Heterogeneity and proliferation of invasive cancer subclones in game theory models of the Warburg effect.

OBJECTIVES: The Warburg effect, a switch from aerobic energy production to anaerobic glycolysis, promotes tumour proliferation and motility by inducing acidification of the tumour microenvironment. Therapies that reduce acidity could impair tumour growth and invasiveness. I analysed the dynamics of cell proliferation and of resistance to therapies that target acidity, in a population of cells, under the Warburg effect. MATERIALS AND METHODS: The dynamics of mutant cells with increased glycolysis and motility has been assessed in a multi-player game with collective interactions in the framework of evolutionary game theory. Perturbations of the level of acidity in the microenvironment have been used to simulate the effect of therapies that target glycolysis. RESULTS: The non-linear effects of glycolysis induce frequency-dependent clonal selection leading to coexistence of glycolytic and non-glycolytic cells within a tumour. Mutants with increased motility can invade such a polymorphic population and spread within the tumour. While reducing acidity may produce a sudden reduction in tumour cell proliferation, frequency-dependent selection enables it to adapt to the new conditions and can enable the tumour to restore its original levels of growth and invasiveness. CONCLUSIONS: The acidity produced by glycolysis acts as a non-linear public good that leads to coexistence of cells with high and low glycolysis within the tumour. Such a heterogeneous population can easily adapt to changes in acidity. Therapies that target acidity can only be effective in the long term if the cost of glycolysis is high, that is, under non-limiting oxygen concentrations. Their efficacy, therefore, is reduced when combined with therapies that impair angiogenesis.

Anterior cervical fusion for radicular-disc conflict performed by three different procedures: clinical and radiographic analysis at long-term follow-up.

PURPOSE: Purpose of the study was to analyze in a retrospective way the clinical and radiographic outcome of three different surgical techniques in patients who underwent anterior cervical fusion. METHODS: Eighty-six patients affected by symptomatic cervical disc herniation or spondylosis underwent cervical anterior fusion. Patients were divided in three groups considering the surgical technique. Clinical outcomes were evaluated by Visual Analog Scale, Odom's criteria, Neck Disability Index. Radiographic evaluation included standard and functional X-rays. RESULTS: At 7 years mean follow-up, a comparable improvement in clinical symptoms was observed in all groups. Radiographic findings showed a solid fusion in all patients but seven cases in group 2 showed a subsidence of the cage. CONCLUSIONS: As shown by the obtained clinical and radiographic results, the anterior interbody fusion with stand-alone peek cage containing ß-tricalcium phosphate could be considered an effective and reliable procedure.

Evolutionary game theory of growth factor production: implications for tumour heterogeneity and resistance to therapies.

BACKGROUND: Tumour heterogeneity is documented for many characters, including the production of growth factors, one of the hallmarks of cancer. What maintains heterogeneity remains an open question that has implications for diagnosis and treatment, as drugs that target growth factors are susceptible to the evolution of resistance. METHODS: I use evolutionary game theory to model collective interactions between cancer cells, to analyse the dynamics of the production of growth factors and the effect of therapies that reduce their amount. RESULTS: Five types of dynamics are possible, including the coexistence of producer and non-producer cells, depending on the production cost of the growth factor, on its diffusion range and on the degree of synergy of the benefit it confers to the cells. Perturbations of the equilibrium mimicking therapies that target growth factors are effective in reducing the amount of growth factor in the long term only if the reduction is extremely efficient and immediate. CONCLUSION: Collective interactions within the tumour can maintain heterogeneity for the production of growth factors and explain why therapies like anti-angiogenic drugs and RNA interference that reduce the amount of available growth factors are effective in the short term but often lead to relapse. Alternative strategies for evolutionarily stable treatments are discussed.

Prospective study of a new dynamic stabilisation system in the treatment of degenerative discopathy and instability of the lumbar spine.

INTRODUCTION: Posterior dynamic stabilisation (PDS) aims at relieving lumbar discogenic pain and preserving adjacent levels from accelerated degeneration. PURPOSE: To evaluate the results of a novel PDS system in 32 adult patients affected by chronic low back pain (CLBP) due to degenerative lumbar spine instability (DLSI). METHOD: A progressive follow-up for 12 months of 32 patients, with collection of complete clinical (ODI and VAS back + leg) and radiological data (resting + functional radiographs and MRI). RESULTS: Mean ODI scores improved from 49 to 6%, VAS back from 5 to 1 and VAS leg from 7 to 2. Twenty-two patients underwent fusion of a lower lumbar segment and stabilisation of an upper segment (hybrid fusion) whereas ten underwent dynamic stabilisation. In 16/32 patients, decompression was added to treat radicular pain. Motion in non-fused instrumented levels was unrestricted on functional X-rays and MRIs did not show significant morphologic changes. Four patients (12.5%) had unchanged functional and pain scores while two (6.3%) suffered worsening low back pain necessitating implant removal and spinal fusion. No infection, no new neurologic deficit or implant failure was recorded. CONCLUSIONS: The 1 year follow-up shows that the tested PDS system is able to provide a significant improvement in pain and disability scores when applied to patients affected by DLSI. The system does not provide better clinical results when compared to similar trials on posterior fusion. Further follow-up is ongoing to investigate the potential preservation of adjacent levels from accelerated degeneration.

