Ala237Lys, and their respective modes of action. Notably, we discovered and verified through minimum inhibitory concentration assays that, while these mutations and their bulkier side chains lead to steric clashes that curtail ampicillin binding, these same groups foster salt bridges with the negatively-charged side-chain of the cephalosporin cefixime, widely used in the clinic to treat multi-resistant bacterial infections. To measure the stability of these unexpected interactions, we used molecular dynamics simulations and found the binding modes to be stable despite the application of biasing forces. Finally, we found that both TEM mutants also bind strongly to other drugs containing negatively-charged R-groups, such as carumonam and ceftibuten. As with cefixime, this increased binding affinity stems from a salt bridge between the compounds' negative moieties and the positively-charged side chain of the arginine or lysine, suggesting a shared mechanism. In addition to reaffirming the power of using simulations as molecular microscopes, our results can guide the rational design of next-generation ß-lactam antibiotics and bring the community closer to retaking the lead against the recurrent threat of multidrug-resistant pathogens.

Density fluctuations, homeostasis, and reproduction effects in bacteria.

Single-cells grow by increasing their biomass and size. Here, we report that while mass and size accumulation rates of single Escherichia coli cells are exponential, their density and, thus, the levels of macromolecular crowding fluctuate during growth. As such, the average rates of mass and size accumulation of a single cell are generally not the same, but rather cells differentiate into increasing one rate with respect to the other. This differentiation yields a density homeostasis mechanism that we support mathematically. Further, we observe that density fluctuations can affect the reproduction rates of single cells, suggesting a link between the levels of macromolecular crowding with metabolism and overall population fitness. We detail our experimental approach and the "invisible" microfluidic arrays that enabled increased precision and throughput. Infections and natural communities start from a few cells, thus, emphasizing the significance of density-fluctuations when taking non-genetic variability into consideration.

Characterization of the vasodilator effect of eugenol in isolated human umbilical cord arteries.

Eugenol (EUG) is a phenylpropanoid widely used in the food and cosmetic industries. It is commonly referred to in the literature by its biological activities such as antioxidant, anti-inflammatory, antimicrobial, and relaxing in organs of laboratory animals, especially in rodent vessels. However, its vasorelaxant potential in human tissue, has not been investigated. Thus, this study characterizes the vasodilatory effect of EUG in the human umbilical artery (HUA). HUAs were isolated, cleaned, sectioned (3-4 mm) and placed in an organ bath (10 mL Krebs Henseleit, 37 °C; and carbogenic mixture). EUG (100-1400 µM), obtained total relaxation of electromechanical contractions induced by KCl (60 mM), and pharmacomechanical contractions (30-1200 µM), induced by serotonin (10 µM) and by histamine (10 µM), showing statistically significant concentrations: 600 µM, 400 µM and 200 µM, and EC50 values: 759.8 ± 6.5 µM, 229.9 ± 7.9 and 279.0 ± 3.4 µM, respectively. EUG (1200 and 1400 µM) prevented the contraction promoted by BaCl2 (0.1-30 mM), similar to the effects of nifedipine (10 µM), sugesting the involvement of EUG in blocking VOCCs. In the presence of tetraethylammonium (10 µM), EUG (30-1200 µM) did not produce a total relaxation (88.6%), suggesting that an alternative pathway where potassium channels, may partially mediate EUG effect. In the presence of 4-aminopyridine (1 mM), glibenclamide (10 µM), and tetraethylammonium (1 mM), EUG relaxed HUAs 100%, although the pharmacological potency was statistically altered, demonstrating the participation of K+ channels (Kv, KATP, BKCa). Our data indicates that EUG has a vasorelaxant effect on HUAs, had a greater pharmacological potency in the serotoninergic pathway, showing effective participation of VOCCs and a partial modulation of K+ channels. These data suggest new possibilities for the use of EUG in human vascular dysfunctions, such as preeclampsia. More studies are necessary to confirm the safety and effectivity in future treatments.

Predicting the viability of beta-lactamase: How folding and binding free energies correlate with beta-lactamase fitness.

