arXiv subjects

Christoph Adami

Publications and source records attributed to Christoph Adami.

At least 91 records · Page 5Linked to original sources

arXiv2005

Quasispecies can exist under neutral drift at finite population sizes

We investigate the evolutionary dynamics of a finite population of RNA sequences adapting to a neutral fitness landscape. Despite the lack of differential fitness between viable sequences, we observe typical properties of adaptive evolution, such as increase of mean fitness over time and punctuated equilibrium transitions. We discuss the implications of these results for understanding evolution at high mutation rates, and extend the relevance of the quasispecies concept to finite populations and time scales. Our results imply that the quasispecies concept and neutral drift are not complementary concepts, and that the relative importance of each is determined by a combination of population size and mutation rate.

q-bio.PE↗

arXiv2005

Why highly expressed proteins evolve slowly

Much recent work has explored molecular and population-genetic constraints on the rate of protein sequence evolution. The best predictor of evolutionary rate is expression level, for reasons which have remained unexplained. Here, we hypothesize that selection to reduce the burden of protein misfolding will favor protein sequences with increased robustness to translational missense errors. Pressure for translational robustness increases with expression level and constrains sequence evolution. Using several sequenced yeast genomes, global expression and protein abundance data, and sets of paralogs traceable to an ancient whole-genome duplication in yeast, we rule out several confounding effects and show that expression level explains roughly half the variation in Saccharomyces cerevisiae protein evolutionary rates. We examine causes for expression's dominant role and find that genome-wide tests favor the translational robustness explanation over existing hypotheses that invoke constraints on function or translational efficiency. Our results suggest that proteins evolve at rates largely unrelated to their functions, and can explain why highly expressed proteins evolve slowly across the tree of life.

q-bio.PE↗

arXiv2004

Thermodynamic Prediction of Protein Neutrality

We present a simple theory that uses thermodynamic parameters to predict the probability that a protein retains the wildtype structure after one or more random amino acid substitutions. Our theory predicts that for large numbers of substitutions the probability that a protein retains its structure will decline exponentially with the number of substitutions, with the severity of this decline determined by properties of the structure. Our theory also predicts that a protein can gain extra robustness to the first few substitutions by increasing its thermodynamic stability. We validate our theory with simulations on lattice protein models and by showing that it quantitatively predicts previously published experimental measurements on subtilisin and our own measurements on variants of TEM1 beta-lactamase. Our work unifies observations about the clustering of functional proteins in sequence space, and provides a basis for interpreting the response of proteins to substitutions in protein engineering applications.

q-bio.BM↗

arXiv2004

A Random Matrix Model of Adiabatic Quantum Computing

We present an analysis of the quantum adiabatic algorithm for solving hard instances of 3-SAT (an NP-complete problem) in terms of Random Matrix Theory (RMT). We determine the global regularity of the spectral fluctuations of the instantaneous Hamiltonians encountered during the interpolation between the starting Hamiltonians and the ones whose ground states encode the solutions to the computational problems of interest. At each interpolation point, we quantify the degree of regularity of the average spectral distribution via its Brody parameter, a measure that distinguishes regular (i.e., Poissonian) from chaotic (i.e., Wigner-type) distributions of normalized nearest-neighbor spacings. We find that for hard problem instances, i.e., those having a critical ratio of clauses to variables, the spectral fluctuations typically become irregular across a contiguous region of the interpolation parameter, while the spectrum is regular for easy instances. Within the hard region, RMT may be applied to obtain a mathematical model of the probability of avoided level crossings and concomitant failure rate of the adiabatic algorithm due to non-adiabatic Landau-Zener type transitions. Our model predicts that if the interpolation is performed at a uniform rate, the average failure rate of the quantum adiabatic algorithm, when averaged over hard problem instances, scales exponentially with increasing problem size.

quant-ph↗

arXiv2004

Information theory in molecular biology

This article introduces the physics of information in the context of molecular biology and genomics. Entropy and information, the two central concepts of Shannon's theory of information and communication, are often confused with each other but play transparent roles when applied to statistical ensembles (i.e., identically prepared sets) of symbolic sequences. Such an approach can distinguish between entropy and information in genes, predict the secondary structure of ribozymes, and detect the covariation between residues in folded proteins. We also review applications to molecular sequence and structure analysis, and introduce new tools in the characterization of resistance mutations, and in drug design.

