The 2019 mathematical oncology roadmap.

Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic Science, there is no denying that mathematics continues to play an increasingly prominent role in cancer research. Mathematical Oncology-defined here simply as the use of mathematics in cancer research-complements and overlaps with a number of other fields that rely on mathematics as a core methodology. As a result, Mathematical Oncology has a broad scope, ranging from theoretical studies to clinical trials designed with mathematical models. This Roadmap differentiates Mathematical Oncology from related fields and demonstrates specific areas of focus within this unique field of research. The dominant theme of this Roadmap is the personalization of medicine through mathematics, modelling, and simulation. This is achieved through the use of patient-specific clinical data to: develop individualized screening strategies to detect cancer earlier; make predictions of response to therapy; design adaptive, patient-specific treatment plans to overcome therapy resistance; and establish domain-specific standards to share model predictions and to make models and simulations reproducible. The cover art for this Roadmap was chosen as an apt metaphor for the beautiful, strange, and evolving relationship between mathematics and cancer.

Steering Evolution with Sequential Therapy to Prevent the Emergence of Bacterial Antibiotic Resistance.

The increasing rate of antibiotic resistance and slowing discovery of novel antibiotic treatments presents a growing threat to public health. Here, we consider a simple model of evolution in asexually reproducing populations which considers adaptation as a biased random walk on a fitness landscape. This model associates the global properties of the fitness landscape with the algebraic properties of a Markov chain transition matrix and allows us to derive general results on the non-commutativity and irreversibility of natural selection as well as antibiotic cycling strategies. Using this formalism, we analyze 15 empirical fitness landscapes of E. coli under selection by different ß-lactam antibiotics and demonstrate that the emergence of resistance to a given antibiotic can be either hindered or promoted by different sequences of drug application. Specifically, we demonstrate that the majority, approximately 70%, of sequential drug treatments with 2-4 drugs promote resistance to the final antibiotic. Further, we derive optimal drug application sequences with which we can probabilistically 'steer' the population through genotype space to avoid the emergence of resistance. This suggests a new strategy in the war against antibiotic-resistant organisms: drug sequencing to shepherd evolution through genotype space to states from which resistance cannot emerge and by which to maximize the chance of successful therapy.

Calibration of Time-Interleaved Errors in Digital Real-Time Oscilloscopes.

A channel mismatch calibration method is proposed for use in time-interleaved digital real-time oscilloscope (DRTO) applications. Linear equations are derived using Fourier transforms of the separated signals from each of the time-interleaved analog-to-digital converters (TIADCs). Thus the errors in the TIADCs can be easily calibrated by inversion of a matrix, as opposed to most previous work where additional filters are employed. The calibration accuracy of the proposed method is limited only by the noise produced after the TIADC circuitry, while other methods depend on the filter design. A transfer function measurement method is then proposed for application to commercially available DRTOs. Two-tone signals are measured using DRTOs from various suppliers to validate the proposed method. The occurrence of signals at spurious frequencies is considerably reduced, as demonstrated by the calibrated results.

Simple neural-like p systems for maximal independent set selection.

Membrane systems (P systems) are distributed computing models inspired by living cells where a collection of processors jointly achieves a computing task. The problem of maximal independent set (MIS) selection in a graph is to choose a set of nonadjacent nodes to which no further nodes can be added. In this letter, we design a class of simple neural-like P systems to solve the MIS selection problem efficiently in a distributed way. This new class of systems possesses two features that are attractive for both distributed computing and membrane computing: first, the individual processors do not need any information about the overall size of the graph; second, they communicate using only one-bit messages.

Model genotype-phenotype mappings and the algorithmic structure of evolution.

Cancers are complex dynamic systems that undergo evolution and selection. Personalized medicine approaches in the clinic increasingly rely on predictions of tumour response to one or more therapies; these predictions are complicated by the inevitable evolution of the tumour. Despite enormous amounts of data on the mutational status of cancers and numerous therapies developed in recent decades to target these mutations, many of these treatments fail after a time due to the development of resistance in the tumour. The emergence of these resistant phenotypes is not easily predicted from genomic data, since the relationship between genotypes and phenotypes, termed the genotype-phenotype (GP) mapping, is neither injective nor functional. We present a review of models of this mapping within a generalized evolutionary framework that takes into account the relation between genotype, phenotype, environment and fitness. Different modelling approaches are described and compared, and many evolutionary results are shown to be conserved across studies despite using different underlying model systems. In addition, several areas for future work that remain understudied are identified, including plasticity and bet-hedging. The GP-mapping provides a pathway for understanding the potential routes of evolution taken by cancers, which will be necessary knowledge for improving personalized therapies.

Deep Learning Classification of 3.5 GHz Band Spectrograms with Applications to Spectrum Sensing.

In the United States, the Federal Communications Commission has adopted rules permitting commercial wireless networks to share spectrum with federal incumbents in the 3.5 GHz Citizens Broadband Radio Service band. These rules require commercial systems to vacate the band when sensors detect radars operated by the U.S. military; a key example being the SPN-43 air traffic control radar. Such sensors require highly-accurate detection algorithms to meet their operating requirements. In this paper, using a library of over 14,000 3.5 GHz band spectrograms collected by a recent measurement campaign, we investigate the performance of thirteen methods for SPN-43 radar detection. Namely, we compare classical methods from signal detection theory and machine learning to several deep learning architectures. We demonstrate that machine learning algorithms appreciably outperform classical signal detection methods. Specifically, we find that a three-layer convolutional neural network offers a superior tradeoff between accuracy and computational complexity. Last, we apply this three-layer network to generate descriptive statistics for the full 3.5 GHz spectrogram library. Our findings highlight potential weaknesses of classical methods and strengths of modern machine learning algorithms for radar detection in the 3.5 GHz band.

