Introduction

Photosynthetic organisms1,2,3,4,5,6,7,8,9 are among the oldest lifeforms and as such feature prominently in current debates about the possibility of life elsewhere in the universe10,11, alien life on Earth12 – and more generally, as potential renewable energy sources13. Among the recent advances in photosynthesis research1,2,13,14,15,16,17,18,19,20 are state-of-the-art AFM maps of the light-harvesting (LH) complexes in bacterial membranes1 and improved estimates for the relevant excitation timescales21,22. Both are essential ingredients for any realistic model of light-harvesting dynamics. Our model for excitation migration in purple bacterium Rsp. Photometricum, an archetypal terrestrial photosynthetic organism, inputs directly large spatial AFM network maps containing approximately 400 complexes (see Fig. 1 and Supplementary Information (SI)) together with these improved excitation timescales. It is well-known that certain environmental extremes would hinder the survival of a photosynthetic bacterium and hence that certain exoplanets would be less likely to support terrestrial photosynthetic life than others – however we know of no prior studies calculating the effect of incident photon arrival times. This is in part because of the previous lack of detailed information concerning the LH network and excitation timescales, but also because the prevailing view holds that it suffices to find planets with a similar incident light intensity.

Figure 1
figure 1

Our model.

Incident photon train produces excitations in purple bacteria (γ(t)) which then migrate across a large network containing approximately 400 light-harvesting complexes. Excitations are then processed at the reaction centers (RC) producing quinol output (ϕ(t)) for chemical metabolism. The AFM structure of the light-harvesting network adapted from Ref. 1, is used as an input to our model. Background shows purple bacteria colony (images courtesy of Drs. W. Lanier and J. Sturgis). Relevant timescales for exciton and charge separation dynamics are shown.

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The time-series of the incident photons creating excitations in the membrane, γ(t) and the quinol output from the RC, ϕ(t), can both be characterized statistically by their burstiness B and memory M, following Goh and Barabasi23. Random arrival with constant probability per unit time constitutes a Poisson process and yields an exponential distribution P(τ) for the time interval τ. Deviations from this exponential hence provide a measure of the burstiness: B ≡ (στ/mτ − 1)/(στ/mτ + 1) where mτ and στ are the mean and standard deviation respectively of the distribution P(τ). The memory M between consecutive intervals is given by23: where nτ is the number of time intervals and m1(m2) and σ1(σ2) are the sample mean and standard deviation of the τi(τi+1)'s respectively (i = 1, …, nτ − 1). By definition, −1 ≤ M ≤ 1 and −1 ≤ B ≤ 1. The γ(t) for thermal sources such as our own Sun is a Poisson-like process with (M, B) ≈ (0, 0) and produces an RC output ϕ(t) which also has (M, B) ≈ (0, 0). However non-thermal sources, such as that recently produced in laboratory silicon systems using stimulated and coherent anti-Stokes Raman scattering24, would not be restricted to having (M, B) ≈ (0, 0) and hence merit investigation. For simplicity our model considers each arriving photon as creating one initial excitation: This avoids adding another layer of statistical analysis for the absorption and does not change our main conclusions.

Results

Figures 2 and 3 present our model's predictions for the survivability of Rsp. Photometricum using three simple inputs whose (M, B) values can be calculated exactly analytically, thereby avoiding questions of finite sample size and hence boosting the robustness of the results. Although for each there are some portions of the (M, B) space that cannot be generated (indicated by diagonal shading), taken collectively they cover almost the entire (M, B) space. Each trajectory of a given color represents the possible RC outputs ϕ(t) generated using a particular input (M, B) value (denoted by a circle of the same color), but with RC closing times chosen from anywhere in the empirically valid range (i.e. 20 to 1000 Hz). If for one of these RC closing times, part of this trajectory lies within some small range of (0, 0) in the (M, B) plot and hence provides a ϕ(t) similar to that on Earth, a terrestrial bacteria with that value of the RC closing time would experience a quinol output from the RC which is identical to that on Earth. All other conditions being equal, it would therefore be likely to survive since its metabolism experiences the same quinol supply chain as on Earth. The corresponding colored circle therefore appears in the white region of the (M, B) space denoting survivability. If the trajectory does not lie close to (0, 0) in the (M, B) plot, then the quinol supply to the metabolism is bursty, which means that quinol molecules would sporadically bunch around the RC. It is known that such molecular crowding can alter the course of biochemical reactions25, which in turn suggests the bacterium's survival would be less likely. The corresponding colored circle now lies in a dotted region. We assume that the terrestrial bacteria's exposure to γ(t) is too abrupt for its membrane structure to adapt, leaving the possibility of mutations and evolutionary effects for future study. The irregular form of these white survivability regions is due to the highly nonlinear nature of the kinetic interplay between exciton migration and RC trapping, meaning extremes with |B| or |M| equal to 1 may allow survival (e.g. orange lines) while more Earth-like regions (i.e. M and B closer to zero) may not. Figure 3 considers a more stringent condition than Fig. 2 for the output range necessary for terrestrial bacteria survival, hence the smaller white regions.

