11institutetext: Kadina E. Johnston 22institutetext: California Institute of
Technology 33institutetext: Clara Fannjiang 44institutetext: University of
California, Berkeley 55institutetext: Bruce J. Wittmann 66institutetext: work
done while at California Institute of Technology, now at Microsoft
77institutetext: Brian L. Hie 88institutetext: Stanford University
99institutetext: Kevin K. Yang 1010institutetext: Microsoft Research New
England 1111institutetext: Zachary Wu 1212institutetext: Correspondence:
<EMAIL_ADDRESS>now at DeepMind 1313institutetext: *All authors
contributed equally

# Machine Learning for Protein Engineering

Kadina E. Johnston  Clara Fannjiang  Bruce J. Wittmann  Brian L. Hie  Kevin K.
Yang  and Zachary Wu

###### Abstract

Directed evolution of proteins has been the most effective method for protein
engineering. However, a new paradigm is emerging, fusing the library
generation and screening approaches of traditional directed evolution with
computation through the training of machine learning models on protein
sequence fitness data. This chapter highlights successful applications of
machine learning to protein engineering and directed evolution, organized by
the improvements that have been made with respect to each step of the directed
evolution cycle. Additionally, we provide an outlook for the future based on
the current direction of the field, namely in the development of calibrated
models and in incorporating other modalities, such as protein structure.

This article has been accepted as an upcoming book chapter published by
Springer Nature. It appears as in its original submission on February 28,
2022.

Proteins are the molecular drivers for many of the processes necessary for
life, performing functions such as binding small molecules, stabilizing other
proteins, or catalyzing vital reactions. They are synthesized as linear
sequences of individual building blocks called amino acids, of which there are
twenty canonical types; these sequences fold into complex and dynamic three-
dimensional structures to accomplish their functions. These sequences undergo
mutation and selection based on the hosts’ abilities to reproduce.

Protein engineers often optimize proteins through a process known as directed
evolution. Directed evolution adapts nature’s evolutionary process to enable
the rapid improvement of proteins for human-desired functions arnold1998design
(1, 2). Specifically, directed evolution iterates between modifying proteins
at the sequence level and identifying protein sequences with improved level of
function. This process has yielded many impactful engineered proteins, ranging
from antibodies for combating disease to enzymes capable of catalyzing non-
natural reactions, and its success has been recognized by the 2018 Nobel Prize
in Chemistry.

Fundamentally, directed evolution is an optimization process for protein
sequences. As such, many recent advances in machine learning have been
successful in improving directed evolution’s ability to identify better
proteins. In this chapter, we review the core concepts that have enabled
successful integration of machine learning in protein engineering by
interpreting the process through the directed evolution cycle. We begin with a
brief background on directed evolution, outlining the steps involved and
casting them in the context of navigating protein fitness landscapes. We then
highlight recent developments in machine learning’s contribution to each of
these steps as well as the experimental constraints it must operate within,
before ending on an outlook for the field.

##  1 Background on Directed Evolution

Directed evolution is an adaption of natural (and artificial) selection to the
modern laboratory. First, consider a simplified view of how a new protein or
function may arise naturally. In nature, evolution occurs within populations
and is largely driven by competition to survive, grow, and reproduce.
Therefore, an attribute which confers an advantage for any of these processes
is selected for, enabling an organism to out-compete the organisms around it.
The advantage could come from a mutation in a protein sequence that imparts a
low level of activity for a new, beneficial function, making the organism and
its offspring more successful. Thus, this protein sequence becomes more common
as well. Through many iterations of this process, that protein sequence and
its function could be further optimized. This process is similar to many
engineering strategies, but contains notable distinctions for proteins,
discussed in the following Sections 1.1 and 1.1.

###  1.1 Directed Evolution Theory

The number of possible protein sequences is immense, presenting a significant
challenge to any protein engineering strategy. A typical protein is several
hundred amino acids long, and at each position there are twenty canonical
amino acids possible. This results in $20^{300}$ ($10^{390}$) possible
sequences, which is around $10^{300}$ times more than the total number of
atoms in the universe. There will never be enough resources to synthesize all
of these sequences let alone screen them.

Interestingly, this does not mean that finding functional proteins or
improving protein fitness is a hopeless endeavor. Maynard Smith made the
critical observation that for natural selection to be possible, functional
protein sequences must neighbor other functional sequences in protein space,
implying that functional proteins exist clustered together within a vast sea
of non-functional ones maynard1970 (3). Therefore, rather than throwing
metaphorical darts at this astronomical space and hoping for a hit, protein
engineers can begin with a small level of activity for their function of
interest and leverage methods for local exploration to improve it.

#### Protein fitness landscapes and epistasis

Due to the iterative nature of the optimization cycle that is directed
evolution, it is commonly conceptualized as a greedy, uphill walk on a protein
fitness landscape towards a fitness peak romero2009exploring (2). Each round
of mutagenesis and screening searches through the local landscape, typically
sampling only a few mutations away from the current position in sequence
space. When a hit is identified, a step up the fitness peak is taken and the
local search is repeated, with the entire process continuing until the fitness
is satisfactory or a peak is reached. Importantly, no downward steps into
valleys of the fitness landscape are typically allowed in directed evolution.

Fitness landscapes are often visualized as smooth, easy-to-navigate surfaces,
but in reality they are discrete, high-dimensional spaces, with many of the
dimensions being quite rugged. This ruggedness is due to a phenomenon in
biology called epistasis, where mutational effects are dependent on higher
order interactions rather than their individual contributions
starr2016epistasis (4). Epistasis arises most commonly from direct structural
contacts, but interactions between residues can also be modulated by ligands,
substrates, allostery, cofactors, or conformational dynamics
miton2021epistasis (5). As a result, it is often reasonable to assume that
distant mutations are independent, but there are important cases where this
assumption breaks down and epistasis must be considered.

It is also important to consider the prerequisite protein properties that must
be satisfied to take fitness measurements, such as expression, stability, and
substrate binding. This means that fitness landscapes are a result of some
combination of these factors, and changes in any of them can modulate fitness
or cause epistasis. For example, romero2009exploring (2) outline how epistasis
can arise from a protein stability threshold, where beneficial, but
destabilizing mutations combine to completely ablate activity
romero2009exploring (2). The protein fitness landscape is a useful analogy for
both intrinsic proteins as well as the methods in this chapter, and we come
back to this concept often.

###  1.2 Chapter Scope

In this chapter, we focus on methods employing machine learning for the
directed evolution of proteins. However, there are many other aspects of
protein modeling that can be explored in biology ching2018opportunities (6)
and chemistry coley2019autonomous (7). Additionally, proteins do not function
in a vacuum. Other molecules, such as nucleotides that encode our genomes
zou2019primer (8, 9) and small molecules vamathevan2019applications (10), can
have profound effects on proteins’ biological functions.

Another view of understanding proteins is through their three-dimensional
structures gao2020deep (11). Protein dynamics noe2020machine (12) and
structure prediction alquraishi2021machine (13) are two rapidly growing
fields, but the connection to protein function is still opaque
greslehner2018molecular (14). Nevertheless, the goal of protein structure-
based design ovchinnikov2021structure (15) is to replace much of the work
required for protein engineering, instead generating optimized proteins in a
single step. However, current best efforts from this approach still benefit
from subsequent rounds of directed evolution. In the next section, we describe
how machine learning methods can improve each step in directed evolution.