Antibiotic collateral sensitivity is contingent on the repeatability of evolution.

Antibiotic resistance represents a growing health crisis that necessitates the immediate discovery of novel treatment strategies. One such strategy is the identification of collateral sensitivities, wherein evolution under a first drug induces susceptibility to a second. Here, we report that sequential drug regimens derived from in vitro evolution experiments may have overstated therapeutic benefit, predicting a collaterally sensitive response where cross-resistance ultimately occurs. We quantify the likelihood of this phenomenon by use of a mathematical model parametrised with combinatorially complete fitness landscapes for Escherichia coli. Through experimental evolution we then verify that a second drug can indeed stochastically exhibit either increased susceptibility or increased resistance when following a first. Genetic divergence is confirmed as the driver of this differential response through targeted and whole genome sequencing. Taken together, these results highlight that the success of evolutionarily-informed therapies is predicated on a rigorous probabilistic understanding of the contingencies that arise during the evolution of drug resistance.

Enhancing the prediction of transcription factor binding sites by incorporating structural properties and nucleotide covariations.

A problem faced by many algorithms for finding transcription factor (TF) binding sites is the high number of false positive hits that result with the increased sensitivity of their prediction. A main contributing factor to this is the short and degenerate nature of these sites which results in a low signal-to-noise ratio. In order to counter this problem, one needs to look beyond the assumption that individual bases of a TF binding site act independently from each other when binding to a transcription factor. In this paper, we present a new method based on templates, designed to exploit the discriminatory features, nucleotide polymorphism, and structural homology present in TF binding sites for distinguishing them from nonbinding sites.

Stochasticity in the Genotype-Phenotype Map: Implications for the Robustness and Persistence of Bet-Hedging.

Nongenetic variation in phenotypes, or bet-hedging, has been observed as a driver of drug resistance in both bacterial infections and cancers. Here, we study how bet-hedging emerges in genotype-phenotype (GP) mapping through a simple interaction model: a molecular switch. We use simple chemical reaction networks to implement stochastic switches that map gene products to phenotypes, and investigate the impact of structurally distinct mappings on the evolution of phenotypic heterogeneity. Bet-hedging naturally emerges within this model, and is robust to evolutionary loss through mutations to both the expression of individual genes, and to the network itself. This robustness explains an apparent paradox of bet-hedging-why does it persist in environments where natural selection necessarily acts to remove it? The structure of the underlying molecular mechanism, itself subject to selection, can slow the evolutionary loss of bet-hedging to ensure a survival mechanism against environmental catastrophes even when they are rare. Critically, these properties, taken together, have profound implications for the use of treatment-holidays to combat bet-hedging-driven resistant disease, as the efficacy of breaks from treatment will ultimately be determined by the structure of the GP mapping.

Simple Algorithms for Distributed Leader Election in Anonymous Synchronous Rings and Complete Networks Inspired by Neural Development in Fruit Flies.

Leader election in anonymous rings and complete networks is a very practical problem in distributed computing. Previous algorithms for this problem are generally designed for a classical message passing model where complex messages are exchanged. However, the need to send and receive complex messages makes such algorithms less practical for some real applications. We present some simple synchronous algorithms for distributed leader election in anonymous rings and complete networks that are inspired by the development of the neural system of the fruit fly. Our leader election algorithms all assume that only one-bit messages are broadcast by nodes in the network and processors are only able to distinguish between silence and the arrival of one or more messages. These restrictions allow implementations to use a simpler message-passing architecture. Even with these harsh restrictions our algorithms are shown to achieve good time and message complexity both analytically and experimentally.

Characterization of the putative operon containing arylamine N-acetyltransferase (nat) in Mycobacterium bovis BCG.

Mycobacterium bovis BCG and Mycobacterium tuberculosis possess a single arylamine N-acetyltransferase whose gene is predicted to occur within a six-gene operon. Deletion of the nat gene caused an extended lag phase in M. bovis BCG and a cell morphology associated with an altered pattern of cell wall mycolates. Analysis of cDNA from M. bovis BCG shows that during in vitro growth all the genes in the putative nat operon are expressed and the open reading frames are contiguous, supporting the existence of an operon. Two genes in the operon, Mb3599c and Mb3600c, are predicted to encode homologues of enzymes annotated as a 2,3-dihydroxybiphenyl 1,2-dioxygenase (bphC5) and a 2-hydroxy-6-oxo-6-phenylhexa-2,4-dienoate hydrolase (bphD2), respectively, in Rhodococcus RHA1. As predicted, M. bovis BCG cell lysates metabolized the BphC substrate 2,3-dihydroxybiphenyl (2,3-DHB) to 2-hydroxy-6-oxo-6-phenylhexa-2,4-dienoic acid (HOPDA), a BphD substrate, which was subsequently hydrolysed. Immunoprecipitation of the BphD homologue from these lysates led to an accumulation of HOPDA. M. bovis BCG growth on both solid and liquid media was inhibited with either 2,3-DHB or an inhibitor of BphC, 3-chlorocatechol (3-CC). In addition, incubation with 2,3-DHB affects the lipid composition of the cell wall resulting in a diminished level of mycolates and an altered cell morphology similar to the Deltanat strain. We propose the enzymes encoded by the putative operon have a similar endogenous role to that of the NAT enzyme and are part of a pathway important for cell wall synthesis.