# Multimodal Attention Merging For Improved Speech Recognition and Audio Event
Classification

###### Abstract

Training large foundation models using self-supervised objectives on unlabeled
data, followed by fine-tuning on downstream tasks, has emerged as a standard
procedure. Unfortunately, the efficacy of this approach is often constrained
by both limited fine-tuning compute and scarcity in labeled downstream data.
We introduce Multimodal Attention Merging (MAM), an attempt that facilitates
direct knowledge transfer from attention matrices of models rooted in high-
resource modalities, text and images, to those in resource-constrained
domains, speech and audio, employing a zero-shot paradigm. MAM reduces the
relative Word Error Rate (WER) of an Automatic Speech Recognition (ASR) model
by up to 6.70%, and relative classification error of an Audio Event
Classification (AEC) model by 10.63%. In cases where some data/compute is
available, we present Learnable-MAM, a data-driven approach to merging
attention matrices, resulting in a further 2.90% relative reduction in WER for
ASR and 18.42% relative reduction in AEC compared to fine-tuning without model
merging.

Index Terms—  Knowledge transfer, cross-modal adaptation, speech recognition,
and acoustic modeling

##  1 Introduction

Current approaches in deep learning train large foundation models using task-
agnostic self-supervised objectives on unlabeled data [1, 2, 3]. The models
are then fine-tuned on downstream tasks, utilizing task-specific inputs and
labels. As foundation models increase in size, fine-tuning is hamstrung by
limitations in compute. Moreover, scarcity of task-specific data compounds
this challenge, particularly for relatively lower-resource modalities like
speech or audio when compared to more widely studied modalities such as text
or images.

Prior research [4, 5, 6, 7] has demonstrated transferability of the
Transformer [8] across modalities with minimal or no fine-tuning of the self-
attention mechanism. [4] shows that text pre-training is sufficient to learn
modality agnostic properties of sequences by demonstrating the success of
frozen text pre-trained Transformers in image classification and protein fold
prediction without self-attention fine-tuning. [9] shows that cross-modality
capabilities in Transformers arises from the transfer of knowledge in the form
of position-aware context. [10] and [11] provide evidence for multimodal
neurons in the Transformer and demonstrate that modality transfer happens in
intermediate layers.

Motivated by these works, we present Multimodal Attention Merging (MAM) to
investigate the possibility of transferring knowledge from models trained on
high-resource modalities such as text and images to models trained on
relatively low-resource modalities such as speech and audio. Given abundant
textual and visual data, self-supervised pre-training using objectives such as
Masked Language Modeling and Masked Patch Prediction utilize the Transformer
to learn generalized representations of natural language text and images.
Chiang and Lee [12] indicate that using Masked Language Modeling allows self-
attention to capture explicit and implicit dependencies at the token level,
which are modality agnostic. Therefore, through MAM we investigate whether
these textual and visual parameter-space representations generalize to speech
and audio. Through a systematic interpolation of attention matrices from
models trained on high-resource modalities (e.g., BERT [13], Vision
Transformer [3]) MAM demonstrates an improvement in performance of models
trained on low-resource modalities (e.g., HuBERT [2], BEATs [14]) on Automatic
Speech Recognition (ASR) and Audio Event Classification (AEC). Our
contributions are:

Fig. 1: Learnable Multimodal Attention Merging. The merged model correctly
transcribes breech.  modules are fine-tuned (trainable) while  are frozen
(non-trainable). In our initial approach, Multimodal Attention Merging, the
interpolation factor $\lambda$ is frozen (non-trainable).

  * •

In contrast to prior research [15, 16, 17, 18, 19], we show attention-merging
on models from different tasks, modalities, and initializations. To the best
of our knowledge, we are the first to extend attention-merging to sequence-to-
sequence tasks, specifically ASR.

  * •

Introducing Multimodal Attention Merging (MAM), we lower HuBERT’s relative
Word Error Rate (WER) on LJ Speech by 6.70% and VCTK by 1.80%, also decreasing
BEATs’ relative classification error on ESC-50 by 10.63%, without additional
fine-tuning (Section 3.1).

  * •

We present a data-driven approach employing the Sliced Wasserstein Distance
[20] between intermediate hidden-layer representations to merge specific
attention layers, reducing the need for empirical experimentation (Section
4.1).

  * •

In the case where some data/compute is available, we present Learnable-MAM
(L-MAM), by learning the interpolation factor during fine-tuning. L-MAM yields
a 2.70% and 2.90% relative reduction in WER on LJ Speech and VCTK and a 18.42%
relative reduction in classification error on ESC-50 compared to regular fine-
tuning (Section 3.3).

##  2 Related Work

Prior work in multimodal merging includes OTKGE [21], that uses Optimal
Transport to align structural knowledge, linguistic information, and image
embeddings in knowledge graphs. However, they do not extend their approach to
merging model weights and focus on embeddings instead. Voice2Series [5] and
Frozen Pretrained Transformer [4] demonstrate knowledge transfer across
modalities through frozen self-attention weights. While both works study the
transferability of self-attention across modalities, they stop short of
merging models trained from different modalities and do not address sequence-
to-sequence tasks such as ASR. In contrast, works such as Fisher merging [22],
local fine-tuning [16], Model Soups [19], DMC [23], AdapterSoup [24], MLM [25]
discuss model merging but do not consider the multimodal scenario. Perhaps the
closest work to ours is Multimodal Model Merging [15], an empirical study of
merging vision and text models for combined vision-language tasks such as
Visual Question Answering [26] and image-text retrieval [27]. The approach
studies the use of simple interpolation, RegMean [15], and Task Vectors [28]
to determine the best model merging approach. However, they require
contrastive model alignment, use a shared seed pre-training phase to
initialize models prior to merging, and address joint vision+language tasks.
In contrast, MAM merges off-the-shelf models from different modalities without
constraints on pre-training tasks or weight initialization. Through L-MAM, we
also present an approach to learn the interpolation factor in the case where
limited data/compute is available, reducing the requirement on empirical
experimentation.

##  3 Method

MAM seeks to determine if the Transformer [8] attention mechanism generalizes
across modalities. It does so by exploring the transferability of parameter-
space sequence representations of Transformers pre-trained on high-resource
modalities (text or vision) to those trained on relatively low-resource
modalities (speech or audio). For convenience, we refer to the high-resource
and low-resource pre-trained models as the Source Model and Target Model
respectively. Figure 1 presents an outline of attention merging. It is
important to note that all our approaches require the source and target models
to have the same number of attention layers and hidden layer sizes.

We apply attention merging to two tasks: Automatic Speech Recognition (ASR)
and Audio Event Classification (AEC). ASR transcribes human speech to text,
while AEC identifies real-life events (e.g. barking, thunderstorm, whistling)
from audio clips.

We use three main approaches to demonstrate MAM: Attention Interpolation,
Layer-wise Attention Interpolation, and Attention-Merging with Learnable
Interpolation.

###  3.1 Attention Interpolation

MAM with attention interpolation uses a convex combination of the source and
target models. Using an interpolation factor $\lambda\in[0,1]$, we merge
Query, Key, and Value matrices ($W_{Q},W_{K},W_{V}$) across all layers
$\mathcal{L}$ in the attention computation. For source and target models
$M_{s}$ and $M_{t}$, the merged model $M_{\textsf{merge}}$’s Query, Key, and
Value matrices for each layer $i$ are defined in Equation 1.
$M_{\textsf{merge}}$ is applied to the same downstream task as $M_{t}$.

