*[page=1,color=gray!60,fontfamily=cmr,fontseries=m,scale=0.4,xpos=0,ypos=130]Preprint in AACD 2021 Workshop Proceedings

# Prospects for Analog Circuits in Deep Networks

Shih-Chii Liu1, John Paul Strachan2, and Arindam Basu3 1Institute of
Neuroinformatics, University of Zurich, Switzerland
2 Hewlett Packard Research Labs, Palo Alto, CA, USA
3Nanyang Technological University, Singapore and City University of Hong Kong,
Hong Kong

###### Abstract

Operations typically used in machine learning algorithms (e.g. adds and soft
max) can be implemented by compact analog circuits. Analog Application-
Specific Integrated Circuit (ASIC) designs that implement these algorithms
using techniques such as charge sharing circuits and subthreshold transistors,
achieve very high power efficiencies. With the recent advances in deep
learning algorithms, focus has shifted to hardware digital accelerator designs
that implement the prevalent matrix-vector multiplication operations. Power in
these designs is usually dominated by the memory access power of off-chip DRAM
needed for storing the network weights and activations. Emerging dense non-
volatile memory technologies can help to provide on-chip memory and analog
circuits can be well suited to implement the needed multiplication-vector
operations coupled with in-computing memory approaches. This paper presents a
brief review of analog designs that implement various machine learning
algorithms. It then presents an outlook for the use of analog circuits in low-
power deep network accelerators suitable for edge or tiny machine learning
applications.

##  I Introduction

Machine-learning systems produce state-of-art results for many applications
including data mining and machine vision. They extract features from the
incoming data on which decisions are made, for example, in a visual
classification task. Current deep neural network approaches in machine
learning (ML) [1] produce state-of-art results in many application domains
including visual processing (object detection [2], face recognition [3] etc),
audio processing (speech recognition [4], keyword spotting etc), and natural
language processing [5], to name a few. This improvement in algorithms and
software stack has eventually led to a drive for better hardware that can run
such ML workloads efficiently.

In recent times, edge computing has become a big research topic and edge
devices that first process the local input sensor data are being developed
within different sensor domains. Many current deep network hardware
accelerators designed for edge devices are implemented through digital
circuits. Less explored are analog/mixed-signal designs that can provide high
energy-efficient implementations of deep network architectures. Custom analog
circuits can exploit the physics of the transistors in implementing
computational primitives needed in deep network architectures. For example,
operations such as summing can be implemented by simpler analog transistor
circuits rather than digital circuits. These designs can provide better area
and energy efficiencies than their digital counterparts in particular for edge
inference applications which require only small networks. With the increasing
availability of dense new non-volatile memory (NVM) technology, the
computation can be co-localized with memory, therefore further savings in
power can be obtained by the reduction of off-chip memory access.

This article reviews analog and mixed-signal hardware chips that implement ML
algorithms including the deep neural network architectures. We discuss the
advantages of analog circuits and also the challenges of using such circuits.
While other reviews have focused on analog circuits for on-chip learning [6],
we focus more on implementations of generic building blocks that can be used
in both training and inference phases.

The paper organization is as follows: First, Sec. II provides a brief review
on analog circuits used for neuromorphic computing and how these circuits can
implement computational primitives useful for neural processor designs and ML
algorithms. It is followed by Sec. III that describes basic operations (such
as vector-matrix multiplications) being accelerated by analog building blocks,
and Sec. IV that reviews the field of non-volatile memory technologies for
deep network accelerators. Section V reviews recent Application-Specific
Integrated Circuits (ASICs) that implement certain ML algorithms. Finally, we
end the paper with a discussion about future prospects of analog-based ML
circuits (e.g. in-memory computing).

##  II Review of circuits for analog computing

With great advances made in digital circuit design through the availability of
both software and hardware design tools, analog circuits have taken a back
seat in mainstream circuits and are now primarily used in high speed analog
domains such as RF, power regulation, PLLs, and interface of sensors and
actuators (e.g. in the analog-digital converter (ADC) readout circuits of
analog microphone or biochemical sensors).

When it was proposed that the exponential properties of running the
transistors in subthreshold can be useful for emulating the structure of
nervous system in the field of neuromorphic engineering [7], analog circuits
became popular for emulating biological structures like the retina [8],
implementing generalized smoothing networks [9, 10], and both simplified and
complex biophysical models of biological neurons. The exponential properties
of a subthreshold transistor also make it easier to design analog VLSI
circuits for implementing basic functions used in many mixed-signal
neuromorphic systems such as the sigmoid, similarity [11], charge-based
vector-matrix calculations [12], and highly distributed operations such as the
winner-take-all [13].