###  1.3 Protein engineering and directed evolution

In this chapter, we view the protein engineering process through the directed
evolution cycle, which adapts natural and artificial selection to the modern
laboratory. In this process, the desired properties of engineered proteins are
directly queried (assayed) by man-made techniques, instead of interpreted
through survival and reproduction (as in natural selection). This allows the
engineer to rapidly evolve proteins for desired properties (such as
thermostability or expression) and functions (such as binding or enzymatic
activity).

The directed evolution cycle (Figure 1 can be segmented into three basic
steps, with two additional steps in cases where protein engineering is driven
by machine learning. In Section 2.3 of this chapter we elaborate on the
experimental constraints and ML considerations of these steps, and in Section
2, we highlight examples where machine learning has enabled advances in each
of the following steps:

First, a protein with a measurable amount of the property of interest must be
identified. Directed evolution relies on accurate physical interrogation of
this scalar value, termed fitness, and a measurable starting point is required
to begin this process. Many protein engineering projects fail at this stage,
as the most biochemical ingenuity is required to identify a protein that is
able to accomplish often novel goals such as breaking down polyethylene
terephthalate (in man-made plastics austin2018characterization (16)) or to
selectively modify DNA (for targeted gene therapy waehler2007engineering
(17)).

Second, the protein sequence is randomized to generate a pool of variants,
often called a library. In nature, this process typically occurs through
random mutagenesis, where random mutations in DNA correspond to random changes
in the protein sequence, or recombination of existing protein fragments. In
the laboratory setting, current experimental techniques give protein engineers
more freedom in selecting which sequences to test. One option lies in biasing
the randomness of these mutations, but rapidly decreasing DNA synthesis costs
also enable the generation of any specific sequence the engineer designs, such
as chimeras (recombined fragments of existing proteins)
smith2013chimeragenesis (18, 19) or sequences generated by language models
madani2021deep (20, 21). While DNA costs are currently dropping, this step can
still be the limiting cost in testing more diverse protein sequences.

Third, the library is tested for the desired property. This step captures a
wide range of assays that have been developed to probe biomolecules. Some
examples of approaches capable of generating the largest amounts of data
(high-throughput assays), are based on protein fluorescence or binding, and
reach hundreds of thousands of labels per month. However, other properties
such as enzymatic activity for generating small molecule substrates are
measured in much lower throughput, typically on the scale of hundreds per
month. This step often limits the amount of data labels the machine learning
modeler can expect to obtain.

In traditional directed evolution, the top $k$ variants (often $k=1$) are fed
back into the second step for further improvement. For methods where directed
evolution is further enabled by machine learning, two other steps may follow.

In these machine-learning-assisted approaches, the next step is to fit models
to the relationship between proteins and their fitness labels. A wide variety
of approaches are available to the machine learning practitioner here, and
there are multiple sources of prior knowledge that can be leveraged for
proteins. One example is the rich historical record of protein sequences,
which can be obtained from sequence databases such as UniRef suzek2007uniref
(22, 23). From such a database, sets of evolutionarily-related sequences
(homologs) can be obtained and aligned in Multiple Sequence Alignments (MSAs),
which can be used as priors on viable sequences. However, while this history
represents sequences retained in nature, it does not necessarily represent the
distribution of allowed sequences for a specific protein on an engineered
task.

Finally, these models are used to select optimal proteins for experimental
validation. Again, a variety of approaches have been employed in this step
such as gradient-based, RL-inspired, and active learning methods (Section
2.5). The sampling strategy often depends on the modeling approach used in the
previous step. Additionally, this step is similar to the second in that both
may be constrained by current molecular biology techniques. These constraints
are often enforced manually, but can be encoded in the design process as well.
From here, directed evolution re-enters the third step, and the cycle is
repeated until the optimum is reached or design criteria are satisfied.

The process of directed evolution with machine learning is depicted in Figure
1, which interprets each step in the analogy of climbing protein fitness
landscapes.

Figure 1: Protein engineering steps viewed as steps in exploring a 1D fitness
landscape. In each plot, the protein fitness (scalar measurement of a function
or property), is on the y-axis, and the protein sequence is on the x-axis. In
(1), a protein with measurable function is identified. In (2), an initial
library of protein variants is built. In (3), the library is tested (assayed)
for desired property. The next steps are additional for protein engineering
methods guided by machine learning, including (4) fitting the models and (5)
selecting the next library based on these models. Finally, the process is
repeated until a maximum is reached, or the desired fitness satisfies a
desired threshold.

###  1.4 Evolutionary Optimization Methods

Evolution is the core optimization process in biology. Naturally, it has
inspired other optimization algorithms, particularly in the gradient-free or
black box optimization settings. Here, we briefly discuss the key similarities
and distinctions between natural evolution, directed evolution, and
evolutionary algorithms.

Natural evolution occurs on the level of organisms interacting with their
environment. Mutations fixed on the individual protein level may not have a
noticeable effect on fitness at the organism level, defined as its ability to
survive and propagate its genes. Additionally, the objective function of
natural evolution is a competition for scarce resources in constantly changing
environments. Diverse solutions are often implicitly rewarded for their
ability to access new ecosystems. However, for the protein engineer with the
goal of optimizing individual molecules, there is not a clear mapping from the
evolutionary history of similar sequences to fitness on the protein level,
defined as how well a protein achieves its target function.

Evolution strategies at the protein level are the subject of this review. Two
key differences distinguish directed evolution of proteins from natural
evolution. In traditional directed evolution campaigns, only a single parent
protein sequence is used to start each round of subsequent evolution, in
contrast to nature which evolves with populations. Recently, approaches where
directed evolution is further guided by machine learning captures information
from all explored variants in trained, surrogate models of the protein fitness
landscape yang2019machine (24), which can also explicitly reward diverse
solutions linder2020generative (25).

Additionally, fitness is more well-defined in directed evolution than in
natural evolution, where fitness is influenced by a complex set of factors and
can change based on environment. For example, the fluorescence of green
fluorescence protein may be directly measured, and variants may be evolved for
brighter fluorescence or alternative emission wavelengths. While this is
largely an advantage, it is important to remember that the process of sample
preparation can also affect the measurement and therefore unintentionally
modify the definition of “fitness” being optimized. For example, the measured
binding efficiency of a protein can also depend on the purification and
expression method used to obtain it. In other words, a protein must pass both
purification and expression to bind effectively to a target to be considered
“fit” in this case. This concept is captured in the directed evolution adage:
”You get what you screen for” arnold1998design (1).

Evolutionary algorithms are a class of optimization algorithms that are
directly inspired by natural evolution, and a subset of these methods have
direct analogs in directed evolution methods back1996evolutionary (26, 27).
For example, genetic algorithms also define fitness as the value of the
objective function to be optimized. During optimization, a population of
individuals (variants) is evaluated against this fitness function, and the
surviving population of solutions is allowed to recombine and mutate for the
next generation of individuals. While the details of genetic selection and
mutation differs from that of natural evolution, the core principles governing
both processes enable successful optimization, often with diverse final
solutions. Additionally, as these methods are computational and act on digital
fitness landscapes, digital evolution is more parallelizable and can be much
easier to study. However, these strategies are also subject to the same
pitfalls as directed evolution methods. Interestingly, a common failure mode
shared with directed evolution is in specification of the fitness landscape:
computational agents often exploit bugs in the modeled physical environments
to achieve the metrics lehman2020surprising (28). Evolutionary algorithms can
also use explicit probability distributions to generate proposal sequences,
which are closely related to Monte Carlo Expectation Maximization methods
brookes2020view (29).

