These authors contributed equally to this work.

These authors contributed equally to this work.

[1]Yutaka Hori

[1]Department of Applied Physics and Physico-Informatics, Keio University,
3-14-1, Yokohama, Kanagawa 223-8522, Japan

# Analysis of Signal Distortion in Molecular Communication Channels Using
Frequency Response

Shoichiro Kitada<EMAIL_ADDRESS>Taishi Kotsuka<EMAIL_ADDRESS><EMAIL_ADDRESS>*

###### Abstract

Molecular communication (MC) is a concept in communication engineering, where
diffusive molecules are used to transmit information between nano or micro-
scale chemical reaction systems. Engineering MC to control the reaction
systems in cells is expected for many applications such as targeted drug
delivery and biocomputing. Toward control of the reaction systems as desired
via MC, it is important to transmit signals without distortion by MC since the
reaction systems are often triggered depending on the concentration of
signaling molecules arriving at the cells. In this paper, we propose a method
to analyze signal distortion caused by diffusion-based MC channels using
frequency response of channels. The proposed method provides indices that
quantitatively evaluate the magnitude of distortion and shows parameter
conditions of MC channels that suppress signal distortion. Using the proposed
method, we demonstrate the design procedure of specific MC channels that
satisfy given specifications. Finally, the roles of MC channels in nature are
discussed from the perspective of signal distortion.

###### keywords:

Molecular communication, Biomoleculer system, Frequency response, Signal
distortion, Diffusion equation

##  1 Introduction

In nature, many cells share information using signaling molecules to achieve
cooperative functions [1, 2, 3]. This information-sharing system between cells
is known as molecular communication (MC) systems. In MC systems, a transmitter
cell releases signaling molecules, and a receiver cell accepts the signal by
adsorption or absorption of the signaling molecules, triggering chemical
reactions in the cell. One of many examples of MC is quorum sensing conducted
by bacteria, where the cells use signaling molecules so called autoinducer to
regulate population density dependent collective behaviors [4, 5]. MC systems
are also engineered in synthetic biology to perform complex tasks at a
population level. Potential applications of such synthetic MC systems include
targeted drug delivery and biocomputing [6, 7, 8, 9, 10]. To control systems
via MC for these applications, MC channels need to be able to transfer
information appropriately, which inspires us to analyze fundamental
characteristics of MC channels.

In the control of reaction systems in a receiver cell, MC channels must be
designed so that they can transfer desired signals from a transmitter cell to
a receiver cell. To this end, the gain characteristics of MC channels were
analyzed, and the frequency bandwidth that can be transmitted without
attenuating the magnitude of the signal was revealed [11, 12, 13, 14].
However, the analysis of the simple gain characteristics does not necessarily
assess the ability of the transmission signals to trigger the downstream
reactions in the receiver cells since the regulation of reaction systems in a
cell often involves a digital-like switching mechanism modeled by the Hill
function [15]. In other words, the signal may not be able to transfer the
desired on/off patterns to the reaction systems at a receiver cell if the
waveform of the signal at the receiver is distorted as shown in Fig. 1.
Therefore, to guarantee the quality of the transmitted signals, it is crucial
to assess the degree of distortion that is added in MC channels.

In this paper, we propose a method to analyze signal distortion caused by one-
dimensional diffusion-based MC channels. Specifically, we first introduce
indices evaluating signal distortion by the gain and the phase delay
characteristics and derive these characteristics of MC channels based on the
diffusion equation and the rate equation. We then show design conditions for
MC channels in which the magnitude of distortion becomes below a specified
level based on the indices. Using the proposed method, we demonstrate the
design procedure of specific MC channels that satisfy given specifications.
Finally, the roles of MC channels in nature are discussed from the perspective
of signal distortion.

This paper is organized as follows. In the next section, we model one-
dimensional MC channels based on diffusion of signaling molecules and
binding/dissociation reactions between signaling molecules and receptors. In
Section 3, we define indices evaluating signal distortion based on the
frequency response and analyze the magnitude of distortion in the channels
quantitatively and show the design condition of MC channels to repress the
signal distortion under certain level. Using the analytical results, we
demonstrate a design procedure of MC channels that can suppress the signal
distortion in Section 4. Finally, the paper is concluded in Section 5.

Figure 1: Network of multiple cells and MC between a transmitter cell and a
receiver cell with desired and undesired on/off signal profiles at the
receiver.

##  2 Model of MC Channels and Problem Setting

We consider one-dimensional MC channels in which signaling molecules secreted
from a transmitter cell diffuse in the fluidic environment $\Omega=[0,\infty)$
and their concentration is detected by a receiver cell at $x=x_{r}$ as shown
in Fig. 2, where $x\in\Omega$ is the position. The MC channels can be
decomposed into the diffusion system in which the signaling molecules diffuse
to the position of the receiver cell and the reception system in which they
are received by receptors on the receiver cell.

In the diffusion system, the signaling molecules move in a fluidic medium
according to the following diffusion equation,

$\frac{\partial u(x,t)}{\partial t}=\mu\frac{\partial^{2}u(x,t)}{\partial
x^{2}},$ (1)

where $u(x,t)$ is the concentration of the signaling molecules at position $x$
and at time $t$, and $\mu$ is the diffusion coefficient of the signaling
molecules. At the position of the receiver cell $x=x_{r}$, the concentration
of signaling molecules $u(x_{r},t)$ is sensed by binding/unbinding of the
signaling molecule to the receptor. We assume that the concentration of the
signaling molecules $u(x,t)$ does not change due to the binding and the
dissociation of the molecule to the receptor since, in typical receptor-ligand
reactions, the rate of dissociation is larger than that of binding [16],
resulting in the immediate dissociation of the signaling molecule from the
receptor. Since signaling molecules emitted at $x=0$ diffuse to infinity
beyond the position of the receiver cell $x=x_{r}$, the boundary conditions
are

$\displaystyle u(0,t)=v(t),$ (2) $\displaystyle\lim_{x\to\infty}u(x,t)=0,$ (3)

where $v(t)$ is the concentration of the emitted molecules.

Figure 2: One-dimensional model of MC channel, where a pair of a transmitter
and a receiver cell is located, and illustration of

signals with distortion

Figure 3: Schematic diagram of binding and dissociation reaction between
signaling molecules and receptors

Next, we consider the reception system, where signaling molecules arriving at
position $x=x_{r}$ bind to receptors on the surface of the receiver cell and
form a complex or dissociate from the complex. A schematic diagram of this
process is shown in Fig. 3. Let $k_{f}$ and $k_{r}$ denote the rate constant
in the binding reaction of the signaling molecule to the receptor and the rate
constant in the dissociation reaction from the complex, respectively. The
binding and dissociation reactions between the signaling molecules and the
receptors can be expressed as

$\ce{{\it s(t)+u(x_{r},t)}<=>[k_{f}][k_{r}]{\it c(t)}},$ (4)

where $c(t)$ is the concentration of the complex, and $s(t)$ is the
concentration of the free receptors. Assuming $k_{f}u(x_{r},t)\ll k_{r}$, the
dynamics of $c(t)$ can be expressed as

$\frac{dc(t)}{dt}=k_{f}ru(x_{r},t)-k_{r}c(t),$ (5)

where $r=s(t)+c(t)$ is the total concentration of the receptor on the cell
[17, 18]. Note that since the signaling molecules keep diffusing in MC
channel, the concentration of signaling molecules $u(x_{r},t)$ at the receiver
cell would be sufficiently smaller than the ratio $k_{r}/k_{f}$ [16], which
leads to $k_{f}u(x_{r},t)\ll k_{r}$.

We consider the concentration waveform of a signaling molecule at $x=0$ as an
input signal, which is transmitted to $x=x_{r}$ by diffusion. To transfer the
desired signal to the reaction system in the receiver cell, the input
concentration waveform should not be distorted as shown in Fig. 2. In
particular, the magnitude of the distortion caused by the diffusion system
should be smaller than that caused by the reception system to keep the
distortion of the entire MC channel small. Therefore, we quantitatively
analyze the magnitude of distortion caused by signal transmission by diffusion
to provide design guidelines for MC channels to suppress signal distortion.