$\displaystyle W_{Q_{i},K_{i},V_{i}}^{M_{\textsf{merge}}}=\lambda\cdot
W_{Q_{i},K_{i},V_{i}}^{M_{s}}+$ $\displaystyle(1-\lambda)\cdot
W_{Q_{i},K_{i},V_{i}}^{M_{t}}$ (1)

###  3.2 Layer-wise Attention Interpolation

Evidenced by research categorizing layers by importance [29], we experiment
with merging a subset of layers $\ell$ from the set of all layers
$\mathcal{L}$ ($|\ell|<|\mathcal{L}|$) and present the modified approach in
Equation 2. We are interested in identifying whether merging all layers is
necessary, or if merging a subset yields better generalization.

$\displaystyle W_{Q_{i},K_{i},V_{i}}^{M_{\textsf{merge}}}=\lambda\cdot
W_{Q_{i},K_{i},V_{i}}^{M_{s}}+(1-\lambda)\cdot W_{Q_{i},K_{i},V_{i}}^{M_{t}}$
(2) $\displaystyle\lambda=0\;\forall{i}\notin\ell$

###  3.3 Attention-Merging with Learnable Interpolation

Finally, we learn the interpolation factor $\lambda$ for individual downstream
tasks. In this setting, $\lambda$ is optimized concurrently with model weights
$M_{t}$ during fine-tuning. We omit optimizing $M_{s}$ as it corresponds to a
different modality from the downstream task. In contrast to the previous two
approaches, we do not impose the requirement for utilizing uniform $\lambda$
across layers. Instead, we view learning $\lambda$ as a gate that enables
flexible information transmission from the high-resource to the low-resource
modality and describe this technique in Equation 3.

$\displaystyle W_{Q_{i},K_{i},V_{i}}^{M_{\textsf{merge}}}=\lambda_{i}\cdot
W_{Q_{i},K_{i},V_{i}}^{M_{s}}+(1-\lambda_{i})\cdot
W_{Q_{i},K_{i},V_{i}}^{M_{t}}$ (3)

##  4 Experiments

For ASR, we merge publicly available HuBERT-large [2] and BERT-large-uncased
[13] models. Both models have 24 attention layers and a width of 1024,
totaling 300 million parameters. HuBERT-large is an encoder model pre-trained
on 60,000 hours of Libri-Light [30] for speech representation learning and
fine-tuned with CTC on 960h of Librispeech [31] for ASR. BERT-large-uncased is
pre-trained via Masked Language Modeling on the Wikipedia corpus and
Bookcorpus. We evaluate merged models on LJ Speech [32], a single-speaker
dataset of 13,100 audio clips from non-fiction books totaling 24 hours, and
VCTK [33], a multi-speaker dataset with 43,000 audio clips totaling 44 hours.
VCTK features diverse speakers from regions like England, Scotland, and
America, reading texts chosen for comprehensive contextual and phonetic
coverage.

For AEC, we merge BEATs [14] and Vision Transformer (ViT) [3] containing 12
attention layers and hidden size of 768, totaling 90 million parameters. BEATs
is pretrained on AudioSet [34] for audio representation learning while ViT is
pretrained on ImageNet [35]. Evaluation focuses on ESC-50 [36], which
comprises 2000 5-second environmental audio recordings across 50 classes.

###  4.1 Case Study 1: Zero-Shot Experiments

The first study evaluates zero-shot performance of merged models on downstream
datasets. We use a dev set to select the interpolation $\lambda$ and report
results on a held-out test set.

Attention-Interpolation. Table 1 contains the results for attention merging of
entire models as described in Section 3.1 for different interpolation factors
$\lambda$. We merge source and target models following the strategy outlined
in Equation 1. As an additional baseline, we also merge target models with
source models sampled from random noise. We experiment with three types of
noise - sampling noise from source model parameters $\mathcal{N}$(Source),
target model parameters $\mathcal{N}$(Target), and a standard normal
distribution $\mathcal{N}$(0,1). For $\mathcal{N}$(Source) and
$\mathcal{N}$(Target), we draw samples with the same mean and variance as the
parameters of the source and target models respectively. The samples are then
used to construct attention matrices with the same dimensions as the Target
model. The results in Table 1 underscore the clear advantage of merging
attention matrices from the source model. Conversely, merging with noise
substantially diminishes performance, especially at higher interpolation
factors.

$\lambda$ |  Source |  $\mathcal{N}$(Source) |  $\mathcal{N}$(Target) | $\mathcal{N}(0,1)$
---|---|---|---|---
LJ Speech - WER(%) Source: BERT Target: HuBERT
0.00 | 9.25 | - | - | -
0.05 | 9.11 | 9.78 | 9.26 | 10.57
0.10 | 9.06 | 32.43 | 10.06 | 74.03
0.15 | 9.20 | 98.30 | 18.13 | 99.95
0.20 | 9.62 | 99.99 | 75.93 | 100.00
0.25 | 11.12 | 100.00 | 100.00 | 100.00
VCTK - WER(%) Source: BERT Target: HuBERT
0.00 | 5.58 | - | - | -
0.05 | 5.48 | 5.84 | 5.54 | 6.26
0.10 | 5.55 | 22.57 | 6.17 | 54.53
0.15 | 5.85 | 91.93 | 12.81 | 99.83
0.20 | 6.45 | 99.42 | 58.57 | 100.00
0.25 | 8.50 | 99.96 | 97.15 | 100.00
ESC-50 - Error(%) Source: ViT Target: BEATs
0.00 | 11.75 | - | - | -
0.10 | 11.50 | 11.76 | 83.40 | 98.25
0.15 | 11.75 | 12.44 | 98.00 | 96.75
0.20 | 17.50 | 14.36 | 98.00 | 97.00
0.25 | 16.75 | 19.12 | 98.00 | 98.50
0.30 | 33.00 | 26.82 | 98.00 | 98.50
Table 1: Error(%) for interpolation of source and target models with factor
$\lambda$. $\mathcal{N}$(Source) and $\mathcal{N}$(Target) are noise sampled
with the same mean and variance as parameters of source and target models.

Interpolation of subset of layers. Table 2 summarizes the results for merging
a subset of layers. We experimented with merging blocks of different sizes and
different interpolation but for the sake of brevity present results on blocks
of 8 layers for ASR and 4 or 8 layers for AEC with the best performing
$\lambda$ selected using a dev set, which was 0.25 for LJ Speech, 0.05 for
VCTK, and 0.1 for ESC-50. For ASR, we identified that merging layers 12-19
resulted in the lowest WER while it was layers 4-11 for AEC.

To determine whether a better subset exists, we employed a data-driven
strategy to pinpoint the most suitable layers to merge. We used audio snippets
and corresponding text transcripts from 10% of the training set of LJ Speech
and VCTK. HuBERT encoded the audio, while BERT encoded the transcripts. For
each sample, hidden representations at the output of each attention block were
extracted from every layer of both networks. These hidden representations were
averaged by sequence length, resulting in a 1024-dimensional vector per layer
for each sample. Similarity between an audio-text pair’s HuBERT and BERT
hidden representations for each layer was computed via Euclidean distance, the
inner product, and motivated by prior work that compares hidden
representations in speech models [37], the Sliced Wasserstein Distance (SWD)
[20]. Sorting layers by similarity, the top-k most similar layers were merged.
Results for distinct k values and distance metrics are presented in Table 3.
For LJ Speech, we find that merging top 6 layers identified using SWD yields
best results while it is the top 10 layers for VCTK. Comparing Tables 2 and 3,
we notice that merging continuous blocks of layers performs better or almost
identical to the data-driven strategy. In contrast, the data-driven strategy
does not require extensive experimentation. We did not perform data-driven
experiments for AEC due to the absence of paired images for audio snippets in
ESC-50.