Analog ML designs using these basic functions included a low-power analog
radial basis function programmable system [14]; a sub-microWatt Support Vector
Machine classifier design [15] with a computational efficiency of $\sim$ 1
TOp/s/W; and the analog deep learning feature extractor system [16] that
processes over 8K input vectors per second and achieves 1 TOp/s/W. The power
efficiency of [16] is achieved by running the transistors in subthreshold and
using floating-gate non-volatile technology for both storage, compensation and
reconfiguration.

Even though analog neural processor circuits were already reported in the
1990s [17], they had taken a back seat partially because of the ease of doing
digital designs; and the care needed for good matching in analog circuits.
Although mismatch is usually reduced by using larger transistors, there are
circuit strategies to minimize the mismatch effect, for example, by techniques
to simplify the circuit complexity (Sec. III), floating-gate techniques to
compensate for the mismatch, and training methods for deep networks to account
for this mismatch as will be discussed in Sec. V.

Figure 1: Simple two-layer Artificial Neural Network (ANN) using a non-linear
transfer function (a) and an implementation using a resistive crossbar array
with differential weights: two non-negative resistors are used to represent a
bipolar weight (b).

(a)

(b)

(c)

Figure 2: Three modes of matrix-vector multipliers using analog circuits: (a)
Charge (b) Time and (c) Current. Figures adapted from [18], [19] and [20].

##  III Analog circuits for matrix-vector multiplication

In a multi-layered neural network, the output of a neuron $i$ in layer $l$ is
given by $y_{i}^{l}=g(z_{i}^{l})=g\smash{(\sum_{j}w_{ij}x_{j}^{l})}$, where
$g()$ is a nonlinear function and the $j$-th input to the $l$-th layer
$x_{j}^{l}$ is the $j$-th output from the previous layer (Fig. 1 (a)). The
basic operations: summation, multiplication by scalars, and simple nonlinear
transformations such as sigmoids can be implemented in analog VLSI circuits
very efficiently. Dropping the index $l$ denoting layer, we can write the most
computationally intensive part as a matrix-vector multiplication (MVM) as
follows:

$\overline{z}=\mathbf{W}\overline{x}$ (1)

where $\overline{x}$ is the vector of inputs to a layer, W denote the matrix
of weights for the layer and $\overline{z}$ denotes the vector of linear
outputs which is then passed through a nonlinear function $g()$ to produce the
final neuronal output. Figure 2 illustrates how the key core computation of
weighted summation can be performed in three modes: (a) Charge, (b) time and
(c) current. Further storage of weight coefficients can be performed in a
volatile or non-volatile manner. More details about these different
possibilities are described next.

#### Charge

Figure 2(a) depicts a capacitive digital analog converter (CDAC) based charge
mode MVM circuit. In this circuit, the weight is stored in the form of binary
weighted capacitor sizes (shown as $C_{1}[i]$ in the figure) and hence
weighting of input happens naturally by charging the desired capacitor value
with the input voltage. Summation happens through the process of charge
redistribution among capacitors via switched capacitor circuit principles. The
charge redistribution can be more accurate if done by using an amplifier in a
negative feedback configuration (as shown on top of Fig. 2(a))–this is
referred to as an active configuration [18, 21]. On the other hand, the
passive configuration without an amplifier (shown below the active one) has
the benefit of high speed operation due to the absence of settling time
limitations from the amplifier. However, it was shown in [18] that the errors
in the passive multiplication amount to a change in the coefficients of the
weighting matrix W and can be accounted for. A disadvantage of this approach
is that it requires $N$ clock cycles to perform a dot product on two $N$
dimensional vectors. Static random access memory (SRAM) is used to store the
weights–hence, it suffers from volatile storage issues. A 6-b input, 3-b
weight implementation of this approach achieved $\approx 7.7-8.7$ TOp/s/W
energy efficiency at clock frequencies of $1-2.5$ GHz clock frequency [18].
Other recent implementations using this approach are reported in [22] and
[23].

#### Time

Another way of implementing addition in the analog domain is by using time
delays. Figure 2(b) shows how addition can be implemented through the
accumulation of delays in cascaded digital buffer stages [19]. By modifying
the delay of each stage according to the weight, a weighted summation can be
achieved. Figure 2(b) shows one example of a delay line based implementation
of this approach. Here, the weight storage is in volatile SRAM cells. The
authors used a thermometer encoded delay line as an unit delay cell to avoid
nonlinearity at the expense of area. A 1-b input, 3-bit weight architecture
achieved very high energy efficiency of $\approx 105$ TOp/s/W at $0.7$ V power
supply [19].

#### Current

By far, the most popular approach for analog VMM implementation is the current
mode approach. This architecture offers flexibility in choosing the way input
is applied (encoding magnitude in current [24], voltage [25] or as pulse-width
of a fixed amplitude pulse [26]) and non-volatile weight storage (Flash [27],
PCM [28], RRAM [25], MRAM [29], Ferroelectric FETs [30], ionic floating-gate
[31], transistor mismatch [32], etc). An example implementation using standard
CMOS compatible Flash transistors shown in Fig. 2(c) was presented as early as
2004 [20].

