On the entropy of protein families

Proteins are essential components of living systems, capable of performing a huge variety of tasks at the molecular level, such as recognition, signalling, copy, transport, ... The protein sequences realizing a given function may largely vary across organisms, giving rise to a protein family. Here, we estimate the entropy of those families based on different approaches, including Hidden Markov Models used for protein databases and inferred statistical models reproducing the low-order (1-and 2-point) statistics of multi-sequence alignments. We also compute the entropic cost, that is, the loss in entropy resulting from a constraint acting on the protein, such as the fixation of one particular amino-acid on a specific site, and relate this notion to the escape probability of the HIV virus. The case of lattice proteins, for which the entropy can be computed exactly, allows us to provide another illustration of the concept of cost, due to the competition of different folds. The relevance of the entropy in relation to directed evolution experiments is stressed.Comment: to appear in Journal of Statistical Physic

Identification of drug resistance mutations in HIV from constraints on natural evolution

Human immunodeficiency virus (HIV) evolves with extraordinary rapidity. However, its evolution is constrained by interactions between mutations in its fitness landscape. Here we show that an Ising model describing these interactions, inferred from sequence data obtained prior to the use of antiretroviral drugs, can be used to identify clinically significant sites of resistance mutations. Successful predictions of the resistance sites indicate progress in the development of successful models of real viral evolution at the single residue level, and suggest that our approach may be applied to help design new therapies that are less prone to failure even where resistance data is not yet available.Comment: 5 pages, 3 figure

For T Cell Receptors, Some Breakups Might Not Last Forever

Does the affinity or half-life of peptide-MHC-T cell receptor (TCR) interactions determine T cell activation? In this issue of Immunity, Aleksic et al. (2010) propose a role for the on rate through multiple rebindings to the same TCR

From HIV protein sequences to viral fitness landscapes: a new paradigm for in silico vaccine design

Background: An inexpensive prophylactic vaccine offers the best hope to curb the HIV/AIDS epidemic gripping sub-Saharan Africa. Systematic means to guide the design of an effective immunogen for this, and other, infectious diseases are not available. What is required is a method to chart the peaks and valleys of viral fitness as a function of amino acid sequence. An efficacious vaccine would eject the virus from the high fitness peaks, and drive it into the valleys where its compromised fitness impairs its ability to replicate and inflict damage to the host. Methods: Appealing to spin glass models in statistical physics, we present a novel approach to translate viral sequence databases into landscapes of viral fitness. These inferred models furnish a quantitative description of viral replicative capacity as a function of amino acid sequence. We illustrate this approach in the development of landscapes for the proteins of HIV-1 clade B Gag. Results: In comparisons to experimental and clinical data, our inferred landscapes demonstrate excellent agreement with: 1) in vitro replicative fitness measurements, 2) clinically observed high-fitness circulating viral strains, 3) documented HLA associated CTL escape mutations, and 4) intra-host temporal adaptation pathways revealed by deep sequencing. These favorable comparisons support our landscapes as reflections of intrinsic viral fitness. We illustrate the value of such descriptions in the computational design of a CTL Gag immunogen. Conclusion: We present a novel methodology to translate viral sequence data into quantitative landscapes of viral fitness. In an application to HIV-1 Gag, we illustrate excellent agreement of our model predictions with experimental and clinical data, and demonstrate a powerful new approach for HIV immunogen design. We anticipate that this approach may represent a heretofore unprecedented means to synthesize fitness landscapes for diverse pathogens, and may provide the basis for the design of improved prophylactic and therapeutic strategies

Deconvolving mutational patterns of poliovirus outbreaks reveals its intrinsic fitness landscape.

Vaccination has essentially eradicated poliovirus. Yet, its mutation rate is higher than that of viruses like HIV, for which no effective vaccine exists. To investigate this, we infer a fitness model for the poliovirus viral protein 1 (vp1), which successfully predicts in vitro fitness measurements. This is achieved by first developing a probabilistic model for the prevalence of vp1 sequences that enables us to isolate and remove data that are subject to strong vaccine-derived biases. The intrinsic fitness constraints derived for vp1, a capsid protein subject to antibody responses, are compared with those of analogous HIV proteins. We find that vp1 evolution is subject to tighter constraints, limiting its ability to evade vaccine-induced immune responses. Our analysis also indicates that circulating poliovirus strains in unimmunized populations serve as a reservoir that can seed outbreaks in spatio-temporally localized sub-optimally immunized populations

Positive Feedback Regulation Results in Spatial Clustering and Fast Spreading of Active Signaling Molecules on a Cell Membrane

Positive feedback regulation is ubiquitous in cell signaling networks, often leading to binary outcomes in response to graded stimuli. However, the role of such feedbacks in clustering, and in spatial spreading of activated molecules, has come to be appreciated only recently. We focus on the latter, using a simple model developed in the context of Ras activation with competing negative and positive feedback mechanisms. We find that positive feedback, in the presence of slow diffusion, results in clustering of activated molecules on the plasma membrane, and rapid spatial spreading as the front of the cluster propagates with a constant velocity (dependent on the feedback strength). The advancing fronts of the clusters of the activated species are rough, with scaling consistent with the Kardar-Parisi-Zhang (KPZ) equation in one dimension. Our minimal model is general enough to describe signal transduction in a wide variety of biological networks where activity in the membrane-proximal region is subject to feedback regulation.Comment: 37 pages, 8 figures. Journal of Chemical Physics (in press

How nonuniform contact profiles of T cell receptors modulate thymic selection outcomes

T cell receptors (TCRs) bind foreign or self-peptides attached to major histocompatibility complex (MHC) molecules, and the strength of this interaction determines T cell activation. Optimizing the ability of T cells to recognize a diversity of foreign peptides yet be tolerant of self-peptides is crucial for the adaptive immune system to properly function. This is achieved by selection of T cells in the thymus, where immature T cells expressing unique, stochastically generated TCRs interact with a large number of self-peptide-MHC; if a TCR does not bind strongly enough to any self-peptide-MHC, or too strongly with at least one self-peptide-MHC, the T cell dies. Past theoretical work cast thymic selection as an extreme value problem, and characterized the statistical enrichment or depletion of amino acids in the post-selection TCR repertoire, showing how T cells are selected to be able to specifically recognize peptides derived from diverse pathogens, yet have limited self-reactivity. Here, we investigate how the degree of enrichment is modified by nonuniform contacts that a TCR makes with peptide-MHC. Specifically, we were motivated by recent experiments showing that amino acids at certain positions of a TCR sequence have large effects on thymic selection outcomes, and crystal structure data that reveal a nonuniform contact profile between a TCR and its peptide-MHC ligand. Using a representative TCR contact profile as an illustration, we show via simulations that the degree of enrichment now varies by position according to the contact profile, and, importantly, it depends on the implementation of nonuniform contacts during thymic selection. We explain these nontrivial results analytically. Our study has implications for understanding the selection forces that shape the functionality of the post-selection TCR repertoire.Comment: 10 pages, 4 figures, submitted to Phys. Rev.