Noise-Induced Mechanism for Biological Homochirality of Early Life Self-Replicators

The observed single-handedness of biological amino acids and sugars has long been attributed to autocatalysis. However, the stability of homochiral states in deterministic autocatalytic systems relies on cross inhibition of the two chiral states, an unlikely scenario for early life self-replicators. Here, we present a theory for a stochastic individual-level model of autocatalysis due to early life self-replicators. Without chiral inhibition, the racemic state is the global attractor of the deterministic dynamics, but intrinsic multiplicative noise stabilizes the homochiral states, in both well-mixed and spatially extended systems. We conclude that autocatalysis is a viable mechanism for homochirality, without imposing additional nonlinearities such as chiral inhibition.

Figure 1

(a) Phase portrait of Frank’s model: the racemic state is an unstable fixed point (the red dot), while the homochiral states are stable fixed points (the green dots). (b) If chiral inhibition is replaced by a linear decay reaction, the ratio of d and l molecules stays constant. (c) Adding even the slightest amount of nonautocatalytic production of d and l molecules makes the racemic state (the green dot) the global attractor of the dynamics.

Figure 2

Comparison between the stationary distribution, Eq. (4) (dashed lines), and Gillespie simulations of the reactions (2) (markers), for different values of $\alpha$. Simulation parameters: $N={10}^3$, $k_a=k_n=k_d=1$.

Figure 3

Parameter ${\alpha }_c^{\text{patch}}$ in the two-patch system as a function of the diffusion rate $\delta$. Gillespie simulations (markers) are compared against Eq. (11) (the solid blue line) and Eq. (13) (the dashed red line). Simulation parameters as in Fig. 2.

Figure 4

Gillespie simulation of scheme (6) for a one-dimensional system of $M=100$ patches, starting from the racemic state and ending with all of the patches in the same homochiral state, $\omega =-1$. Simulation parameters: $N=1000$, $k_a=k_d=1$, $\delta =10^{-3}$, and $k_n=0$.