In these approaches, a crossbar array of NVM devices are used to store the
weights W. In the case of Flash, the inputs $x_{j}$ can be encoded in current
magnitude ($I_{j}^{+}-I_{j}^{-}$) and presented along the columns (word-lines)
while current summation occurs along the rows (bit-lines) by virtue of
Kirchhoff’s Current Law (KCL) to produce the output $z_{j}$. Here, the
weighting happens through a sub-threshold current mirror operation of the
input diode-connected Flash transistor and the NVM device in the crossbar with
weight being encoded as charge difference between the two devices. Since then,
several variants of these Flash-based VMM architectures have been published
using amplifier based active current mirrors [33] for higher speed, source
coupled VMM for higher accuracy [34] and special Flash process based VMM [27]
with promise of scaling down to 28nm. These approaches generally achieve
energy efficiencies in the range of $5-10$ TOp/s/W.

An interesting alternative is to use the threshold voltage mismatch in-built
in transistors as a weight quantity. This leads to ultra-compact arrays for
VMM operation [24]. However, since these weights are random, they may only be
used to implement a class of randomized neural networks such as reservoir
computing, neural engineering framework, extreme learning machines etc. While
these networks are typically only two layers deep, they have advantages of
good generalization and quick retraining. Such approaches have been used for
brain-machine interfaces [35], tactile sensing [36] and image classification
[37].

The recent trend in this architecture is to use resistive memory elements,
sometimes dubbed memristors, as the NVM device in the crossbar. They are less
mature but offer advantages of longer retention, higher endurance, low write
energy, and promise of scaling to sizes smaller than Flash transistors. They
have also been shown to support back-propagation based weight updates with
small modifications to the architecture. Due to their increasing popularity in
deep network implementations, we will discuss them further in the next
section.

##  IV Non-volatile resistive crossbars

A popular approach for performing the matrix-vector multiplications in ML -
and especially in the deep neural networks of today - is to leverage emerging
non-volatile memory technologies such as phase change (PCM), oxide-based
resistive RAM (RRAM or memristors), and spin-torque magnetic technologies
(STT-MRAM). The equivalent of an ANN implemented in a resistive memory array
is shown in Fig. 1 (b). As further illustrated in Fig. 3, a dense crossbar
circuit is constructed with these resistive elements or memristors at every
junction. Each resistor is analog tunable to encode multiple bits of
information (from binary to over seven bits [38, 39]). Most importantly, the
devices retain this analog resistive programming in a non-volatile manner.
This is appropriate for encoding the heavily reused weights in deep neural
networks, such as convolution kernels or fully connected layers. And, as noted
earlier, this allows for the dominant vector-matrix computations to be
performed in-memory without the costly fetching of neural network (synaptic)
weights.

Figure 3: Performing vector-matrix multiplication in non-volatile resistive
(memristive) crossbar arrays. The input can be encoded in voltage amplitude
with fixed pulse width, as shown here, or other approaches such as fixed
amplitude and variable pulse width. At each crossbar junction, a variable
resistor is present representing a matrix weight element, modulating the
amount of current injected into the column wires through Ohm’s law. On each
column, the currents from each row are summed through Kirchhoff’s current law,
yielding the desired output vector representing the vector-matrix product.
Pairs of differential weights can be utilized as in Fig. 1(b) to allow bipolar
representations.

To take full advantage of analog non-volatile crossbars in deep neural
networks, it is necessary to devise a larger architecture that supplements the
vector-matrix computations performed in-memory, with a range of additional
data orchestration and processing performed by traditional digital circuits.
These include operations such as data routing, sigmoidal or other nonlinear
activation functions, max-pooling, and normalization. Several prior works have
explored this design-space [40, 41] for resistive crossbars, with the
inclusion of schemes to encode arbitrarily high precision weights across
multiple resistive elements (”bit-slicing”) and the overhead in constantly
converting all intermediate calculations performed within analog resistive
crossbars back into the digital domain to avoid error accumulation in deep
networks of potentially tens of layers. An architecture and performance
analysis was first done for CNNs [40], and then extended to nearly all modern
deep neural networks including flexible compiler support [42].