Layers Merged |  LJ Speech $\lambda=0.25$ |  VCTK $\lambda=0.05$ |  Layers Merged |  ESC-50 $\lambda=0.1$
---|---|---|---|---
0 - 7 | 9.33 | 5.53 | 0 - 3 | 13.00
4 - 11 | 9.59 | 5.55 | 4 - 7 | 12.50
8 - 15 | 9.28 | 5.54 | 8 - 11 | 12.00
12 - 19 | 8.63 | 5.52 | 0 - 7 | 11.75
16 - 23 | 10.07 | 5.54 | 4 - 11 | 10.50
None | 9.25 | 5.58 | None | 11.75
Table 2: Model Merging on a subset of layers - WER(%) on LJ Speech and VCTK and Error(%) on ESC-50 $\lambda$ | k |  Euclidean Distance |  SWD |  Inner Product
---|---|---|---|---
LJ Speech
0.1 | 4 | 9.18 | 8.74 | 9.28
6 | 8.87 | 8.73 | 9.38
8 | 9.19 | 8.92 | 9.32
VCTK
0.05 | 6 | 5.53 | 5.55 | 5.54
8 | 5.51 | 5.52 | 5.52
10 | 5.51 | 5.51 | 5.52
Table 3: Comparison of selecting Top-k most similar layers based on different distance metrics, WER(%) on the ASR task |  Baseline |  MAM
---|---|---
| LJ Speech
1 |  the commission believes that the motorcade rout selected by agent lawson upon the advice of agent in charge sorrels |  the commission believes that the motorcade route selected by agent lawson upon the advice of agent in charge sorrels
2 |  here a couple of pye men had been selling their wares the basket of one of them which was raised upon a four legged stool was upset |  here a couple of piemen had been selling their wares the basket of one of them which was raised upon a four legged stool was upset
3 |  besides his employers a jeweler named humphreys was in the swim at whose shop in red lion square was discovered a quantity of bass gold |  besides his employers a jeweler named humphreys was in the swim at whose shop in red lion square was discovered a quantity of base gold
4 |  aproximately thirty to forty five seconds after oswalds lunch room encounter with baker and truley |  approximately thirty to forty five seconds after oswalds lunchroom encounter with baker and truly
| VCTK
5 |  on the contrary they stant togain |  on the contrary they stand to gain
6 |  flanke gordon simpson may also feature in that much |  flanke gordon simpson may also feature in that match
7 |  the marshal at the tern was great |  the marshal at the turn was great
8 |  they were behind the field |  they were behind the wheel
Table 4: Analysis of improvements on LJ Speech and VCTK

###  4.2 Case Study 2: Fine-Tuning Experiments

While previous results were based on zero-shot evaluation, we also examined
fine-tuned performance. A comparison of different approaches is provided in
Table 5. The top row represents the baseline of downstream evaluation without
attention merging or fine-tuning. By employing MAM, we improve the original
model’s performance without additional fine-tuning. We report the better of
Attention Interpolation (3.1) and Layer-wise Attention Interpolation (3.2) as
the best performing MAM approach. Another baseline involves fine-tuning models
on target data alone (third row), with results averaged over 3 runs. We fine-
tune using AdamW [38] using a learning rate of 1e-5 for ASR and 1e-3 for AEC.
We fine-tune for 2 epochs on LJ Speech, 1 epoch for VCTK, and 3 epochs for
ESC-50 with a batch size of 32. For ASR, we fine-tune HuBERT using CTC Loss.
Fine-tuning on target data outperforms MAM for LJ Speech and ESC-50, while MAM
is the better approach for VCTK. We speculate that the similarity in
distribution between VCTK (a larger, multi-speaker dataset) and the pre-
training data (Libri-light and Librispeech) limits the efficacy of fine-tuning
while the single-speaker nature of LJ Speech allows fine-tuning to adapt
better to the dataset.

In the situation some data/compute is available, we explore fine-tuning based
approaches. We notice improved performance when combining MAM and fine-tuning
as compared to using either approach independently. We utilize the best
performing model obtained through model-merging (Tables 1 and 2) followed by
fine-tuning, shown in the fourth row of Table 5. Our top-performing model
emerges when jointly learning the interpolation factor and model weights
during fine-tuning, as shown in the last row of Table 5. With L-MAM followed
by fine-tuning, we achieve a 2.70% relative WER reduction on LJ Speech, a
2.90% reduction on VCTK, and an 18.42% reduction in classification error on
ESC-50 compared to the regular fine-tuning baseline.

MAM |  FT |  L-MAM |  WER (%) LJ Speech |  WER (%) VCTK |  Error (%) ESC-50
---|---|---|---|---|---
- | - | - | 9.25 | 5.58 | 11.75
✓ | - | - | 8.63 | 5.48 | 10.50
- | ✓ | - | 8.52 | 5.52 | 9.50
✓ | ✓ | - | 8.40 | 5.44 | 7.75
- | ✓ | ✓ | 8.29 | 5.36 | 7.75
Table 5: Ablation study to compare MAM, Fine-Tuning (FT), and Learnable-MAM
for ASR and AEC

###  4.3 Analysis of Improvements

We now analyze the improvements observed on the ASR task. Table 4 contrasts
transcriptions from the baseline (without attention merging or fine-tuning)
with those from MAM. MAM improves transcriptions for homophonic words,
exemplified by ‘route’, ‘piemen’, and ‘base’ in LJ Speech. VCTK, encompassing
various speakers, contains non-standard pronunciations, wherein MAM
successfully transcribes ambiguous words accurately. Instances include
‘stand’, ‘match’, ‘turn’, and ‘wheel’, as shown in rows 5 to 8 of Table 4. We
further categorize improvements based on character insertion, substitution, or
deletion in Table 6. While LJ Speech improvements primarily stem from
insertion and substitutions, VCTK shows a more balanced distribution among
these types of errors.

Improvement | Insertion | Substitution | Deletion
---|---|---|---
LJ Speech | 61.89 % | 35.13 % | 2.98 %
VCTK | 36.36 % | 28.28 % | 35.35 %
Table 6: Categorization of Improvements

##  5 Conclusion

This paper introduces Multimodal Attention Merging (MAM), which transfers
knowledge from attention matrices of high-resource modality models (e.g., text
and images) to low-resource ones (e.g., speech and audio). MAM improves zero-
shot performance of HuBERT (ASR) and BEATs (Audio Event Classification) by
merging attention matrices with BERT and Vision Transformer. Additionally,
Learnable-MAM (L-MAM) jointly learns interpolation and model weights during
fine-tuning, achieving up to 2.90% relative WER reduction and 18.42%
classification error reduction on ASR and Audio Classification compared to
regular fine-tuning, respectively.

While MAM and L-MAM demonstrate improvements, our work is nascent and we
believe there are several avenues for future work warranting investigation.
Future work could address merging larger, billion-parameter models
representing the state of the art. Developing methods to merge models of
differing architectures and merging three or more modalities are other
dimensions to extend this work. While we merge attention matrices, future work
could address the problem from a parameter efficiency perspective by merging
adapter modules [39] or low-rank representations [40]. Finally, we believe
that equipping merged models with cross-modality capabilities to build a
generalized multi-task architecture holds promise and urge future work in this
direction.

