Block network mapping approach to quantitative trait locus analysis.

BACKGROUND: Advances in experimental biology have enabled the collection of enormous troves of data on genomic variation in living organisms. The interpretation of this data to extract actionable information is one of the keys to developing novel therapeutic strategies to treat complex diseases. Network organization of biological data overcomes measurement noise in several biological contexts. Does a network approach, combining information about the linear organization of genomic markers with correlative information on these markers in a Bayesian formulation, lead to an analytic method with higher power for detecting quantitative trait loci? RESULTS: Block Network Mapping, combining Similarity Network Fusion (Wang et al., NM 11:333-337, 2014) with a Bayesian locus likelihood evaluation, leads to large improvements in area under the receiver operating characteristic and power over interval mapping with expectation maximization. The method has a monotonically decreasing false discovery rate as a function of effect size, unlike interval mapping. CONCLUSIONS: Block Network Mapping provides an alternative data-driven approach to mapping quantitative trait loci that leverages correlations in the sampled genotypes. The evaluation methodology can be combined with existing approaches such as Interval Mapping. Python scripts are available at http://lbm.niddk.nih.gov/vipulp/ . Genotype data is available at http://churchill-lab.jax.org/website/GattiDOQTL .

The jigsaw puzzle of sequence phenotype inference: Piecing together Shannon entropy, importance sampling, and Empirical Bayes.

A nucleotide sequence 35 base pairs long can take 1,180,591,620,717,411,303,424 possible values. An example of systems biology datasets, protein binding microarrays, contain activity data from about 40,000 such sequences. The discrepancy between the number of possible configurations and the available activities is enormous. Thus, albeit that systems biology datasets are large in absolute terms, they oftentimes require methods developed for rare events due to the combinatorial increase in the number of possible configurations of biological systems. A plethora of techniques for handling large datasets, such as Empirical Bayes, or rare events, such as importance sampling, have been developed in the literature, but these cannot always be simultaneously utilized. Here we introduce a principled approach to Empirical Bayes based on importance sampling, information theory, and theoretical physics in the general context of sequence phenotype model induction. We present the analytical calculations that underlie our approach. We demonstrate the computational efficiency of the approach on concrete examples, and demonstrate its efficacy by applying the theory to publicly available protein binding microarray transcription factor datasets and to data on synthetic cAMP-regulated enhancer sequences. As further demonstrations, we find transcription factor binding motifs, predict the activity of new sequences and extract the locations of transcription factor binding sites. In summary, we present a novel method that is efficient (requiring minimal computational time and reasonable amounts of memory), has high predictive power that is comparable with that of models with hundreds of parameters, and has a limited number of optimized parameters, proportional to the sequence length.

A network characteristic that correlates environmental and genetic robustness.

As scientific advances in perturbing biological systems and technological advances in data acquisition allow the large-scale quantitative analysis of biological function, the robustness of organisms to both transient environmental stresses and inter-generational genetic changes is a fundamental impediment to the identifiability of mathematical models of these functions. An approach to overcoming this impediment is to reduce the space of possible models to take into account both types of robustness. However, the relationship between the two is still controversial. This work uncovers a network characteristic, transient responsiveness, for a specific function that correlates environmental imperturbability and genetic robustness. We test this characteristic extensively for dynamic networks of ordinary differential equations ranging up to 30 interacting nodes and find that there is a power-law relating environmental imperturbability and genetic robustness that tends to linearity as the number of nodes increases. Using our methods, we refine the classification of known 3-node motifs in terms of their environmental and genetic robustness. We demonstrate our approach by applying it to the chemotaxis signaling network. In particular, we investigate plausible models for the role of CheV protein in biochemical adaptation via a phosphorylation pathway, testing modifications that could improve the robustness of the system to environmental and/or genetic perturbation.

Quantitative dynamics of adipose cells.

