38 research outputs found
Folding of small proteins: A matter of geometry?
We review some of our recent results obtained within the scope of simple
lattice models and Monte Carlo simulations that illustrate the role of native
geometry in the folding kinetics of two state folders.Comment: To appear in Molecular Physic
Interplay between pleiotropy and secondary selection determines rise and fall of mutators in stress response
Dramatic rise of mutators has been found to accompany adaptation of bacteria
in response to many kinds of stress. Two views on the evolutionary origin of
this phenomenon emerged: the pleiotropic hypothesis positing that it is a
byproduct of environmental stress or other specific stress response mechanisms
and the second order selection which states that mutators hitchhike to fixation
with unrelated beneficial alleles. Conventional population genetics models
could not fully resolve this controversy because they are based on certain
assumptions about fitness landscape. Here we address this problem using a
microscopic multiscale model, which couples physically realistic molecular
descriptions of proteins and their interactions with population genetics of
carrier organisms without assuming any a priori fitness landscape. We found
that both pleiotropy and second order selection play a crucial role at
different stages of adaptation: the supply of mutators is provided through
destabilization of error correction complexes or fluctuations of production
levels of prototypic mismatch repair proteins (pleiotropic effects), while rise
and fixation of mutators occur when there is a sufficient supply of beneficial
mutations in replication-controlling genes. This general mechanism assures a
robust and reliable adaptation of organisms to unforeseen challenges. This
study highlights physical principles underlying physical biological mechanisms
of stress response and adaptation
Use of machine learning algorithms to classify binary protein sequences as highly-designable or poorly-designable
<p>Abstract</p> <p>Background</p> <p>By using a standard Support Vector Machine (SVM) with a Sequential Minimal Optimization (SMO) method of training, Naïve Bayes and other machine learning algorithms we are able to distinguish between two classes of protein sequences: those folding to highly-designable conformations, or those folding to poorly- or non-designable conformations.</p> <p>Results</p> <p>First, we generate all possible compact lattice conformations for the specified shape (a hexagon or a triangle) on the 2D triangular lattice. Then we generate all possible binary hydrophobic/polar (H/P) sequences and by using a specified energy function, thread them through all of these compact conformations. If for a given sequence the lowest energy is obtained for a particular lattice conformation we assume that this sequence folds to that conformation. Highly-designable conformations have many H/P sequences folding to them, while poorly-designable conformations have few or no H/P sequences. We classify sequences as folding to either highly – or poorly-designable conformations. We have randomly selected subsets of the sequences belonging to highly-designable and poorly-designable conformations and used them to train several different standard machine learning algorithms.</p> <p>Conclusion</p> <p>By using these machine learning algorithms with ten-fold cross-validation we are able to classify the two classes of sequences with high accuracy – in some cases exceeding 95%.</p
Mutation Bias Favors Protein Folding Stability in the Evolution of Small Populations
Mutation bias in prokaryotes varies from extreme adenine and thymine (AT) in obligatory endosymbiotic or parasitic bacteria to extreme guanine and cytosine (GC), for instance in actinobacteria. GC mutation bias deeply influences the folding stability of proteins, making proteins on the average less hydrophobic and therefore less stable with respect to unfolding but also less susceptible to misfolding and aggregation. We study a model where proteins evolve subject to selection for folding stability under given mutation bias, population size, and neutrality. We find a non-neutral regime where, for any given population size, there is an optimal mutation bias that maximizes fitness. Interestingly, this optimal GC usage is small for small populations, large for intermediate populations and around 50% for large populations. This result is robust with respect to the definition of the fitness function and to the protein structures studied. Our model suggests that small populations evolving with small GC usage eventually accumulate a significant selective advantage over populations evolving without this bias. This provides a possible explanation to the observation that most species adopting obligatory intracellular lifestyles with a consequent reduction of effective population size shifted their mutation spectrum towards AT. The model also predicts that large GC usage is optimal for intermediate population size. To test these predictions we estimated the effective population sizes of bacterial species using the optimal codon usage coefficients computed by dos Reis et al. and the synonymous to non-synonymous substitution ratio computed by Daubin and Moran. We found that the population sizes estimated in these ways are significantly smaller for species with small and large GC usage compared to species with no bias, which supports our prediction