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# Twisted carotenoids do not support efficient intramolecular singlet fission
in the orange carotenoid protein

George A. Sutherland  Plants, Photosynthesis and Soil, School of Biosciences,
University of Sheffield, Sheffield S10 2TN, UK  James P. Pidgeon  Department
of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, UK
Harrison Ka Hin Lee  SPECIFIC, Faculty of Science and Engineering, Swansea
University, Swansea SA1 8EN, UK  Matthew S. Proctor  Plants, Photosynthesis
and Soil, School of Biosciences, University of Sheffield, Sheffield S10 2TN,
UK  Andrew Hitchcock  Plants, Photosynthesis and Soil, School of Biosciences,
University of Sheffield, Sheffield S10 2TN, UK  Shuangqing Wang  Department of
Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, UK  Dimitri
Chekulaev  Department of Chemistry, University of Sheffield, Sheffield S3 7HF,
UK  Wing Chung Tsoi  SPECIFIC, Faculty of Science and Engineering, Swansea
University, Swansea SA1 8EN, UK  Matthew P. Johnson  Plants, Photosynthesis
and Soil, School of Biosciences, University of Sheffield, Sheffield S10 2TN,
UK  C. Neil Hunter  Plants, Photosynthesis and Soil, School of Biosciences,
University of Sheffield, Sheffield S10 2TN, UK  Jenny Clark
<EMAIL_ADDRESS>Department of Physics and Astronomy, University of
Sheffield, Sheffield S3 7RH, UK

###### Abstract

Singlet exciton fission is the spin-allowed generation of two triplet
electronic excited states from a singlet state. Intramolecular singlet fission
has been suggested to occur on individual carotenoid molecules within protein
complexes, provided the conjugated backbone is twisted out-of-plane (giving a
4 $\sim$980\text{\,}{\mathrm{cm}}^{-1}$$ resonance Raman peak). However, this
hypothesis has only been forwarded in protein complexes containing multiple
carotenoids and bacteriochlorophylls in close contact. To test the hypothesis
on twisted carotenoids in a ‘minimal’ one-carotenoid system, we study the
orange carotenoid protein (OCP). OCP exists in two forms: in its orange form
(OCPo), the single bound carotenoid is twisted, whereas in its red form
(OCPr), the carotenoid is planar. To enable room-temperature spectroscopy on
canthaxanthin-binding OCPo and OCPr without laser-induced photoconversion, we
trap them in trehalose glass. Using transient absorption spectroscopy, we show
that there is no evidence of long-lived triplet generation through
intramolecular singlet fission, despite the canthaxanthin twist in OCPo.

###### keywords:

singlet exciton fission, singlet fission, orange carotenoid protein,
carotenoid, canthaxanthin

These authors contributed equally. These authors contributed equally. +44
(0)114 222 3526 IR,NMR,UV

##  1 Introduction

Singlet exciton fission (SF) is the conversion of a spin-0 singlet exciton 1
(or excited singlet state) into a pair of spin-1 triplet excitons 2, 3, 4, 5.
This multiexciton generation process has been studied over the past decade
primarily because of its promise to improve solar cell efficiency 6, 7, 8, 9,
10; one-high energy photon creates two low-energy excited states, which could
be harvested by conventional photovoltaic devices in a process minimizing
energetic losses due to thermalization. SF has other potential applications
for non-linear optics 11, 12, 13, OLEDs 14 or even quantum technologies 15,
16, 17, 18 by taking advantage of the virtue that a single photon creates a
pair of spin-entangled quantum states. However, despite promising results 19,
20, practical applications have yet to be realized, in part due to the limited
library of materials that undergo SF, none of which is yet ideal 7, 4.

In the search for other SF materials, the polyenes, ‘class III’ SF materials
according to Smith and Michl’s categorization 2, form an intriguing materials
class. In these materials, the lowest-lying singlet excited state (S1) has
dominant triplet-pair character, denoted 1(TT) (see Refs. 21, 22, 3) and thus
demonstrates negligible one-photon absorption from the ground-state. S1 is
instead accessed by internal conversion following excitation to the strongly
absorbing S2 state.

This SF class includes conjugated polymers such as polydiacetylene23, 24, 25,
poly(alkyl-thienylenevinylene)26, 27, 28, a new generation of donor-acceptor
singlet fission polymers29, 30, 31, 32, quinoidal thiophenes 33, 34, 35, 36,
37, carbene-based diradicaloids 38 and antiaromatic core-structured molecules
39, 40. The polyene family also includes the carotenoids, a large class of
over 1000 naturally occurring molecules,41, 42 represented here by
canthaxanthin (CAN) which forms the subject of this work (see structure in
Fig. 1a).

Figure 1: The OCP photoswitches from orange (OCPo) to red (OCPr) forms with
different carotenoid conformations. The OCP studied here binds a single CAN
carotenoid whose skeletal structure is shown in panel (a). The bound CAN
conformation depends on the OCP form, as shown in panel (b): when CAN is bound
in OCPo (green, data from X-ray diffraction structure PDB 4XB5 43, 44) it has
a twisted conformation; when bound in an OCPr N-terminal homolog (blue, data
from X-ray diffraction structure of red carotenoid protein, RCP: PDB 4XB4 43,
45) it is planar. (c) In solution, OCPo converts to OCPr under white-light
illumination ($1600\text{\,}\mathrm{\SIUnitSymbolMicro
mol}\text{\,}\mathrm{photon}\text{\,}{\mathrm{m}}^{-2}\text{\,}{\mathrm{s}}^{-1}$)
resulting in a change in color (see inset) and absorbance spectrum (main
panel). The spectra were taken in $1\text{\,}\mathrm{min}$ intervals under
constant white-light illumination. In the dark, OCPr converts back to OCPo
(see SI Fig. 6). The optical path length for solution measurements was
$1\text{\,}\mathrm{mm}$.

In comparison with better-studied ‘class I’ SF materials 2, 46, 47, 48, 49,
mostly based on molecules such as pentacene50, 51 or tetracene 52, 53, 54, 55,
SF in polyenes is less well understood. This is attributable in part to their
complex manifold of low-lying triplet-pair states 56, 57, 58 and strong
vibronic coupling59, 60, and also partly due to the sensitivity of the
photophysics to conjugation length and molecular geometry. In polyenes, the
lowest-lying 1(TT) state that makes up the dominant contribution of S1 21, 22,
61, 62 contains tightly-bound triplets that are unlikely to easily separate
into free triplets 63 without additional energy 56.

Indeed, while intramolecular singlet fission (iSF) has been observed in a
variety of long-chain polyenes in solution 23, 24, 25, 26, 27, 28, 29, 30, 31,
32, unlike the recently designed ‘class I’ iSF systems 49, 48, 47, 64, the
triplet-pairs in polyenes decay rapidly
($\text{\,}\mathrm{ps}$-$\text{\,}\mathrm{ns}$) to the S0 ground-state 3. Even
in carotenoid aggregates, where intermolecular SF occurs between neighboring
chromophores 65, 66, 67, 68, 69, 70, the majority of triplet excited states
decay to S0 surprisingly quickly (within a nanosecond) 65, 3, 70. In isolated
carotenoids in solution, the dominant deactivation channel from the
photoexcited S2 state is internal conversion to S1. To our knowledge, there is
no evidence that isolated carotenoids in solution demonstrate intramolecular
SF (iSF).

Nevertheless, similarly to recent reports that torsion or twisting along a
molecular backbone can allow both rapid iSF and formation of long-lived
triplets in ‘class I’ SF materials 48, 64, iSF along a single _twisted_
carotenoid chain to produce long-lived ($\text{\,}\mathrm{\SIUnitSymbolMicro
s}$) triplets has been suggested to occur in some photosynthetic light-
harvesting complexes 71, 72, 73, 74, 75. In these systems, the protein binds
the carotenoid so that it is constrained in a twisted geometry. This twist
reportedly stabilizes a triplet at either end of the molecule 71, 73.

This hypothesis was initially proposed to explain the presence of SF in the
light-harvesting antenna (LH1) from Rhodospirillum rubrum, because of the
large intermolecular distances between neighboring carotenoids
($>$$10\text{\,}\mathrm{\text{}}$) 71. More recently, Yu et al.73 observed a
correlation between the presence of SF and the so-called 4 resonance Raman
peak ($\sim$980\text{\,}{\mathrm{cm}}^{-1}$$) in light-harvesting complexes
(LH1-RC and LH2) from Thermochromatium tepidum and Rhodobacter sphaeroides
2.4.1. The intensity of 4 is related to carotenoid backbone twisting,73, 76 so
this finding led to the conclusion that backbone twisting of the carotenoid
directly enables iSF.