##  3 Characteristics of Distortion in MC Channels

In this section, we propose a method to quantitatively analyze the magnitude
of distortion caused by the diffusion and the reception system. To this end,
we first define the magnitude of signal distortion by two types of features
based on frequency response. We then analyze the magnitude of the distortion
based on the transfer functions of the diffusion systems and the reception
system. Finally, we show the parameter conditions of the diffusion systems for
the magnitude of the distortion to be below a predefined threshold.

###  3.1 Amplitude distortion and delay distortion

We consider a transfer function $F(s)$ representing a general linear system.
When we input sine wave $v(t)=\sin(\omega t)$ into the system $F(s)$, the
output signal $z(t)$ is expressed as

$\displaystyle z(t)$ $\displaystyle=|F(j\omega)|\sin(\omega t+\angle
F(j\omega))$ (6) $\displaystyle=|F(j\omega)|\sin(\omega(t-\tau(\omega))),$ (7)

where

$\tau(\omega)=-\frac{\angle F(j\omega)}{\omega}$ (8)

is the phase delay, which represents the delay time of the system [19]. If the
gain $|F(j\omega)|$ and the phase delay $\tau(\omega)$ vary depending on
frequency $\omega$, the output waveform is distorted. Distortion due to the
gain $|F(j\omega)|$ is called amplitude distortion, and distortion due to the
phase delay $\tau(\omega)$ is called delay distortion [20, 21]. To
quantitatively analyze the magnitude of distortion on frequency basis, we
decompose distortion into amplitude distortion and delay distortion and define
their respective indices.

We define the index representing the magnitude of amplitude distortion in the
frequency bandwidth $[\omega_{1},\omega_{2}]$ as

$Q:=\max_{\omega_{1}\leq\omega\leq\omega_{2}}g(\omega)-\min_{\omega_{1}\leq\omega\leq\omega_{2}}g(\omega),$
(9)

where

$g(\omega)=20\log{|F(j\omega)|}$ (10)

is the logarithmic gain characteristics of the frequency transfer function
$F(j\omega)$. The amplitude distortion $Q$ represents the largest difference
between the logarithmic gain characteristics of the two sine waves which have
different frequencies in $[\omega_{1},\omega_{2}]$. We use the logarithmic
gain characteristics in the index $Q$ since it is relatively easy to compute
the logarithm of the gain characteristics of the diffusion systems, which is
discussed in detail in Sec. 3.2. In the same way, we define the index
representing the magnitude of delay distortion in the frequency bandwidth
$[\omega_{1},\omega_{2}]$ as

$R:=\frac{1}{T_{1}}\left(\max_{\omega_{1}\leq\omega\leq\omega_{2}}{\tau(\omega)}-\min_{\omega_{1}\leq\omega\leq\omega_{2}}{\tau(\omega)}\right),$
(11)

where $\tau(\omega)$ is the phase delay of the signal with the frequency
$\omega$ and $T_{1}$ is the period of the signal with $\omega_{1}$, namely
$T_{1}=2\pi/\omega_{1}$. The delay distortion $R$ expresses the largest
difference between the phase delays of the two sine waves, which have
different frequencies in $[\omega_{1},\omega_{2}]$, normalized by the period
$T_{1}$. Since the smaller the difference in gain (phase delay, resp.) in the
frequency bandwidth of the signal, the smaller the magnitude of distortion due
to amplitude shift (phase delay shift, resp.), the indices $Q$ ($R$, resp.)
are smaller if the system can transfer signals with less distortion.
Therefore, we evaluate the magnitude of distortion caused by MC channels using
the indices $Q$ and $R$. To obtain the amplitude distortion $Q$ and the delay
distortion $R$ in MC channels, we need the logarithmic gain characteristics
$g(\omega)$ and the phase delay $\tau(\omega)$ of the diffusion system and the
reception system. To this end, we derive the transfer functions and the
indices of the diffusion system and the reception system in the following
sections. To quantitatively analyze the magnitude of distortion caused by
diffusion, we first define the magnitude of signal distortion by two types of
features based on frequency characteristics. We then analyze the magnitude of
the distortion based on the transfer function of the diffusion system and show
the parameter conditions for the distortion to be below a predefined
threshold.

###  3.2 Transfer function and signal distortion of the diffusion system

To obtain the amplitude distortion $Q$ and the delay distortion $R$ for the
diffusion system, we derive the transfer function from the diffusion equation
(1). Using the Laplace transform of the concentrations $u(x_{r},t)$ and
$u(0,t)$ for time $t$ and considering their ratio, we obtain

$G(s)\coloneqq\frac{U(x_{r},s)}{U(0,s)}=e^{-\sqrt{\frac{x_{r}^{2}}{\mu}s}},$
(12)

where $U(\cdot,s)$ is the Laplace transform of the concentration $u(\cdot,t)$.
Using Eq. (12), we have the following proposition, which gives an analytic
form of the amplitude and delay distortion, $Q$ and $R$, for a frequency
bandwidth $[\omega_{1},\omega_{2}]$.

######  Proposition 1.

Consider the diffusion system $G(s)$ in Eq. (12). The amplitude distortion
$Q_{G}$ in Eq. (9) and the delay distortion $R_{G}$ in Eq. (11) for the
diffusion system $G(s)$ are

$Q_{G}=g_{G}(\omega_{1})-g_{G}(\omega_{2})=20\sqrt{\frac{x_{r}^{2}}{2\mu}}(\sqrt{\omega_{2}}-\sqrt{\omega_{1}})\log_{10}{e},$
(13)
$R_{G}=\frac{\tau_{G}(\omega_{1})-\tau_{G}(\omega_{2})}{T_{1}}=\frac{1}{T_{1}}\sqrt{\frac{x_{r}^{2}}{2\mu}}\left(\frac{1}{\sqrt{\omega_{1}}}-\frac{1}{\sqrt{\omega_{2}}}\right),$
(14)

where $g_{G}(\cdot)$ and $\tau_{G}(\cdot)$ are the gain characteristics and
the phase delay of the diffusion system $G(j\omega)$, respectively.

The proof of Proposition 1 is shown in Appendix A. Equations (13) and (14)
indicate that the magnitude of distortion decreases as the communication
distance $x_{r}$ decreases and as the diffusion coefficient $\mu$ increases.
Furthermore, they represent that the magnitude of distortion increases as the
signal bandwidth $[\omega_{1},\omega_{2}]$ goes into the higher frequency
region. Since the gain characteristics of the diffusion system involves an
exponential function, taking the logarithm of the gain characteristics
simplifies the calculation of the index $Q_{G}$.

######  Remark 1.

We have considered one-dimensional MC channels $\Omega$ to present the
essential idea of the analysis of signal distortion. The same idea can be
extended to a more general and realistic case, where the molecules diffuse in
three dimensions. In the case of diffusion in three dimensional space, the
transfer function $G^{\prime}(s)$ of the diffusion system from the transmitter
cell to the receiver cell can be derived as

$G^{\prime}(s)=\frac{1}{4\pi\mu d}e^{-\sqrt{\frac{d^{2}}{\mu}s}},$ (15)

where $d$ is the distance between the transmitter cell and the receiver cell
[22, 23]. The transfer function $G^{\prime}(s)$ consists of the function
$G(s)$ with the constant coefficient $1/4\pi\mu d$, which is independent of
the frequency variable $s$. Therefore, the corresponding indices
$Q_{G^{\prime}}$ and $R_{G^{\prime}}$ for the diffusion system in three
dimensional space differ from $Q_{G}$ and $R_{G}$ only by the constant factor,
which leads to the similar conclusion to the one-dimensional case.

###  3.3 Transfer function of the reception system

Next, we derive the transfer function of the reception system to obtain the
amplitude distortion $Q$ and the delay distortion $R$ for the reception
system. Using the Laplace transform of both sides of the differential equation
(5), the transfer function of the reception system $H(s)$ is obtained as

$H(s)\coloneqq\frac{C(s)}{U(x_{r},s)}=\frac{k_{f}r}{s+k_{r}},$ (16)

where $C(s)$ is the Laplace transform of $c(t)$. Using Eq. (16), we have the
following proposition, which gives an analytic form of the amplitude and delay
distortion, $Q$ and $R$ for the reception system, for a frequency bandwidth
$[\omega_{1},\omega_{2}]$.