To date, non-volatile resistive crossbars have been explored for both the
inference and training modes of deep neural networks. In the case of
inference, the main advantage from NVM comes from reduced data-fetching and
movement, while reprogramming of the crossbars is infrequent, requiring lower
endurance from the resistive technology (PCM or RRAM), but potentially higher
retention and programming yield accuracy [43]. To handle device faults,
programming errors, or noise, novel techniques for performing error-detection
and correction for the computations performed within these crossbar arrays
have been devised recently [44, 45] and experimentally demonstrated [46]. On
the other hand, implementation of training in NVM crossbars [47, 48, 49] can
take advantage of efficient update schemes for tuning each of the resistive
weights in parallel (e.g., ”outer product” updates such as in [50]). In turn,
the implementation of neural network training puts a larger burden on the
underlying NVM technology from an endurance perspective, and requirements for
a symmetric and linear change in the device resistance when programmed up or
down. While the technology remains highly promising, the current state of
resistive NVM suffers from large programming asymmetries and uniformity
challenges. As the technology continues to mature, some current approaches are
able to mitigate these setbacks by complementing the resistive technology with
short term storage in capacitors [51], or operating in a more binary mode
[52], but with cost of either area or prediction accuracy. Nonetheless,
practical demonstrations using resistive crossbar networks have already
included, to name just a few, image filtering and signal processing [53],
fully connected and convolutional networks [48, 39, 51], LSTM recurrent neural
networks [25], and reinforcement learning [54].

(a)

(b)

Figure 4:  Machine learning hardware trends: Peak energy efficiency vs
throughput (a) and area efficiency (b) for recent ASIC implementations
reported in ISSCC, SOVC, and JSSC (see main text).

##  V Future of analog deep neural network architectures

Analog circuits can be more compact than digital circuits, especially for
certain low-precision operations like the add operation needed in neural
network architectures or the in-memory computing circuits for summing up
weighted currents [55]. While mismatch variations could be a feature for
certain network architectures like the Extreme Learning Networks, they need to
be addressed in analog implementations of deep networks by using design
techniques such as the schemes described in Sec. III or through training
methods that account for the statistics of the fabricated devices.

The work of [56] shows that it is possible to use neural network training
methods as an effective optimization framework to automatically compensate for
the device mismatch effects of analog VLSI circuits. The response
characteristics of the individual VLSI neurons are added as constraints in an
off-line training process, thereby compensating for the inherent variability
of chip fabrication and also taking into account the particular analog
neuron’s transfer function achievable in a technology process. The measured
inference results from the fabricated analog ASIC neural network chip [56]
matches that from the simulations, while offering lower power consumption over
a digital counterpart. A similar retraining scheme was used to correct for
memristor defects in a memristor-based synaptic network trained on a
classification task [57].

###  V-A Trends in machine learning ASICs

To understand the energy and area efficiency trends in recent ASIC designs of
ML systems, we present a survey [58] of papers published in IEEE ISSCC and
IEEE SOVC conferences from 2017-2020 (similar to the ADC survey in [59]), and
in the IEEE Journal of Solid-state Circuits (JSSC).

Using the data from [60], we show two plots. The first plot shows the
throughput vs. peak energy efficiency tradeoff for digital and mixed-signal
designs (Fig. 4(a)). It can be seen that while throughput is comparable for
analog and digital approaches, the energy efficiency for mixed-signal designs
is superior to their digital counterparts. Figure 4(b) plots the area
efficiency vs peak energy efficiency for these designs and further classifies
the digital designs according to the bit-width of the multiply-accumulate
(MAC) unit. It can again be seen that the mixed-signal designs have better
tradeoff than the digital counterparts. Furthermore, as expected, lower bit
widths lead to higher efficiencies in terms of both area and energy. Lastly,
the efficiency of mixed-signal designs seem significantly better than digital
designs only for these with very low-precision 1-bit MACs.

##  VI Conclusion

While deep network accelerator designs are implemented primarily using digital
circuits, in-memory computing systems can benefit from analog and mixed-signal
circuits for niche ultra low-power edge or biomedical applications. The peak
energy efficiency trends in Fig. 4 show that mixed-signal designs can be
competitive at lower-bit precision parameters for network accelerators. Some
of the analog machine learning circuit blocks such as the sigmoid and the
winner-take-all designs can implement directly the sigmoid transfer function
of the neuron, and the soft-max function of the final classification layers of
a deep network. It will be interesting to see how these circuits will be
incorporated further into in-memory computing systems in the future.

##  VII Acknowledgment

The authors would like to thank Mr. Sumon K. Bose and Dr. Joydeep Basu for
help with figures; and T. Delbruck for comments.

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Hexamethylenetetramine (HMT) was detected in carbonaceous meteorites and can
be degraded to formaldehyde and ammonia upon hydrothermal treatment.111 HMT
was shown to be formed by photochemical reactions and warming of interstellar
ice analogs.112, 113, 114 Since formaldehyde and ammonia are reactants in our
proposed vitamin B3 synthesis pathway (see Reaction Pathway and eqs. 1 and 2),
HMT decomposing in the aqueous interiors of carbonaceous planetesimals could
be another potential source of vitamin B3 not included in the present model.
If the presence of HMT in the interstellar medium is detected by observations,
future studies might be able to estimate the initial concentration of HMT in
the solar nebula and explore whether it has the potential to contribute
significantly to vitamin B3 synthesis in meteorite parent bodies.

