The context-dependence of mutations: a linkage of formalisms

Defining the extent of epistasis - the non-independence of the effects of mutations - is essential for understanding the relationship of genotype, phenotype, and fitness in biological systems. The applications cover many areas of biological research, including biochemistry, genomics, protein and systems engineering, medicine, and evolutionary biology. However, the quantitative definitions of epistasis vary among fields, and its analysis beyond just pairwise effects remains obscure in general. Here, we show that different definitions of epistasis are versions of a single mathematical formalism - the weighted Walsh-Hadamard transform. We discuss that one of the definitions, the backgound-averaged epistasis, is the most informative when the goal is to uncover the general epistatic structure of a biological system, a description that can be rather different from the local epistatic structure of specific model systems. Key issues are the choice of effective ensembles for averaging and to practically contend with the vast combinatorial complexity of mutations. In this regard, we discuss possible approaches for optimally learning the epistatic structure of biological systems.Comment: 6 pages, 3 figures, supplementary informatio

Protein Sectors: Evolutionary Units of Three-Dimensional Structure

SummaryProteins display a hierarchy of structural features at primary, secondary, tertiary, and higher-order levels, an organization that guides our current understanding of their biological properties and evolutionary origins. Here, we reveal a structural organization distinct from this traditional hierarchy by statistical analysis of correlated evolution between amino acids. Applied to the S1A serine proteases, the analysis indicates a decomposition of the protein into three quasi-independent groups of correlated amino acids that we term “protein sectors.” Each sector is physically connected in the tertiary structure, has a distinct functional role, and constitutes an independent mode of sequence divergence in the protein family. Functionally relevant sectors are evident in other protein families as well, suggesting that they may be general features of proteins. We propose that sectors represent a structural organization of proteins that reflects their evolutionary histories

Inviscid instability of two-fluid free surface flow down an incline

The inviscid temporal stability analysis of two-fluid parallel shear flow with a free surface, down an incline, is studied. The velocity profiles are chosen as piecewise-linear with two limbs. The analysis reveals the existence of unstable inviscid modes, arising due to wave interaction between the free surface and the shear jump interface. Surface tension decreases the maximum growth rate of the dominant disturbance. Interestingly, in some limits, surface tension destabilises extremely short waves in this flow. This can happen because of the interaction with the shear-jump interface. This flow may be compared with a corresponding viscous two-fluid flow. Though viscosity modifies the stability properties of the flow system both qualitatively and quantitatively, there is qualitative agreement between the viscous and inviscid stability analysis when the less viscous fluid is closer to the free surface

Heracles: Improving Resource Efficiency at Scale

User-facing, latency-sensitive services, such as web-search, underutilize their computing resources during daily periods of low traffic. Reusing those resources for other tasks is rarely done in production services since the contention for shared resources can cause latency spikes that violate the service-level objectives of latency-sensitive tasks. The resulting under-utilization hurts both the affordability and energy-efficiency of large-scale datacenters. With technology scaling slowing down, it becomes important to address this opportunity. We present Heracles, a feedback-based controller that enables the safe colocation of best-effort tasks alongside a latency-critical service. Heracles dynamically manages multiple hardware and software isolation mechanisms, such as CPU, memory, and network isolation, to ensure that the latency-sensitive job meets latency targets while maximizing the resources given to best-effort tasks. We evaluate Heracles using production latency-critical and batch workloads from Google and demonstrate average server utilizations of 90% without latency violations across all the load and colocation scenarios that we evaluated

Stabilization of Hydrodynamic Flows by Small Viscosity Variations

Motivated by the large effect of turbulent drag reduction by minute concentrations of polymers we study the effects of a weakly space-dependent viscosity on the stability of hydrodynamic flows. In a recent Letter [Phys. Rev. Lett. {\bf 87}, 174501, (2001)] we exposed the crucial role played by a localized region where the energy of fluctuations is produced by interactions with the mean flow (the "critical layer"). We showed that a layer of weakly space-dependent viscosity placed near the critical layer can have a very large stabilizing effect on hydrodynamic fluctuations, retarding significantly the onset of turbulence. In this paper we extend these observation in two directions: first we show that the strong stabilization of the primary instability is also obtained when the viscosity profile is realistic (inferred from simulations of turbulent flows with a small concentration of polymers). Second, we analyze the secondary instability (around the time-dependent primary instability) and find similar strong stabilization. Since the secondary instability develops around a time-dependent solution and is three-dimensional, this brings us closer to the turbulent case. We reiterate that the large effect is {\em not} due to a modified dissipation (as is assumed in some theories of drag reduction), but due to reduced energy intake from the mean flow to the fluctuations. We propose that similar physics act in turbulent drag reduction.Comment: 10 pages, 17 figs., REVTeX4, PRE, submitte