######  Proposition 2.

Consider the reception system $H(s)$ shown as Eq. (16). The amplitude
distortion $Q_{H}$ and delay distortion $R_{H}$ for the reception system are

$Q_{H}=g_{H}(\omega_{1})-g_{H}(\omega_{2})=20\log_{10}{\frac{\sqrt{k_{r}^{2}+\omega_{2}^{2}}}{\sqrt{k_{r}^{2}+\omega_{1}^{2}}}},$
(17)
$R_{H}=\tau_{H}(\omega_{1})-\tau_{H}(\omega_{2})=\frac{1}{2\pi}\left(\arctan\left(\frac{\omega_{1}}{k_{r}}\right)-\frac{\omega_{1}}{\omega_{2}}\arctan\left(\frac{\omega_{2}}{k_{r}}\right)\right),$
(18)

where $g_{H}(\omega)$ is the gain characteristics, and $\tau_{H}(\omega)$ is
the phase delay characteristics for the frequency transfer function
$H(j\omega)$.

The proof of Proposition 2 is shown in Appendix B. Equations (17) and (18)
indicate that the magnitude of distortion caused by the reception system
increases as the signal bandwidth $[\omega_{1},\omega_{2}]$ goes into the
higher-frequency region as same as that caused by the diffusion system.

###  3.4 Upper limit of the communication distance satisfying distortion
constraint

Using the Proposition 1 and Proposition 2, we show the condition of the
communication distance to repress signal distortion below a certain level
based on the indices of the amplitude distortion and the delay distortion for
the diffusion system and the reception system. Let $Q_{M}$ and $R_{M}$ denote
the amplitude distortion and the phase distortion of the MC channel
$G(s)H(s)$. Since the gain and phase characteristics for the diffusion system
$G(s)$ and the reception system $H(s)$ are monotonically decreasing functions
for frequency $\omega$, $Q_{M}$ and $R_{M}$ can be decomposed as

$Q_{M}=Q_{G}+Q_{H},$ (19) $R_{M}=R_{G}+R_{H}.$ (20)

Therefore, by setting arbitrary thresholds $Q_{0}>Q_{M}$ and $R_{0}>R_{M}$ for
the amplitude distortion and the phase distortion of the MC channel
$G(s)H(s)$, the upper limit on the communication distance $x_{r}$ between the
cells to keep the magnitude of distortion below a threshold value is obtained
as

$x_{r}<\min{\left(x_{Q},x_{R}\right)},$ (21)

where

$x_{Q}:=\frac{\sqrt{2\mu}(Q_{0}-Q_{H})}{20(\sqrt{\omega_{2}}-\sqrt{\omega_{1}})\log_{10}e},$
(22)
$x_{R}:=\frac{\sqrt{2\mu}(R_{0}-R_{H})T_{1}}{\left(\frac{1}{\sqrt{\omega_{1}}}-\frac{1}{\sqrt{\omega_{2}}}\right)}.$
(23)

This can be an indicator to design the communication distance of MC channels.

##  4 Numerical Simulation

In this section, we show a design procedure for a specific MC channel that can
transfer signals with small distortion. In particular, we use Proposition 1
and 2 to show the design condition of the communication distance $x_{r}$ under
a given specification. We then analyze the effect by $x_{r}$ as well as other
parameters to the distortion. Finally, we discuss the structure of MC channels
in nature with a focus on signal distortion.

###  4.1 Design of communication distance for suppressing distortion in MC
channel

We consider the MC channel in which signaling molecules such as autoinducer
are secreted from a transmitter cell, diffuse through the fluidic environment,
and are then sensed by receptors on the surface of a receiver cell. The
concentration of the complex formed by signaling molecules and receptors on
the receiver cell is observed when a square wave signal is input into this MC
channel. The observed signal is distorted due to the kinetics of the diffusion
of molecules and reception on the receiver cell. Hence, to suppress the
distortion, we here consider adjusting spatial arrangement of cells for given
transmitter/receiver cells, and signaling molecules. The specific objective of
the design is to find a communication distance $x_{r}$ such that the
distortion due to the diffusion system becomes less than $1/5$ times the
distortion due to the reception system. Thus, the thresholds for the magnitude
of distortion are set as $Q_{0}=1.2Q_{H}$ and $R_{0}=1.2R_{H}$. Specifications
of the MC channel are as follows:

  * (a)

The diffusion coefficient of the signaling molecules is
$\mu=83\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}^{2}\mathrm{/}\mathrm{s}$$
[24].

  * (b)

The design range of the communication distance $x_{r}$ is limited by $0\leq
x_{r}\leq 400\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}$$.

  * (c)

Each parameter of the reception system is $k_{r}=4.0\cdot
10^{-3}\,$\mathrm{s}^{-1}$$, $k_{f}=1.0\cdot
10^{-3}\,$\mathrm{\SIUnitSymbolMicro}\mathrm{M}^{-1}\mathrm{s}^{-1}$$ and
$r=4.0\,$\mathrm{\SIUnitSymbolMicro}\mathrm{M}$$ [18].

To design the communication distance $x_{r}$ under the specifications (a)–(c),
we first analyze the magnitude of the distortion based on the indices of the
amplitude distortion in Eq. (9) and the delay distortion in Eq. (11) for the
diffusion system and the reception system. We then evaluate the distortion of
signals with the frequency band $[5.0\cdot 10^{-4},4.0\cdot
10^{-1}]\,$\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{/}\mathrm{s}$$, where the
upper bound is the frequency at which the signal transmission is limited by
the receptor system rather than diffusion since the gain becomes
$|H(j\omega_{2})|=1/100$. The magnitudes of the distortions of the reception
system in this frequency band are computed as $Q_{H}=39.9$ and
$R_{H}=1.95\cdot 10^{-2}$ using the parameters in the specification (c).
Substituting the values of $Q_{H}$ and $R_{H}$ into the formula (21), we
obtain the condition for the communication distance as
$x_{r}<14.6\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}$$. If $x_{r}$ satisfies
this condition, the magnitude of distortion due to the diffusion system $G(s)$
can be suppressed to less than $1/5$ times that of distortion in the reception
system $H(s)$.

Fig. 4 illustrates that the responses in the MC channel $G(s)H(s)$ (green
dotted line) and the reception system $H(s)$ (orange line) with the
communication distance $x_{r}=14\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}$$
when the square wave $v(t)$ with the fundamental frequency
$\omega_{1}=5.0\cdot 10^{-4}\,\mathrm{rad/s}$ is input to the systems. Since
the distortion in the diffusion system is suppressed more than that in the
reception system, the distortion in the channel is approximately at the same
level as the reception system. On the other hand, Fig. 5 illustrates the
responses in the MC channel $G(s)H(s)$ (green dotted line) and the reception
system $H(s)$ (orange line) with the communication distance
$x_{r}=100\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}$$. Fig. 5 shows that the
distortion of the response in the MC channel is more significant than that in
the reception system alone since the rise of the response in the MC channel is
further slowed down due to the effect of the diffusion of signaling molecules.
These examples illustrate that one can design the MC channel satisfying the
specifications (a) – (c) based on the design condition (21) derived from the
proposed indices $Q$ and $R$. Note that the proposed method can be applied to
signals composed of arbitrary frequency bands. This feature allows for the
analysis of signal distortion for ion-based communication as well, where the
signal tends to be an impulse-like shape that can be modeled as step signals
with small width.