Figure 2
figure 2

Survivability of terrestrial bacteria.

Three simple input time-series γ(t) are considered as illustration, with the sum of the white and dotted areas representing possible burstiness B and memory M values for that input process. Since the output ϕ(t) needs to be similar to on Earth (i.e. where ), white regions correspond to γ(t) inputs for which the bacteria would in principle survive while dotted regions correspond to γ(t) inputs for which survival is less favorable. Trajectories show the (M, B) output values obtained as the range of physically reasonable RC closure times is spanned, for a particular (M, B) input indicated by a circle of the same color. Right-hand column shows magnified version. Photon inputs correspond to (a) bunched input, (b) power-law step input and (c) step input.

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Figure 3
figure 3

As in Fig. 2, but now the condition for survival is more stringent. .

Additional histograms show waiting times τ between the incident photon arrivals.

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Discussion

Further specification of the bacterium's likely survival will require more detailed empirical information about the environmental and biochemical changes that a non-thermal light source such as in Ref. 24 would induce. Our results simply provide a proof-of-principle that, all other conditions being equal, light sources with extreme photon statistics24 could allow survival of the photosynthetic bacterium (white regions). In particular, since the temperature of objects receiving energy from such a source depends only on the time-average incident energy flux, one can vary the photon arrival statistics without changing the light intensity and hence without changing the temperature of the bacterium or its environment. If an extraterrestrial environment were identified with an Earth-like incident energy flux, temperature, humidity etc., the photon statistics could therefore make the difference between life and death. Our results are also relevant to the scenario of our own sun suddenly developing extremal temporal statistics, e.g. through sudden instabilities in the plasma flow dynamics modulating the irradiance properties at the Earth's surface26; the scenario of using artificial light sources as in Ref. 24 to manipulate photosynthesis; and the scenario where the bacteria's chromatophores are artificially modified in such a way that the absorption of our sun's photons takes on statistical properties with M ≠ 0 and B ≠ 0. Our results may also help with engineering designer-harvesting structures having charge transfer times possessing a particular desired statistic.

Methods

We model the excitation migration process as shown in Fig. 1, with details in the Supplementary Information (SI). The transfer rate values that we use (Fig. 1) are measured from pump-probe experiments and agree with generalized Förster calculated rates18, assuming intra-complex delocalization. The LH2→ LH1 transfer is estimated as t21 = 3.3 ps27, while LH2→LH2 transfer timescale is t22 = 10 ps18. The LH1→LH1 mean transfer time t11 has been calculated using a generalized Förster interaction6 as 20 ps, while the back-transfer LH1→ LH2 is approximately t12 = 15.5 ps. The lowest exciton state is thought to cause the LH1→ RC (reaction center) transfer at 77 K, whose non-vanishing dipole strength arises from ring symmetry breaking. Involvement of the bright second and third low lying states at higher temperatures, improves the transfer time to t1,RC = 25 ps22,28. Back-transfer from an RC's fully populated lowest exciton state to the second and third bright LH1 states, occurs in a calculated time of tRC,1 = 8.1 ps29. This is close to the empirically determined value 7–9 ps30. Charge separation at the RC complex will occur within t+ = 3 ps depending on whether a charge carrier is available, i.e. the RC is in an open state. In the RC, two electron transfer steps produce quinol (QBH2) after which the RC is then closed for a few milliseconds before quinol undocks and an available quinone QB replaces it. This reinitiates the charge carrier cycle and sets the RC in an open state. A proton gradient is generated across the periplasm and cytoplasm, inducing a voltage difference across the chromatophore membrane and hence enabling activation of the bacterial metabolism.