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Cell fate reprogramming by control of intracellular network dynamics
Jorge G. T. Zañudo, Réka Albert
TL;DR
Cell-fate reprogramming requires controlling intracellular network dynamics, while conventional approaches face limitations for large, switch-like biological networks. The paper develops stable motif control, a logical-network framework that integrates network structure and function to identify transient interventions guiding cells toward desired attractors. Applied to cancer and immune-cell differentiation, the approach identifies effective control targets, although its control sets are not guaranteed to be minimal and blocking can produce similar unwanted attractors.
Problem
Cell-fate reprogramming requires driving cells between states, but conventional control approaches are limited by network size, linear dynamics, and complete-controllability assumptions.
Method
The authors combine logical network dynamics, stable motifs, and network reduction to identify transient interventions that guide systems toward selected attractors.
Results
The approach identifies control interventions that guide cells toward desired fates or away from undesired fates in blood-cancer and immune-cell differentiation applications.
Takeaways & Limitations
Stable motif control provides a network-based way to identify intervention targets for intracellular dynamics and cell-fate reprogramming.
Takeaways & Limitations
Control sets are not guaranteed to be small or minimal, and blocking an attractor can generate similar new attractors that remain biologically consistent with the unwanted fate.
Abstract
from arXiv · showhide
Identifying control strategies for biological networks is paramount for practical applications that involve reprogramming a cell's fate, such as disease therapeutics and stem cell reprogramming. Here we develop a novel network control framework that integrates the structural and functional information available for intracellular networks to predict control targets. Formulated in a logical dynamic scheme, our approach drives any initial state to the target state with 100% effectiveness and needs to be applied only transiently for the network to reach and stay in the desired state. We illustrate our method's potential to find intervention targets for cancer treatment and cell differentiation by applying it to a leukemia signaling network and to the network controlling the differentiation of helper T cells. We find that the predicted control targets are effective in a broad dynamic framework. Moreover, several of the predicted interventions are supported by experiments.
AUTHOR SUMMARY
The paper presents a network-control approach that integrates structural and functional information to guide cells toward desired fates or away from undesired ones. It demonstrates the approach in blood cancer and immune-cell differentiation.
- The framework identifies interventions that stabilize selected components to drive cells toward desired fates or away from undesired fates.
- The method integrates structural and functional information from intracellular networks.
- Applications address therapeutic-target discovery and stem cell reprogramming.
INTRODUCTION
The introduction motivates cell-fate control through logical network models that represent regulatory structure and dynamics. It presents stable motifs and network reduction as the basis for identifying attractors and control targets while addressing limits of conventional controllability methods.
- Cell-fate reprogramming means driving a cell from an initial internal state to a final target state.
- Conventional control theory is limited by network size, linear regulatory functions, and its focus on complete rather than biologically admissible controllability.
- Prior approaches include Boolean control theory, maximal matching, and feedback vertex sets, with reported control requirements ranging from roughly 80% of nodes to five or fewer genes.
- Logical models encode binary node states and Boolean regulatory functions, using asynchronous updating to represent differing timescales.
- Stable motifs are function-dependent network components that stabilize in fixed states and help identify attractors without exhaustive state-space search.
- Iterative network reduction traces stable motifs’ downstream effects and produces quasi-attractors that exactly capture steady states.
Stable motif control implies network control
Stable motif control uses the partial fixed-point structure of stable motifs to guide a network along motif sequences leading to a chosen attractor. The method can reduce intervention targets, though it does not guarantee minimum or small control sets.
- Stable motif states act as points of no return, allowing controlled motif sequences to guide the system toward selected attractors.
- A motif succession sequence uniquely determines an attractor, so controlling each motif in that sequence directs the system toward it.
- The example control set contains {E=0, A=1} for target attractor A2, regardless of which of its two motif sequences is used.
- For the example network, controlling A and E suffices to guide the system to all four attractors using the corresponding CAi state combinations.
- The example method uses half as many controlled nodes as a minimal feedback vertex set, but it does not guarantee the smallest possible control sets.
Blocking stable motifs may obstruct specific attractors
Stable motif blocking negates motif states associated with an undesired attractor to obstruct its reachability. Its success depends on the resulting attractors and whether transient intervention reduces long-term access to the unwanted state.
- Stable motif blocking targets motifs whose sequences lead to an unwanted attractor, with the goal of preventing or reducing access to that attractor.
