The executable pathway to biological networks

Abstract

As time goes by, it becomes more and more apparent that the puzzles of life involve more and more molecular pieces that fit together in increasingly complex ways. Genomics and Proteomics technologies nowadays, produce reliable and quantitative data that could potentially reveal all the molecular pieces of a particular puzzle. However, this is akin to the opening of Pandora's box; and we are now facing the problem of integrating this vast amount of data with its incredible complexity into some coherent whole. With the aid of engineering methods designed to build and analyze computerized man-made systems, a new emerging field called 'Executable Biology' aims to create computer programmes that put together the pieces in ways that allows capturing their dynamicity and ultimately elucidating how molecular function generates cellular function. This review aspires to highlight the main features characterizing these kinds of executable models and what makes them uniquely qualified to reason about and analyze biological networks.

Figure 1:

A contact map. One view of the rule set is the contact map, which is akin to a protein–protein interaction map. This is a graph where nodes with interfaces represent agents and edges between interface sites represent possible bindings between sites. This system has three agents: a kinase (K), a target (T) with two phosphorylation sites (x and y), and a phosphatase (P). The Kinase K can bind to either the X or the Y site of T and changes their state to phosphorylated (change of state on binding indicated by green). Similarly, P can act on X and Y and changes their state from phosphrylated to dephosphorylated [20]. Figure reproduced with permission from Danos et al. [20].

Figure 2:

StateCharts model of an autonomous pancreatic cell. (A) The cell is composed of a nucleus and a membrane and additional parts that control differentiation and proliferation. The Nucleus contains parts that follow the expression state of a few genes (Exp. or Unexp.), and the Membrane contains parts that follow the state of receptors and controls motion. (B) A histological cross-section of the pancreas (left), the emerging structure in the model at approximately the same developmental day (middle), and the result of an in silico experiment, in which the aorta was disabled, leading to a complete loss of structure (right) [8]. Figure reproduced with permission from Setty et al. [8].

Figure 3:

Dual compilation. A high-level description through a set of rules can be compiled to a deterministic ODE model or to a stochastic CTMC model. Existing ODE models can be translated to rules and CTMCs, facilitating further refinement and affording additional analysis. Existing CTMC models can be translated to ODEs and compared to reference models.

Figure 4:

Proposed sequence of events leading to a stable and unstable fate patterns as predicted by model checking. Time flows from top to bottom. Two events that appear on the same vertical line are ordered according to the time flow. The dashed lines synchronize the different vertical lines. All events that appear above a synchronization line occur before all events that appear below the synchronization line. The time-order between two events that appear on parallel vertical lines without a synchronization line is unknown. (A) Proposed sequence of events leading to a stable pattern. The left time line starts with a high inductive signal (IS) and the right time line with a medium IS. (B) Three diagrams that represent possible sequences of events leading to different fate patterns in the absence of IS (the AC is absent). Execution 1 represents the case where two cells are strongly coupled and they both reduce their lin-12 level simultaneously, send LS, which is ignored, and assume primary fates. Execution 2 represents the case where the left cell sends the lateral signal slightly before its neighbour reduces the level of lin-12, thus resulting in a 1⁰–2⁰ pattern. Execution 3 is the dual of execution 2 where the cell on the right inhibits the cell on the left. Figure reproduced with permission from Fisher et al. [34].

Figure 5:

Results of model checking for the MAPK stochastic model. (A) The expected percentage of activated MAPK at time instant t, (B) the expected number of reactions between MAPK and MAPKK up until time t, and (C) the expected time until all MAPK are activated at the same time according to the number of MAPK, MAPKK, and MAPKKK that are initially available (N) [36]. These results demonstrate that, as the size of N grows, the percentage of MAPK that is activated increases and the time until all MAPK are activated decreases. They also show the expected dynamics that raising species quantities increases the number of reactions that occur between them. Figure reproduced with permission from Kwiatkowska et al. [36].

Figure 6:

Modelling with Cellucidate. (A) A model representing part of the EGFR cascade. Proteins and their interaction sites are the nodes with edges connecting interaction sites. (B) A zoom-in on MEK with its interaction sites and their connections. (C) A different view of Raf and its interactions, where activating relations are in green and inhibiting relations are in red. (D) A zoom-in into a rule: if sites Y and T of ERK are phosphorylated and may or may not be bound, and site S of SoS is ubiquitinated then site s of ERK and site S of SoS can bind, which changes their state from unbound (left) to bound (right). (E) A simulation of the model showing the change in number of molecules over time. Figure reproduced with permission from Plectix [46].

Figure 7:

Hybrid Functional Petri Nets model of EGFR pathway in Cell Illustrator. (A) Sets of entities and processes are classified into discrete, continuous, and generic types, and entities and processes can be replaced with pictures reflecting the biological images. This replacement makes the hybrid functional Petri nets (HFPNe) model of a biological pathway more comprehensible for biologists. (B) For entities and processes, pictures reflecting the biological images may be used [52]. Figure reproduced with permission from Tasaki et al. [52].

Figure 8:

A snapshot of the simulation during run time of the StateCharts Thymus model. This is a high-level front-end view of a lobule during execution. The buttons in the bottom left control the statistical representation of the data; pause the simulation; chemokine representation; different zooming in-and-out abilities; connection between the animation and simulation. The other buttons give different colour codes relevant to the display, enable the user to trace the motion of specific cells, control the connection between the simulation and specific statistical tool (such as Matlab), give the user the ability to avoid clutter made by overlapping cells, give the user the ability to receive visual indication to interactions, and more. The small circles are the visual representation of thymocytes [6]. Figure reproduced with permission from Efroni et al. [6].