To test the hypothesis that singlet fission (SF) can occur along a single
twisted carotenoid chain, we examine a protein that binds a single carotenoid:
the orange carotenoid protein (OCP). In OCP the protein exists in two forms,
orange and red (OCPo and OCPr) with the carotenoid in either a twisted or
planar conformation, respectively (see Fig. 1). By studying both forms with
the protein fixed in a trehalose-sucrose glass, we demonstrate that a twisted
backbone is not sufficient to enable iSF in a protein-bound carotenoid. In
light of recent work understanding magnetic field effects (MFEs) in SF systems
77, 78, we also discuss published reports of MFE in light-harvesting complexes
from purple bacteria 79, 80, 81, 82, 83, 84 and find that the reported MFEs
are also inconsistent with iSF. Overall, we conclude that iSF is not supported
on carotenoids bound to the OCP and unlikely to occur in light-harvesting
complexes.

##  2 Results

In this study, the OCP was produced in Escherichia (E.) coli by virtue of a
dual plasmid system comprised of pET28a with the Synechocystis sp. PCC 6803
OCP gene (slr1963) and pAC-CANTHipi, which provides near-100% accumulation of
CAN.85 Carotenoid-containing protein was isolated according to the method
described in the methods Section.

In solution, upon illumination with white light, the dark-adapted OCPo form
undergoes a conformational switch to the OCPr form, with a concomitant red-
shift of its steady-state absorbance spectrum due to the effective conjugation
length extension of the bound carotenoid 86, 87, 76, 88, see Fig. 1c. The
change is reversible, with back-conversion from OCPr to OCPo occurring in the
dark, see SI Fig. 6.

Previously published X-ray diffraction structures by Leverenz, Sutter, and co-
workers 43 show that the conjugated backbone of the bound carotenoid is
twisted out of the plane of conjugation in OCPo (PDB 4XB5 44), while in OCPr
N-terminal domain homologs such as red carotenoid protein (RCP) it is
relatively planar (PDB 4XB4 45). The difference between the two conformations
of CAN is depicted in Fig. 1b using data from X-ray diffraction structures 43.
The different protein conformations containing a twisted and non-twisted form
of CAN provide an uncomplicated model system to study the role of carotenoid
geometry on iSF.

To avoid the problems associated with using spectroscopy to probe a light-
activated conformational switch, we prevent the conformational change by
trapping the protein in either its OCPo or OCPr conformations in a trehalose-
sucrose glass as previously described70. This glass matrix prevents OCPo
$\rightleftharpoons$ OCPr conversion, as demonstrated in Fig. 2(a,b), and
allows us to probe each conformation in isolation at room temperature, without
altering its conformation or photophysics89, 90.

Figure 2: OCPo and OCPr trapped in trehalose glass films. The steady-state
absorbance spectra of the OCPo film (a) were taken in $1\text{\,}\mathrm{min}$
intervals under constant white-light illumination
($1600\text{\,}\mathrm{\SIUnitSymbolMicro
mol}\text{\,}\mathrm{photon}\text{\,}{\mathrm{m}}^{-2}\text{\,}{\mathrm{s}}^{-1}$)
and the spectra of the OCPr film (b) were taken in $1\text{\,}\mathrm{min}$
intervals at $22\text{\,}\mathrm{\SIUnitSymbolCelsius}$ in darkness. No
changes in spectra were observed over $900\text{\,}\min$. (c) The resonance
Raman spectra of OCPo (green) and OCPr (blue) films in trehalose glass show
vibrational peaks typical of carotenoids, labelled following convention. The
spectra show a significant difference in the intensity of the 4 vibrational
peak between OCPo and OCPr and a shift of the 1 peak. The Raman measurements
were performed using a $532\text{\,}\mathrm{nm}$ laser. Data is averaged from
two successive scans, and normalized to the peak 1 intensity.

To confirm the twisted/planar conformations of CAN in OCPo/OCPr glass films,
we turn to resonance Raman spectroscopy. As described above73, 76, the
presence of a so-called 4 peak at $\sim$$980\text{\,}{\mathrm{cm}}^{-1}$ in
the resonance Raman spectrum of carotenoids (due to out-of-plane C-H wagging
modes 91) is generally associated with a backbone twist of the carotenoid 73,
76. Fig. 2c shows the resonance Raman spectrum of OCPo (blue) and OCPr
(green). Consistent with previous measurements on an echinenone-binding OCP
76, we observe a larger twist-induced 4 peak in OCPo than in OCPr, confirming
native geometry is maintained in trehalose-encapsulated OCPo and OCPr.

Figure 3: Transient absorption spectra of CAN-binding OCPo (a) and OCPr (b)
trapped in trehalose films. The spectral timeslices have been averaged between
the times indicated on the figure and are consistent with an S2 $\rightarrow$
S1 $\rightarrow$ S0 decay scheme in both cases, with no discernible long-lived
features (see also global lifetime analysis of the data in the SI note on
Global lifetime analysis and Ref. 89). The films were excited with
$532\text{\,}\mathrm{nm}$, $5\text{\,}\mathrm{kHz}$,
$\sim$$100\text{\,}\mathrm{fs}$, $200\text{\,}\mathrm{\SIUnitSymbolMicro
J}\text{\,}{\mathrm{cm}}^{-2}$ pump pulses. Figure 4: Transient absorption
dynamics of CAN-binding OCPo (a) and OCPr (b) in trehalose glass. The dynamics
have been averaged between the wavelengths indicated in the legend and
demonstrate that no discernible long-lived features are seen. The films were
excited with $532\text{\,}\mathrm{nm}$, $5\text{\,}\mathrm{kHz}$,
$\sim$$100\text{\,}\mathrm{fs}$, $200\text{\,}\mathrm{\SIUnitSymbolMicro
J}\text{\,}{\mathrm{cm}}^{-2}$ pulses. Note the plots have a linear time-axis
up to $1\text{\,}\mathrm{ps}$, and subsequently logarithmic up to
$40\text{\,}\mathrm{ps}$.

Having established that the CAN backbone is more twisted in OCPo than OCPr, we
test the suggestion that such a twist is the determinant for iSF reactivity72,
73, 75. Picosecond transient absorption spectroscopy spectra and dynamics are
shown in Figs. 3 and 4. Global lifetime analysis of the data is shown in SI
Fig. 9 and 10, but simply from inspection of the raw data in Fig. 3, we see
that all spectral features in both OCPo (green) and OCPr (blue) decay to $<$1%
of the initial population within $30\text{\,}\mathrm{ps}$. Importantly, we
observe no obvious formation of SF-generated triplets, as reported in light-
harvesting complexes in purple bacteria 73, 71. Instead both OCPo and OCPr
broadly demonstrate the expected isolated carotenoid behavior characterized by
rapid internal conversion from S2 to S1 (evidenced by the instrument-limited
decay of an excited-state absorption (ESA) in the near infrared region), and
subsequent decay of S1-like states to the ground-state. Therefore, a twist
along the carotenoid backbone is not sufficient to enable iSF.

##  3 Discussion

The lack of intramolecular singlet fission (iSF) in the protein-twisted
carotenoid in OCPo appears to counter the currently accepted explanation for
singlet fission (SF) in light-harvesting complexes (LHCs) in purple bacteria
71, 72, 73, 74, 75. We therefore return to the original studies of SF in these
LHC systems and discuss them in light of recent work on the nature of
intermediate triplet-pair states involved in singlet fission 77, 78.