- Blocking interventions negate node states of the target attractor and therefore eliminate the intended attractor, but similar new attractors may arise.
- For attractor A3, candidate interventions include A=1, E=0, D=0, or combinations of these states.
- Interventions A=1 and E=0 leave only original attractors that exclude A3 and remain effective after intervention stops.
- The D=0 intervention is not long-term successful because it increases the likelihood that arbitrary initial states reach A3.
Verification of the method’s effectiveness in test cases
The framework is applied to two cell-fate reprogramming cases: a leukemia signaling network and helper T cell differentiation.
- The authors apply the framework to predict interventions in a leukemia signaling network and a helper T cell differentiation network.
T Cell Large Granular Lymphocyte Leukemia Network
The T-LGL network models cytotoxic T-cell survival and distinguishes apoptosis from leukemia as alternative attractors. Stable motif analysis identifies intervention targets that can steer or block these fates.
- T-LGL leukemia involves cytotoxic T cells avoiding activation-induced apoptosis and surviving abnormally.
- The Boolean model contains 60 nodes and 142 regulatory edges representing genes, proteins, receptors, small molecules, external signals, and biological functions.
- Seven stable motifs and their succession diagram were identified under Stimuli and IL15, with some P2-associated motifs omitted from the diagram.
- Activation of any of three S1P-related motifs can drive the system toward either apoptosis or T-LGL leukemia, consistent with apoptosis after S1P signaling blockade.
- All stable motif control interventions reached the desired state from every initial condition and remained successful after transient intervention.
- Among 12 single-node interventions, Ceramide=ON was 100% effective and long-term successful.
Helper T Cell Differentiation Network
The helper T cell network models subtype differentiation under specified environmental conditions. Stable motif analysis maps subtype-associated motifs to intervention strategies with differing effectiveness.
- Helper T cells regulate immune responses through cytokine release, and known subtypes include Th1, Th2, Th17, and Treg.
- The selected helper T cell network contains 55 nodes and 121 edges under APC=ON, TGFB e=ON, and IL2 e=ON.
- The network yields 17 stable motifs and a succession diagram containing 697 sequences.
- Stable motifs associated with each attractor regulate the characteristic transcription factor of the corresponding helper T cell subtype.
- All stable motif control interventions reached the desired state with 100% effectiveness, whereas blocking interventions were usually successful but not always completely effective.
- Some single-node interventions succeeded, but none achieved 100% effectiveness.
The control targets transcend the logical modeling framework
The authors test whether stable motif control targets depend on Boolean modeling by translating the networks into ODE models and seeking experimental support. The interventions remain effective across these checks.
- Boolean networks were translated into ODE models using smooth Hill-type functions that preserve the Boolean model’s fixed-point attractors.
- Stable motif control interventions remained 100% effective or very close in ODE models for both permanent and transient interventions.
- Several predicted single interventions for leukemic apoptosis or specific T cell types were also successful experimentally.
DISCUSSION
The proposed control framework combines network structure and dynamics to identify interventions for cancer treatment and cell differentiation. Its interventions are guaranteed to reach desired attractors, can be transient, use few nodes, and receive experimental support.
- The method combines structural and functional information in a logical network model to identify control targets for T-LGL leukemia and helper T cell differentiation.
- 100% effectiveness is guaranteed regardless of the initial state, and interventions need only be applied transiently for the network to reach and remain at the desired attractor.
- Multi-target interventions are generally combinatorial, while the case studies require only one to five controlled nodes out of more than fifty.
- The framework is applicable beyond logical cell-fate models to qualitative Boolean dynamics, although extending stable motifs to continuous models remains future work.
Computational methods
The computational analyses used custom Java code and MATLAB-based procedures for logical-model analysis and ODE simulation.
- Logical-model simulations, attractor finding, and stable-motif succession analysis were performed with custom Java code.
- ODE models were generated with the MATLAB implementation of Wittman et al.'s method.
- Numerical integration of the ODE models used MATLAB's ode45 function.
General asynchronous updating scheme
In the general asynchronous scheme, one node is randomly selected and updated at each discrete time step while all others retain their previous states. This permits every update order and samples the processes' relative timescales.
- Node states are updated at discrete time steps from an initial condition at t = 0.
- At each time step, one variable is chosen uniformly at random and updated using its function and regulators' previous states.
