Mathematical modeling of the metastatic process

Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include the competition between healthy and normal tissue, carcinogenesis, therapy and metastasis. It is the latter topic, metastasis, on which we will focus this short review, specifically discussing various computational and mathematical models of different portions of the metastatic process, including: the emergence of the metastatic phenotype, the timing and size distribution of metastases, the factors that influence the dormancy of micrometastases and patterns of spread from a given primary tumor.Comment: 24 pages, 6 figures, Revie

A simple approach to counterterms in N=8 supergravity

We present a simple systematic method to study candidate counterterms in N=8 supergravity. Complicated details of the counterterm operators are avoided because we work with the on-shell matrix elements they produce. All n-point matrix elements of an independent SUSY invariant operator of the form D^{2k} R^n +... must be local and satisfy SUSY Ward identities. These are strong constraints, and we test directly whether or not matrix elements with these properties can be constructed. If not, then the operator does not have a supersymmetrization, and it is excluded as a potential counterterm. For n>4, we find that R^n, D^2 R^n, D^4 R^n, and D^6 R^n are excluded as counterterms of MHV amplitudes, while only R^n and D^2 R^n are excluded at the NMHV level. As a consequence, for loop order L<7, there are no independent D^{2k}R^n counterterms with n>4. If an operator is not ruled out, our method constructs an explicit superamplitude for its matrix elements. This is done for the 7-loop D^4 R^6 operator at the NMHV level and in other cases. We also initiate the study of counterterms without leading pure-graviton matrix elements, which can occur beyond the MHV level. The landscape of excluded/allowed candidate counterterms is summarized in a colorful chart.Comment: 25 pages, 1 figure, published versio

R^4 counterterm and E7(7) symmetry in maximal supergravity

The coefficient of a potential R^4 counterterm in N=8 supergravity has been shown previously to vanish in an explicit three-loop calculation. The R^4 term respects N=8 supersymmetry; hence this result poses the question of whether another symmetry could be responsible for the cancellation of the three-loop divergence. In this article we investigate possible restrictions from the coset symmetry E7(7)/SU(8), exploring the limits as a single scalar becomes soft, as well as a double-soft scalar limit relation derived recently by Arkani-Hamed et al. We implement these relations for the matrix elements of the R^4 term that occurs in the low-energy expansion of closed-string tree-level amplitudes. We find that the matrix elements of R^4 that we investigated all obey the double-soft scalar limit relation, including certain non-maximally-helicity-violating six-point amplitudes. However, the single-soft limit does not vanish for this latter set of amplitudes, which suggests that the E7(7) symmetry is broken by the R^4 term.Comment: 33 pages, typos corrected, published versio

Comparison of various microbial inocula for the efficient anaerobic digestion of Laminaria hyperborea

Background: The hydrolysis of seaweed polysaccharides is the rate limiting step in anaerobic digestion (AD) of seaweeds. Seven different microbial inocula and a mixture of these (inoculum 8) were therefore compared in triplicate, each grown over four weeks in static culture for the ability to degrade Laminaria hyperborea seaweed and produce methane through AD. Results: All the inocula could degrade L. hyperborea and produce methane to some extent. However, an inoculum of slurry from a human sewage anaerobic digester, one of rumen contents from seaweed-eating North Ronaldsay sheep and inoculum 8 used most seaweed volatile solids (VS) (means ranged between 59 and 68% used), suggesting that these each had efficient seaweed polysaccharide digesting bacteria. The human sewage inoculum, an inoculum of anaerobic marine mud mixed with rotting seaweed and inoculum 8 all developed to give higher volumes of methane (means between 41 and 62.5 ml g-1 of seaweed VS by week four) ,compared to other inocula (means between 3.5 and 27.5 ml g-1 VS). Inoculum 8 also gave the highest acetate production (6.5 mmol g-1 VS) in a single-stage fermenter AD system and produced most methane (8.4 mL mmol acetate-1) in phase II of a two-stage AD system. Conclusions: Overall inoculum 8 was found to be the most efficient inoculum for AD of seaweed. The study therefore showed that selection and inclusion of efficient polysaccharide hydrolysing bacteria and methanogenic archaea in an inoculum offer increased methane productivity in AD of L. hyperborea. This inoculum will now being tested in larger scale (10L) continuously stirred reactors optimised for feed rate and retention time to determine maximum methane production under single-stage and two-stage AD systems.Marie Curie Senior Researcher Fellowship (SEAWEED AD

High-dose alkylating chemotherapy in BRCA-altered triple-negative breast cancer:the randomized phase III NeoTN trial