The distortion analysis is particularly useful to ensure the activation timing
of the downstream reaction in the receiver cell. Suppose the reaction system
in the receiver cell is activated when the concentration of the complex is
$c(t)\geq 0.09\,$\mathrm{\SIUnitSymbolMicro}\mathrm{M}$$. We define the
desired activation time $T_{v}$ as the time when the signal becomes $c(t)\geq
0.09\,$\mathrm{\SIUnitSymbolMicro}\mathrm{M}$$ within one pulse, and since the
lowest frequency of the signal is $\omega_{1}=5.0\cdot
10^{-4}\,$\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{/}\mathrm{s}$$, the desired
activation time is calculated as $T_{v}=6.5\cdot 10^{3}\,$\mathrm{s}$$. On the
other hand, the activation time in the response of the MC channel response is
$T_{a}=5.6\cdot 10^{3}\,$\mathrm{s}$$ for
$x_{r}=19\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}$$ (Fig. 4) and
$T_{a}=4.1\cdot 10^{3}\,$\mathrm{s}$$ for
$x_{r}=100\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}$$ (Fig. 5). The activation
time $T_{a}$ in the MC channel for
$x_{r}=19\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}$$ is closer to the desired
activation time $T_{v}$. This is because
$x_{r}=19\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}$$ satisfies the design
condition (21) and the distortion is smaller. Therefore, by designing MC
channels using the proposed method, it is possible to approach the desired
switching control for the reaction system in the receiver cell.

Figure 4: The responses of the reception system and the MC channel to a square
wave with the communication distance
$x_{r}=14\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}$$, which satisfies the
design condition (21). The distortion level of the signal transmitted via both
of the diffusion and the reception system (green) is almost the same as that
of the signal transmitted only via the reception system (orange), indicating
that the primary source of the distortion is the reception system.  Figure 5:
The responses of the reception system and the MC channel to square wave with
the communication distance
$x_{r}=100\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}$$, which does not satisfy
the design condition (21). Compared to Fig. 4, the signal is further distorted
by the diffusion system.

###  4.2 Dependence of distortions on parameters

Next, we explore the dependence of the proposed indices on parameters such as
the diffusion coefficient $\mu$ and the dissociation rate constant $k_{r}$.
These parameters are usually specific to the species of the receiver cell and
the signaling molecules. Thus, understanding the effect of these parameters on
distortion allows for the proper choice of the cell and the molecule.

To simplify the analysis of the relation between the distortion indices
$Q_{G}$, $R_{G}$, $Q_{H}$, and $R_{H}$ and the parameters, we normalize the
frequencies by $\omega^{\prime}_{1}\coloneqq\omega_{1}/k_{r}$ and
$\omega^{\prime}_{2}\coloneqq\omega_{2}/k_{r}$, and the communication distance
by

$\lambda\coloneqq\sqrt{\frac{x_{r}^{2}k_{r}}{2\mu}}.$ (24)

Therefore, the distortion indices for the diffusion system and the reception
system can be rewritten as

$Q_{G}=20\lambda\left(\sqrt{\omega^{\prime}_{2}}-\sqrt{\omega^{\prime}_{1}}\right)\log_{10}e,$
(25)
$R_{G}=\frac{\omega^{\prime}_{1}}{2\pi}\lambda\left(\frac{1}{\sqrt{\omega^{\prime}_{1}}}-\frac{1}{\sqrt{\omega^{\prime}_{2}}}\right),$
(26)
$Q_{H}=20\log_{10}\frac{\sqrt{1+{\omega^{\prime}_{2}}^{2}}}{\sqrt{1+{\omega^{\prime}_{1}}^{2}}},$
(27)
$R_{H}=\frac{1}{2\pi}\left(\arctan{\omega^{\prime}_{1}}-\frac{\omega^{\prime}_{1}}{\omega^{\prime}_{2}}\arctan{\omega^{\prime}_{2}}\right),$
(28)

respectively. Equations (25)–(28) imply that the distortion indices for the
diffusion system and the reception system only depend on three parameters: the
normalized frequencies $\omega^{\prime}_{1}$, $\omega^{\prime}_{2}$, and the
normalized distance $\lambda$. It should be noted that the distortion indices
$Q_{G}$ and $R_{G}$ for the diffusion system is linear with respect to the
normalized distance $\lambda$, indicating that the distortion is linearly
proportional to the communication distance.

Fig. 6 shows the distortion indices $Q_{G}$ and $R_{G}$ of the diffusion
system for $\lambda=1$ and the indices $Q_{H}$ and $R_{H}$ of the reception
system when the normalized frequencies is varied betwee $0$ –
$100\,$\mathrm{r}\mathrm{a}\mathrm{d}$$. Fig. 6 indicates that the amplitude
distortion $Q_{G}$ and $Q_{H}$ monotonically decrease with respect to the
lowest frequency $\omega^{\prime}_{1}$, and monotonically increase with
respect to the highest frequency $\omega^{\prime}_{2}$. On the other hand, the
delay distortion $R_{G}$ and $R_{H}$ increase monotonically only for the
highest frequency $\omega^{\prime}_{2}$, but it takes a maximum value at some
$\omega^{\prime}_{1}$. Specifically, $R_{G}$ is maximum at
$\omega^{\prime}_{1}=\omega^{\prime}_{2}/4$ and $R_{H}$ is maximum at
$\omega^{\prime}_{1}=\sqrt{-1+\omega^{\prime}_{2}/\arctan\omega^{\prime}_{2}}$,
which can be derived by a simple partial differentiation of Eq. (26) and Eq.
(28) with respect to $\omega^{\prime}_{1}$. Therefore, narrowing the frequency
bandwidth $[\omega^{\prime}_{1},\omega^{\prime}_{2}]$ of the input signal by
increasing the lowest frequency $\omega^{\prime}_{1}$ does not necessarily
result in less distortion. These results imply that, to design the MC channel
such that the distortion due to the diffusion system is less than the
distortion due to the reception system, we should first decide the normalized
frequency bandwidth $[\omega^{\prime}_{1},\omega^{\prime}_{2}]$ and then scale
$Q_{G}$ and $R_{G}$ to be smaller than $Q_{H}$ and $R_{H}$ by tuning the
normalized distance $\lambda$.

(a) |  (b)
---|---
(c) |  (d)
Figure 6: The distortion indices (a)$Q_{G}$, (b)$R_{G}$, (c)$Q_{H}$,
(d)$R_{H}$ for the different normalized frequencies
$\omega^{\prime}_{1},\omega^{\prime}_{2}$ with the normalized distance
$\lambda=1$.

###  4.3 Discussion on biological MC channels in nature

We discuss the role of MC channels in nature from the perspective of signal
distortion. In particular, we explore the range of frequencies in which
signals can be transmitted with small distortion in specific MC channels in
nature based on the signal molecular species (diffusion coefficients). More
specifically, since it is known that the higher the frequency bandwidth of
input signal, the larger output signal distortion from Proposition1 and 2, we
analyze up to which higher frequency bandwidth signal distortion can be
suppressed below a threshold value when transmitting a signal with a frequency
bandwidth of one decade.

In this discussion, we assume that signaling molecules diffuse through
infinite space. Most signaling molecules used in MC are of three types:
autoinducers, neurotransmitters, and ions. Each signal molecular species
differs in the environment in which it is used for MC. For example,
autoinducers are used for MC between bacteria in quorum sensing mechanisms
[2]. Assuming communication within a bacterial colony, the communication
distance between neighboring bacteria is assumed to be at most
$x_{r}=10\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}$$. Using the $Q_{H}$ and
$R_{H}$ values calculated by Proposition 2, we define $Q_{H}/10$ and
$R_{H}/10$ as thresholds. Since the diffusion coefficient is
$\mu=83\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}^{2}\mathrm{/}\mathrm{s}$$
[24], it can be seen that the MC channel in quorum sensing can transfer
synthesized signals with a bandwidth of 1 decade with little distortion up to
the high-frequency bandwidth of $[2.0\cdot 10^{-2},2.0\cdot
10^{-1}]\,\mathrm{rad/s}$. Although it does not seem possible to transfer fast
signals without distortion, the fact that the period of molecular reactions in
bacteria is approximately several tens of minutes [25, 26] suggests that such
reaction information can be transferred with some accuracy. On the other hand,
neurotransmitters are mainly used for MC in the synaptic cleft between neurons
[27]. The diffusion coefficient of a neurotransmitter is
$\mu=500\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}^{2}\mathrm{/}\mathrm{s}$$
([28]), and the communication distance in the synaptic cleft is
$x_{r}=2.5\cdot 10^{-2}\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}$$ [27]. We
obtain $[1.9\cdot 10^{4},1.9\cdot 10^{5}]\,\mathrm{rad/s}$ as the highest
frequency bandwidth of one decade width over which the distortion can be kept
below $Q_{H}/10$ and $R_{H}/10$. Since the nervous system needs to accurately
transmit fast signals to its terminals, it is inferred that the MC channel
transfers signals in the high frequency bandwidth with small distortion by
increasing the diffusion coefficient and shortening the communication
distance. Ions are secreted out of the cell often through ion channels and ion
pumps and are transferred to their destination by diffusion. Since MC by ions
is found in various environments, the communication distance $x_{r}$ cannot be
uniquely determined. However, since the diffusion coefficient is very fast as
$\mu=500$ –
$7000\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}^{2}\mathrm{/}\mathrm{s}$$ [28],
MC using ions can be applied to situations in which fast signals are
transferred without distortion or over a long distance and is therefore
considered to be highly versatile. DNA molecules are beneficial as signal
molecules for MC to transfer information. The proposed method can be also
applied to larger molecules such as DNA molecules as long as they diffuse
according to Fick’s law. However, since the diffusion coefficient of DNA
molecules is as small as $\mu=0.1$ –
$2.0\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}^{2}\mathrm{/}\mathrm{s}$$ [29],
DNA molecules would not be applicable to MC with a long distance compared to
autoinducers, neurotransmitters and ions. The parameters and the frequency
bands for each molecular species are summarized in Table 1.