q-bio.BM↗

arXiv2004

The Physics of Information

Information theory is a statistical theory concerned with the relative state of detectors and physical systems. As a consequence, the classical framework of Shannon needs to be extended to deal with quantum detectors, possibly moving at relativistic speeds, conceivably within curved space-time. Considerable progress toward such a theory has been achieved in the last ten years, while much is still not understood. This review recapitulates some milestones along this road, and speculates about future ones.

quant-ph↗

arXiv2004

Stability and the Evolvability of Function in a Model Protein

Functional proteins must fold with some minimal stability to a structure that can perform a biochemical task. Here we use a simple model to investigate the relationship between the stability requirement and the capacity of a protein to evolve the function of binding to a ligand. Although our model contains no built-in tradeoff between stability and function, proteins evolved function more efficiently when the stability requirement was relaxed. Proteins with both high stability and high function evolved more efficiently when the stability requirement was gradually increased than when there was constant selection for high stability. These results show that in our model, the evolution of function is enhanced by allowing proteins to explore sequences corresponding to marginally stable structures, and that it is easier to improve stability while maintaining high function than to improve function while maintaining high stability. Our model also demonstrates that even in the absence of a fundamental biophysical tradeoff between stability and function, the speed with which function can evolve is limited by the stability requirement imposed on the protein.

q-bio.BM↗

arXiv2003

Towards photostatistics from photon-number discriminating detectors

We study the properties of a photodetector that has a number-resolving capability. In the absence of dark counts, due to its finite quantum efficiency, photodetection with such a detector can only eliminate the possibility that the incident field corresponds to a number of photons less than the detected photon number. We show that such a {\em non-photon} number-discriminating detector, however, provides a useful tool in the reconstruction of the photon number distribution of the incident field even in the presence of dark counts.

quant-ph↗

arXiv2003

Modeling stochastic clonal interference

We study the competition between several advantageous mutants in an asexual population (clonal interference) as a function of the time between the appearance of the mutants, their selective advantages, and the rate of deleterious mutations. We find that the overall probability of fixation (the probability that at least one of the mutants becomes the ancestor of the entire population) does not depend on the time interval between the appearance of these mutants, and equals the probability that a genotype bearing all of these mutations reaches fixation. This result holds also in the presence of deleterious mutations, and for an arbitrary number of competing mutants. We also show that if mutations interfere, an increase in the mean number of fixation events is associated with a decrease in the expected fitness gain of the population.

physics.bio-ph↗

arXiv2003

Entangled Light in Moving Frames

We calculate the entanglement between a pair of polarization-entangled photon beams as a function of the reference frame, in a fully relativistic framework. We find the transformation law for helicity basis states and show that, while it is frequency independent, a Lorentz transformation on a momentum-helicity eigenstate produces a momentum-dependent phase. This phase leads to changes in the reduced polarization density matrix, such that entanglement is either decreased or increased, depending on the boost direction, the rapidity, and the spread of the beam.

quant-ph↗

arXiv2003

Compensatory mutations cause excess of antagonistic epistasis in RNA secondary structure folding

Background: The rate at which fitness declines as an organism's genome accumulates random mutations is an important variable in several evolutionary theories. At an intuitive level, it might seem natural that random mutations should tend to interact synergistically, such that the rate of mean fitness decline accelerates as the number of random mutations is increased. However, in a number of recent studies, a prevalence of antagonistic epistasis (the tendency of multiple mutations to have a mitigating rather than reinforcing effect) has been observed. Results: We studied in silico the net amount and form of epistatic interactions in RNA secondary structure folding by measuring the fraction of neutral mutants as a function of mutational distance d. We found a clear prevalence of antagonistic epistasis in RNA secondary structure folding. By relating the fraction of neutral mutants at distance d to the average neutrality at distance d, we showed that this prevalence derives from the existence of many compensatory mutations at larger mutational distances. Conclusions: Our findings imply that the average direction of epistasis in simple fitness landscapes is directly related to the density with which fitness peaks are distributed in these landscapes.

physics.bio-ph↗

arXiv2003

Selective pressures on genomes in molecular evolution

We describe the evolution of macromolecules as an information transmission process and apply tools from Shannon information theory to it. This allows us to isolate three independent, competing selective pressures that we term compression, transmission, and neutrality selection. The first two affect genome length: the pressure to conserve resources by compressing the code, and the pressure to acquire additional information that improves the channel, increasing the rate of information transmission into each offspring. Noisy transmission channels (replication with mutations) gives rise to a third pressure that acts on the actual encoding of information; it maximizes the fraction of mutations that are neutral with respect to the phenotype. This neutrality selection has important implications for the evolution of evolvability. We demonstrate each selective pressure in experiments with digital organisms.

