Amos Maritan

Global protein function prediction from protein-protein interaction networks

Determining protein function is one of the most challenging problems of the post-genomic era. The availability of entire genome sequences and of high-throughput capabilities to determine gene coexpression patterns has shifted the research focus from the study of single proteins or small complexes to that of the entire proteome. In this context, the search for reliable methods for assigning protein function is of primary importance. There are various approaches available for deducing the function of proteins of unknown function using information derived from sequence similarity or clustering patterns of co-regulated genes, phylogenetic profiles, protein-protein interactions (refs. 5–8 and Samanta, M.P. and Liang, S., unpublished data), and protein complexes. Here we propose the assignment of proteins to functional classes on the basis of their network of physical interactions as determined by minimizing the number of protein interactions among different functional categories. Function assignment is proteome-wide and is determined by the global connectivity pattern of the protein network. The approach results in multiple functional assignments, a consequence of the existence of multiple equivalent solutions. We apply the method to analyze the yeast Saccharomyces cerevisiae protein-protein interaction network. The robustness of the approach is tested in a system containing a high percentage of unclassified proteins and also in cases of deletion and insertion of specific protein interactions.

Size and form in efficient transportation networks

Many biological processes, from cellular metabolism to population dynamics, are characterized by allometric scaling (power-law) relationships between size and rate. An outstanding question is whether typical allometric scaling relationships—the power-law dependence of a biological rate on body mass—can be understood by considering the general features of branching networks serving a particular volume. Distributed networks in nature stem from the need for effective connectivity, and occur both in biological systems such as cardiovascular and respiratory networks and plant vascular and root systems,,, and in inanimate systems such as the drainage network of river basins. Here we derive a general relationship between size and flow rates in arbitrary networks with local connectivity. Our theory accounts in a general way for the quarter-power allometric scaling of living organisms, recently derived under specific assumptions for particular network geometries. It also predicts scaling relations applicable to all efficient transportation networks, which we verify from observational data on the river drainage basins. Allometric scaling is therefore shown to originate from the general features of networks irrespective of dynamical or geometric assumptions.

Neutral theory and relative species abundance in ecology.

The theory of island biogeography asserts that an island or a local community approaches an equilibrium species richness as a result of the interplay between the immigration of species from the much larger metacommunity source area and local extinction of species on the island (local community). Hubbell generalized this neutral theory to explore the expected steady-state distribution of relative species abundance (RSA) in the local community under restricted immigration. Here we present a theoretical framework for the unified neutral theory of biodiversity and an analytical solution for the distribution of the RSA both in the metacommunity (Fishers log series) and in the local community, where there are fewer rare species. Rare species are more extinction-prone, and once they go locally extinct, they take longer to re-immigrate than do common species. Contrary to recent assertions, we show that the analytical solution provides a better fit, with fewer free parameters, to the RSA distribution of tree species on Barro Colorado Island, Panama, than the lognormal distribution.

A universal model for mobility and migration patterns

Introduced in its contemporary form in 1946 (ref. 1), but with roots that go back to the eighteenth century, the gravity law is the prevailing framework with which to predict population movement, cargo shipping volume and inter-city phone calls, as well as bilateral trade flows between nations. Despite its widespread use, it relies on adjustable parameters that vary from region to region and suffers from known analytic inconsistencies. Here we introduce a stochastic process capturing local mobility decisions that helps us analytically derive commuting and mobility fluxes that require as input only information on the population distribution. The resulting radiation model predicts mobility patterns in good agreement with mobility and transport patterns observed in a wide range of phenomena, from long-term migration patterns to communication volume between different regions. Given its parameter-free nature, the model can be applied in areas where we lack previous mobility measurements, significantly improving the predictive accuracy of most of the phenomena affected by mobility and transport processes.

Modeling of Protein Interaction Networks

We introduce a graph-generating model aimed at representing the evolution of protein interaction networks. The model is based on the hypothesis of evolution by duplication and divergence of the genes which produce proteins. The obtained graphs have multifractal properties recovering the absence of a characteristic connectivity as found in real data of protein interaction networks. The error tolerance of the model to random or targeted damage is in very good agreement with the behavior obtained in real protein network analyses. The proposed model is a first step in the identification of the evolutionary dynamics leading to the development of protein functions and interactions.