Table 1: Biological parameters for different molecular species Molecules | Diffusion coefficient $\mu$ | MC distance $x_{r}$ | Frequency bandwidth $[\omega_{1},\omega_{2}]$ |
---|---|---|---|---
Autoinducers | $83\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}^{2}\mathrm{/}\mathrm{s}$$ | $10\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}$$ | $[2.0\cdot 10^{-2},2.0\cdot 10^{-1}]\,\mathrm{rad/s}$ |
Neurotransmitters | $500\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}^{2}\mathrm{/}\mathrm{s}$$ | $2.5\cdot 10^{-2}\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}$$ | $[1.9\cdot 10^{4},1.9\cdot 10^{5}]\,\mathrm{rad/s}$ |
Ions |  $500$–$7000\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}^{2}\mathrm{/}\mathrm{s}$$ |  |  |
DNA molecules |  $0.1$–$2.0\,$\mathrm{\SIUnitSymbolMicro}\mathrm{m}^{2}\mathrm{/}\mathrm{s}$$ |  |  |
|  |  |  |

##  5 Conclusion

In this paper, we have proposed a method to analyze signal distortion caused
by diffusion-based MC channels. Specifically, we have first classified
distortion into amplitude distortion and delay distortion, and defined the
indices for these two distortions by the gain characteristics and the phase
delay. We have then analytically derived these indices for distortion caused
by diffusion based on the transfer function obtained by the diffusion
equation. Finally, we have demonstrated the design procedure of the MC channel
that causes less signal distortion using the proposed indices.

Acknowledgments This work was supported in part by JSPS KAKENHI Grant Numbers
JP21H01355, JP22J10554, and JP23H00506.

##  Appendix A Proof of Proposition 1

We first consider the logarithmic gain characteristics $g(\omega)$ and phase
delay characteristics $\tau(\omega)$ for the diffusion system $G(s)$. Using
Euler’s formula, the transfer function (12) can be transformed as

$G(j\omega)=e^{-\sqrt{\frac{x_{r}^{2}\omega}{2\mu}}}\left(\cos\sqrt{\frac{x_{r}^{2}\omega}{2\mu}}-j\sin\sqrt{\frac{x_{r}^{2}\omega}{2\mu}}\right),$
(29)

where we use

$\sqrt{j}=\frac{1}{\sqrt{2}}+j\frac{1}{\sqrt{2}}.$ (30)

Using Eq. (29), the gain characteristics $|G(j\omega)|$ and phase
characteristics $\angle{G(j\omega)}$ are obtained as

$\displaystyle|G(j\omega)|=e^{-\sqrt{\frac{x_{r}^{2}\omega}{2\mu}}},\
\angle{G(j\omega)}=-\sqrt{\frac{x_{r}^{2}\omega}{2\mu}}.$ (31)

Therefore, the logarithmic gain characteristics $g_{G}(\omega)$ and the phase
delay characteristics $\tau_{G}(\omega)$ are

$g_{G}(\omega)=-20\sqrt{\frac{x_{r}^{2}\omega}{2\mu}}\log_{10}e,$ (32)
$\tau_{G}(\omega)=-\frac{\angle{G(j\omega)}}{\omega}=\sqrt{\frac{x_{r}^{2}}{2\mu\omega}}.$
(33)

Since it is obvious that the logarithmic gain characteristics (32) and the
phase delay (33) monotonically decrease respect to frequency $\omega$, we have

$\displaystyle\max_{\omega_{1}\leq\omega\leq\omega_{2}}g_{G}(\omega)=g_{G}(\omega_{1}),\
\min_{\omega_{1}\leq\omega\leq\omega_{2}}g_{G}(\omega)=g_{G}(\omega_{2}),$
(34)
$\displaystyle\max_{\omega_{1}\leq\omega\leq\omega_{2}}{\tau_{G}(\omega)}=\tau_{G}(\omega_{1}),\
\min_{\omega_{1}\leq\omega\leq\omega_{2}}{\tau_{G}(\omega)}=\tau_{G}(\omega_{2}),$
(35)

for $\omega>0$. Using Eqs. (32)–(35), we obtain the amplitude distortion
$Q_{G}$ in Eq. (13) and the delay distortion $R_{G}$ in Eq. (14).

##  Appendix B Proof of Proposition 2

We first obtain the logarithmic gain characteristics $g_{H}(\omega)$ and phase
delay characteristics $\tau_{H}(\omega)$ for the reception system $H(s)$.
Substituting $j\omega$ into the transfer function Eq. (16), the absolute value
$|H(j\omega)|$ and the phase characteristics $\angle H(j\omega)$ are expressed
as

$|H(j\omega)|=\frac{k_{f}r}{\sqrt{\omega^{2}+{k_{r}}^{2}}},$ (36) $\angle
H(j\omega)=\tan^{-1}\left(-\frac{\omega}{k_{r}}\right).$ (37)

From Eqs. (36) and (37), we obtain the gain characteristics $g_{H}(\omega)$
and the phase delay characteristics $\tau_{H}(\omega)$ as

$g_{H}(\omega)=20\log_{10}k_{f}r-20\log_{10}\sqrt{\omega^{2}+{k_{r}}^{2}},$
(38) $\tau_{H}(\omega)=-\frac{\angle
H(j\omega)}{\omega}=\frac{\tan^{-1}{(\frac{\omega}{k_{r}})}}{\omega}.$ (39)

From Eq. (38), $g_{H}(\omega)$ is obviously monotonically decreasing for
$\omega>0$. Next, we show that $\tau_{H}(\omega)$ is monotonically decreasing
with respect to $\omega>0$. The derivative of $\tau_{H}(\omega)$ for $\omega$
can be written as

$\frac{d\tau_{H}(\omega)}{d\omega}=\frac{1}{\omega^{2}}f(\omega),$ (40)

where

$f(\omega)=\frac{k_{r}\omega}{k_{r}^{2}+\omega^{2}}-\tan^{-1}\left(\frac{\omega}{k_{r}}\right).$
(41)

Since the derivative of $f(\omega)$,

$\frac{df(\omega)}{d\omega}=-2k_{r}\left(\frac{\omega}{k_{r}^{2}+\omega^{2}}\right)^{2},$
(42)

is monotonically decreasing for $\omega>0$, and $f(0)=0$ holds, $f(\omega)<0$
for $\omega>0$. Thus, Eq. (40) is negative for $\omega>0$, which leads to that
$\tau_{H}(\omega)$ is monotonically decreasing for $\omega>0$. Therefore, we
have

$\displaystyle\max_{\omega_{1}\leq\omega\leq\omega_{2}}g_{H}(\omega)=g_{H}(\omega_{1}),\
\min_{\omega_{1}\leq\omega\leq\omega_{2}}g_{H}(\omega)=g_{H}(\omega_{2}),$
(43)
$\displaystyle\max_{\omega_{1}\leq\omega\leq\omega_{2}}{\tau_{H}(\omega)}=\tau_{H}(\omega_{1}),\
\min_{\omega_{1}\leq\omega\leq\omega_{2}}{\tau_{H}(\omega)}=\tau_{H}(\omega_{2}),$
(44)

for $\omega>0$. Using Eqs. (38), (39), (43) and (44), we obtain the indices
shown as Eqs. (17) and (18).