Figure 5: Magnetic field effect (MFE) of _Rhodobacter sphaeroides_. Data
reproduced from Ref. 79 and used with permission from Elsevier. The data is
plotted as the normalized change in fluorescence $\Delta$F/F (detected at
$890\text{\,}\mathrm{nm}$) as a function of the magnetic field strength upon
$515\text{\,}\mathrm{nm}$ excitation in oxidized cells of _Rba. sphaeroides_
2.4.1., with $1\text{\,}\mathrm{mM}$ K3Fe(CN)6 added. $A_{\textrm{850--
960}}=0.35$; optical path length $2\text{\,}\mathrm{mm}$.

Singlet fission in LHCs was first observed in a series of experiments that
probed their magnetic field-dependent fluorescence 81, 80, 79. Representative
data for oxidized cells from Rhodobacter sphaeroides 2.4.1 from Ref. 79 are
reproduced in Fig. 5; similar behavior has been reported for whole cells and
isolated LHCs from several strains of purple bacteria 80, 79, 84, 81. The
shape of the magnetic field effect (MFE in Fig. 5), with an initial dip in
fluorescence as the field increases from 0 to $40\text{\,}\mathrm{mT}$, and
then a rise in fluorescence to saturation beyond $100\text{\,}\mathrm{mT}$, is
a characteristic signature of SF.

This behavior is very well described by the kinetic model of SF by Johnson and
Merrifield92, 93, 51, 94, 95, published in the 1960s and 70s. Recent work
shows 77, 78 that this low-field Merrifield-type MFE behavior can only be
observed when the inter-triplet exchange interaction $J$ is negligible, or
more precisely when $J\ll D$ 96, where $D$ is the intra-triplet dipolar zero-
field splitting parameter. In carotenoids, and indeed most organic
chromophores, $D$ is relatively small, on the order of
$4$–$10\text{\,}\mathrm{\SIUnitSymbolMicro eV}$ 97, 98. If $J$ increases
beyond $D$, the MFE has a different behavior, showing dips in fluorescence at
much higher field strengths 77, 78, 99, 100. Therefore, to determine whether
SF along a single carotenoid chain is capable of producing the measured MFEs
in LHCs, we must estimate the values of $J$ and $D$.

Before doing so we make several observations about the carotenoids involved in
SF in LHCs of purple bacteria: (1) the S0$\rightarrow$S2 absorbance spectra of
the carotenoids in light-harvesting antenna are similar to their all-trans
forms in organic solvent and depend sensitively on carotenoid conjugation
length 74, 101. A full break in conjugation along the chain would lead to a
dramatic blue-shift of the carotenoid absorption feature that is not observed.
(2) The carotenoid T1$\rightarrow$Tn excited-state absorption feature seen in
transient absorption of LHCs71, 72, 74, 75 is very similar to that seen in
aggregated carotenoids of comparable conjugation lengths forming triplets by
intermolecular SF65, 66, 67, 70. The T1$\rightarrow$Tn feature is also
sensitive to carotenoid conjugation length,102, 103, 74 and a conjugation
break along the chain would similarly lead to a blue-shift that is not
observed. (3) The dipolar $D$ and $E$ parameters of the SF-generated triplets
in LHCs from transient electron parametric resonance (EPR) spectroscopy are
similar to full-chain triplet $D$ and $E$ parameters, rather than to their
half-chain alternatives 84. These observations suggest that the conjugation
along the chain is not broken, even in the protein, and therefore that the
triplets at either end of the chain maintain orbital overlap and, presumably,
non-negligible $J$.

The exchange interaction, $J$, between triplets within a pair is equal to one
sixth of the energy difference between the pure singlet triplet-pair, denoted
1(TT), and the pure quintet, 5(TT). In addition, to first approximation, the
energy of 5(TT) is equal to twice the free triplet energy 104, 3, 56. In
carotenoids, as described above, the lowest energy singlet state (S1) is
predominantly a pure singlet 1(TT) state. Therefore, comparison between twice
the energy of a triplet on half a chain against the energy of S1 on a full
chain provides an indication of the exchange interaction.

Recent high-level density matrix renormalization group (DMRG) calculations of
the Pariser-Parr-Pople-Peierls Hamiltonian56 calculate that $2\times
E(\textrm{T}_{1})$ for a half chain is higher in energy than S1
($\approx$1(TT)) for a full chain at all conjugation lengths. This is
supported by experimentally determined energies: for diphenylexatriene with
$N=5$ conjugated double bonds, $2\times
E(\textrm{T}_{1})=3.02\pm$0.1\text{\,}\mathrm{eV}$$ 102, 105, while for
spheroidene with twice the number of double bonds ($N=10$),
$E(\textrm{S}_{1})=$1.77\text{\,}\mathrm{eV}$$ 106. This would indicate an
exchange interaction of $J=$0.2\text{\,}\mathrm{eV}$$, which is orders of
magnitude larger than the dipolar parameter $D\sim
4$–$10\text{\,}\mathrm{\SIUnitSymbolMicro eV}$ 97, 98. These energies indicate
that the triplets within 1(TT) should be strongly exchange coupled.

The triplets within a single carotenoid chain are therefore exchange coupled
($J\gg D$), even in a protein that twists the carotenoid backbone 73, as no
breaks in conjugation along the carotenoid chain have been observed (i.e. no
observable shifts in absorption spectra 74 or changes in dipolar $D$ and $E$
parameters84). Therefore, MFEs such as those reproduced in Fig. 5, that were
the initial proof of SF in purple bacteria, cannot be explained with an
intramolecular model of SF.

##  4 Conclusions

We conclude that singlet fission (SF) to produce long-lived triplets does not
occur along a single twisted carotenoid chain in the OCP and is unlikely to
occur in purple bacterial LHCs, contrary to the current notion 71, 72, 74, 73,
75. We conclude this because (1) immobilized OCPo – an uncomplicated, minimal
carotenoprotein – shows similar twisted carotenoid geometry to LHCs, but shows
no evidence of SF, and (2) the MFEs that identified SF in purple bacteria are
irreconcilable with iSF without a significant break in conjugation (which is
not observed). These findings therefore call into question the mechanism of SF
that is observed in LHCs.

##  5 Supplementary Information

###  5.1 Materials and Methods

####  5.1.1 Sample preparation

OCP containing $\sim$100% canthaxanthin (CAN) was produced from BL21(DE3)
_Escherichia coli_ (_E. coli_) using a dual-plasmid system comprised of pAC-
CANTHipi 85 and pET28a containing the gene encoding OCP (slr1963) from
_Synechocystis_ sp. PCC 6803. Briefly, $500\text{\,}\mathrm{ml}$ cultures were
grown at $37\text{\,}\mathrm{\SIUnitSymbolCelsius}$
($200\text{\,}\mathrm{rev}\text{\,}{\mathrm{min}}^{-1}$ agitation) in
$2\text{\,}\mathrm{l}$ baffled Erlenmeyer flasks using lysogeny broth (LB)
medium containing the appropriate concentrations of antibiotics. When the
optical density of the medium at $600\text{\,}\mathrm{nm}$ (OD600) had reached
a value of 0.6, protein production was induced by addition of
$0.5\text{\,}\mathrm{mM}$ isopropyl -D-1-thiogalatopyranoside and the cultures
incubated for $16\text{\,}\mathrm{h}$ at
$18\text{\,}\mathrm{\SIUnitSymbolCelsius}$.