##  2 ML Contributes to many steps in directed evolution

The directed evolution cycle powered by machine learning methods can be
segmented into five steps, as described previously. In this section, we
summarize important contributions machine learning has made, and promises to
make, to improve over the directed evolution baseline over each of its steps.

###  2.1 Identifying starting variants

The first consideration in a directed evolution experiment is selecting the
protein variant to evolve, which can be a nontrivial task. In the most extreme
setting, there may be no known proteins that perform the desired function; a
more common but related setting is when the desired output of the directed
evolution experiment needs to be substantially different from all known
proteins due to considerations of scientific novelty or intellectual property.

In such settings, machine learning can be a useful tool to help identify a
sufficiently novel starting variant, typically with weak or suboptimal
fitness, that can subsequently be given to a traditional or machine-learning-
guided directed evolution pipeline. The two main approaches for doing so are
(1) to screen a large and diverse collection of proteins for any that have a
nonzero fitness value shin2021protein (21, 30, 20) or (2) to de-novo design
the initial, functional protein cao2021robust (31, 32, 33). Machine learning
has contributed to both approaches, particularly for the design of protein-
protein binding.

As an example of the first approach, shin2021protein (21) use an
autoregressive language model, trained on approximately 1.2 million natural
llama nanobody sequences, to generate a nanobody library that is screened to
potentially identify novel binders to a target protein shin2021protein (21).
The generative model enables improved sequence diversity over previous
synthetic libraries, enabling the authors to identify new proteins with high
binding affinity using an efficient set of approximately $10^{5}$ generated
sequences, which is 1000-fold smaller than other libraries.

As an example of the second approach, cao2021robust (31) de-novo design
miniproteins that bind to a known, target structure cao2021robust (31). They
use a multistep computational pipeline, which includes supervised machine
learning models that guide physics-based approaches to protein design, to
engineer de-novo binders with some affinity for a target protein. These
initial binders are then improved via traditional directed evolution to
produce the final binder.

While we have mostly considered cases in which the starting variant is unknown
or must be substantially different from existing proteins, this is not a
constraint in many other settings where a good, functional variant exists and
the goal is simply to improve fitness. Even in such settings, however,
directly evolving the best-known variant may not be the most effective
strategy. A known, high-fitness variant may be in a local optimum of the
fitness landscape such that the evolutionary path to the unknown global
optimum (or the highest-fitness variant) requires crossing a fitness valley
(where some intermediate mutations along the path decrease fitness).

Therefore, it may be desirable to begin evolution at a lower-fitness variant
from which multiple fitness peaks (both locally- and globally-optimal) are
accessible via a greedy uphill walk strategy typical in protein engineering.
Engineering a more evolvable starting variant, even at some fitness cost, is
currently an open question trudeau2018protein (34) for which machine learning
could play an important role. Proteins with high intrinsic stability are
thought to be more evolvable bloom2006protein (35), and many machine learning
models have been developed that either directly (via supervision) or
indirectly (as an emergent property of an unsupervised model) predict
stability cao2019deepddg (36, 37, 38, 39). Moreover, we note that directed
evolution that begins at a local optimum could still cross fitness valleys via
more complex, model-guided strategies beyond greedy exploration, which we
review in the following sections.

###  2.2 Building initial library

The data used to train a machine learning model determines what it learns and,
by extension, in what situations it can be used to make effective predictions.
For protein engineering, this means that the design of the library that will
provide training data is critical to the eventual effectiveness of the trained
model in finding improved sequences.

Machine learning models tend to be more effective at interpolation than
extrapolation and so will typically perform best when used to make predictions
in the same domain as the data used to train them. In general, for a given
design space of allowed proteins, this translates to collecting maximally
diverse training data that best covers that space. For proteins, this means
that training data with maximal sequence diversity will be most informative
for modeling an underlying true fitness landscape: 111Strictly speaking,
training data that is maximizes diversity in the encoded sequences will be the
most informative the more diverse the training sequences are, the more of the
design space that is covered by the training data and the less a model must
extrapolate to previously unseen regions of sequence space. For example,
romero2013navigating (40), bedbrook2017machine (41), and greenhalgh2021machine
(42) maximize the information entropy of the initial set of sequences when
engineering P450s, channelrhodopsins, and acyl-ACP reductase, respectively
romero2013navigating (40, 41, 42).

Randomly collecting sequences from a fixed design space (e.g., a combinatorial
space defined by a given number of positions in a protein) can thus be a
valuable strategy for training data collection, as this will on average result
in the collection of highly diverse sequences. Random collection of training
data is also an attractive approach from an applications point of view, as
fully random libraries can be easily constructed in a multiplexed fashion
using degenerate oligomers or strategies like error-prone Polymerase Chain
Reaction (epPCR) kille2013reducing (43) (see Section 2.3 for more
information), and this strategy has been combined with machine learning to
engineer halohydrin dehalogenase fox2007improving (44), fluorescent proteins
saito2018machine (45, 46), and an adenovirus capsid protein bryant2021deep
(47).

While building a perfect map of a fitness landscape would be ideal for model-
guided engineering, it is not always feasible given our limited ability to
collect experimental data. More complex fitness landscapes considering larger
sections of sequence space require more data to model and a small amount of
randomly selected training data may be spread too thinly across the design
space to build a comprehensive map brookes2022sparsity (48). The goal of ML-
assisted protein engineering is not to comprehensively map fitness landscapes,
but to use ML to guide exploration of fitness landscapes to reach higher-
fitness protein variants, as discussed further in Section 2.4. As a result, if
training data is expensive to collect, then it can be advantageous to build
focused initial libraries that are biased toward protein variants believed a
priori to be higher in fitness. It is more important to be able to identify
the highest-fitness variants from the set of high-fitness variants than the
lowest-fitness variants from the set of low-fitness variants, and so the idea
of this strategy is to model (potentially) higher-fitness regions of the
protein fitness landscape at higher resolution and lower-fitness regions of
the protein fitness landscape at lower resolution.

Focused libraries can be particularly helpful when navigating hole-filled
protein fitness landscapes wittmann2021informed (49). As more mutations are
made to a protein, the probability that it retains function decreases
exponentially bloom2006protein (35), and so fitness landscapes consisting of
combinations of mutations at multiple positions (combinatorial landscapes)
tend to be dominated by proteins with zero or extremely low fitness. These
variants are commonly referred to as holes in the fitness landscape as they
only provide information on which mutations destroy protein fitness. These
variants are conceptually distinct from fitness valleys mentioned previously,
as they do not provide information about the extent to which a mutation
impacts protein fitness, which is valuable information for training the
regression models typically employed for ML-assisted protein engineering.
wittmann2021informed (49) demonstrated that by using so-called zero-shot
predictor—models or strategies that can predict protein fitness prior to
collection of new experimental data—focused training sets can be constructed
that minimize inclusion of holes in training data wittmann2021informed (49).
Through simulation on a complex, hole-filled, combinatorial fitness landscape,
they showed that models trained with these focused training sets tended to be
far more effective at identifying the highest-fitness variants than models
trained with data drawn randomly from the landscape.