Long-term results of the direct repair of spondylolisthesis.

Direct repair of spondylolisthesis can save a functional segment in young patients with slight slipping. Since 1968 many surgeons have proposed different technical solutions to obtain the isthmic repair. Their results changed according to the technique used, the extent of listhesis and the age of the patient. The aim of our study was to perform a retrospective review on the long-term results of the direct repair of spondylolisthesis, according to the different techniques used. We operated 62 patients for isthmic repair, with three different techniques, from 1994 to 2007. We analysed the clinical and radiographic results of 52 cases, with an average follow-up of 9 ± 3 years (range 2-15). Ten patients were lost to the follow-up. The results were different depending on the technique used. Good or excellent clinical outcome by Odom's criteria were observed in the 83.3% of patients operated with the modified Scott technique. These results are better than those obtained in the group of patients operated with the Scott (62.5%) and the Buck technique (28.5%). Patients with clinical and radiological failure, who then underwent spinal fusion, were 57% with the Buck technique, 12.5% with the Scott technique and 2.7% with the Scott modified technique. The reasons for a new operation were symptomatic pseudarthrosis and progression of slipping. In conclusion, the pars defect repair is a helpful technique in lumbar spondylolisthesis, especially in young patient with slight slipping and painful symptoms resistant to conservative treatment. In our experience, the modified Scott technique seems to provide a better outcome than the Scott and Buck techniques.

Evolution of monogamous marriage by maximization of inclusive fitness.

The majority of human societies allow polygynous marriage, and the prevalence of this practice is readily understood in evolutionary terms. Why some societies prescribe monogamous marriage is however not clear: current evolutionary explanations--that social monogamy increases within-group co-operation, giving societies an advantage in competition with other groups--conflict with the historical and ethnographic evidence. We show that, within the framework of inclusive fitness theory, monogamous marriage can be viewed as the outcome of the strategic behaviour of males and females in the allocation of resources to the next generation. Where resources are transferred across generations, social monogamy can be advantageous if partitioning of resources among the offspring of multiple wives causes a depletion of their fitness value, and/or if females grant husbands higher fidelity in exchange for exclusive investment of resources in their offspring. This may explain why monogamous marriage prevailed among the historical societies of Eurasia: here, intensive agriculture led to scarcity of land, with depletion in the value of estates through partitioning among multiple heirs. Norms promoting high paternity were common among ancient societies in the region, and may have further facilitated the establishment of social monogamy. In line with the historical and ethnographic evidence, this suggests that monogamous marriage emerged in Eurasia following the adoption of intensive agriculture, as ownership of land became critical to productive and reproductive success.

Cooperation as a volunteer's dilemma and the strategy of conflict in public goods games.

Conflict and cooperation for the exploitation of public goods are usually modelled as an N-person prisoner's dilemma. Many social dilemmas, however, would be described more properly as a volunteer's dilemma, in which a certain number of individuals are necessary to produce a public good. If volunteering is costly, but so is failure to produce the public good, cheaters can invade and form a stable mixed equilibrium with cooperators. The dilemma is that the benefit for the group decreases with group size because the larger the group is, the less likely it is that someone volunteers. This problem persists even in the presence of a high degree of relatedness between group members. This model provides precise, testable predictions for the stability of cooperation. It also suggests a counterintuitive but practical solution for this kind of social dilemmas: increasing the damage resulting from the failure to produce the public good increases the probability that the public good is actually produced. Adopting a strategy that entails a deliberate risk (brinkmanship), therefore, can lead to a benefit for the society without being detrimental for the individual.

Survival of the steepest: hypersensitivity to mutations as an adaptation to soft selection.