- All other variables retain their states, allowing every update order and sampling all relative process timescales.
Stable motif control algorithm
The stable motif control algorithm identifies motif sequences leading to a target attractor, minimizes the required motifs, derives sufficient node-state subsets, and combines and prunes candidate control sets.
- Stable motif control algorithm: The algorithm begins by identifying stable-motif sequences leading to the attractor of interest from the succession diagram.
- Stable motif control algorithm: Each sequence is shortened to the minimum motifs required to reach the target attractor, removing motifs that are not necessary.
- Stable motif control algorithm: For each motif, the method finds minimal subsets of motif states whose fixation forces every motif node into its target state.
- Stable motif control algorithm: Candidate control sets are formed by choosing one subset from each motif and taking the union of their node states.
- Stable motif control algorithm: Duplicate candidates and any candidate that is a superset of another are removed to avoid redundancy.
Stable motif blocking algorithm
The stable motif blocking algorithm identifies interventions that obstruct a specified attractor by negating node states in stable motifs associated with paths leading to it.
- The algorithm begins by identifying stable-motif sequences that lead to the attractor A using the stable motif succession diagram.
- It collects every stable motif state Mi from those sequences into the set MA = {Mi}.
- For each node state σj ⊂ Mi in MA, it creates BA from the negations of those node states.
- The node states in BA, alone or in combination, are identified as potential interventions for blocking attractor A.
- Pseudocode for the algorithm's steps is provided in Text S7.
Intervention target validation
Intervention targets are validated by fixing prescribed node states, simulating many uniformly random initial conditions until attractors are reached, and estimating attractor-reaching probabilities.
- 100,000 uniformly chosen initial conditions and 50,000 time steps are used to estimate the probability of reaching each attractor under an intervention.The validation also tests transient interventions by fixing node states before releasing them and simulating for another 50,000 time steps.
- The estimated probability of reaching the attractor of interest has standard deviation 3 · 10−3 [pAttr(1 − pAttr)]1/2.
A. Attractor-finding method
The method identifies stable motifs in an expanded Boolean network and uses iterative network reduction to represent attractors as quasi-attractors. It establishes that stable-motif sequences preserve attractor structure and can support control interventions targeting desired attractor classes.
- Motivation: Attractor finding is computationally difficult because Boolean state spaces grow exponentially with network size, limiting exhaustive searches to small networks.The alternative method addresses this limitation for intracellular or sparse networks.
- Method: Stable motifs are identified from logical network structure and functions, then used iteratively for network reduction until quasi-attractors or attractors are obtained.Quasi-attractors exactly capture steady states while compressing complex attractors.
- Method: For every asynchronous attractor, the method finds a corresponding quasi-attractor that fixes the attractor’s Sred nodes while placing remaining nodes in or downstream of an oscillating motif.This is the theorem-level guarantee combining Lemmas 1–3.
- Attractor characterization: A stable-motif sequence uniquely determines an equivalence class of attractors sharing the same Sred nodes and their states.The equivalence class contains attractors that agree on fixed-state nodes independent of oscillating-node states.
- Control implication: Fixing the node states specified by a stable-motif sequence produces a Boolean network whose attractors are exactly those in the corresponding attractor equivalence class.This conservation result is the basis for the stable motif control algorithm’s effectiveness.
C. Analysis of the stable motif decision diagram for helper T cell differentiation network
The helper T cell decision diagram identifies minimal stable-motif subsets associated with each subtype, generally through regulation of its characteristic transcription factor. ODE validation examines whether interventions remain effective under continuous dynamics and varied implementation conditions.
- 17 stable motifs generate a stable motif decision diagram containing 697 sequences for helper T cell differentiation.
- Most minimal motif subsets contain the defining transcription factor for Th1, Th2, Th17, or Treg differentiation.The corresponding markers are TBET=ON, GATA3=ON, RORGT=ON, and FOXP3=ON.
- Some subsets lacking a subtype’s characteristic transcription factor depend on another motif that stabilizes or differentially expresses that factor.
- Logical-to-ODE conversion preserves Boolean fixed-point attractors but may create non-equivalent ODE attractors and does not always yield 100% effective interventions.
- 50.0%, 45.4%, 2.8%, and 1.8% are the reported Th1, Th2, Th17, and Treg subtype percentages, respectively.