The prior information needed to construct focused libraries can come from many
sources. For instance, prediction of protein thermal stability
wittmann2021informed (49), use of meta-predictors of protein fitness
gray2018quantitative (50), or strategies based on evolutionary conservation
can all be used to make zero-shot predictions of protein fitness
liao2007engineering (51, 52, 53, 54, 38). The exact strategy that will be most
effective, however, will vary depending on the fitness and protein being
optimized. Take, for for instance, the zero-shot strategies that rely on
sequence conservation. Such strategies assume that evolutionary fitness aligns
with whatever fitness is being predicted; that is, they assume that mutant
proteins more closely resembling known protein sequences (found in databases
of protein sequence such as UniProt uniprot2021uniprot (55)) are more likely
to be functional than others. Should this assumption not hold (for instance,
the fitness of a protein being engineered for a new-to-nature activity may not
correlate well with evolutionary fitness), or if there are simply not enough
homologous protein sequences available to build an effective sequence-based
zero-shot prediction model, then the zero-shot predictions are likely to be
inaccurate. Inaccurate zero-shot predictions are unhelpful for focused library
design: indeed, they may even be detrimental to effective learning by focusing
training data collection on regions of the fitness landscape dominated by
holes.

Ultimately, the decision between random library design and focused library
design will depend on a number of factors. If the fitness landscape to be
explored is expected to be minimally complex with few holes and large amounts
of training data can be easily collected for it, then random library design is
a reasonable approach, as the library itself will be simple to construct, and
training data gathered from it will be sufficient to build a comprehensive map
of the fitness landscape. If the fitness landscape to be explored is complex,
full of holes, and it is challenging to gather training data for it, then
focused libraries may be a viable option, particularly if high-confidence
zero-shot predictions can be made for the fitness landscape. Such libraries
may be more challenging to construct in the laboratory, but they will likely
result in more efficient machine learning-guided engineering.

###  2.3 Experimental considerations for applying machine learning to protein
engineering in vitro

The process of directed evolution is relatively simple in theory and can also
be so in practice. However, the process must operate within current
experimental constraints imposed by a variety of factors, including available
technology, cost, and time. Current laboratory methods for directed evolution
have been reviewed extensively packer2015methods (56, 57), so we focus here on
facets that can impact the usefulness of machine learning methods. As alluded
to in the previous section, there is often a trade-off between lab-work
complexity or cost and efficiency of ML-guided engineering, and we discuss
these trade-offs below.

Notably, both the input protein sequences and the output experimental labels
both depend on physical constraints. In the first section, we discuss
different approaches to generating protein libraries. In the second section,
we discuss varying experimental methods (assays) for obtaining protein labels.
Finally, in the third section we discuss methods for pairing protein sequence
and function information.

#### Methods for library generation

Random mutagenesis is one of the most straightforward methods for creating
initial sequence diversity. Errors are introduced throughout an initial DNA
sequence by either randomly damaging DNA or by introducing errors during
replication such as via epPCR, a process that introduces mutations randomly by
increasing the error rate of the copying enzyme, the polymerase. However, it
is important to note that errors introduced via “random” mutagenesis are not
perfectly random in two major ways. First, mutations from one nucleotide to
another do not occur at identical frequencies, so the original base can
dictate what mutations are most likely at a given position
vanhercke2005reducing (58). Second, the genetic code is redundant, with the 20
canonical amino acids encoded by 61, three-nucleotide codons. Although it is
possible for multiple nucleotides within a single codon to mutate
simultaneously, this is rare, and generally only one nucleotide mutation
occurs per codon during random mutagenesis, limiting the mutations available
at the amino acid level. Importantly for ML methods hoping to build upon
random mutagenesis strategies, there are very few parameters that can be tuned
in this process—error rate can be modulated to shift the Poisson distribution
of number of mutations, different regions of the sequence of interest can be
targeted, and bias towards particular nucleotide swaps can be imposed. In
comparison to other mutagenesis methods, the protein engineer has much less
control over the generated library.

Targeted mutagenesis, of which the focused mutagenesis discussed in the
previous section is a subset, is an alternative to random mutagenesis that
affords more control over the final library. Unlike random mutagenesis,
targeted mutagenesis typically assumes that either (1) specific sites in the
protein sequence are important to mutate or (2) it is important to be able to
access all amino acids at a given position. Site selection usually requires
structural knowledge or other biochemical insights into the protein system. To
perform targeted mutagenesis, degenerate oligos—mixtures of individual primers
that together encode a distribution of mutations—are used to induce randomness
at a specific codon/amino acid position or positions. Unlike random
mutagenesis, multiple mutations can now be made within a single codon,
allowing access to any amino acid if desired. The pool of degenerate oligos
can also be modified to achieve a relatively even distribution across all
twenty canonical amino acids kille2013reducing (43) or to achieve a different
distribution of interest weinstein2021optimal (59). Targeted mutagenesis can
also be performed simultaneously at multiple sites, enabling the exploration
of more complex, epistatic landscapes. By tuning the distribution of mutations
encoded in such simultaneous site-saturation libraries, focused libraries such
as those described in the previous section can be created. Importantly, as the
desired amino acid distribution becomes more complex and more sites are
mutated simultaneously, both difficulty of laboratory implementation and the
cost of oligos can become untenable. There are a number of computational
strategies available that can assist with such complex library designs;
however, all are fundamentally limited by the set of amino acid distributions
made possible by the genetic code shimko2020decode (60, 61, 59). Therefore, ML
methods relying on targeted mutagenesis for either training set design or
evaluation of predicted designs must keep in mind these constraints.

A final strategy for library generation is recombination, which pieces
together, or “recombines”, initial diversity into different arrangements to
create new diversity. Recombination is a very broad category of diversity
generation, and due to the array of recombination strategies available, we do
not explain them here, but they are well reviewed by packer2015methods (56)
packer2015methods (56). The choice of recombination strategy typically relies
on the type of initial diversity on hand. Such diversity could be comprised of
a set of functional, homologous proteins, the top variants from a random
mutagenesis library, or the top variants from a targeted mutagenesis library.
One recombinatorial approach of note is the use of SCHEMA libraries
voigt2002protein (62), where fragments of multiple parent proteins are
swapped, and which has been successfully engineered with machine learning
methods romero2013navigating (40, 63). Importantly, some recombination
strategies are quite experimentally straightforward and a single round of
recombination on top variants can yield much higher improvements in fitness
than a single round of random or targeted mutagenesis. Therefore, when
comparing ML methods for protein engineering to lab-only methods, using a wet-
lab recombination strategy as a baseline is highly recommended when possible.

There is promise to disrupt these traditional paradigms of library generation
with the advent of cheap gene synthesis technologies kosuri2014DNAsynth (64).
Rather than starting with an initial sequence or pool of sequences and
building diversity with mutagenesis or recombination, a set of desired
sequences can be synthesized directly for under $100 per gene block. Ordering
pools of sequences with targeted or random mutations is also possible, and
synthesis technologies can impart more control over the final distribution. As
these DNA synthesis technologies improve, ML methods for protein engineering
can shake the constraints imposed by existing library construction
technologies, allowing researchers to design libraries with specific
distributions of mutations.

#### Assaying protein fitness

With proteins performing such a wide variety of different functions, the
protein engineering community has had to devise countless different assays to
measure them all. As such, assays for protein function vary widely in both
accuracy and throughput, with ranges from tens to millions of protein
variants. This amount is typically dependent on the project definition of
fitness. For instance, if the measurement of fitness can be directly coupled
to a sequencing assay (as in deep mutational scanning), then large datasets
($10^{5}$ to $10^{6}$) can be rapidly created. Many assays for fitness,
however, are limited to comparatively low-throughput chromatographic methods
(e.g., HPLC, LCMS, GCMS, etc.), which rely on physical separation of a mixture
through a column, producing smaller datasets ($10^{1}$ to $10^{4}$). The
amount of data available for training a model will dictate how much of
sequence space can be explored and how accurate the predictions of fitness for
new sequences will be. At the same time, however, the goal of ML in protein
engineering is to reduce the burden of experimental screening and expedite the
process, so a balance must be found between the amount of data collected and
the accuracy of predictions of models trained on that data.