Cells were harvested by centrifugation (4,400$\times$$g$,
$30\text{\,}\mathrm{min}$, $4\text{\,}\mathrm{\SIUnitSymbolCelsius}$) and
resuspended in binding buffer ($50\text{\,}\mathrm{mM}$ HEPES, pH 7.4,
$500\text{\,}\mathrm{mM}$ NaCl, $5\text{\,}\mathrm{mM}$ imidazole). Cells were
lysed by sonication and then centrifuged (53,000$\times$$g$,
$30\text{\,}\mathrm{min}$, $4\text{\,}\mathrm{\SIUnitSymbolCelsius}$). The
supernatant was collected and filtered
($0.22\text{\,}\mathrm{\SIUnitSymbolMicro m}$ filter pores) and applied to a
Chelating Sepharose Fast Flow column (GE Healthcare) pre-equilibrated with
NiSO4. The column was washed with binding buffer, wash buffer
($50\text{\,}\mathrm{mM}$ HEPES, pH 7.4, $500\text{\,}\mathrm{mM}$ NaCl,
$50\text{\,}\mathrm{mM}$ imidazole) and elution buffer
($50\text{\,}\mathrm{mM}$ HEPES, pH 7.4, $100\text{\,}\mathrm{mM}$ NaCl,
$400\text{\,}\mathrm{mM}$ imidazole) with the elution pooled for further
purification. The protein sample was buffer exchanged into buffer A
($50\text{\,}\mathrm{mM}$ HEPES, pH 7.4) loaded onto a Fast Flow Q-Sepharose
column (GE Healthcare) and a linear gradient of 0–$1\text{\,}\mathrm{M}$ NaCl
was applied. Fractions were analyzed by SDS-PAGE and appropriate samples taken
forward for size exclusion chromatography on a Superdex 200 Increase column
(GE Healthcare) in buffer B ($50\text{\,}\mathrm{mM}$ HEPES, pH 7.4,
$200\text{\,}\mathrm{mM}$ NaCl). Where necessary OCP samples were concentrated
using centrifugal dialysis (VivaSpin, Sartorius).

OCPo samples were fixed in sucrose-trehalose glasses in strict darkness by
mixing $100\text{\,}\mathrm{\SIUnitSymbolMicro l}$ of concentrated protein
solution (ODmax $\sim 2$) in aqueous buffer ($50\text{\,}\mathrm{mM}$ HEPES,
$200\text{\,}\mathrm{mM}$ NaCl, pH 7.4) with
$100\text{\,}\mathrm{\SIUnitSymbolMicro l}$ of a trehalose-sucrose mixture
($0.5\text{\,}\mathrm{M}$ trehalose, $0.5\text{\,}\mathrm{M}$ sucrose).
$200\text{\,}\mathrm{\SIUnitSymbolMicro l}$ of the protein-trehalose mixture
was drop-cast in the center of a quartz-coated glass substrate (S151, Ossila;
15$\times$20$\times$$1.1\text{\,}\mathrm{mm}$). The substrate was incubated
under vacuum ($-70\text{\,}\mathrm{kPa}$) with an excess of calcium sulfate
desiccant (Drierite) at room temperature for at least 48 hours. OCPr trehalose
glasses were made in an identical manner, with samples illuminated for
$30\text{\,}\mathrm{min}$ ($1600\text{\,}\mathrm{\SIUnitSymbolMicro
mol}\text{\,}\mathrm{photon}\text{\,}{\mathrm{m}}^{-2}\text{\,}{\mathrm{s}}^{-1}$)
prior to the addition of the trehalose-sucrose solution and constant weaker
illumination ($500\text{\,}\mathrm{\SIUnitSymbolMicro
mol}\text{\,}\mathrm{photon}\text{\,}{\mathrm{m}}^{-2}\text{\,}{\mathrm{s}}^{-1}$)
for the duration of the desiccation.

OCPo and OCPr samples measured with the resonance Raman setup were
additionally encapsulated with imaging spacers and a cover slip to protect the
trehalose against atmospheric rehydration. For these samples, a stack of two
imaging spacers (SecureSeal, Grace BioLabs; $9\text{\,}\mathrm{mm}$ diameter,
$0.12\text{\,}\mathrm{mm}$ thickness) were attached to the quartz-coated glass
substrate (S151, Ossila; 15$\times$20$\times$$1.1\text{\,}\mathrm{mm}$) and
$40\text{\,}\mathrm{\SIUnitSymbolMicro l}$ of the protein-trehalose mixture
drop-cast in the center of the imaging spacer. The substrate was then placed
in vacuum as above; pressure was released under a continuous flow of ultra-
pure nitrogen gas and a glass microscope cover slip (ThermoScientific;
22$\times$$22\text{\,}\mathrm{mm}$, No.1 thickness) was attached to the upper
imaging spacer.

####  5.1.2 Transient absorption spectroscopy

Short-time transient absorption spectroscopy was undertaken with a commercial
spectrometer (Helios, Ultrafast Systems) outfitted with a Ti:Sapphire seed
laser (MaiTai, Spectra Physics) providing $800\text{\,}\mathrm{nm}$ pulses
($84\text{\,}\mathrm{MHz}$, $25\text{\,}\mathrm{fs}$ nominal FWHM) and a
Ti:Sapphire chirped-pulse amplifier (Spitfire Ace PA-40) amplifying
$800\text{\,}\mathrm{nm}$ pulses ($10\text{\,}\mathrm{kHz}$,
$12\text{\,}\mathrm{W}$ average power, $40\text{\,}\mathrm{fs}$ nominal FWHM).
Tuneable pump pulses for excitation were generated by seeding a part of the
$800\text{\,}\mathrm{nm}$ beam in an optical parametric amplifier (TOPAS
Prime, Light Conversion). An optical chopper was used to modulate the pump
frequency to $5\text{\,}\mathrm{kHz}$. An intensity spectrum for the pump used
in visible-probe measurements is shown in Fig. 8. Pump beam spot sizes were
measured at the sample position with a CCD beam profiler (BC106N-VIS/M,
Thorlabs), and used in subsequent calculations to tune a
$200\text{\,}\mathrm{\SIUnitSymbolMicro J}\text{\,}{\mathrm{cm}}^{-2}$ pump
fluence. Supercontinuum probes were generated with a part of the
$800\text{\,}\mathrm{nm}$ pulse focused on either a sapphire crystal for
visible probes (450–$800\text{\,}\mathrm{nm}$) or a YAG crystal for NIR probes
(800–$1600\text{\,}\mathrm{nm}$). Pump-probe delay was controlled with a
motorized delay stage with a random stepping order. The signal was dispersed
with a grating and detected with CMOS or InGaAs sensors for visible or NIR
probes, respectively. The pump and probe polarizations were set to the magic
angle.

Surface Xplorer 4.3.0 (Ultrafast Systems) was used in processing the transient
absorption datasets. Noisy edges of the spectra were trimmed, and the
program’s bad spectra replacement procedure was applied. A background
correction (‘subtract scattered light’) was then applied using the spectra
before any apparent response from the sample. Chirp correction was applied,
choosing points at the first apparent signal for a given kinetic. Time zero is
adjusted to the time of maximum initial signal. Further processing and some
analysis was performed with original Python code.

####  5.1.3 Resonance Raman spectroscopy

Resonance Raman measurements were performed with a Renishaw inVia Raman system
(Renishaw plc., Wotton-Under-Edge, UK) in a backscattering configuration. A
$532\text{\,}\mathrm{nm}$ laser (150–$750\text{\,}\mathrm{\SIUnitSymbolMicro
W}$ power) and a 50$\times$ objective were used (NA 0.50, spot size
$\sim$$1\text{\,}\mathrm{\SIUnitSymbolMicro m}$). Acquisition times used were
in the range 5–$30\text{\,}\mathrm{s}$.

###  5.2 Figure preparation

OriginPro 9.6.0.172 (OriginLab) and home-built Python code was used to prepare
the plots.