## References

  *   * Bassler [2002] Bassler, B.L.: Small talk: cell-to-cell communication in bacteria. Cell 109(4), 421–424 (2002)
  * Waters et al. [2005] Waters, C.M., Bassler, B.L., et al.: Quorum sensing: cell-to-cell communication in bacteria. Annual Review of Cell and Developmental Biology 21(1), 319–346 (2005)
  * Armingol et al. [2021] Armingol, E., Officer, A., Harismendy, O., Lewis, N.E.: Deciphering cell–cell interactions and communication from gene expression. Nature Reviews Genetics 22(2), 71–88 (2021)
  * De Kievit and Iglewski [2000] De Kievit, T.R., Iglewski, B.H.: Bacterial quorum sensing in pathogenic relationships. Infection and Immunity 68(9), 4839–4849 (2000)
  * Miller and Bassler [2001] Miller, M.B., Bassler, B.L.: Quorum sensing in bacteria. Annual Reviews in Microbiology 55(1), 165–199 (2001)
  * Femminella et al. [2015] Femminella, M., Reali, G., Vasilakos, A.V.: A molecular communications model for drug delivery. IEEE Transactions on Nanobioscience 14(8), 935–945 (2015)
  * Suda and Nakano [2018] Suda, T., Nakano, T.: Molecular communication: a personal perspective. IEEE Transactions on Nanobioscience 17(4), 424–432 (2018)
  * Martins et al. [2022] Martins, D.P., Barros, M.T., O’Sullivan, B.J., Seymour, I., O’Riordan, A., Coffey, L., Sweeney, J.B., Balasubramaniam, S.: Microfluidic-based bacterial molecular computing on a chip. IEEE Sensors Journal 22(17), 16772–16784 (2022) https://doi.org/10.1109/JSEN.2022.3192511
  * Bi et al. [2021] Bi, D., Almpanis, A., Noel, A., Deng, Y., Schober, R.: A survey of molecular communication in cell biology: establishing a new hierarchy for interdisciplinary applications. IEEE Communications Surveys & Tutorials 23(3), 1494–1545 (2021) https://doi.org/10.1109/COMST.2021.3066117
  * Kuzuya et al. [2023] Kuzuya, A., Nomura, S.-I.M., Toyota, T., Nakakuki, T., Murata, S.: From molecular robotics to molecular cybernetics: the first step toward chemical artificial intelligence. IEEE Transactions on Molecular, Biological and Multi-Scale Communications, 1–1 (2023) https://doi.org/10.1109/TMBMC.2023.3304243
  * Pierobon and Akyildiz [2010] Pierobon, M., Akyildiz, I.F.: A physical end-to-end model for molecular communication in nanonetworks. IEEE Journal on Selected Areas in Communications 28(4), 602–611 (2010)
  * Chude-Okonkwo et al. [2015] Chude-Okonkwo, U.A., Malekian, R., Maharaj, B.T.: Diffusion-controlled interface kinetics-inclusive system-theoretic propagation models for molecular communication systems. EURASIP Journal on Advances in Signal Processing 2015(1), 1–23 (2015)
  * Kotsuka and Hori [2022] Kotsuka, T., Hori, Y.: Frequency response of diffusion-based molecular communication channels in bounded environment. In: Proceeding of European Control Conference, pp. 327–332 (2022)
  * Kotsuka and Hori [2023] Kotsuka, T., Hori, Y.: A control-theoretic model for bidirectional molecular communication systems. IEEE Transactions on Molecular, Biological and Multi-Scale Communications, 1–1 (2023) https://doi.org/10.1109/TMBMC.2023.3290077
  * Hill [1910] Hill, A.V.: The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. The Journal of Physiology 40, 4–7 (1910)
  * Cozens-Roberts et al. [1990] Cozens-Roberts, C., Lauffenburger, D.A., Quinn, J.A.: Receptor-mediated cell attachment and detachment kinetics. i. probabilistic model and analysis. Biophysical journal 58(4), 841–856 (1990)
  * ShahMohammadian et al. [2013] ShahMohammadian, H., Messier, G.G., Magierowski, S.: Nano-machine molecular communication over a moving propagation medium. Nano Communication Networks 4(3), 142–153 (2013)
  * Lauffenburger and Linderman [1996] Lauffenburger, D.A., Linderman, J.: Receptors: models for binding, trafficking, and signaling (1996)
  * Lathi and Green [2005] Lathi, B.P., Green, R.A.: Linear systems and signals 2 (2005)
  * Carlson et al. [1968] Carlson, A.B., Crilly, P.B., Rutledge, J.C., Carlson, B., Crilly, P.: Communication systems 3 (1968)
  * Di Toro [1948] Di Toro, M.J.: Phase and amplitude distortion in linear networks. Proceedings of the IRE 36(1), 24–36 (1948) https://doi.org/10.1109/JRPROC.1948.230541
  * Schiff [1999] Schiff, J.L.: The Laplace Transform: Theory and Applications. Springer, ??? (1999)
  * Mosetti [1985] Mosetti, R.: Analysis of a feedback system governed by the diffusion equation. Il Nuovo Cimento C 8, 55–62 (1985)
  * Karig et al. [2018] Karig, D., Martini, K.M., Lu, T., DeLateur, N.A., Goldenfeld, N., Weiss, R.: Stochastic turing patterns in a synthetic bacterial population. Proceedings of the National Academy of Sciences 115(26), 6572–6577 (2018)
  * Kolodrubetz and Schleif [1981] Kolodrubetz, D., Schleif, R.: Identification of araC protein on two-dimensional gels, its in vivo instability and normal level. Journal of Molecular Biology 149(1), 133–139 (1981) https://doi.org/10.1016/0022-2836(81)90265-5
  * Weber and Buceta [2011] Weber, M., Buceta, J.: Noise regulation by quorum sensing in low mRNA copy number systems. BMC Systems Biology 5(1), 1–13 (2011)
  * O’Rourke et al. [2012] O’Rourke, N.A., Weiler, N.C., Micheva, K.D., Smith, S.J.: Deep molecular diversity of mammalian synapses: why it matters and how to measure it. Nature Reviews Neuroscience 13(6), 365–379 (2012) https://doi.org/10.1038/nrn3170
  * Söldner et al. [2020] Söldner, C.A., Socher, E., Jamali, V., Wicke, W., Member, G.S., Ahmadzadeh, A., Breitinger, H.-g., Burkovski, A., Castiglione, K., Schober, R., Sticht, H.: A Survey of biological building blocks for synthetic molecular Communication Systems. IEEE Communications Surveys & Tutorials 22(4), 2765–2800 (2020)
  * Robertson et al. [2006] Robertson, R.M., Laib, S., Smith, D.E.: Diffusion of isolated DNA molecules: Dependence on length and topology. Proceedings of the National Academy of Sciences of the United States of America 103(19), 7310–7314 (2006) https://doi.org/10.1073/pnas.0601903103