Additionally, one should consider where an ML method for protein engineering
may have the biggest impact on efficiency, cost, and time. Protein functions
that can be assayed in high-throughput provide more data for training
downstream ML models; however, applying an ML-based engineering method to such
a function may not impart as much benefit as it would being applied to
engineering a function with a low-throughput assay. Therefore, many recent
efforts for building ML methods for protein engineering have focused on the
low-N regime, where few samples are used for training wittmann2021informed
(49, 65, 66, 67, 63, 68).

Final considerations, for both the protein engineer choosing an assay and the
ML scientist choosing a dataset, are the assay noise and bias. As interest has
grown in applying ML to protein engineering, method developers have sought out
sequence-fitness datasets with which to benchmark their approaches. This has
typically resulted in the pursuit of large datasets built from high-throughput
screening methods, such as deep mutational scanning (DMS) fowler2014deep (69)
and fluorescence-activated cell sorting (FACS) bonner1972FACS (70), but
inherent biases in such protein fitness datasets are left under-discussed. DMS
fitness measurements can be heavily impacted by the input library and can
result in highly non-uniform error across a dataset rubin2017statistical (71).
FACS-based assays can result in bias due to binning that occurs when gates are
chosen for sorting cells trippe2022randomized (72). Note that all fitness
assays have their own noise and bias which should be thoroughly considered
when developing an ML method on a particular dataset.

#### Pairing sequences to fitness data through sequencing

Uncommon in the broader ML discipline, datasets that result from typical
protein engineering campaigns are label-rich and feature-poor, with many
assayed fitnesses and relatively few variant sequences. Because only function
is being optimized in directed evolution, this process does not technically
require sequencing. Indeed, only the top few variants from each round are
sequenced for validation in practice, and sequencing all of the variants is
considered an unnecessary, unjustifiable expense. Thus, the remainder of the
unimproved variants are discarded without sequencing, resulting in fitness
labels that are rendered useless. Notably, this is not true for deep
mutational scanning libraries, where fitness is directly coupled to
sequencing, which is why many ML approaches are currently developed on these
types of datasets wu2019combination (67, 49, 73, 74, 75).

Variant sequencing, especially for low-throughput assays, has traditionally
been done via Sanger sequencing, but this method scales linearly with the
number of variants, costing a few dollars per sequence. Depending on the assay
used for evaluating protein fitness, sequencing could easily become the most
expensive part of a protein engineering campaign.

Fortunately, next generation sequencing (NGS) technologies Slatko2018NGS (76)
have begun disrupting this paradigm. The deep mutational scanning strategies
mentioned in the previous section rely on sequencing to measure fitness,
meaning sequencing and assaying fitness happen simultaneously fowler2014deep
(69). New sequencing methods that incorporate NGS show promise to continue
shifting the sequencing paradigm by spreading reads over many, multiplexed
sequences Currin2019multiplexed (77, 78, 79). Currently, such methods still
have limitations, ranging from the requirement to fill an entire flow cell,
which can cost upwards of $1000 per run Currin2019multiplexed (77, 79), to
only sequencing short amplicons from within an entire gene wittmann2021evSeq
(78), which are restricted to only a few hundred amino acids, complicating its
application to mutations over longer sequences. Nonetheless, both sequencing
technologies and sequencing methods for the protein engineering community have
been growing rapidly in the past few years, showing promise to address these
shortcomings in the near future.

###  2.4 Modeling protein fitness

Fitness datasets obtained as described above and can be used to fit models of
the sequence-fitness relationship. Here, we first describe the methods for
representing a protein sequence before diving into the model classes used to
predict fitness from sequence.

#### Representing protein sequences

Proteins are variable-length sequences of twenty canonical amino acids. Due to
both the variability in sequence length and the categorical nature of amino
acids, an important and long-standing problem has been how to best represent a
protein sequence to facilitate machine learning. Roughly speaking, there are
two general approaches for doing this: (1) hand-crafting features based on,
for example, statistical summaries or biophysical properties of a sequence or
its constituent amino acids, and (2) using evolutionarily related sequences to
learn likelihoods or embeddings as representations.

Statistical summaries of a sequence: higher-order terms and k-mers. One of the
simplest ways to represent a protein sequence is to concatenate one-hot
encodings of the amino acid at each position in the sequence. Despite its
simplicity, even a linear model with this representation can be a surprisingly
effective baseline in some settings—for example, when we focus on predictive
performance on sequences near a wild type dallago2021flip (73, 65). Amino acid
similarities may also be directly encoded through matrices based on
substitution probabilities of one amino acid for another henikoff1992amino
(80). Beyond encoding just the amino acid identities at each sequence
position, one can also encode the identities of the amino acids at pairs of
structurally contacting positions romero2013navigating (40, 41).

Generalizing this idea further, one-hot encodings of groups of amino acids,
which we call _higher-order terms_ —for example, the identities of the amino
acids at three positions for a third-order term—have been shown to be both
theoretically principled and empirically useful representations for learning
protein fitness functions stadler1996landscapes (81, 82, 83, 84, 85, 75, 48,
86). In particular, it has been shown that any fitness function defined over
sequences of a fixed length can be expressed exactly as a linear function of
all possible higher-order terms of all orders between sequence positions
stadler1996landscapes (81). The number of such terms grows exponentially with
sequence length. However, there is increasing evidence that many realistic
protein fitness functions can be well-approximated by a linear model of just a
small number of these terms ballal2020sparse (87, 88, 48); an effective
baseline representation may therefore be to one-hot encode all terms up to,
for example, second- or third-order poelwijk2019learning (84, 65, 86).

Beyond higher-order terms, the frequencies of different _k-mers_ —contiguous
subsequences of $k$ amino acids—are another kind statistical summary that has
been used to represent sequences and learn fitness functions ofer2015profet
(89, 90).

Physicochemical features. Beyond one-hot encodings of a sequence’s residues,
or the higher-order terms between them, features based on physicochemical
properties of a sequence have been used to learn fitness functions. For
example, each amino acid can be featurized as a vector of various
physicochemical properties sandberg1998new (91, 92) or by a low-dimensional
representation thereof georgiev2009interpretable (93, 94, 95). These
properties can also be combined with structural information qiu2007structural
(96, 97, 98), or with the aforementioned statistical summary representations
ofer2015profet (89).

However, it not generally clear which physicochemical properties will be
relevant for any particular fitness function. Consequently, in recent years
considerable attention has turned to learning relevant features by fitting
low-dimensional representations of evolutionarily related sequences.