Aspartic acid, which is one of the intermediate amino acids S2 in Reaction
Pathway, was found in meteorites.80, 81 This indicates that a part of the
available stock of amino acids participated in the vitamin B3 synthesis and
the rest remained in the parent body until after its phase of aqueous
activity. Pearce et al.44 showed that simulating the formation of several
different prebiotic organics in thermochemical equilibrium models
simultaneously often results in zero abundances or fails to reproduce the
measurements in meteorites, as the model does not converge correctly due to
its increased complexity. This limitation of the model means that we always
obtain the upper possible limit using the whole pool of reactants for one
specific pathway. The actual abundances are a weighted combination of the
results for the synthesis of different organic molecules in parallel and
partially yet unknown chemical mechanisms, drawing from overlapping sets of
reactants, as mentioned above. This limitation of the thermochemical models
would also be a challenge in future combined formose and vitamin B3 models.

Not only the amount and allocation of the available reactants (which still
needs to be explored further), but also processes involving the products might
explain the overestimates in the simulations. In comparison to other vitamins,
B3 is relatively stable. On the other hand, B3 is one of the least complex
vitamins. Compared to the stability of other prebiotic molecules found in
meteorites, e.g., nucleobases,115 vitamin B3 (in this case nicotinamide)
decomposes orders of magnitude faster,116 especially under hot
($\geq$80\text{\,}\mathrm{\SIUnitSymbolCelsius}$$) and alkaline conditions as
presumed for carbonaceous parent body interiors, as mentioned earlier. This
follows from comparing the pH-dependent decomposition rates and Arrhenius
plots of nucleobases115 with the percentage of vitamin B3 degradation at
$80\text{\,}\mathrm{\SIUnitSymbolCelsius}$ over $60\text{\,}\mathrm{min}$,116
and might explain the overproduction in the present simulations. Potential
destruction mechanisms of aqueous vitamin B3 have not been included in the
model but might reduce its final abundance found in meteoritic samples,
especially over the long periods of radiogenic heating inside parent bodies.46
It is difficult to quantify the exact pH and duration of aqueous activity in
the parent body of a specific meteorite and therefore was not included in the
model. Nevertheless, Smith et al.12 found a clear correlation between
increasing aqueous alteration of the studied CM2 meteorites and a decreasing
vitamin B3 abundance, confirming that decomposition by hydrolysis plays a role
in meteorite parent bodies.

Smith et al.12 also studied the hydrolysis of nicotinamide under the
procedures employed to extract the organics from the meteorites. When using
acid-hydrolyzed hot water ($6\text{\,}\mathrm{M}$ HCl,
$150\text{\,}\mathrm{\SIUnitSymbolCelsius}$, $3\text{\,}\mathrm{h}$) for
extraction, a common method also used by Oba et al. (2023),14 purchased
nicotinamide was $100\text{\,}\mathrm{\char 37\relax}$ converted to nicotinic
acid. This might also explain why nicotinamide could only be detected by the
more gentle method by Oba et al. (2022),13 using water extraction and ultra-
sonication for $10\text{\,}\mathrm{min}$ at room temperature without involving
high temperatures or acids. In their other study Oba et al. (2023),14 they
could only find it in hot water extracts of the Orgueil CI meteorite at
$105\text{\,}\mathrm{\SIUnitSymbolCelsius}$ over $20\text{\,}\mathrm{h}$,
which is at a lower temperature and over a shorter period in comparison to hot
water extraction performed by Smith et al.12 In the same study Oba et al.
(2023),14 acid-hydrolyzed extraction ($6\text{\,}\mathrm{M}$ HCl, same as
acid-hydrolyzed extraction by Smith et al.12) of the same sample yielded no
nicotinamide, but a slightly higher nicotinic acid abundance. This might
indicate that in the acidic conditions of the extraction, nicotinamide was
partially decomposed116 and partially converted to nicotinic acid.12 The
method of extraction in meteorites itself seems to reduce the amount of
organic material recovered, and hence might explain the discrepancy between
the presented simulations and measurements.

In Figures 2 and 3, we also included the sum of all isomers of nicotinic acid
(isonicotinic acid, picolinic acid) and nicotinamide (isonicotinamide,
picolinamide) found in meteorites.12, 13, 14 This is due to the fact that
thermochemical equilibrium simulations can not distinguish between isomers.45,
46 Following from this limitation it might be that the simulated abundances
actually represent the sum of all isomers.