Adipose cells are unique in the dynamism of their sizes, a requisite for their main function of storing and releasing lipid. Lipid metabolism is crucial for energy homeostasis. However, the regulation of lipid storage capacity in conditions of energy excess and scarcity is still not clear. It is not technically feasible to monitor every process affecting storage capacity such as recruitment, growth/shrinkage and death of individual adipose cells in real time for a sufficiently long period. However, recent computational approaches have allowed an examination of the detailed dynamics of adipose cells using statistical information in the form of precise measurements of adipose cell-size probability distributions. One interesting finding is that the growth/shrinkage of adipose cells (> 50 µm diameter) under positive/negative energy balance is proportional to the surface area of cells, limiting efficient lipid absorption/release from larger adipose cells. In addition to the physical characteristics of adipose cells, quantitative modeling integrates dynamics of adipose cells, providing the mechanism of cell turnover under normal and drug-treated conditions. Thus, further use of mathematical modeling applied to experimental measurements of adipose cell-size probability distributions in conjunction with physiological measurements of metabolic state may help unravel the intricate network of interactions underlying metabolic syndromes in obesity.

Scaling behavior of quantum nanosystems: emergence of quasi-particles, collective modes, and mixed exchange symmetry states.

Examples of quantum nanosystems are graphene nanoribbons, molecular wires, and superconducting nanoparticles. The objective of the multiscale theory presented here is to provide a new perspective on the coupling of processes across scales in space and time underlying the dynamics of these systems. The long range objective for this multiscale approach is to serve as an efficient computational algorithm. Long space-time dynamics is derived using a perturbation expansion in the ratio ɛ of the nearest-neighbor distance to a nanometer-scale characteristic length and a theorem on the equivalence of long time-averages and expectation values. This dynamics is shown to satisfy a coarse-grained wave equation (CGWE) which takes a Schrödinger-like form with modified masses and interactions. The scaling of space and time is determined by the orders of magnitude of various contributions to the N-body potential. If the spatial scale of the coarse-graining is too large, the CGWE would imply an unbounded growth of gradients; if it is too short, the system's size would display uncontrolled growth inappropriate for the bound states of interest, i.e., collective motion or migration within a stable nanoassembly. The balance of these two extremes removes arbitrariness in the choice of the scaling of space-time. Since the long-scale dynamics of each Fermion involves its interaction with many others, we hypothesize that the solutions of the CGWE have mean-field character to good approximation, i.e., can be factorized into single-particle functions. This leads to a coarse-grained mean-field approximation that is distinct in character from traditional Hartree-Fock theory. A variational principle is used to derive equations for the single-particle functions. This theme is developed and used to derive an equation for low-lying disturbances from the ground state corresponding to long wavelength density disturbances or long-scale migration. An algorithm for the efficient simulation of quantum nanosystems is suggested.

Deriving principles of microbiology by multiscaling laws of molecular physics.

It has long been an objective of the physical sciences to derive principles of biology from the laws of physics. At the angstrom scale for processes evolving on timescales of 10(-14) s, many systems can be characterized in terms of atomic vibrations and collisions. In contrast, biological systems display dramatic transformations including self-assembly and reorganization from one cell phenotype to another as the microenvironment changes. We have developed a framework for understanding the emergence of living systems from the underlying atomic chaos.

Effect of competitive complex formation on patterning and front propagation in periodic precipitation.

The Co(OH)2 Liesegang pattern (from Co2+ and NH4OH) propagates in space by periodic band formation at the head due to precipitation and band disappearance at the tail due to dissolution in excess NH4OH. Introduction of Ni2+, which competes with Co2+ for complex formation with ammonia, into the system led to several interesting observations: slower propagation, fewer bands, and increased spacing between them. Above a cutoff concentration of Ni2+ (0.13 M for [Co2+]0 = 0.100 M), only a uniform precipitation zone was observed. The quantity delta X = |XNi-Xfree|, namely, the difference in the position of last band in the system with nickel relative to that without nickel attained at a fixed time (93 h), was found to oscillate as the initial concentration of NH4OH ([NH4OH]0) was varied. It was shown that variations in the concentration of intermediate NH4+ act as precursors for these oscillations: [NH4+] was measured with an ammonia-specific electrode, and the difference delta [NH4+] = |[NH4+]Ni-[NH4+]free| at 93 h exhibited oscillations with [NH4OH]0 similar to those obtained in delta X. Theoretical calculations based on the model of Müller and Polezhaev agreed with the experimental results.