###  5.3 Additional steady-state absorbance data

Figure 6: Backconversion of OCPr to OCPo in solution. Steady-state absorbance
spectra of OCPr in solution taken in $1\text{\,}\mathrm{min}$ intervals at
$22\text{\,}\mathrm{\SIUnitSymbolCelsius}$ in darkness. The optical path
length was $1\text{\,}\mathrm{mm}$.

###  5.4 Additional resonance Raman data

Figure 7: Resonance Raman spectra of blank trehalose glass and OCPo in
trehalose. The blank trehalose spectrum (black) is almost entirely noise,
confirming that the trehalose-sucrose glass is not contributing significant
Raman signal in any of the samples incorporating trehalose glass. OCPo in
trehalose (green) is shown as a comparison, normalized to the peak 1
intensity. The blank spectrum has been scaled to give a similar noise
magnitude at the high-wavenumber end. Both spectra are single scans (not
averaged). Measurements were undertaken at room temperature. A
$532\text{\,}\mathrm{nm}$ pump was used.

###  5.5 Additional transient absorption data

####  5.5.1 Pump spectrum

Figure 8: Intensity spectrum of the pump used in the short-time transient
absorption experiments while using the visible probe. This
$532\text{\,}\mathrm{nm}$-centered (set in WinTopas4) excitation profile was
used in taking the visible-probe data shown in main text. The
$532\text{\,}\mathrm{nm}$-centered profile used in taking the NIR-probe data
was not taken, and may have had a slightly different spectrum owing to day-to-
day variation in the tunable pump generation. The spectrum has been normalized
to the maximum intensity.

####  5.5.2 Additional note: global lifetime analysis

Global lifetime analysis on the visible-probe transient absorption data of
OCPo and OCPr was performed. This was done using the Glotaran 1.5.1 software
package(http://glotaran.org) 107, a GUI for the R package TIMP108. Data used
had already been processed with the steps outlined in Section 5.1.2; in
particular, a chirp correction had already been applied, so that a term to
account for chirp did not need to be included in the fitting. Noisy regions in
the data due to pump scatter were excluded for all times to ensure a good fit
of the rest of the data. Noisy red and blue ends in the data associated with
tails of the probe were also excluded, so that the fitted wavelengths were
$430\text{\,}\mathrm{nm}$ to $780\text{\,}\mathrm{nm}$. The fitting was
weighted favourably at later delay times for good fits of any long-lived
features; Table 1 shows the weighting applied. Due to the strong coherent
artifact feature in the first $0.5\text{\,}\mathrm{ps}$, only data beyond that
time was fitted. Thus, in the model, terms to account for the coherent
artifact and S2 states were not included. This left a relatively simple fitted
model of a number of wavelength-dependent decay-associated difference spectra
(DADS) decaying exponentially in parallel.

Time range ($\text{\,}\mathrm{ps}$) |  Weighting
---|---
0.5 – 10 |  1
10 – 20 |  2
20 – 30 |  3
30 – 35 |  4
$>$35 |  5
Table 1: Weightings applied to time-ranges of the visible
$\text{\,}\mathrm{ps}$ transient absorption data for the global lifetime
analysis. Note that only data $>$$0.5\text{\,}\mathrm{ps}$ was fitted, and
that the maximum time delay in these experiments was
$\sim$$40\text{\,}\mathrm{ps}$.

Global lifetime analysis of the OCP data does not indicate any significant
population of longer-lived features. 2-component global lifetime analysis of
the CAN-binding OCPo and OCPr data are shown in Fig. 9 and 10, respectively.
Fitting a 2-component parallel decay model in an artifact-free region of the
visible-probe data beyond the initial coherent artifact and S2-associated
response gives two decay-associated difference spectra (DADS) for both the
OCPo data and OCPr data, with the longer time-constant DADS relatively weaker
and blueshifted in both cases. Both components are likely associated with
mixed S1 decay, internal vibrational redistribution, and vibrational
cooling.60 A single component is not sufficient to adequately fit the region
of the data, and a fitting a third component gives results with spurious DADS
profiles.

Figure 9: Results of global lifetime analysis with a 2-component parallel
model on transient absorption data of CAN-binding OCPo in trehalose with peak
pump wavelength $532\text{\,}\mathrm{nm}$ and a visible probe: DADS (top) and
residuals (bottom). Only the wavelength range 430–$780\text{\,}\mathrm{nm}$
and times $>$$0.5\text{\,}\mathrm{ps}$ were fitted, and noisy data from
520.5–$549.5\text{\,}\mathrm{nm}$ due to significant pump scatter was excluded
from the fit. DADS lifetimes are specified in the legend.
$\textrm{Residuals}=\textrm{Data}-\textrm{Fit}$. See text for further details.
Figure 10: Results of global lifetime analysis with a 2-component parallel
model on transient absorption data of CAN-binding OCPr in trehalose with peak
pump wavelength $532\text{\,}\mathrm{nm}$ and a visible probe: DADS (top) and
residuals (bottom). Only the wavelength range 430–$780\text{\,}\mathrm{nm}$
and times $>$$0.5\text{\,}\mathrm{ps}$ were fitted, and noisy data from
522–$548\text{\,}\mathrm{nm}$ due to significant pump scatter was excluded
from the fit. DADS lifetimes are specified in the legend; multiplications
refer to scalings applied to the DADS.
$\textrm{Residuals}=\textrm{Data}-\textrm{Fit}$. See text for further details.

We note that sample degradation (caused the
$\sim$$200\text{\,}\mathrm{\SIUnitSymbolMicro J}\text{\,}{\mathrm{cm}}^{-2}$
pump fluence) likely affects the fitted time constants and DADS profiles, and
that the maximum time delay used was about $40\text{\,}\mathrm{ps}$.

The authors thank James D. Shipp, Sayantan Bhattacharya and David G. Bossanyi
for assistance with transient absorption measurements.

Funding: G.A.S. and C.N.H. acknowledge ERC Synergy Grant 854126. J.P.P. thanks
the EPSRC for support through a Doctoral Training Partnership Scholarship
(EP/R513313/1). The authors thank the EPSRC for a Capital Equipment Award
(EP/L022613/1 and EP/R042802/1) which funded the Lord Porter Laser facility
used in this study. J.C., C.N.H, G.A.S. and S.W. thank the EPSRC for funding
through EP/S002103/1. J.C. and S.W. also thank the EPSRC for funding through
EP/N014022/1. M.S.P. and M.P.J. were supported by Leverhulme Trust award
RPG-2019-045. A.H. acknowledges The Royal Society (award URF\R1\191548).
H.K.H.L. and W.C.T. acknowledge the SPECIFIC Innovation and Knowledge Centre
(EP/N020863/1) grant for providing financial support.

Author contributions: G.A.S. conceived the study. G.A.S., J.P.P., S.W. and
J.C. designed the experiments. G.A.S., M.S.P. and A.H. prepared protein
samples under the supervision of M.P.J. and C.N.H. Steady-state measurements
were performed by G.A.S. Resonance Raman measurements were performed by
H.K.H.L. under the supervision of W.C.T. Transient absorption was conducted by
J.P.P. and S.W. within the Lord Porter Laser, with D.C. providing facility
management. J.P.P. and G.A.S. analyzed the data. J.P.P., G.A.S. and J.C. wrote
the manuscript and prepared the figures with input from all authors.

  * •

Supplementary information (SI): Canthaxanthin-binding OCP production, OCPo and
OCPr in sugar glasses preparation, spectroscopic setups, and data analysis
procedures are detailed. A figure showing back-conversion of solution OCPr to
OCPo in the dark is included. Figures showing a short-time transient
absorption pump spectrum and a resonance Raman spectrum of blank trehalose are
included. The results of global lifetime analysis on the transient absorption
data is detailed.

  * •

Data will be available on Sheffield University’s repository, ORDA, once the
paper has been accepted for publication.

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