In all the carbonaceous meteorite and asteroid extracts of Oba et al.,13, 14
no picolinic acid was detected. Picolinamide was not detected in the Ryugu
asteroid samples and the CI meteorite Orgueil, and in very minor amounts
($\leq$10\text{\,}\mathrm{p}\mathrm{p}\mathrm{b}$$), which is similar to the
background noise, in the CM2 meteorites Murchison and Murray as well as the
ungrouped C2 meteorite Tagish Lake. Dominance of the nicotin- and isonicotin-
isomers over picolin- isomers might be a direct consequence of the newly
proposed mechanism in Reaction Pathway. The decarboxylation by charge
migration from 6 to 10 excludes that a carboxyl/amide group is at the
2-position of the pyridine ring of the final molecule. However, this is the
case for the picolin- isomers or quinolinic acid mentioned above. On the other
hand, starting with 4-oxobutanoic acid/4-oxobutanamide instead of S1 results
in glutamic acid/glutamine in the Strecker reaction. Combining this directly
with glycolaldehyde F1 (instead of glyceraldehyde F4/F7) to form an imine
equivalent to 1 in Reaction Pathway yields the isonicotin- isomers, following
the same newly proposed mechanism. This is supported by the fact that glutamic
acid was also found in meteorites.80, 81

Nevertheless, Smith et al.12 found picolinic acid in their extracts from
several CM2 meteorites, which is in direct contradiction to the missing
detection in Murchison and Murray by Oba et al. (2022),13 all members of the
same meteorite group CM2 and potentially sharing the same parent body. They
also performed proton-irradiation experiments of pyridine and CO2 ice
mixtures. The underlying idea is that prebiotic organics formed in the
interstellar and interplanetary medium on ice grains at low temperatures, and
were incorporated into the source material of planetesimals. Meteorites might
have inherited these organics and not (only) formed them in situ by aqueous
chemistry, as presented here. Smith et al.12 claim to have found more picolin-
than other isomers in these experiments, similar to the pyridine carboxylic
acids detected in the extract of their most aqueously unaltered meteorite LEW
85311 studied. However, no respective chromatography-mass spectroscopy data
were provided to support these findings. It is questionable if pyridine is
readily available on ice grains, as this rather complex molecule was never
detected in the interstellar medium.117, 118, 119, 120

Anyway, there needs to be an explanation as to why Smith et al.12 found
picolin- isomers in dominating amounts in meteorites, and Oba et al.13, 14 did
not. They might be inherited from ice grain processes and either very
heterogeneously distributed in the same parent body, or the CM2 chondrites
originate from several different bodies with different chemical histories.
Another reason could be the contamination of the meteorite samples before
their retrieval. At the same time, the asteroid material studied by Oba et al.
(2023)14 might have the highest chance of evading Earth’s biosphere. Oba et
al. (2022)13 also refer to previous experiments on photon-irradiated H2O, CO,
NH3, and CH3OH ice mixtures (Oba et al. (2019)121) to explain the synthesis of
the N-heterocycles found in their meteoritic samples. The measured acid/amide
ratios in the photochemical products were $0.81.0$, and $9.372.8$ in the
meteorite extracts.13 Oba et al. explained the high ratios in meteorites with
aqueous processing of photochemical products inherited from interstellar ice
grains into the meteorite parent bodies. As an alternative to in situ aqueous
chemistry, we recognize reactions on and inheritance from ice grains as
another possible source of the vitamin B3 in extraterrestrial carbonaceous
material. More experimental work is needed here to find pathways feasible for
vitamin B3 synthesis in the interstellar medium. The same is true for aqueous
pathways other than demonstrated by Cleaves & Miller79 to study their
interconnection with the mechanisms in Reaction Pathway. This is necessary to
better understand the origin of vitamin B3 and its isomers in these extreme
environments very different from the typical conditions studied in most
chemical laboratories (extreme temperatures, no free oxygen available, etc.).
It is an open question whether inheritance from ice grains or in situ aqueous
synthesis is the primary source of vitamin B3 and other prebiotic organics in
meteorites.

## Conclusion

Aqueous chemistry inside the warm porous rock of carbonaceous chondrite parent
body planetesimals is a promising candidate for the prebiotic synthesis of
vitamin B3 in the early solar system. This could be a way to provide prebiotic
molecules that are fundamental to all life as we know it and universal to all
forming (exo)planetary systems. For the first time, we provide a detailed
reaction mechanism suitable for this environment without any obvious caveats.
Neither free oxygen nor electrical discharges are required, and the
availability of necessary reactants is plausible. The origin of meteoritic
organics and their contribution to the origins of life can only be understood
by carefully assessing the physical setting and applying it to detailed
chemical reaction mechanisms in an interdisciplinary approach.

We tested the thermodynamic favorability of our newly proposed reaction (see
Reaction Pathway) and evaluated the resulting abundances in comparison to
measurements in carbonaceous chondrites and asteroids. We conclude that it
fits well into the complex network of other prebiotic pathways, e.g.,
Strecker,55, 69 Fischer-Tropsch,42, 44, 122, 46 or formose45 reactions active
in the aqueous phase of planetesimals. More detailed modeling of competition
between these pathways is needed, e.g., the interplay with the formose
reaction. Additionally, decomposition reactions of vitamin B3 either by
hydrolysis in planetesimals or meteorite extraction in the laboratory need to
be explored further to fully understand the abundances found by measurements
in meteorites.