One of the long-standing holy grails of molecular evolution has been the ability to predict an organism's fitness directly from its genotype. With such predictive abilities in hand, researchers would be able to more accurately forecast how organisms will evolve and how proteins with novel functions could be engineered, leading to revolutionary advances in medicine and biotechnology. In this work, we assemble the largest reported set of experimental TEM-1 ß-lactamase folding free energies and use this data in conjunction with previously acquired fitness data and computational free energy predictions to determine how much of the fitness of ß-lactamase can be directly predicted by thermodynamic folding and binding free energies. We focus upon ß-lactamase because of its long history as a model enzyme and its central role in antibiotic resistance. Based upon a set of 21 ß-lactamase single and double mutants expressly designed to influence protein folding, we first demonstrate that modeling software designed to compute folding free energies such as FoldX and PyRosetta can meaningfully, although not perfectly, predict the experimental folding free energies of single mutants. Interestingly, while these techniques also yield sensible double mutant free energies, we show that they do so for the wrong physical reasons. We then go on to assess how well both experimental and computational folding free energies explain single mutant fitness. We find that folding free energies account for, at most, 24% of the variance in ß-lactamase fitness values according to linear models and, somewhat surprisingly, complementing folding free energies with computationally-predicted binding free energies of residues near the active site only increases the folding-only figure by a few percent. This strongly suggests that the majority of ß-lactamase's fitness is controlled by factors other than free energies. Overall, our results shed a bright light on to what extent the community is justified in using thermodynamic measures to infer protein fitness as well as how applicable modern computational techniques for predicting free energies will be to the large data sets of multiply-mutated proteins forthcoming.

Selection on mutators is not frequency-dependent.

The evolutionary fate of mutator mutations - genetic variants that raise the genome-wide mutation rate - in asexual populations is often described as being frequency (or number) dependent. Mutators can invade a population by hitchhiking with a sweeping beneficial mutation, but motivated by earlier experiments results, it has been repeatedly suggested that mutators must be sufficiently frequent to produce such a driver mutation before non-mutators do. Here, we use stochastic, agent-based simulations to show that neither the strength nor the sign of selection on mutators depend on their initial frequency, and while the overall probability of hitchhiking increases predictably with frequency, the per-capita probability of fixation remains unchanged.

Genomic clustering of fitness-affecting mutations favors the evolution of chromosomal instability.

Most solid cancers are characterized by chromosomal instability (CIN)-an elevated rate of large-scale chromosomal aberrations and ploidy changes. Chromosomal instability may arise through mutations in a range of genomic integrity loci and is commonly associated with fast disease progression, poor prognosis, and multidrug resistance. However, the evolutionary forces promoting CIN-inducing alleles (hereafter, CIN mutators) during carcinogenesis remain poorly understood. Here, we develop a stochastic, individual-based model of indirect selection experienced by CIN mutators via genomic associations with fitness-affecting mutations. Because mutations associated with CIN affect large swaths of the genome and have the potential to simultaneously comprise many individual loci, we show that indirect selection on CIN mutators is critically influenced by genome organization. In particular, we find strong support for a key role played by the spatial clustering of loci with either beneficial or deleterious mutational effects. Genomic clustering of selected loci allows CIN mutators to generate favorable chromosomal changes that facilitate their rapid expansion within a neoplasm and, in turn, accelerate carcinogenesis. We then examine the distribution of oncogenic and tumor-suppressing loci in the human genome and find both to be potentially more clustered along the chromosome than expected, leading us to speculate that human genome may be susceptible to CIN hitchhiking. More quantitative data on fitness effects of individual mutations will be necessary, though, to assess the true levels of clustering in the human genome and the effectiveness of indirect selection for CIN. Finally, we use our model to examine how therapeutic strategies that increase the deleterious burden of genetically unstable cells by raising either the rate of CIN or the cost of deleterious mutations affect CIN evolution. We find that both can inhibit CIN hitchhiking and delay carcinogenesis in some circumstances, yet, in line with earlier work, we find the latter to be considerably more effective.

Migration promotes mutator alleles in subdivided populations.