Optimal enumeration of state space of finitely buffered stochastic molecular networks and exact computation of steady state landscape probability
Mathematical modeling and comparison of protein size distribution in different plant, animal, fungal and microbial species reveals a negative correlation between protein size and protein number, thus providing insight into the evolution of proteomes
<p>Abstract</p> <p>Background</p> <p>The sizes of proteins are relevant to their biochemical structure and for their biological function. The statistical distribution of protein lengths across a diverse set of taxa can provide hints about the evolution of proteomes.</p> <p>Results</p> <p>Using the full genomic sequences of over 1,302 prokaryotic and 140 eukaryotic species two datasets containing 1.2 and 6.1 million proteins were generated and analyzed statistically. The lengthwise distribution of proteins can be roughly described with a gamma type or log-normal model, depending on the species. However the shape parameter of the gamma model has not a fixed value of 2, as previously suggested, but varies between 1.5 and 3 in different species. A gamma model with unrestricted shape parameter described best the distributions in ~48% of the species, whereas the log-normal distribution described better the observed protein sizes in 42% of the species. The gamma restricted function and the sum of exponentials distribution had a better fitting in only ~5% of the species. Eukaryotic proteins have an average size of 472 aa, whereas bacterial (320 aa) and archaeal (283 aa) proteins are significantly smaller (33-40% on average). Average protein sizes in different phylogenetic groups were: Alveolata (628 aa), Amoebozoa (533 aa), Fornicata (543 aa), Placozoa (453 aa), Eumetazoa (486 aa), Fungi (487 aa), Stramenopila (486 aa), Viridiplantae (392 aa). Amino acid composition is biased according to protein size. Protein length correlated negatively with %C, %M, %K, %F, %R, %W, %Y and positively with %D, %E, %Q, %S and %T. Prokaryotic proteins had a different protein size bias for %E, %G, %K and %M as compared to eukaryotes.</p> <p>Conclusions</p> <p>Mathematical modeling of protein length empirical distributions can be used to asses the quality of small ORFs annotation in genomic releases (detection of too many false positive small ORFs). There is a negative correlation between average protein size and total number of proteins among eukaryotes but not in prokaryotes. The %GC content is positively correlated to total protein number and protein size in prokaryotes but not in eukaryotes. Small proteins have a different amino acid bias than larger proteins. Compared to prokaryotic species, the evolution of eukaryotic proteomes was characterized by increased protein number (massive gene duplication) and substantial changes of protein size (domain addition/subtraction).</p
Protein 3D Structure Computed from Evolutionary Sequence Variation
The evolutionary trajectory of a protein through sequence space is constrained by its function. Collections of sequence homologs record the outcomes of millions of evolutionary experiments in which the protein evolves according to these constraints. Deciphering the evolutionary record held in these sequences and exploiting it for predictive and engineering purposes presents a formidable challenge. The potential benefit of solving this challenge is amplified by the advent of inexpensive high-throughput genomic sequencing
Development of a knowledge-based potential for crystals of small organic molecules: Calculation of energy surfaces for C=0 center dot center dot center dot H-N hydrogen bonds
This paper describes the derivation of a Knowledge-Based Potential for intermolecular interactions from the statistical information stored in the Cambridge Structural Database. We develop a statistical mechanical method that relates the occurrences of intermolecular contacts in the database to their energies. Our approach allows us to quantify (in the form of energy) the geometrical preferences of interactions. We use our method to construct energy maps for a hydrogen bond between carbonyl oxygen and amino hydrogen. Our results demonstrate high orientational selectivity of this type of hydrogen bonding