Representations learned from evolutionarily related sequences. In directed
evolution, one generally starts by identifying a wild-type protein (or
multiple such wild types) that exists naturally in the genome of some organism
and exhibits the function of interest to an appreciable degree. In many cases,
that function of interest is needed by more than one organism, and natural
selection has yielded multiple homologs residing in a variety of organisms.
Though the precise fitness value differs across homologs, due to evolutionary
constraints homologs are generally functional as opposed to non-functional.
Based on the premise that homologs are mostly functional, a great body of work
in recent years has focused on learning the distribution of homologous
sequences, as a proxy for the distribution of functional sequences. The
density, or approximations thereof, of the resulting learned sequence
distribution has been shown to correlate with fitness in many cases, whether
modeling the homologs with a hidden Markov model shihab2013predicting (99, 65,
100), Potts model mann2014fitness (101, 53), variational autoencoder
riesselman2018deep (54, 102, 103), or autoregressive model shin2021protein
(21), leading to its use as an informative correlate of fitness that does not
require any experimental measurements.

Currently, variational autoencoders such as riesselman2018deep (54) appear to
provide the highest correlations with fitness for a variety of fitness data
sets, presumably due to their ability to learn evolutionary constraints on
higher-order interactions between sequence positions, though autoregressive
models shin2021protein (21) and transformers meier2021language (38) also
achieve comparable performance. Due to this correlation, approximations of the
density such as the evidence lower bound (ELBO) have shown to be an effective
feature when used with supervised learning approaches hsu2022learning (65);
the latent space learned by variational autoencoders has also been used to
represent proteins for learning fitness functions ding2019deciphering (102).
Finally, generative models fit to homologs have also been used to sample novel
functional proteins russ2020evolution (104, 20, 105).

Beyond homologs, which, by virtue of natural selection, contain sequence
patterns necessary for the function of interest, the set of all proteins
sequenced so far may similarly reveal patterns necessary for basic properties
of all functional proteins, such as the ability to fold into a stable
structure. Based on this hypothesis, a growing body of work has trained
various deep learning models on massive databases of known proteins, such as
UniProt uniprot2021uniprot (55), UniRef suzek2015uniref (23), and UniParc
uniprot2021uniprot (55), which contain up to hundreds of millions of sequence
as of this writing. The model architectures are almost all borrowed from
natural language processing (NLP), ranging from relatively simple skip-gram
neural networks asgari2015continuous (106, 107) and its extensions to
embedding text documents kimothi2016distributed (108, 109) to recurrent
alley2019unified (110, 111, 66) and convolutional neural networks
schwartz2018deep (112) to, most recently, transformers rao2019evaluating (113,
74, 114, 115, 38, 116). These models are generally trained using self-
supervision tasks, where the goal is, for example, to predict the amino acid
at a certain position given the amino acids at other positions (though other
approaches such as multi-task learning using function labels schwartz2018deep
(112) and incorporating protein structural information bepler2019learning
(111) have also been used). The outputs of intermediate layers in these
models, which we will call deep embeddings, can then be used to represent
protein sequences for learning fitness functions.

Estimates of the density from transformers have also been shown to correlate
with a variety of fitness functions meier2021language (38, 115), presumably
both because the model learns sequence patterns required for basic properties
of all functional proteins, such as stability, and because the training data
contains all homologs corresponding to all known functions. Whether using them
for deep embeddings or density estimates, if homologs of a functional wild
type are also available for a function of interest, these models can also be
further trained or “fine-tuned” on them biswas2021low (66, 20, 115) to focus
on a particularly relevant region of sequence space.

Despite promising results on capturing phylogenetic relationships and various
clustering tasks, these deep embeddings have shown limited success in learning
fitness functions. For example, when used with ridge regression or Gaussian
process regression, they do not appear to systematically outperform simpler
baselines yang2018learned (109, 65, 73) such as concatenating the
aforementioned density of a homolog sequence distribution to a one-hot
encoding hsu2022learning (65), particularly when there is limited training
data.

#### Modeling the sequence-fitness relationship

Given a representation of protein sequences, a variety of model classes have
been used to learn the sequence-fitness relationship. In general, however,
note that models that excel under more traditional evaluation metrics—for
example, prediction error on held-out sequences from the same distribution as
the training data—may or may not be appropriate for use with directed
evolution, since in the latter we focus on sequences the model predicts to
have high fitness. That is, a model that facilitates directed evolution needs
to be reliable even in regions of sequence space far from the training data,
particularly in regions on which it predicts high fitness.

With that in mind, a few domain-specific models have been designed with the
particular goal of jointly learning (1) a density model over homologs and (2)
the fitness function from experimentally labeled sequences barrat2016improving
(117, 118), under the premise that the density of homologs is positively
correlated with the fitness and that therefore both models should stand to
gain from sharing information via joint training.

In the more common setting of using only experimentally labeled sequences, two
models have been shown to be very strong baselines across a variety of fitness
data sets, particularly in the regime of limited training data (i.e., at most
a few hundred labeled sequences): linear regression, for example on one-hot
encodings fox2007improving (44, 119, 73), optionally concatenated with the
density of a homolog sequence distribution hsu2022learning (65), and Gaussian
process regression with either domain-specific kernels (e.g., structurally
informed romero2013navigating (40, 120, 41) or mismatch string
leslie2004mismatch (121, 109) kernels, which count shared subsequences between
proteins) or more general-purpose kernels bedbrook2019machine (63, 98, 90, 45,
109, 122).

Other kernel methods have been used as well, such as support vector machines
for modeling enzyme enantioselectivity zaugg2017learning (123), membrane
protein expression saladi2018statistical (124), and protein thermostability
tian2010predicting (125, 126, 127, 128, 129, 130, 97, 131). The latter task,
which has been of widespread interest due to its necessity in industrial
applications, has also been approached using regression trees and their
extensions tian2010predicting (125, 126, 127).

When labeled sequences are abundant (that is, at least tens to hundreds of
thousands), deep learning models can also be effective for learning the
fitness function. Models range from simple feedforward networks, which have
been used to predict fluorescence sarkisyan2016local (132, 133), histidine
synthesis efficacy pokusaeva2019experimental (134), and viral capsid packaging
ability zhu2021machine (85), to convolutional neural networks
shanehsazzadeh2020transfer (135, 136, 73, 47), recurrent neural networks
rao2019tape (137, 110, 47), and transformers rao2019tape (137, 73), which have
been assessed on a variety of protein tasks including fluorescence,
thermostability, and binding affinity prediction.

Limitations of current model comparisons. Our understanding of what
representations and models are most effective is limited by the constraints of
the molecular biology techniques available to generate fitness data sets. For
example, the vast majority of currently available fitness data sets only
assess the fitnesses of mutants one or two mutations away from a wild type,
excluding insertions and deletions hopf2017mutation (53, 50, 54, 21, 65). This
choice is usually justified by the assumption that most mutations are
deleterious bloom2005thermodynamic (138); therefore, to generate data with
informative, non-zero labels, it is beneficial to stay near sequences already
known to be functional. Pragmatically, the resource and throughput constraints
on mutagenesis and sequencing protocols described in Section 2.3 further
discourage protein engineers from making more simultaneous mutations. If one
intends on generating training data near a functional wild type, comparing
representations and models using these data sets may be sufficiently
informative. However, beyond this limited setting, fitness data sets with
measurements for proteins more broadly dispersed in sequence space are needed
to comprehensively understand what machine learning strategies are most
effective for learning fitness functions. dallago2021flip (73) have collected
several such datasets in recent work; there are also a few data sets with
fitness measurements for all possible protein sequences varying at a small
number (typically less than twenty) of positions poelwijk2019learning (84,
139, 134), which comprehensively expose the effects of all possible
combinations of (albeit a limited number of) mutations.