Mutator alleles that elevate the genomic mutation rate may invade nonrecombining populations by hitchhiking with beneficial mutations. Mutators have been repeatedly observed to take over adapting laboratory populations and have been found at high frequencies in both microbial pathogen and cancer populations in nature. Recently, we have shown that mutators are only favored by selection in sufficiently large populations and transition to being disfavored as population size decreases. This population size-dependent sign inversion in selective effect suggests that population structure may also be an important determinant of mutation rate evolution. Although large populations may favor mutators, subdividing such populations into sufficiently small subpopulations (demes) might effectively inhibit them. On the other hand, migration between small demes that otherwise inhibit hitchhiking may promote mutator fixation in the whole metapopulation. Here, we use stochastic, agent-based simulations and evolution experiments with the yeast Saccharomyces cerevisiae to show that mutators can, indeed, be favored by selection in subdivided metapopulations composed of small demes connected by sufficient migration. In fact, we show that population structure plays a previously unsuspected role in promoting mutator success in subdivided metapopulations when migration is rare.

Evolutionary constraints in fitness landscapes.

In the last years, several genotypic fitness landscapes-combinations of a small number of mutations-have been experimentally resolved. To learn about the general properties of "real" fitness landscapes, it is key to characterize these experimental landscapes via simple measures of their structure, related to evolutionary features. Some of the most relevant measures are based on the selectively acessible paths and their properties. In this paper, we present some measures of evolutionary constraints based on (i) the similarity between accessible paths and (ii) the abundance and characteristics of "chains" of obligatory mutations, that are paths going through genotypes with a single fitter neighbor. These measures have a clear evolutionary interpretation. Furthermore, we show that chains are only weakly correlated to classical measures of epistasis. In fact, some of these measures of constraint are non-monotonic in the amount of epistatic interactions, but have instead a maximum for intermediate values. Finally, we show how these measures shed light on evolutionary constraints and predictability in experimentally resolved landscapes.

The Influence of Higher-Order Epistasis on Biological Fitness Landscape Topography.

The effect of a mutation on the organism often depends on what other mutations are already present in its genome. Geneticists refer to such mutational interactions as epistasis. Pairwise epistatic effects have been recognized for over a century, and their evolutionary implications have received theoretical attention for nearly as long. However, pairwise epistatic interactions themselves can vary with genomic background. This is called higher-order epistasis, and its consequences for evolution are much less well understood. Here, we assess the influence that higher-order epistasis has on the topography of 16 published, biological fitness landscapes. We find that on average, their effects on fitness landscape declines with order, and suggest that notable exceptions to this trend may deserve experimental scrutiny. We conclude by highlighting opportunities for further theoretical and experimental work dissecting the influence that epistasis of all orders has on fitness landscape topography and on the efficiency of evolution by natural selection.

Patterns of musculoskeletal growth and dimensional changes associated with selection and developmental plasticity in domestic and wild strain turkeys.

Domestication is a type of experimental evolution in which humans have artificially selected for specific desired traits. Selected strain animals can be utilized to identify correlated responses by comparing them to the wild strain. In particular, domestic turkeys have been selected for increased body mass and high-growth rate, most significantly over the past 60 years. Yet it remains unclear how artificial selection has affected the morphology and evolution of the musculoskeletal system as a whole. Here, we compare growth rate over 21 weeks, hind limb bone scaling across ontogeny via in vivo CT scanning, and muscle proportions in wild and domestic turkeys to identify differences in structural scaling and the potential contributions of selection and developmental plasticity to whole-organism morphology. The domestic turkeys grew at a higher rate (0.14 kg/day vs. 0.05 kg/day) and reached over 3 times the body mass of wild birds. Comparing the proportional muscle masses in adult turkeys, only the trunk had a greater mass ratio in the domestic turkey, driven solely by M. pectoralis (2.8 times larger). The proportional increase in only breast meat and no other muscles highlights the surgical precision attainable with artificial selection. The domestic turkey femur and tibiotarsus displayed increases in polar moment of area, apparently maintaining torsional strength as body mass increased. The lack of dimensional change in the more vertically held tarsometatarsus is consistent with the pattern expected due to developmental plasticity. These results from the domestic turkey emphasize that there are morphological limits to preserving the balance between growth and function, and varying rates of trait evolution can further complicate this equilibrium.

Sign of selection on mutation rate modifiers depends on population size.