Dynamic modeling of gene expression data

We describe the time evolution of gene expression levels by using a time translational matrix to predict future expression levels of genes based on their expression levels at some initial time. We deduce the time translational matrix for previously published DNA microarray gene expression data sets by modeling them within a linear framework by using the characteristic modes obtained by singular value decomposition. The resulting time translation matrix provides a measure of the relationships among the modes and governs their time evolution. We show that a truncated matrix linking just a few modes is a good approximation of the full time translation matrix. This finding suggests that the number of essential connections among the genes is small.

A backbone-based theory of protein folding.

Under physiological conditions, a protein undergoes a spontaneous disorder ⇌ order transition called “folding.” The protein polymer is highly flexible when unfolded but adopts its unique native, three-dimensional structure when folded. Current experimental knowledge comes primarily from thermodynamic measurements in solution or the structures of individual molecules, elucidated by either x-ray crystallography or NMR spectroscopy. From the former, we know the enthalpy, entropy, and free energy differences between the folded and unfolded forms of hundreds of proteins under a variety of solvent/cosolvent conditions. From the latter, we know the structures of ≈35,000 proteins, which are built on scaffolds of hydrogen-bonded structural elements, α-helix and β-sheet. Anfinsen showed that the amino acid sequence alone is sufficient to determine a proteins structure, but the molecular mechanism responsible for self-assembly remains an open question, probably the most fundamental open question in biochemistry. This perspective is a hybrid: partly review, partly proposal. First, we summarize key ideas regarding protein folding developed over the past half-century and culminating in the current mindset. In this view, the energetics of side-chain interactions dominate the folding process, driving the chain to self-organize under folding conditions. Next, having taken stock, we propose an alternative model that inverts the prevailing side-chain/backbone paradigm. Here, the energetics of backbone hydrogen bonds dominate the folding process, with preorganization in the unfolded state. Then, under folding conditions, the resultant fold is selected from a limited repertoire of structural possibilities, each corresponding to a distinct hydrogen-bonded arrangement of α-helices and/or strands of β-sheet.

Supply–demand balance and metabolic scaling

It is widely accepted that metabolic rates scale across species approximately as the 3/4 power of mass in most if not all groups of organisms. Metabolic demand per unit mass thus decreases as body mass increases. Metabolic rates reflect both the ability of the organisms transport system to deliver metabolites to the tissues and the rate at which the tissues use them. We show that the ubiquitous 3/4 power law for interspecific metabolic scaling arises from simple, general geometric properties of transportation networks constrained to function in biological organisms. The 3/4 exponent and other observed scaling relationships follow when mass-specific metabolic demands match the changing delivery capacities of the network at different body sizes. Deviation from the 3/4 exponent suggests either inefficiency or compensating physiological mechanisms. Our conclusions are based on general arguments incorporating the minimum of biological detail and should therefore apply to the widest range of organisms.

Patterns of relative species abundance in rainforests and coral reefs

A formidable many-body problem in ecology is to understand the complex of factors controlling patterns of relative species abundance (RSA) in communities of interacting species. Unlike many problems in physics, the nature of the interactions in ecological communities is not completely known. Although most contemporary theories in ecology start with the basic premise that species interact, here we show that a theory in which all interspecific interactions are turned off leads to analytical results that are in agreement with RSA data from tropical forests and coral reefs. The assumption of non-interacting species leads to a sampling theory for the RSA that yields a simple approximation at large scales to the exact theory. Our results show that one can make significant theoretical progress in ecology by assuming that the effective interactions among species are weak in the stationary states in species-rich communities such as tropical forests and coral reefs.

On Hack's Law

Hacks law is reviewed, emphasizing its implications for the elongation of river basins as well as its connections with their fractal characteristics. The relation between Hacks law and the internal structure of river basins is investigated experimentally through digital elevation models. It is found that Hacks exponent, elongation, and some relevant fractal characters are closely related. The self-affine character of basin boundaries is shown to be connected to the power law decay of the probability of total contributing areas at any link and to Hacks law. An explanation for Hacks law is derived from scaling arguments. From the results we suggest that a statistical framework referring to the scaling invariance of the entire basin structure should be used in the interpretation of Hacks law.