Current evidence suggests that, when focusing on relatively small regions of
sequence space—for example, clustered around a wild type—simple models such as
ridge regression on one-hot encodings can be much more effective than more
complex models dallago2021flip (73, 65), but when considering predictive
performance on a broader region, given sufficient training data there may be
benefits from using transformers pretrained on massive protein databases
dallago2021flip (73). Further work is needed to systematically investigate the
machine learning strategies appropriate for the different types of training
and test data that arise in protein engineering.

###  2.5 Protein selection and optimization

After obtaining a trained sequence-fitness model, the goal is to use it as
part of an acquisition function (in the Bayesian optimization sense) to decide
which sequences from the theoretical library to characterize next.

#### Defining the design space

Although evaluating the sequence-fitness model is faster and cheaper than
actually obtaining laboratory measurements, it is frequently impossible to
evaluate it on all possible protein sequences. One approach is to explicitly
define a more limited design space of proteins. Example design spaces include
traditional library designs for protein engineering such as all single- or
double-mutants, all the possible mutations at a small number of sites
wu2019combination (67, 49, 139), a recombination library defined by mixing and
matching parts of homologous parent sequences romero2013navigating (40, 62,
18, 19), or libraries that are easy to make using current DNA synthesis
techniques weinstein2021optimal (59). If a differentiable predictive oracle is
trained on sequence-fitness data, another approach is to optimize the sequence
using gradient ascent linder2020fast (140).

Another approach is to use a generative model to implicitly define the design
space by learning a probability distribution over sequences. A generative
model performs one or both of two fundamental tasks: (1) assigning every
possible sequence a likelihood of being in the desired distribution, and (2)
generating examples of sequences from a desired distribution. The simplest
models assume this distribution can be modeled by considering sites
independently or by relationships between pairs of sites hopf2017mutation (53,
104). More recently, researchers have used deep generative models to learn
more complex sequence distributions and propose sequences for evaluation
wu2021protein (141); relevant neural architectures include variational
autoencoders (VAEs) kingma2013auto (142, 54), generative adversarial networks
(GANs) goodfellow2014generative (143, 144, 145), and autoregressive language
models hochreiter1997long (146, 111, 21, 74, 20).

#### Defining the acquisition function

An acquisition function uses sequence information and the surrogate model to
prioritize sequences from the theoretical library for experimental
measurements. A simple example of an acquisition function is greedy selection
of the top prediction (or the top few predictions) according to the sequence-
function model. Greedy acquisition is common in practice and can work well
fox2007improving (44, 67, 47, 66, 49, 147), but can become trapped in more
complex fitness landscapes. Many standard acquisition functions are designed
to select only a single example in each round. Often, however, it is faster to
obtain many experimental measurements in parallel. While simply acquiring
several of the top-ranked sequences is possible, this approach may result in
the acquisition of many similar sequences. Special methods for batched
acquisition are therefore designed to encourage acquiring more diverse
sequences gonzalez2016batch (148, 149, 40, 150, 151, 152), but this remains an
open area of methodological development.

Given a theoretical library and an acquisition function, the simplest method
for choosing sequences is to compute the surrogate score on as many members of
the library as is computationally feasible, and then to use those scores to
select sequences. However, when the library is defined by a generative model,
the sequence-fitness model can be used to shift the generated distribution
toward more optimal sequences. For example, in adaptive sampling, sequences
are sampled from a generative model, the outputs of a surrogate model are used
to re-estimate the parameters of the generative model, and the process
iterates until convergence brookes2018design (153). brookes2018design (153)
use adaptive sampling with a VAE to optimize DNA sequences for protein
expression abundance brookes2018design (153). gupta2018feedback (154) use
adaptive sampling based with a GAN to design antimicrobial peptides
gupta2018feedback (154). To perform de novo protein design anishchenko2021novo
(155) use adaptive sampling with a mutation-based generative model to identify
sequences with valid folds.

By default, adaptive sampling assumes a trustworthy sequence-fitness model;
however, in practice, these models are imperfect and can be prone to poor
predictions in many regions of the protein space. To address this problem,
adaptive sampling can avoid these degeneracies in the surrogate model by
constraining sampling to be close to the training distribution for the
surrogate model brookes2019conditioning (133, 155). In each iteration, it is
also possible to retrain the surrogate model to avoid pathologies
fannjiang2020autofocused (156). Sequence generation can also be improved by
sampling from an ensemble of generative models angermueller2020rmodel (157,
158).

A closely-related approach uses genetic algorithms to heuristically balance
both mutation and recombination to produce new sequences hansen2006cma (159)
by adaptively querying a sequence-fitness model to preserve sequence designs
sinai2020adalead (152). Another approach inverts the sequence-fitness model by
finding the elements from the generative model’s distribution that are most
likely to have a desirable value according to the sequence-fitness model. An
inverse of the sequence-fitness model can be trained via an iterative
procedure similar to adaptive sampling kumar2019model (160), or the inverse of
a differentiable surrogate model can be computed using gradient-based methods
liu2020antibody (30, 25, 140).

While it is computationally convenient to exactly specify the sequences to
measure next, specifying a new library and sampling from that library may
allow many more sequences to be measured for the same cost as directly
synthesizing a small number of sequences. This library may be optimized for
expected improvement yang2020batched (151), to balance diversity and expected
function zhu2021machine (85), or to match a desired distribution over
sequences weinstein2021optimal (59).

#### Updating the sequence-function model

So far, we have discussed methods for using an acquisition function based on a
sequence-fitness model to choose sequences from a theoretical library that are
optimized for a desired function. However, in some cases it may be possible to
sequentially update the sequence-fitness model with new measurements.

Greedy acquisition across experimental rounds (uphill climbing the fitness
landscape) is the simplest implementation of sequential optimization and is
used widely in practice fox2007improving (44). Going beyond greedy acquisition
means tolerating more risk for a potentially higher reward, which is often
described as a tradeoff between exploitation (equivalent to greedy
acquisition) and exploration robbins1952some (161, 162, 163, 164), in which an
algorithm acquires proteins where the model is uncertain about its predictions
(or that are are dissimilar from sequences in the training set) to improve
future predictions and to explore new regions of sequence space.

Bayesian optimization is a popular framework for sequential optimization
snoek2012practical (163) that leverages Bayesian uncertainty in the sequence-
fitness predictions to guide the exploration-exploitation tradeoff. Bayesian
optimization relies on an acquisition function that systematically weighs the
sequence-fitness model’s prediction with its associated uncertainty. The upper
confidence bound (UCB) acquisition function adds the prediction value with a
weighted uncertainty term that lets the user control the influence of
uncertainty on the prediction, with a larger weight encouraging more
exploration auer2002using (162, 165). UCB has good theoretical properties
snoek2012practical (163) and is used widely in practice romero2013navigating
(40, 41, 42, 166). Other notable acquisition functions select an example that
is predicted to, in expectation, have the largest improvement compared to the
best example in the training set or compared to a randomly drawn example from
the training set wilson2018maximizing (167). Uncertainty can also help improve
exploration in parallel acquisition azimi2010batch (149, 40, 150, 148, 151).

Gaussian process models rasmussen2006gaussian (168) are a popular kernel
method for Bayesian optimization because of their theoretical elegance,
flexibility, and good performance in practice. However, Bayesian optimization
can also leverage more bespoke Bayesian models and algorithms for exact or
approximate inference. The wide interest in neural network models over the
last decade has also led to increased interest in uncertainty prediction
through Bayesian neural networks, in which the parameters of the network are
themselves random variables with associated prior distributions, though
efficient and accurate inference in these models can be challenging
neal2012bayesian (169). One particularly interesting approach is to combine a
fitness-space prior (e.g. stability predictions) with the standard neural
network weight-space prior nisonoff2022augmenting (170), and more examples are
described in Section 2.4.