The influence of population size (N) on natural selection acting on alleles that affect fitness has been understood for almost a century. As N declines, genetic drift overwhelms selection and alleles with direct fitness effects are rendered neutral. Often, however, alleles experience so-called indirect selection, meaning they affect not the fitness of an individual but the fitness distribution of its offspring. Some of the best-studied examples of indirect selection include alleles that modify aspects of the genetic system such as recombination and mutation rates. Here, we use analytics, simulations, and experimental populations of Saccharomyces cerevisiae to examine the influence of N on indirect selection acting on alleles that increase the genomic mutation rate (mutators). Mutators experience indirect selection via genomic associations with beneficial and deleterious mutations they generate. We show that, as N declines, indirect selection driven by linked beneficial mutations is overpowered by drift before drift can neutralize the cost of the deleterious load. As a result, mutators transition from being favored by indirect selection in large populations to being disfavored as N declines. This surprising phenomenon of sign inversion in selective effect demonstrates that indirect selection on mutators exhibits a profound and qualitatively distinct dependence on N.

Cavernous Nerve Injury by Radiation Therapy May Potentiate Erectile Dysfunction in Rats.

PURPOSE/OBJECTIVES: Radiation-induced erectile-dysfunction (RiED) is one of the most common side effects of radiation therapy (RT) and significantly reduces the quality of life (QoL) of cancer patients. Approximately 50% of prostate cancer patients experience RiED within 3 to 5 years after completion of RT. A series of vascular, muscular, and neurogenic injuries after prostate RT lead to RiED; however, the precise role of RT-induced neurogenic injury in RiED has not been fully established. The cavernous nerves (CN) are postganglionic parasympathetic nerves located beside the prostate gland that assist in penile erection. This study was designed to investigate the role of CN injury, tissue damage, and altered signaling pathways in an RiED rat model. METHODS AND MATERIALS: Male rats were exposed to a single dose of 25 Gy prostate-confined RT. Erectile function was evaluated by intracavernous pressure (ICP) measurements conducted both 9 and 14 weeks after RT. Neuronal injury was evaluated in the CN using quantitative polymerase chain reaction, conduction studies, transmission electron microscopy, and immunoblotting. Masson trichrome staining was performed to elucidate fibrosis level in penile tissues. RESULTS: There were significant alterations in the ICP (P<.0001) of RT rats versus non-RT rats. TEM analysis showed decreased myelination, increased microvascular damage, and progressive axonal atrophy of the CN fibers after RT. Electrophysiologic analysis showed significant impairment of the CN conduction velocity after RT. RT also significantly increased RhoA/Rho-associated protein kinase 1 (ROCK1) mRNA and protein expression. In addition, penile tissue showed increased apoptosis and fibrosis 14 weeks after RT. CONCLUSIONS: RT-induced CN injury may contribute to RiED; this is therefore a rationale for developing novel therapeutic strategies to mitigate CN and tissue damage. Moreover, further investigation of the RhoA/ROCK pathway's role in mitigating RiED is necessary.

Enzyme Efficiency but Not Thermostability Drives Cefotaxime Resistance Evolution in TEM-1 ß-Lactamase.

A leading intellectual challenge in evolutionary genetics is to identify the specific phenotypes that drive adaptation. Enzymes offer a particularly promising opportunity to pursue this question, because many enzymes' contributions to organismal fitness depend on a comparatively small number of experimentally accessible properties. Moreover, on first principles the demands of enzyme thermostability stand in opposition to the demands of catalytic activity. This observation, coupled with the fact that enzymes are only marginally thermostable, motivates the widely held hypothesis that mutations conferring functional improvement require compensatory mutations to restore thermostability. Here, we explicitly test this hypothesis for the first time, using four missense mutations in TEM-1 ß-lactamase that jointly increase cefotaxime Minimum Inhibitory Concentration (MIC) ∼1500-fold. First, we report enzymatic efficiency (kcat/KM) and thermostability (Tm, and thence ΔG of folding) for all combinations of these mutations. Next, we fit a quantitative model that predicts MIC as a function of kcat/KM and ΔG. While kcat/KM explains ∼54% of the variance in cefotaxime MIC (∼92% after log transformation), ΔG does not improve explanatory power of the model. We also find that cefotaxime MIC rises more slowly in kcat/KM than predicted. Several explanations for these discrepancies are suggested. Finally, we demonstrate substantial sign epistasis in MIC and kcat/KM, and antagonistic pleiotropy between phenotypes, in spite of near numerical additivity in the system. Thus constraints on selectively accessible trajectories, as well as limitations in our ability to explain such constraints in terms of underlying mechanisms are observed in a comparatively "well-behaved" system.