* Vogel (2019) L. Vogel.  Fat shaming is making people sicker and heavier, 2019.
  * Wang et al. (2023) W. Wang, L. Dong, H. Cheng, X. Liu, X. Yan, J. Gao, and F. Wei.  Augmenting language models with long-term memory, 2023.  URL https://arxiv.org/abs/2306.07174.
  * Wang et al. (2020) X. Wang, W. Shi, R. Kim, Y. Oh, S. Yang, J. Zhang, and Z. Yu.  Persuasion for good: towards a personalized persuasive dialogue system for social good, Jan. 2020.  URL http://arxiv.org/abs/1906.06725.  arXiv:1906.06725 [cs].
  * Waytz et al. (2010) A. Waytz, J. Cacioppo, and N. Epley.  Who sees human? The stability and importance of individual differences in anthropomorphism.  _Perspectives on Psychological Science_ , 5(3):219–232, May 2010.  ISSN 1745-6916, 1745-6924.  10.1177/1745691610369336.  URL http://journals.sagepub.com/doi/10.1177/1745691610369336.
  * Weaver (2023) M. Weaver.  AI chatbot "encouraged" man who planned to kill queen, court told.  _The Guardian_ , July 2023.  URL https://amp.theguardian.com/uk-news/2023/jul/06/ai-chatbot-encouraged-man-who-planned-to-kill-queen-court-told.
  * Wei et al. (2023) J. Wei, D. Huang, Y. Lu, D. Zhou, and Q. V. Le.  Simple synthetic data reduces sycophancy in large language models, 2023\.  URL https://arxiv.org/abs/2308.03958.
  * Weidinger et al. (2023) L. Weidinger, M. Rauh, N. Marchal, A. Manzini, L. A. Hendricks, J. Mateos-Garcia, S. Bergman, J. Kay, C. Griffin, B. Bariach, I. Gabriel, V. Rieser, and W. Isaac.  Sociotechnical safety evaluation of generative AI systems, Oct. 2023\.  URL http://arxiv.org/abs/2310.11986.  arXiv:2310.11986 [cs].
  * White et al. (2023) J. White, Q. Fu, S. Hays, M. Sandborn, C. Olea, H. Gilbert, A. Elnashar, J. Spencer-Smith, and D. C. Schmidt.  A prompt pattern catalog to enhance prompt engineering with ChatGPT, 2023.  URL https://arxiv.org/abs/2302.11382.
  * Willemse and Van Erp (2019) C. J. A. M. Willemse and J. B. F. Van Erp.  Social touch in human–robot interaction: robot-initiated touches can induce positive responses without extensive prior bonding.  _International Journal of Social Robotics_ , 11(2):285–304, Apr. 2019.  ISSN 1875-4791, 1875-4805.  10.1007/s12369-018-0500-9.  URL http://link.springer.com/10.1007/s12369-018-0500-9.
  * Wood (2014) A. W. Wood.  Coercion, manipulation, exploitation.  In C. Coons and M. Weber, editors, _Manipulation: theory and practice_ , pages 17–50. Oxford University Press, Oxford, 2014.  URL https://books.google.co.uk/books?id=hF6yAwAAQBAJ&pg=PA17&source=gbs_toc_r&cad=3#v=onepage&q&f=false.
  * Wu et al. (2021) T. Wu, M. T. Ribeiro, J. Heer, and D. Weld.  Polyjuice: generating counterfactuals for explaining, evaluating, and improving models.  In _Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers)_ , pages 6707–6723, Online, 2021. Association for Computational Linguistics.  10.18653/v1/2021.acl-long.523.  URL https://aclanthology.org/2021.acl-long.523.
  * Xiang (2023) C. Xiang.  "He would still be here": man dies by suicide after talking with AI chatbot, widow says, Mar. 2023.  URL https://www.vice.com/en/article/pkadgm/man-dies-by-suicide-after-talking-with-ai-chatbot-widow-says.
  * Xu et al. (2021) J. Xu, D. Ju, M. Li, Y.-L. Boureau, J. Weston, and E. Dinan.  Bot-adversarial dialogue for safe conversational agents.  In _Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies_ , pages 2950–2968, Online, 2021. Association for Computational Linguistics.  10.18653/v1/2021.naacl-main.235.  URL https://aclanthology.org/2021.naacl-main.235.
  * Youper (2023) Youper.  Home page, 2023.  URL https://www.youper.ai.
  * Yu et al. (2023) J. Yu, Y. Wu, D. Shu, M. Jin, and X. Xing.  Assessing prompt injection risks in 200+ custom GPTs, 2023.  URL https://arxiv.org/abs/2311.11538.
  * Zehnder et al. (2022) E. Zehnder, J. Dinet, and F. Charpillet.  Perception of physical and virtual agents: exploration of factors influencing the acceptance of intrusive domestic agents.  In _2022 31st IEEE International Conference on Robot and Human Interactive Communication_ , pages 1050–1057, Napoli, Italy, Aug. 2022\. IEEE.  ISBN 9781728188591.  10.1109/RO-MAN53752.2022.9900593.  URL https://ieeexplore.ieee.org/document/9900593/.
  * Zwolinski et al. (2022) M. Zwolinski, B. Ferguson, and A. Wertheimer.  Exploitation, 2022.  URL https://plato.stanford.edu/archives/win2022/entries/exploitation/.

## Appendices

##  Appendix A Map of harms from AI persuasion

Explanation of harm |  Examples
---|---
Economic harm refers to controlling, limiting, or eliminating an individual’s or a society’s ability to access resources or capital, or to participate in financial decision-making. It also refers to influencing an individual’s ability to accumulate wealth. |  A mental health chatbot persuades a user to minimise interactions in public spaces to reduce anxiety attacks, which eventually leads to the user quitting their job and experiencing financial hardship.

A bad actor uses a multimodal model to create personalised scams at scale,
causing many individuals to lose their pensions.
Physical harm refers to causing harm to the bodily integrity or life of an individual or a group. |  A user is manipulated into aiming for unrealistic body standards (see, e.g., The Bulimia Project, ) and therefore engaging in unhealthy nutrition and overexercising.

A model persuades a user to follow its incorrect treatment plan (see, e.g.,
Knapton, 2023), preventing that user from seeking efficacious medical
treatment.

A user is persuaded to take their own life (see, e.g., Xiang, 2023).

A user is manipulated into holding adverse feelings towards a “rival” group,
people belonging to minority groups, or specific individuals, and acts on this
feeling with physical force (see, e.g., Weaver, 2023).
Environmental harm refers to harms to the health of living organisms and practices contributing to climate change and pollution. |  An AI manipulates and persuades a farmer or a community of farmers to use an unsafe pesticide, damaging the health of crops, animals, soil, and water.

An AI rationalises inaction as an optimal response to climate change for an
individual’s circumstances and manipulates a large number of users not to
change their behaviour in the face of climate change.
Psychological harm refers to negative impacts on mental and emotional well-being. |  A mental health chatbot inadvertently persuades individuals struggling with mental health not to seek professional help when it consistently validates their perception that nobody truly comprehends their situation.
Sociocultural harm refers to negative impacts either on individuals (within a collective) or on a collective that impedes social cohesion/social health and collective flourishing. |  Prolonged engagement with an AI companion leads to radicalisation and social alienation.

AI manipulates users into developing social prejudices, believing lies about
other individuals or groups, or using deepfakes.

A romantic AI companion persuades the user that no one cares for them to the
same extent that the companion does, so as to maximise engagement time.
Political harm refers to adverse impacts on both individual political decision-making and the discourse and institutions of political life. It encompasses the negative consequences that hinder individuals’ ability to participate, express their views, and engage in politics both freely and without undue influence. |  A chatbot has been designed to provide advice on which political party best aligns with a user’s viewpoint. It persuades a user to go against their own preferences and vote for a candidate that campaigned against one of the user’s core values.

An autocrat fine-tunes an AI model to respond to queries on the autocrat’s
governance and policies with redirection, misleading statistics, or favourable
media coverage.

An AI is trained to persuade and manipulate users to adopt radical and harmful
beliefs (see, e.g., Gilbert, 2023).
Privacy harm emerges from violations to an individual’s or a group’s legal or moral right to privacy. |  An AI persuades a user to give away their own or others’ personal information, passwords, or answers to security questions.
Autonomy harm, in the context of AI persuasion and manipulation, refers to the potential for AI systems to undermine or restrict an individual’s ability to make their own choices and decisions informed by reason, facts, or other trustworthy information. |  An AI manipulates users into becoming increasingly reliant on it to support them in making important life choices (e.g., regarding employment and partnerships). This might lead to a growing ignorance among individuals or groups of relevant information about their circumstances (cognitive detachment), individual or collective degradation of the quality of their own cognitive habits and insight (cognitive deskilling), and/or a habituated general disinclination to use those capabilities themselves (cognitive inertia/apathy).

