Complexity and algorithms for copy-number evolution problems

Background

Cancer is an evolutionary process characterized by the accumulation of somatic mutations in a population of cells that form a tumor. One frequent type of mutations is copy number aberrations, which alter the number of copies of genomic regions. The number of copies of each position along a chromosome constitutes the chromosome’s copy-number profile. Understanding how such profiles evolve in cancer can assist in both diagnosis and prognosis.

Results

We model the evolution of a tumor by segmental deletions and amplifications, and gauge distance from profile \(\mathbf {a}\) to \(\mathbf {b}\) by the minimum number of events needed to transform \(\mathbf {a}\) into \(\mathbf {b}\). Given two profiles, our first problem aims to find a parental profile that minimizes the sum of distances to its children. Given k profiles, the second, more general problem, seeks a phylogenetic tree, whose k leaves are labeled by the k given profiles and whose internal vertices are labeled by ancestral profiles such that the sum of edge distances is minimum.

Conclusions

For the former problem we give a pseudo-polynomial dynamic programming algorithm that is linear in the profile length, and an integer linear program formulation. For the latter problem we show it is NP-hard and give an integer linear program formulation that scales to practical problem instance sizes. We assess the efficiency and quality of our algorithms on simulated instances.

Availability

https://github.com/raphael-group/CNT-ILP

     

TOR inhibition primes immunity and pathogen resistance in tomato in a salicylic acid-dependent manner

All organisms need to sense and process information about the availability of nutrients, energy status, and environmental cues to determine the best time for growth and development. The conserved target of rapamycin (TOR) protein kinase has a central role in sensing and perceiving nutritional information. TOR connects environmental information about nutrient availability to developmental and metabolic processes to maintain cellular homeostasis. Under favourable energy conditions, TOR is activated and promotes anabolic processes such as cell division, while suppressing catabolic processes. Conversely, when nutrients are limited or environmental stresses are present, TOR is inactivated, and catabolic processes are promoted. Given the central role of TOR in regulating metabolism, several previous works have examined whether TOR is wired to plant defence. To date, the mechanisms by which TOR influences plant defence are not entirely clear. Here, we addressed this question by testing the effect of inhibiting TOR on immunity and pathogen resistance in tomato. Examining which hormonal defence pathways are influenced by TOR, we show that tomato immune responses and disease resistance to several pathogens increase on TOR inhibition, and that TOR inhibition-mediated resistance probably requires a functional salicylic acid, but not jasmonic acid, pathway. Our results support the notion that TOR is a master regulator of the development–defence switch in plants.     

Oligonucleotides are potent antioxidants acting primarily through metal ion chelation

We report on a rather unknown feature of oligonucleotides, namely, their potent antioxidant activity. Previously, we showed that nucleotides are potent antioxidants in Fe^II/Cu^I/II–H₂O₂ systems. Here, we explored the potential of 2′-deoxyoligonucleotides as inhibitors of the Fe^II/Cu^I/II-induced ·OH formation from H₂O₂. The oligonucleotides [d(A)_5,7,20; d(T)₂₀; (2′-OMe-A)₅] proved to be highly potent antioxidants with IC₅₀ values of 5–17 or 48–85 μM in inhibiting Fe^II/Cu^I- or Cu^II-induced H₂O₂ decomposition, respectively, thus representing a 40–215-fold increase in potency as compared with Trolox, a standard antioxidant. The antioxidant activity is only weakly dependent on the oligonucleotides’ length or base identity. We analyzed by matrix-assisted laser desorption/ionization time of flight mass spectrometry and ¹H-NMR spectroscopy the composition of the d(A)₅ solution exposed to the aforementioned oxidative conditions for 4 min or 24 h. We concluded that the primary (rapid) inhibition mechanism by oligonucleotides is metal ion chelation and the secondary (slow) mechanism is radical scavenging. We characterized the Cu^I–d(A)₅ and Cu^II–d(A)₇ complexes by ¹H-NMR and ³¹P-NMR or frozen-solution ESR spectroscopy, respectively. Cu^I is probably coordinated to d(A)₅ via N1 and N7 of two adenine residues and possibly also via two phosphate/bridging water molecules. The ESR data suggest Cu^II chelation through two nitrogen atoms of the adenine bases and two oxygen atoms (phosphates or water molecules). We conclude that oligonucleotides at micromolar concentrations prevent Fe^II/Cu^I/II-induced oxidative damage, primarily through metal ion chelation. Furthermore, we propose the use of a short, metabolically stable oligonucleotide, (2′-OMe-A)₅, as a highly potent and relatively long lived (t _1/2 ~ 20 h) antioxidant.     

Structure-based rational design of streptavidin mutants with pseudo-catalytic activity

Introduction of enzymatic activity into proteins or other types of polymers by rational design is a major objective in the life sciences. To date, relatively low levels of enzymatic activity could be introduced into antibodies by using transition-state analogues of haptens. In the present study, we identify the structural elements that contribute to the observed hydrolytic activity in egg white avidin, which promote the cleavage of active biotin esters (notably biotinyl p-nitrophenyl ester). The latter elements were then incorporated into bacterial streptavidin via genetic engineering. The streptavidin molecule was thus converted from a protector to an enhancer of hydrolysis of biotin esters. The conversion was accomplished by the combined replacement of a "lid-like loop" (L3,4) and a leucine-to-arginine point mutation in streptavidin. Interestingly, neither of these elements play a direct role in the hydrolytic reaction. The latter features were thus shown to be responsible for enhanced substrate hydrolysis. This work indicates that structural and non-catalytic elements of a protein can be modified to promote the induced fit of a substrate for subsequent interaction with either a catalytic residue or water molecules. This approach complements the conventional design of active sites that involves direct modifications of catalytic residues.     

A cell-specific,prenylation-independent mechanism regulates targeting of type II RACs

The RHO proteins, which regulate numerous signaling cascades, undergo prenylation, facilitating their interaction with membranes and with proteins called RHO.GDP dissociation inhibitors. It has been suggested that prenylation is required for RHO function. Eleven RHO-related proteins were identified in Arabidopsis. Eight of them are putatively prenylated. We show that targeting of the remaining three proteins, AtRAC7, AtRAC8, and AtRAC10, is prenylation independent, requires palmitoylation, and occurs by a cell-specific mechanism. AtRAC8 and AtRAC10 could not be prenylated by either farnesyltransferase or geranylgeranyltransferase I, whereas AtRAC7 could be prenylated by both enzymes in yeast. The association of AtRAC7 with the plasma membrane in plants did not require farnesyltransferase or a functional CaaX box. Recombinant AtRAC8 was palmitoylated in vitro, and inhibition of protein palmitoylation relieved the association of all three proteins with the plasma membrane. Interestingly, AtRAC8 and a constitutively active mutant, Atrac7mV(15), were not associated with the plasma membrane in root hair cells, whose elongation requires the localization of prenylated RHOs in the plasma membrane at the cell tip. Moreover, Atrac7mV(15) did not induce root hair deformation, unlike its prenylated homologs. Thus, AtRAC7, AtRAC8, and AtRAC10 may represent a group of proteins that have evolved to fulfill unique functions.