Variability in fitness effects can preclude selection of the fittest.

Evolutionary biologists often predict the outcome of natural selection on an allele by measuring its effects on lifetime survival and reproduction of individual carriers. However, alleles affecting traits like sex, evolvability, and cooperation can cause fitness effects that depend heavily on differences in the environmental, social, and genetic context of individuals carrying the allele. This variability makes it difficult to summarize the evolutionary fate of an allele based solely on its effects on any one individual. Attempts to average over this variability can sometimes salvage the concept of fitness. In other cases evolutionary outcomes can only be predicted by considering the entire genealogy of an allele, thus limiting the utility of individual fitness altogether. We describe a number of intriguing new evolutionary phenomena that have emerged in studies that explicitly model long-term lineage dynamics and discuss implications for the evolution of infectious diseases.

Oligodendrocyte death, neuroinflammation, and the effects of minocycline in a rodent model of nonarteritic anterior ischemic optic neuropathy (rNAION).

Purpose: Optic nerve (ON) damage following nonarteritic anterior ischemic optic neuropathy (NAION) and its models is associated with neurodegenerative inflammation. Minocycline is a tetracycline derivative antibiotic believed to exert a neuroprotective effect by selective alteration and activation of the neuroinflammatory response. We evaluated minocycline's post-induction ability to modify early and late post-ischemic inflammatory responses and its retinal ganglion cell (RGC)-neuroprotective ability. Methods: We used the rodent NAION (rNAION) model in male Sprague-Dawley rats. Animals received either vehicle or minocycline (33 mg/kg) daily intraperitoneally for 28 days. Early (3 days) ON-cytokine responses were evaluated, and oligodendrocyte death was temporally evaluated using terminal deoxynucleotidyl transferase dUTP nick end labeling (TUNEL) analysis. Cellular inflammation was evaluated with immunohistochemistry, and RGC preservation was compared with stereology of Brn3a-positive cells in flat mounted retinas. Results: Post-rNAION, oligodendrocytes exhibit a delayed pattern of apoptosis extending over a month, with extrinsic monocyte infiltration occurring only in the primary rNAION lesion and progressive distal microglial activation. Post-induction minocycline failed to improve retinal ganglion cell survival compared with the vehicle treated (893.14 vs. 920.72; p>0.9). Cytokine analysis of the rNAION lesion 3 days post-induction revealed that minocycline exert general inflammatory suppression without selective upregulation of cytokines associated with the proposed alternative or neuroprotective M2 inflammatory pathway. Conclusions: The pattern of cytokine release, extended temporal window of oligodendrocyte death, and progressive microglial activation suggests that selective neuroimmunomodulation, rather than general inflammatory suppression, may be required for effective repair strategies in ischemic optic neuropathies.

Measuring epistasis in fitness landscapes: The correlation of fitness effects of mutations.

Genotypic fitness landscapes are constructed by assessing the fitness of all possible combinations of a given number of mutations. In the last years, several experimental fitness landscapes have been completely resolved. As fitness landscapes are high-dimensional, simple measures of their structure are used as statistics in empirical applications. Epistasis is one of the most relevant features of fitness landscapes. Here we propose a new natural measure of the amount of epistasis based on the correlation of fitness effects of mutations. This measure has a natural interpretation, captures well the interaction between mutations and can be obtained analytically for most landscape models. We discuss how this measure is related to previous measures of epistasis (number of peaks, roughness/slope, fraction of sign epistasis, Fourier-Walsh spectrum) and how it can be easily extended to landscapes with missing data or with fitness ranks only. Furthermore, the dependence of the correlation of fitness effects on mutational distance contains interesting information about the patterns of epistasis. This dependence can be used to uncover the amount and nature of epistatic interactions in a landscape or to discriminate between different landscape models.