Abstract
Cell differentiation is an important process in living organisms. Differentiation is mostly based on binary decisions with the progenitor cells choosing between two specific lineages. The differentiation dynamics have both deterministic and stochastic components. Several theoretical studies suggest that cell differentiation is a bifurcation phenomenon, well-known in dynamical systems theory. The bifurcation point has the character of a critical point with the system dynamics exhibiting specific features in its vicinity. These include the critical slowing down, rising variance and lag-1 autocorrelation function, strong correlations between the fluctuations of key variables and non-Gaussianity in the distribution of fluctuations. Recent experimental studies provide considerable support to the idea of criticality in cell differentiation and in other biological processes like the development of the fruit fly embryo. In this Review, an elementary introduction is given to the concept of criticality in cell differentiation. The correspondence between the signatures of criticality and experimental observations on blood cell differentiation in mice is further highlighted.
Footnotes
Glossary: Basic Terminologies of Nonlinear Dynamics
- Dynamical system
- a system the state of which evolves as a function of time.
- State at time t
- defined by the magnitudes of the key variables at time t.
- State space
- the space of all states. For an N-variable system the state space is N-dimensional with one coordinate axis for each variable.
- Time evolution
- described by differential rate equations, one equation for each variable.
- Trajectory in state space
- each state is defined by a single point in state space. A trajectory is obtained by joining the points representing the states of the system at successive time intervals. A knowledge of the state at time is obtained by solving the differential rate equations.
- Steady state
- a state in which all rates of change are zero, defines the fixed point of the dynamics.
- Stability of steady state
- a steady state is stable (unstable) if the system comes back to (goes away from) the steady state after being weakly perturbed from it.
- Bistability
- two stable steady states are possible for the same parameter values. Basin of attraction of a stable steady state: defined by a region in state space. All trajectories in this region end up at the fixed point representing the stable steady state.
- Attractors of dynamics
- trajectories in state space end up in the attractors which include both fixed points and limit cycles. In the latter case, the attractor is a cycle of states repeatedly traversed by the system indicative of periodic motion.
- Bifurcation
- occurs at specific parameter values at which there is a change in the dynamical regime, involves changes in the number and/or the stability properties of steady state solutions of the differential rate equations.
