Model checking to assess T-helper cell plasticity

Abstract

Computational modeling constitutes a crucial step toward the functional understanding of complex cellular networks. In particular, logical modeling has proven suitable for the dynamical analysis of large signaling and transcriptional regulatory networks. In this context, signaling input components are generally meant to convey external stimuli, or environmental cues. In response to such external signals, cells acquire specific gene expression patterns modeled in terms of attractors (e.g., stable states). The capacity for cells to alter or reprogram their differentiated states upon changes in environmental conditions is referred to as cell plasticity. In this article, we present a multivalued logical framework along with computational methods recently developed to efficiently analyze large models. We mainly focus on a symbolic model checking approach to investigate switches between attractors subsequent to changes of input conditions. As a case study, we consider the cellular network regulating the differentiation of T-helper (Th) cells, which orchestrate many physiological and pathological immune responses. To account for novel cellular subtypes, we present an extended version of a published model of Th cell differentiation. We then use symbolic model checking to analyze reachability properties between Th subtypes upon changes of environmental cues. This allows for the construction of a synthetic view of Th cell plasticity in terms of a graph connecting subtypes with arcs labeled by input conditions. Finally, we explore novel strategies enabling specific Th cell polarizing or reprograming events.

Keywords: T-helper lymphocyte; cell differentiation; cell plasticity; logical modeling; model checking; signaling networks.

Figure 1

Typical workflow to tackle a central biological question using logical model construction and analysis. A model is defined, relying on literature and experimental data (box Model Definition). The model is then analyzed (boxes Static analysis and Dynamical analysis). The identification of the attractors is performed either by static methods (see Sections 2.2.1 and 2.2.2) or by inspecting the dynamics (see Sections 2.2.3 and 2.3). Dynamics are represented at different levels of abstraction, from the comprehensive state transition graphs to the reprograming graphs. Resulting properties are confronted with biological observations, leading to predictions and/or to model revision. Ellipsoid boxes relate to the different model versions and behavior representations. Green boxes denote methods that are available in GINsim, whereas gray boxes denote analyses performed with other software tools.

Figure 2

Regulatory graph of Th differentiation logical model. The model encompasses 101 components (among which 21 input nodes) and 221 interactions. The components denoting the inputs are in blue, those denoting the secreted cytokines in olive. Green edges correspond to activations, whereas red blunt ones denote inhibitions. Ellipses denote Boolean components, whereas rectangles denote ternary ones. Gray-out components are those selected for reduction.

Figure 3

Reprograming graph, considering all canonical Th subtypes, generated with the model checker NuSMV-ARCTL. Nodes represent sets of states characterizing the canonical Th subtypes defined in Table 2. There is an arc labeled with e, going from node c₁ to node c₂, whenever the following ARCTL temporal logic formula is verified: INIT c₁; EAF (e) (c₂ ∧ AAG (e)(c₂)). It should be noted that the existence of a single reprograming path from a Th subtype to another one does not necessarily imply the stability of the target Th subtype, since NuSMV-ARCTL considers that a property is true if and only if it is verified by the whole set of states in the initial conditions. Hence, if at least one state associated with a given subtype points to a state not associated with this subtype (for given input conditions), then the stability of the Th subtype is not represented (see for example, Th9 subtype, which is not considered stable under proTh9 input condition).