Darwinian evolution favours genotypes with high fitness ('survival of the fittest'). Models of quasi-species evolution, however, suggest that in some cases selection may favour genotypes that are more robust against the impact of mutations ('survival of the flattest') even if these genotypes have lower fitness. I show that the opposite effect will be observed if competition occurs during development (e.g. among embryos or ovules) or before the adult phase (e.g. among the progeny of an individual). If viability is not affected by selection at these initial stages (soft selection), the genotypes that are more sensitive to the effects of mutations may increase in frequency because they get rid more easily of deleterious mutations. In a simple theoretical model of mutation and selection, genotypes located in steeper regions of the fitness surface are favoured ('survival of the steepest') even if they do not have higher viability, and even if they have slightly deleterious effects. Hypersensitive genes are potentially harmful for the individual, but with soft selection during the juvenile phase they persist in the genome because they reduce competition with their mutants. Soft selection occurs in practically all vascular plants and in many animals, therefore antirobustness may be a very common feature of the genome of multicellular organisms.

Coevolution and the adaptive value of autumn tree colours: colour preference and growth rates of a southern beech aphid.

The evolutionary explanation for the change in leaf colour during autumn is still debated. Autumn colours could be a signal of defensive commitment towards insects (coevolution) or an adaptation against physical damage because of light at low temperatures (photoprotection). These two hypotheses have different predictions: (1) under the coevolution hypothesis, insects should not prefer red leaves in autumn and grow better in spring on trees with green autumn leaves; and (2) under the photoprotection hypothesis, insects should prefer and grow better on trees with red leaves because they provide better nutrition. Studying colour preference in autumn and growth rates in spring of a southern beech aphid species (Neuquenaphis staryi) on Nothofagus alessandrii, we found preference for green leaves in autumn but no differential performance of aphids in spring. We suggest that aphid preference for green might have evolved to exploit better their host during the autumn rather than to improve their performance in spring.

Genetic robustness and selection at the protein level for synonymous codons.

Synonymous codons are neutral at the protein level, therefore natural selection at the protein level should have no effect on their frequencies. Synonymous codons, however, differ in their capacity to reduce the effects of errors: after mutation, certain codons keep on coding for the same amino acid or for amino acids with similar properties, while other synonymous codons produce very different amino acids. Therefore, the impact of errors on a coding sequence (genetic robustness) can be measured by analysing its codon usage. I analyse the codon usage of sequenced nuclear and cytoplasmic genomes and I show that there is an extensive variation in genetic robustness at the DNA sequence level, both among genomes and among genes of the same genome. I also show theoretically that robustness can be adaptive, that is natural selection may lead to a preference for codons that reduce the impact of errors. If selection occurs only among the mutants of a codon (e.g. among the progeny before the adult phase), however, the codons that are more sensitive to the effects of mutations may increase in frequency because they manage to get rid more easily of deleterious mutations. I also suggest other possible explanations for the evolution of genetic robustness at the codon level.

Recombination and loss of complementation: a more than two-fold cost for parthenogenesis.

Certain types of asexual reproduction lead to loss of complementation, that is unmasking of recessive deleterious alleles. A theoretical measure of this loss is calculated for apomixis, automixis and endomitosis in the cases of diploidy and polyploidy. The effect of the consequent unmasking of deleterious recessive mutations on fitness is also calculated. Results show that, depending on the number of lethal equivalents and on the frequency of recombination, the cost produced by loss of complementation after few generations of asexual reproduction may be greater than the two-fold cost of meiosis. Maintaining complementation may, therefore, provide a general short-term advantage for sexual reproduction. Apomixis can replace sexual reproduction under a wide range of parameters only if it is associated with triploidy or tetraploidy, which is consistent with our knowledge of the distribution of apomixis.

Loss of complementation and the logic of two-step meiosis.

Meiosis is usually a two-step process: two divisions preceded by a duplication. One-step meiosis, a single division without prior replication, is a more logical way to produce haploid gametes; moreover, one-step meiosis leads to higher variabilty in the progeny than two-step meiosis. Yet one-step meiosis is very rare in nature, and may not even exist at all. I suggest that this is because one-step meiosis, in contrast to two-step meiosis, can be easily invaded and replaced by asexual reproduction. I discuss why other existing peculiar forms of division leading to the production of haploid gametes, but not one-step meiosis, have the same effect as two-step meiosis.

The origin of autumn colours by coevolution.

We lack an adaptive explanation for a striking phenomenon, that of bright colours displayed in autumn by the leaves of many deciduous trees. The usual explanation is that it is simply a non-adaptive secondary effect of leaf senescence. A game-theoretic model of biological signalling provides an adaptive hypothesis for autumn colours showing that they can be the result of a process of coevolution between insects and trees: if leaf colour acts as a warning indicator of the tree's vigour to autumn parasite insects, trees can gain advantage from the reduction of parasite load and insects can gain advantage from location of the most profitable hosts to lay their eggs. The results of the model are consistent with Zahavi's handicap principle. Possible explanations for the origin of the system and evidence from natural history are discussed.