Inheritance of organics formed on the surface of ice grains by irradiation in
the interstellar medium (often including reactions between radicals) is
another promising synthesis pathway that needs to be acknowledged.12 After
inheritance into meteoritic material, this might influence the final available
organic reservoir brought to the early Earth by impacts, but this is beyond
the scope of the present study.

It might be interesting to make 3-oxopropanoic acid, 3-oxopropanamide,
4-oxobutanoic acid, and 4-oxobutanamide new targets in surveys hunting for
organics in comets. We hope the present work emphasizes the importance of
these aldehydes for prebiotic synthesis in the early solar system and is able
to stimulate cometary surveys to search for them despite their rather high
complexity and specificity. If future surveys can detect these key reactants,
this might bring us closer to understanding the prebiotic synthesis of the
vital vitamin B3 as well as proteinogenic amino acids in the interplanetary
space of the arising solar system.

We hope the newly proposed mechanism in Reaction Pathway, building on the
previous work of Cleaves & Miller,79 might encourage more research into
prebiotic vitamin B3. In the context of prebiotic synthesis, little attention
seems to be given to it. This is despite the fact that it has the potential to
connect the competing “RNA first” and “metabolism first” hypotheses in a
unifying scenario, much like the central dogma of molecular biology in present
life.

## Computational Methods

Figure 5: Gibbs free energies of formation $\Delta G_{f,\mathrm{(aq)}}$ as a
function of temperature $T$ for the molecules not included in the CHNOSZ
database. All energies are given in an aqueous solution at a pressure of
$100\text{\,}\mathrm{b}\mathrm{a}\mathrm{r}$, assuming an ideal infinite
dilution.

### Thermochemical Calculations and Data

The software ChemApp (version 740) provided by GTT Technologies was used to
perform the thermochemical equilibrium calculations.123 As inputs this
software requires Gibbs free energies of formation for the molecules involved
in the reaction (see also next Section on Gibbs Free Energy of Formation).
These were mostly obtained from the database CHNOSZ (version 1.3.6, 2020 March
16), providing a huge library of consistent Gibbs free energies of formation,
obtained from a large set of experimental and theoretical studies.124

The source code to set up and run the simulations, excluding the proprietary
software ChemApp, is openly available on Zenodo125 and as a Git repository
(https://github.com/klauspaschek/prebiotic_synthesis_planetesimal). More
details can be found in our previous study.46

### Gibbs Free Energy of Formation

Each chemical molecule that takes part in a reaction as a reactant or product
has a Gibbs free energy of formation $\Delta G_{f}$ that depends on
temperature and pressure. The lower the value of $\Delta G_{f}$ the higher the
probability that the molecule will form. The molecules should form
spontaneously in the case of negative $\Delta G_{f}$ when the required
reactants are available.

The $\Delta G_{f}$ as a function of temperature $T$ and pressure $p$ can be
calculated by fitting the corresponding thermodynamic data $\Delta G_{f}$ from
the CHNOSZ database to the function

$G_{f}(T,P)=a+bT+cTln(T)+dT^{2}+eT^{3}+f/T+gP.$ (3)

The Gibbs coefficients $a$ through $g$ are necessary inputs for the
equilibrium chemistry software ChemApp, which is used for the chemical
reaction simulations.

As shown in previous studies,69, 44, 46 in the temperature range of liquid
water the Gibbs free energies are independent of pressure. This independence
of pressure allows the pressure of the thermodynamic system to be set to a
constant $100\text{\,}\mathrm{b}\mathrm{a}\mathrm{r}$, making temperature and
initial reactant concentrations the only dynamic simulation variables. This
value is chosen as it is typically representing the conditions in porous
planetesimals of up to hundreds of kilometers in radius due to lithospheric
pressure.44, 105

As the pressure dependence of $\Delta G_{f}$ is negligible, the Gibbs
coefficient $g$ can be neglected.44 Nevertheless, the boiling point of water
remains the only pressure-dependent parameter of the model that needs to be
considered. Our modeled reactions operate in the aqueous phase. It is assumed
that when water evaporates, the prebiotic synthesis ceases, and lately formed
organic molecules retain their present abundance. Each reaction must have a
negative Gibbs free energy of reaction $\Delta G_{r}$ to be thermodynamically
favorable, expressed as

$\Delta G_{r}=\sum_{\mathrm{products}}\Delta
G_{f}-\sum_{\mathrm{reactants}}\Delta G_{f}.$ (4)

Conversely, reactions with positive $\Delta G_{r}$ require activation energy
to progress. This means that this would increase the total Gibbs free energy
of the system $\Delta G$.