An interdomain sector mediating allostery in Hsp70 molecular chaperones

The Hsp70 family of molecular chaperones provides a well defined and experimentally powerful model system for understanding allosteric coupling between different protein domains.New extensions to the statistical coupling analysis (SCA) method permit identification of a group of co-evolving amino-acid positions—a sector—in the Hsp70 that is associated with allosteric function.Literature-based and new experimental studies support the notion that the protein sector identified through SCA underlies the allosteric mechanism of Hsp70.This work extends the concept of protein sectors by showing that two non-homologous protein domains can share a single sector when the underlying biological function is defined by the coupled activity of the two domains

A Dynamic Model of Interactions of Ca^(2+), Calmodulin, and Catalytic Subunits of Ca^(2+)/Calmodulin-Dependent Protein Kinase II

During the acquisition of memories, influx of Ca^(2+) into the postsynaptic spine through the pores of activated N-methyl-D-aspartate-type glutamate receptors triggers processes that change the strength of excitatory synapses. The pattern of Ca^(2+) influx during the first few seconds of activity is interpreted within the Ca^(2+)-dependent signaling network such that synaptic strength is eventually either potentiated or depressed. Many of the critical signaling enzymes that control synaptic plasticity, including Ca^(2+)/calmodulin-dependent protein kinase II (CaMKII), are regulated by calmodulin, a small protein that can bind up to 4 Ca^(2+) ions. As a first step toward clarifying how the Ca^(2+)-signaling network decides between potentiation or depression, we have created a kinetic model of the interactions of Ca^(2+), calmodulin, and CaMKII that represents our best understanding of the dynamics of these interactions under conditions that resemble those in a postsynaptic spine. We constrained parameters of the model from data in the literature, or from our own measurements, and then predicted time courses of activation and autophosphorylation of CaMKII under a variety of conditions. Simulations showed that species of calmodulin with fewer than four bound Ca^(2+) play a significant role in activation of CaMKII in the physiological regime, supporting the notion that processing ofCa^(2+) signals in a spine involves competition among target enzymes for binding to unsaturated species of CaM in an environment in which the concentration of Ca^(2+) is fluctuating rapidly. Indeed, we showed that dependence of activation on the frequency of Ca^(2+) transients arises from the kinetics of interaction of fluctuating Ca^(2+) with calmodulin/CaMKII complexes. We used parameter sensitivity analysis to identify which parameters will be most beneficial to measure more carefully to improve the accuracy of predictions. This model provides a quantitative base from which to build more complex dynamic models of postsynaptic signal transduction during learning

A Generalized Allosteric Mechanism for cis-Regulated Cyclic Nucleotide Binding Domains

Cyclic nucleotides (cAMP and cGMP) regulate multiple intracellular processes and are thus of a great general interest for molecular and structural biologists. To study the allosteric mechanism of different cyclic nucleotide binding (CNB) domains, we compared cAMP-bound and cAMP-free structures (PKA, Epac, and two ionic channels) using a new bioinformatics method: local spatial pattern alignment. Our analysis highlights four major conserved structural motifs: 1) the phosphate binding cassette (PBC), which binds the cAMP ribose-phosphate, 2) the “hinge,” a flexible helix, which contacts the PBC, 3) the β2,3 loop, which provides precise positioning of an invariant arginine from the PBC, and 4) a conserved structural element consisting of an N-terminal helix, an eight residue loop and the A-helix (N3A-motif). The PBC and the hinge were included in the previously reported allosteric model, whereas the definition of the β2,3 loop and the N3A-motif as conserved elements is novel. The N3A-motif is found in all cis-regulated CNB domains, and we present a model for an allosteric mechanism in these domains. Catabolite gene activator protein (CAP) represents a trans-regulated CNB domain family: it does not contain the N3A-motif, and its long range allosteric interactions are substantially different from the cis-regulated CNB domains