quant-ph↗

arXiv2002

Quantum Entanglement of Moving Bodies

We study the properties of quantum information and quantum entanglement in moving frames. We show that the entanglement between the spins and the momenta of two particles can be interchanged under a Lorentz transformation, so that a pair of particles that is entangled in spin but not momentum in one reference frame, may, in another frame, be entangled in momentum at the expense of spin-entanglement. Similarly, entanglement between momenta may be transferred to spin under a Lorentz transformation. While spin and momentum entanglement each is not Lorentz invariant, the joint entanglement of the wave function is.

quant-ph↗

arXiv2002

Viral evolution under the pressure of an adaptive immune system - optimal mutation rates for viral escape

Based on a recent model of evolving viruses competing with an adapting immune system [1], we study the conditions under which a viral quasispecies can maximize its growth rate. The range of mutation rates that allows viruses to thrive is limited from above due to genomic information deterioration, and from below by insufficient sequence diversity, which leads to a quick eradication of the virus by the immune system. The mutation rate that optimally balances these two requirements depends to first order on the ratio of the inverse of the virus' growth rate and the time the immune system needs to develop a specific answer to an antigen. We find that a virus is most viable if it generates exactly one mutation within the time it takes for the immune system to adapt to a new viral epitope. Experimental viral mutation rates, in particular for HIV (human immunodeficiency virus), seem to suggest that many viruses have achieved their optimal mutation rate. [1] C.Kamp and S. Bornholdt, Phys. Rev. Lett., 88, 068104 (2002)

cond-mat.stat-mech↗

arXiv2002

Critical and Near-Critical Branching Processes

Scale-free dynamics in physical and biological systems can arise from a variety of causes. Here, we explore a branching process which leads to such dynamics. We find conditions for the appearance of power laws and study quantitatively what happens to these power laws when such conditions are violated. From a branching process model, we predict the behavior of two systems which seem to exhibit near scale-free behavior--rank-frequency distributions of number of subtaxa in biology, and abundance distributions of genotypes in an artificial life system. In the light of these, we discuss distributions of avalanche sizes in the Bak-Tang-Wiesenfeld sandpile model.

cond-mat.dis-nn↗

arXiv2001

Optimal adaptive performance and delocalization in NK fitness landscapes

We investigate the evolutionary dynamics of a finite population of sequences adapting to NK fitness landscapes. We find that, unlike in the case of an infinite population, the average fitness in a finite population is maximized at a small but finite, rather than vanishing, mutation rate. The highest local maxima in the landscape are visited for even larger mutation rates, close to a transition point at which the population delocalizes (i.e., leaves the fitness peak at which it was localized) and starts traversing the sequence space. If the mutation rate is increased even further, the population undergoes a second transition and loses all sensitivity to fitness peaks. This second transition corresponds to the standard error threshold transition first described by Eigen. We discuss the implications of our results for biological evolution and for evolutionary optimization techniques.

physics.bio-ph↗

arXiv2001

Interaction between directional epistasis and average mutational effects

We investigate the relationship between the average fitness decay due to single mutations and the strength of epistatic interactions in genetic sequences. We observe that epistatic interactions between mutations are correlated to the average fitness decay, both in RNA secondary structure prediction as well as in digital organisms replicating in silico. This correlation implies that during adaptation, epistasis and average mutational effect cannot be optimized independently. In experiments with RNA sequences evolving on a neutral network, the selective pressure to decrease the mutational load then leads to a reduction of the amount of sequences with strong antagonistic interactions between deleterious mutations in the population.

physics.bio-ph↗

arXiv2000

Evolution of Biological Complexity

In order to make a case for or against a trend in the evolution of complexity in biological evolution, complexity needs to be both rigorously defined and measurable. A recent information-theoretic (but intuitively evident) definition identifies genomic complexity with the amount of information a sequence stores about its environment. We investigate the evolution of genomic complexity in populations of digital organisms and monitor in detail the evolutionary transitions that increase complexity. We show that because natural selection forces genomes to behave as a natural ``Maxwell Demon'', within a fixed environment genomic complexity is forced to increase.

physics.bio-ph↗