When the system reaches equilibrium, the chemical reactions cease, as at the
current concentrations there is no longer a set of reactions that results in a
negative $\Delta G_{r}$. This highlights the overall concept of thermodynamic
chemical reaction simulation, which involves establishing initial
concentrations of reactant molecules in the system and then calculating the
resulting reactant and product concentrations that minimize $\Delta G$. The
total Gibbs free energy of the system $\Delta G$ can be written as the
combination of the Gibbs free energy of formation $\Delta G_{f}$ of each
molecule

$\Delta G=\sum_{\mathrm{all}}\Delta G_{f}.$ (5)

Catalysts have no role in minimizing Gibbs free energy computations because
they do not commit molecules to the reaction. Catalysts only accelerate the
reaction time by reducing the activation energy, which is a variable not used
in equilibrium calculations.

### Gibbs Free Energies of Formation for Species Missing in CHNOSZ

The CHNOSZ database contains only the Gibbs energy of formation for
nicotinamide in its solid form $\Delta G_{f,\mathrm{(s)}}$. To obtain the
Gibbs energy in an aqueous solution $\Delta G_{f,\mathrm{(aq)}}$, we used the
formula

$\Delta G_{f,\mathrm{(aq)}}(T)=\Delta
G_{f,\mathrm{(s)}}(T)+RT\ln(s_{\mathrm{sat}}(T)),$ (6)

where $T$ is the temperature, $R$ is the ideal gas constant, and
$s_{\mathrm{sat}}$ is the ideal saturated solubility in water in units of ,
assuming infinite dilution and that Henry’s law applies.126 We used measured
temperature-dependent solubilities of nicotinamide in water127 and fit the
data with a polynomial of second degree as a simple approximation of the
temperature dependence. This allows us to extrapolate the measured data points
for $s_{\mathrm{sat}}(T)$ over the whole considered temperature range. fig. 5
shows the resulting temperature dependence of the aqueous Gibbs energies of
formation, using eq. 6.

Nicotinic acid is missing in CHNOSZ. We used measured literature values for
the thermodynamic properties at standard conditions128, 129 and imported them
into CHNOSZ. This allowed to calculate the Gibbs energies of formation over
the whole considered temperature range.

Glycolaldehyde is also missing in the database, but we performed quantum
chemistry calculations in a previous study45 to obtain its Gibbs energies of
formation. The same techniques were used to calculate the Gibbs energies of
formation for the aldehydes 3-oxopropanoic acid and 3-oxopropanamide for the
first time in a private communication with B. K. D. Pearce (Department of
Earth and Planetary Science, Johns Hopkins University, July 2023).

Using the software package Gaussian 09,130 the atomic and molecular energies
and entropies were determined to calculate the Gibbs free energy of formation.
The Becke-3–Lee–Yang–Parr (B3LYP) hybrid density functional131, 132, 133 and
the polarizable continuum model (PCM) for aqueous solution effects134, 135
were used, with geometry optimizations conducted using the 6-31G(d,p) basis
set. Single-point energies and frequency were calculated using the
6-311++G(2df,2p) basis set. The Gibbs free energy of formation was determined
using Ochterski’s three-step method,136 incorporating enthalpy and entropy
calculations at different temperatures. Some values were obtained from
experiments137 and thermodynamic tables,138 while an adjustment was made to
the entropy of carbon (graphite) based on similar calculations for hydrogen
and oxygen. A small error was introduced due to the use of gas-state carbon
instead of carbon (graphite) for an enthalpy correction. More details can be
found in the previous study45 and the given references. fig. 5 shows all the
Gibbs energies of formation used in our simulation that are not available in
the CHNOSZ database.

## Acknowledgements

The authors would like to thank Oliver Trapp for helping to understand the
chemical reactions toward vitamin B3 and deriving parts of the candidate
prebiotic pathway. We would also like to thank Ben K. D. Pearce for performing
quantum chemistry calculations to obtain Gibbs free energies of formation for
some molecules missing in the CHNOSZ database. We thank Christelle Hiemstra
for the stylistic review of the manuscript. K.P. acknowledges financial
support by the Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) under Germany’s Excellence Strategy EXC 2181/1 - 390900948 (the
Heidelberg STRUCTURES Excellence Cluster). K.P. is a fellow of the
International Max Planck Research School for Astronomy and Cosmic Physics at
the University of Heidelberg (IMPRS-HD). D.A.S. and T.K.H. acknowledge
financial support by the European Research Council under the Horizon 2020
Framework Program via the ERC Advanced Grant Origins 83 24 28.

## Conflict of Interest

The authors declare no conflict of interest.

Keywords:

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## Entry for the Table of Contents

Aqueous chemistry inside meteorite parent bodies allows the formation of
prebiotic molecules crucial for all life in the early solar system. We present
a reaction mechanism suitable for vitamin B3 synthesis in this environment,
which is experimentally verified in the literature. Vitamin B3 was transported
to the Hadean Earth by meteorite falls and initiated redox chemistry in the
form of NAD(P)H, potentially participating in the origins of life.