Probabilistic surrogate models can also be implemented by model ensembles
laks2017ensemble (171), which train multiple sequence-to-fitness models on the
same data and rely on variance in model predictions, due to different model
architectures or randomness in the training procedure, to estimate uncertainty
liu2020antibody (30). Ensembles are not Bayesian by default, so incorporating
prior information into these models can be challenging amini2019deep (172,
173).

Finally, conformal prediction (CP) is an approach for rigorous uncertainty
quantification that can be used with any predictive model in a black-box
manner, including the aforementioned Gaussian process models or any deep
learning model gammerman1998learning (174, 175, 176). The framework leverages
the assumption of exchangeable (e.g., independently and identically
distributed) training and test data to construct confidence sets around
predictions that provably satisfy _coverage_ , a frequentist guarantee on how
often the confidence sets contain the true label of test inputs. Beyond
exchangeable data, CP has been generalized to handle various forms of
distribution shift, including label shift aleks2021distribution (177),
covariate shift tibshirani2019conformal (178, 179), distribution shifts in an
online setting gibbs2021adaptive (180), and test distributions that are close
to the training distribution cauchois2020robust (181). Notably, in recent work
fannjiang2022conformal (86) generalized CP for the setting of protein design,
in which any of the aforementioned optimization procedures induces a
distribution shift wherein the distribution of test (i.e., designed) sequences
is dependent on the training data fannjiang2022conformal (86). This method
enables practitioners to assess the predictive uncertainty of any optimization
procedure, using any machine learning model, and as such can be a principled
approach for selecting an optimization procedure (or any component thereof,
including any hyperparameters or the machine learning model class).

##  3 Outlook and Concluding Remarks

In this chapter, we have discussed current efforts to improve protein
engineering with machine learning. The field has grown rapidly over the past
five years, as the development of deep learning methods and methods to obtain
and organize biomolecular data have reached inflection points. We anticipate
continued growth in this area of research from both directions, particularly
in the following directions.

###  3.1 Model Confidence

The space of possible amino acid combinations is vast, but the space of
functional proteins is much smaller, with estimates ranging from one in
$10^{11}$ keefe2001functional (182) to as low as one in $10^{77}$
axe2004estimating (183). This manifold of functional proteins may not have
been completely explored by nature, which has search strategies that are
biased toward existing functional proteins, and we are still identifying new
proteins through metagenomic analysis mitchell2020mgnify (184). Therefore, it
is unclear whether relying on the evolutionary history of identified proteins
is sufficient to identify the manifold of functional proteins.

For protein engineering, it is clear that there is a balance to maintain
between exploring new protein sequences and staying within predictive models’
confident regions. In the directed evolution context, where rounds of
experimental data are used to train predictive oracles (or used directly),
various methods encode these trust regions heuristically or probabilistically
brookes2019conditioning (133, 86, 66, 185), and retraining oracles for
specific regions has also been successful fannjiang2020autofocused (156).
However, there are few fully enumerated protein landscapes to validate these
approaches against. A nearly comprehensive GB1 study wu2016adaptation (139)
has been remarkably useful, as have synthetic datasets, but the field would
benefit from more, diverse, epistatic landscapes with which to validate.

While model confidence represents one challenge in protein engineering, noisy
labels present another. The sample preparation methods used often introduce
noise, may have limited linear range of measurement, and can be difficult to
reproduce, particularly for newly developed assays designed for to probe more
complex biological phenomena. While robust training under noisy labels has
gained some traction in deep learning, especially for more subjective and
error-prone tasks, natarajan2013learning (186, 187), handling noisy labels is
typically treated as a data pre-processing step (such as by labeling the data
with Gaussian Mixture Models bryant2021deep (47, 21)), although a recent
method demonstrates that biophysical priors on functional labels can improve
prediction accuracy nisonoff2022augmenting (170).

###  3.2 Protein-specific data modalities

Much of this chapter is focused on the guided acquisition of data for a
particular protein function, which is being collected and curated by ProtaBank
wang2018protabank (188). However, the amount of information available for
proteins in other data modalities is also rapidly increasing. Many databases
exist for various properties of proteins, ranging from protein stability to
binding. Of particular note are UniProt uniprot2021uniprot (55) and the
Protein Data Bank (PDB) berman2000protein (189, 190).

UniProt contains a large amount of information about proteins beyond their
sequence, including cross-references to functional labels, disease-association
and Protein family (Pfam) classifications at the per-residue level
mistry2021pfam (191), Gene Ontologies on the per-protein example
ashburner2000gene (192, 193), and links to several other databases. UniProt
also releases reference protein clusters (UniRef uniprot2021uniprot (55,
194)), which are currently almost ubiquitous as the training set for large
protein language models rives2021biological (114). This dataset will continue
to grow as more metagenomes are sequenced mitchell2020mgnify (184) and more
unique proteins are identified. Some approaches to modeling proteins are
conditioned on protein functional labels gligorijevic2021function (33) or
other data available in UniProt madani2020progen (74), but there is no clear
optimal approach to incorporating annotations about all proteins for protein
engineering campaigns, which are often focused on specific protein families.

The PDB is the primary source of protein structure data, and it largely
consists of static protein structures obtained through protein
crystallography, although the number of structures obtained through cryo-EM
and NMR are also increasing. Protein structures are invaluable to biologists
in providing much-needed context for molecules that are otherwise difficult to
probe. However, mutations may have effects that are not captured by static
structures. For example, they may bias the protein’s Boltzmann distribution
toward different conformational states in the ensemble without perturbing the
ground state crystal structure, or the crystal structure may simply have too
low resolution to capture small changes. Nonetheless, structure can be a
useful prior in directed evolution bepler2019learning (111, 49).

While protein data continues to grow, methods with inductive biases tailored
for biology are comparatively underdeveloped, particular for protein
engineering applications. A few notable exceptions have been developed in
application to protein structure modeling. For example, the MSA Transformer
rao2021msa (115) develops a variant of axial attention specific for MSAs,
which contain an aligned homolog sequence in each row. The protein sequences
in an MSA likely share similar structure, and the MSA transformer is able to
leverage this structure by tying row attention maps. Famously, AlphaFold
jumper2021highly (195) incorporated several biophysical inductive biases in
the CASP14 protein structure prediction contest. These include a variant of
attention to account for the triangle inequality on distances, a lowered
emphasis on the linear input sequence of a protein (which folds into a three-
dimensional structure), and a variant of axial attention for the MSA. These
methods have been successful for improving protein structure prediction, and
it is likely that machine learning methods developed to balance evolutionary
history, structure, and function will be successful in protein engineering as
well.

###  3.3 Summary

Protein engineering is an optimization strategy, and many recent advances in
machine learning have been successfully applied or developed to the directed
evolution of proteins. In this chapter, we have highlighted studies where
machine learning contributes to each step of the optimization process. As we
continue to gather more protein information and develop methods to bootstrap
and guide engineering from these data, machine learning will play an
increasingly important role in protein engineering.

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##  4 Funding

This work was funded by

  * •

NSF Division of Chemical, Bioengineering, Environmental, and Transport Systems
(CBET 1937902)

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Amazon AI4Science

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Caltech Biotechnology Leadership Program (NIH 5 T32 GM 112592-5)