Exploratory analyses of high-dose alkylating chemotherapy trials have suggested that BRCA1 or BRCA2-pathway altered (BRCA-altered) breast cancer might be particularly sensitive to this type of treatment. In this study, patients with BRCA-altered tumors who had received three initial courses of dose-dense doxorubicin and cyclophosphamide (ddAC), were randomized between a fourth ddAC course followed by high-dose carboplatin-thiotepa-cyclophosphamide or conventional chemotherapy (initially ddAC only or ddAC-capecitabine/decetaxel [CD] depending on MRI response, after amendment ddAC-carboplatin/paclitaxel [CP] for everyone). The primary endpoint was the neoadjuvant response index (NRI). Secondary endpoints included recurrence-free survival (RFS) and overall survival (OS). In total, 122 patients were randomized. No difference in NRI-score distribution (p = 0.41) was found. A statistically non-significant RFS difference was found (HR 0.54; 95% CI 0.23–1.25; p = 0.15). Exploratory RFS analyses showed benefit in stage III (n = 35; HR 0.16; 95% CI 0.03–0.75), but not stage II (n = 86; HR 1.00; 95% CI 0.30–3.30) patients. For stage III, 4-year RFS was 46% (95% CI 24–87%), 71% (95% CI 48–100%) and 88% (95% CI 74–100%), for ddAC/ddAC-CD, ddAC-CP and high-dose chemotherapy, respectively. No significant differences were found between high-dose and conventional chemotherapy in stage II-III, triple-negative, BRCA-altered breast cancer patients. Further research is needed to establish if there are patients with stage III, triple negative BRCA-altered breast cancer for whom outcomes can be improved with high-dose alkylating chemotherapy or whether the current standard neoadjuvant therapy including carboplatin and an immune checkpoint inhibitor is sufficient. Trial Registration: NCT01057069

Diversity of HIV-1 Subtype B: Implications to the Origin of BF Recombinants

BACKGROUND: The HIV-1 subtype B epidemic in Brazil is peculiar because of the high frequency of isolates having the GWGR tetramer at V3 loop region. It has been suggested that GWGR is a distinct variant and less pathogenic than other subtype B isolates. METHODOLOGY/PRINCIPAL FINDINGS: Ninety-four percent of the HIV-1 subtype B worldwide sequences (7689/8131) obtained from the Los Alamos HIV database contain proline at the tetramer of the V3 loop of the env gene (GPGR) and only 0.74% (60/8131) have tryptophan (GWGR). By contrast, 48.4% (161/333) of subtype B isolates from Brazil have proline, 30.6% (102/333) contain tryptophan and 10.5% (35/333) have phenylalanine (F) at the second position of the V3 loop tip. The proportion of tryptophan and phenylalanine in Brazilian isolates is much higher than in worldwide subtype B sequences (chi-square test, p = 0.0001). The combined proportion of proline, tryptophan and phenylalanine (GPGR+GWGR+GFGR) of Brazilian isolates corresponds to 89% of all amino acids in the V3 loop. Phylogenetic analysis revealed that almost all subtype B isolates in Brazil have a common origin regardless of their motif (GWGR, GPGR, GGGR, etc.) at the V3 tetramer. This shared ancestral origin was also observed in CRF28_BF and CRF29_BF in a genome region (free of recombination) derived from parental subtype B. These results imply that tryptophan substitution (e.g., GWGR-to-GxGR), which was previously associated with the change in the coreceptor usage within the host, also occurs at the population level. CONCLUSIONS/SIGNIFICANCE: Based on the current findings and previous study showing that tryptophan and phenylalanine in the V3 loop are related with coreceptor usage, we propose that tryptophan and phenylalanine in subtype B isolates in Brazil are kept by selective mechanisms due to the distinct coreceptor preferences in target cells of GWGR, GFGR and GFGR viruses

Phase II study of helical tomotherapy in the multidisciplinary treatment of oligometastatic colorectal cancer

<p>Abstract</p> <p>Background</p> <p>Complete metastasectomy provides a real chance for long-term survival in patients with oligometastatic colorectal cancer (CRC). For inoperable patients, we evaluated in this study intensity-modulated and image-guided radiotherapy (IMRT-IGRT) by helical tomotherapy.</p> <p>Methods</p> <p>Twenty-four CRC patients with ≤ 5 metastases were enrolled, receiving a dose of 50 Gy in fractions of 5 Gy. No limitations concerning dimension or localization of the metastases were imposed. Whole body PET-CT was performed at baseline and 3 months after the initiation of RT to evaluate the metabolic response rate according to PET Response Criteria in Solid Tumors (PERCIST) version 1.0.</p> <p>Results</p> <p>A total of 53 metastases were treated. Seventeen patients (71%) received previously ≥ 1 line of chemotherapy for metastatic disease, displaying residual (n = 7) or progressive (n = 10) metabolic active oligometastatic disease at time of inclusion. Most common sites were the lung, liver and lymphnodes. One patient (4%) experienced grade 3 dysphagia. Twenty-two patients were evaluated by post-treatment PET-CT. Twelve patients achieved a complete (n = 6) or partial (n = 6) metabolic response, resulting in an overall metabolic response rate of 55%. At a median follow-up of 10 months, 7 patients (29%) are in remission, of which 5 received previous chemotherapy with residual oligometastatic disease at time of inclusion. The actuarial 1-year local control, progression-free survival, and overall survival were 54%, 14% and 78%.</p> <p>Conclusions</p> <p>Helical tomotherapy delivering 10 fractions of 5 Gy resulted in a metabolic response rate of 55%, and appeared to be attractive as consolidation of inoperable oligometastatic disease after effective chemotherapy.</p> <p>Trial registration</p> <p>Eudract 2008-008300-40; <a href="http://www.clinicaltrials.gov/ct2/show/NCT00807313">NCT00807313</a></p