Term Paper Presentation

OnCancer Hybrid

AutomataPresented by:Name: Ankita BhallaRoll No: 2012CSB2003

This paper discuss about the cancer hybrid automata to prepare automata model for the progression of the cancer through discrete phenotypes.

CHA is basically computational model for the cancer progression. This paper discusses the transition between the discrete states in real time.

Introduction

Cancer-a progressive diseaseTimed AutomataHybrid AutomataRectangular AutomataVarious Hallmarks in Cancer Hybrid AutomataTimed CHAAutomatically generating therapiesConclusionLimitation

Things to be discussed

Cancer is a disease caused by an uncontrolled division of cells in various parts of the body. Cancer is a progressive disease which exhibit certain cancer phenotypes that represented or modeled as a finite set of discrete states, and reaches towards terminal cancer phenotypes i.e. Metastasis.

Cancer

A timed automaton is a finite automaton with a

set of real-valued variables, called clocks.

clocks increase synchronously at the same rate.

It is extended classical Automata in real time

system.

Timed Automata

It is a formal model for mixed discrete continuous system. A

hybrid automaton is a finite state machine with a finite set of

continuous variables.

In timed automata clocks increase synchronously at the

same rate where as in hybrid automata, clocks can run at

different rates, which can change independently with the

transition to another state.

Hybrid Automata

A Rectangular Automata is an automaton in which

the clock constraint on each edge is a rectangular

region of continuous states. In this automata the

controlling problems are decidable.

It is a sub class of hybrid automata.

Rectangular Automata

SSG: Self-Sufficiency in Growth signals.

IAG: Insensitivity to Anti-Growth signals.

Ang: Sustained Angiogenesis.

LRP: Limitless Replicative Potential.

M: Metastasis.

Various Hallmarks in Cancer Hybrid Automata

We assume a global set D of drugs.

Definition: A Cancer Hybrid Automaton (CHA) is a tuple H = (V, E, v’),

WhereV is a set of states, corresponding to hallmarks.E⊆ V × 2D × V is a set of directed edges labeled

with sets of drugs, andv’ is the initial state.

An edge (v, D, v’) represents a transition from state v to state v’ which can be restrained by any drug from the set D

Formal model

In timed CHA, transitions would take certain durations of time, and drugs can slow down the transition process but earlier the transitions occur spontaneously and drugs can switch off transitions completely.

Timed CHA

A timed CHA is a tuple H = (V, E, v’, l, ) where𝜌V is a set of states, corresponding to hallmarks,E ⊆ V ×C(X) × V is a set of directed edges each

labeled with a clock constraint, v’ is the initial state,l: V×X→N is a partial function specifying the time

limit for each clock that the system can remain in a given state and

𝜌::V×D×X → R yields a function specifying how a given drug influences the clocks at a given state.

Formal Model of Timed CHA

Drug d modifies the clock rate, by slowing down or speeding up the clock.

When =1 then the drug has no effect on the 𝜌clock.

When =0 then drug effectively stops the clock 𝜌from progressing.

Timed CHA

In CHA, simple verification and control problems like reachability and safety are undecidable.

There exist rectangular hybrid automata which is a subclass of hybrid automata in which control problems are decidable. So it is important to translate from timed CHAs into rectangular hybrid automata, so that therapies can be generated automatically.

Automatically generating therapies

The aim was to design a conceptually clear framework or structure based on realistic biological foundations.

This model is used to describe cancer hallmarks and their dynamics.

This paper established a general formalism for describing cancer progression, without depending on any detailed mechanistic model of cancer.

Conclusion

More general clocks: Clocks are so far referred only as measuring time in CHA, but they could be measuring different properties like size of tumor, spatial properties.

Heterogeneity in tumors: States of CHA are so far considered as unique dominant phenotype of tumor cell population but most form of the cancer involves several sub population of tumor cells , each having different dominant phenotype.

Some Limitations

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