Gene Regulatory Networks (GRNs) represent the interactions among genes regulating the activation of specific cell functionalities, such as reception of (chemical) signals or reaction to environmental changes. Studying and understanding these processes is crucial: they are the fundamental mechanism at the basis of cell functioning, and many diseases are based on perturbations or malfunctioning of some gene regulation activities. In this paper, we provide an overview on computational approaches to GRN modelling and analysis. We start from the biological and quantitative modelling background notions, recalling differential equations and the Gillespie’s algorithm. Then, we describe more in depth qualitative approaches such as Boolean networks and some computer science formalisms, including Petri nets, P systems and reaction systems. Our aim is to introduce the reader to the problem of GRN modelling and to guide her/him along the path that goes from classical quantitative methods, through qualitative methods based on Boolean network, up to some of the most relevant qualitative computational methods to understand the advantages and limitations of the different approaches.

The most challenging task in colorectal cancer research nowadays is to understand the development of acquired resistance to anti-EGFR drugs. The key reason for this problem is the KRAS mutations appearance after the treatment with monoclonal antibodies (moAb). Here we present a mathematical model for the analysis of KRAS mutations behavior in colorectal cancer with respect to moAb treatments. To evaluate the drug performance we have developed equations for two types of tumors cells, KRAS mutated and KRAS wild-type. Both tumor cell populations were treated with a combination of moAb and chemotherapy drugs. It was observed that even the minimal initial concentration of KRAS mutation before the treatment has the ability to make the tumor refractory to the treatment. Minor population of KRAS mutations has strong influence on large number of wild-type cells as well rendering them resistant to chemotherapy. Patient׳s immune responses are specifically taken into considerations and it is found that, in case of KRAS mutations, the immune strength does not affect medication efficacy. Finally, cetuximab (moAb) and irinotecan (chemotherapy) drugs are analyzed as first-line treatment of colorectal cancer with few KRAS mutated cells. Results show that this combined treatment could be only effective for patients with high immune strengths and it should not be recommended as first-line therapy for patients with moderate immune strengths or weak immune systems because of a potential risk of relapse, with KRAS mutant cells acquired resistance involved with them.

Background: Carassius gibelio, a cyprinid fish from Eurasia, has the ability to reproduce both sexually and asexually. This fish is also known as an invasive species which colonized almost all continental Europe, most likely originating from Asia and Eastern Europe. Populations of both sexually and asexually reproducing individuals exist in sympatry. In this study we try to elucidate the advantages of such a mixed type of reproduction. We investigate the dynamics of two sympatric populations with sexual and asexual reproduction in a periodically fluctuating environment. We define an individual-based computational model in which genotypes are represented byLloci, and the environment is composed ofLresources for which the two populations compete.Results: Our model demonstrates advantageous population dynamics where the optimal percentage of asexual reproduction depends on selection strength, on the number of selected loci and on the timescale of environmental fluctuations. We show that the sexual reproduction is necessary for "generating" fit genotypes, while the asexual reproduction is suitable for "amplifying" them. The simulations show that the optimal percentage of asexual reproduction increases with the length of the environment stability period and decrease with the strength of the selection and the number of loci.Conclusions: In this paper we addressed the advantages of a mixed type of sexual and asexual reproduction in a changing environment and explored the idea that a species that is able to adapt itself to environmental fluctuation can easily colonize a new habitat. Our results could provide a possible explanation for the rapid and efficient invasion of species with a variable ratio of sexual and asexual reproduction such asCarassius gibelio.

Bisimulations are well-established behavioural equivalences that are widely used to study properties of computer science systems. Bisimulations assume the behaviour of systems to be described as labelled transition systems, and properties of a system can be verified by assessing its bisimilarity with a system one knows to enjoy those properties. In this paper we show how semantics based on labelled transition systems and bisimulations can be defined for two formalisms for the description of biological systems, both capable of describing membrane interactions. These two formalisms are the Calculus of Looping Sequences (CLS) and Brane Calculi, and since they stem from two different approaches (rewrite systems and process calculi) bisimulation appears to be a good candidate as a general verification method. We introduce CLS and define a labelled semantics and bisimulations for which we prove some congruence results. We show how bisimulations can be used to verify properties by way of two examples: the description of the regulation of lactose degradation in Escherichia coli and the description of the EGF signalling pathway. We recall the PEP calculus (the simplest of Brane Calculi) and its translation into CLS, we define a labelled semantics and some bisimulation congruences for PEP processes, and we prove that bisimilar PEP processes are translated into bisimilar CLS terms.