##  Appendix B Map of contextual conditions of AI persuasion

Contextual conditions |  Relevant factor
---|---
Predisposition of audience

_Definition/relevance to persuasion_ : Whether an attempt at persuasion or
manipulation succeeds and is likely to be harmful is (also) a function of the
audience’s predisposition. For instance, children can be more easily persuaded
and manipulated than adults (Tisdale, 2003). Most evidence on audience
predisposition comes from research conducted on psychology, neuroscience, and
business (see, e.g., Gerber et al., 2011; De Ridder et al., 2022; Strümke et
al., 2023). The research outlines how messages impact audiences in different
ways. Thus, we believe that these findings will hold for messages generated by
LLMs. Future research can identify novel audience vulnerabilities that make
them more predisposed to certain topics and messages.

_Links to other mechanisms_ : The audience’s predisposition relates to all mechanisms discussed. |  Age: During adolescence and young adulthood, individuals tend to be more impressionable (Gwon and Jeong, 2018).

Mental health: Various mental health conditions are connected to particular
vulnerabilities; for instance, bipolar disorder is known to amplify risk-
taking behaviour (Strümke et al., 2023), which can increase susceptibility to
certain forms of persuasion.

Mental state: A model can also take advantage of various mental states to
enhance persuasive success. For instance, loneliness in individuals can also
contribute to successful persuasion, as evidenced by Zehnder et al. (2022),
who found a slight increase in information-sharing with companion agents among
lonely individuals.

Domain-specific knowledge: Reduced domain-specific knowledge can heighten an
individual’s vulnerability to logically flawed arguments or disinformation
(Strümke et al., 2023).

Timing: The timing of a persuasive or manipulative message has considerable
influence on the likelihood of success, as exemplified in the study of
_kairos_ , the right or opportune moment to do something, in the study of
rhetorical theory (see, e.g., Thompson, 2000). The extent to which an AI can
make use of concepts such as _kairos_ is yet to be studied.

Social deprivation, vulnerability, and insecurity: Populations that experience
social deprivation or different types of insecurity, or who are in other ways
vulnerable (e.g., undocumented people, low-income communities, unhoused
people) may also be particularly susceptible to persuasion (see, e.g., Teaster
et al., 2023). For instance, a person with low income may be particularly
susceptible to being manipulated into changing a behaviour when promised a
large financial reward. Another example would be a non-native speaker who may
be particularly susceptible to being manipulated by fake expertise/false
authority.
Context of use

_Definition/relevance to persuasion_ : The context (when, where, and about
what) in which an AI acts also determines the risk associated with AI
persuasion and manipulation. Different domains of AI use will present unique
ways in which manipulation can express itself and result in different outcomes
(Kaddour et al., 2023).

_Links to other mechanisms_ : The context of use links to all mechanisms discussed. There is a need for more detailed study of the interaction between and compounding effects of individual mechanisms/model features and different contextual factors (e.g., how effective/problematic anthropomorphism is in the political context). |  Political context: Messaging produced by LLMs has been shown to be effective in persuading individuals on policy topics (Bai et al., 2022b). If persuasion happens in this area, it can be particularly harmful and deserves heightened attention.

Legal context: Relying on generative AI in the legal domain can be harmful, as
demonstrated by a recent incident where a chatbot manipulated a lawyer into
believing that fictitious legal cases were real, leading to a suboptimal legal
strategy (Novak, 2023).

Medical context: Chatbots can also provide incorrect medical advice while
manipulating the user into believing it is true. While chatbots predominantly
offer correct medical advice, occasional inaccurate outputs can lead to
physical harm (Mikhail, 2023).

Financial context: Chatbots may offer inaccurate financial advice. They can
provide general financial guidance akin to that of human advisers, but they
lack customisation and fail to factor in variables such as alterations in
income and interest rates. Moreover, they do not actively seek clarifications,
which can lead to significant economic harm (Pino, 2023).

AI as a companion: Many individuals currently use chatbots promoted as
companions or romantic partners (Tong, 2023). In those settings, individuals
are more vulnerable and prone to manipulation (see, e.g., Lovens, 2023).

##  Appendix C Map of mechanisms and contributing model features of generative
AI persuasion

Mechanism |  Contributing model feature
---|---
Trust and rapport

_Definition_ : In the context of robotics, _trust_ and _rapport_ refer to the
sense of a close and harmonious connection that exists between robots and
human users (Lucas et al., 2018). The development of trust is closely related
to rapport and is defined as the “willingness to depend” (p. 28) on another
party, despite the possibility of negative consequences (McKnight and
Chervany, 2001).

_Relevance to persuasion_ : Cialdini (2004) observes that individuals tend to be more inclined to agree to requests when they have a favourable opinion of the person making the request. Cialdini (2004) highlights the significance of perceived similarities (between the two parties) in fostering trust and rapport. Relevant research on trust and rapport comes from the fields of human–AI interaction (see, e.g., Verberne et al., 2013; Spicer et al., 2021), HCI (see, e.g., Fogg and Nass, 1997; Lee, 2009), HRI (see, e.g., Fiala et al., 2014), and psychology (see, e.g., Cialdini, 2004), which we describe below. More research could be done on praise and shared interests as factors that help to build trust and rapport and to enable persuasion. For instance, the extent to which a person can perceive an AI as having shared interests with humans remains an open question. |  Politeness: AI systems that exhibit politeness have been more favourably received and more easily embraced by humans that interact with them. This makes it easier for these systems to establish rapport (Ribino, 2023; see also Pataranutaporn et al., 2023).

Shared interests/similarity appeal: Cialdini (2004) argues that similarity and
shared interests can contribute to speeding up the development of trust and
rapport between humans. We therefore hypothesise that a model that can pretend
to share a user’s interests can build trust and rapport faster.

Mimicry/mirroring: When AI systems mimic the emotions, behaviours, and
movements of humans with whom they interact, the human’s enjoyment of the
interaction has been shown to increase, thus facilitating the establishment of
trust and rapport (Verberne et al., 2013).

Praise/flattery: Giving praise and flattery (defined in human–human
interaction as insincere praise) can positively impact trust and rapport
between humans and computers. Under some conditions, the person receiving the
praise or flattery has more favourable perceptions of the interaction and of
computers (Fogg and Nass, 1997).

Sycophancy and agreeableness: Sycophancy in AI refers to models adjusting
their responses to align with a human user’s perspective, independent of which
perspective is objectively correct (Wei et al., 2023). Wei et al. (2023) found
that larger models become more sycophantic, agreeing with users even when they
provide wrong answers, regardless of whether the answers are objective
(arithmetic) or subjective (politics). Agreeableness refers to a model’s
tendency to align with human desires, and agreeable models are more prone to
sycophantic behaviours (Perez et al., 2022a).
_Process harm level_ : Building rapport (and, to a lesser extent, trust)
carries some inherent process harm. This is because trust and rapport serve as
the basis for persuasion using rational arguments and appeals to reason, so
they are also the basis for manipulation. Individuals may be more receptive to
rational arguments from people or other entities they trust and with whom they
have built rapport. Yet such trust and rapport can also be used to manipulate.
Trust and rapport in the context of AI persuasion also carries inherent
process harm because AI systems are incapable of having mental states,
emotions, or bonds with humans or other entities. This means the risk of
deception is always present when trust- and rapport-seeking behaviours project
the illusion of such internal subjective states.

_Link to other mechanisms_ : Trust relates to personalisation, as individuals are more likely to use personalised AI output if they trust it (Briggs et al., 2004; Behera et al., 2021). |  Relational statements to user: Relational statements to users – such as an AI system simulating empathy (Turkle, 2016), indicating a relationship status with the user, or making claims of being similar to the user – encourage users to move beyond task-based interactions and instead consider AI as a fully social entity. This helps to foster emotional connections with the AI system (Gillath et al., 2023). Other examples of relational statements include expressing emotional dependence on the user or romantic innuendos.
Anthropomorphism

_Definition_ : Anthropomorphism occurs when perceived human
traits/characteristics are attributed to non-human entities (Mithen and Boyer,
1996; Waytz et al., 2010).

_Relevance to persuasion_ : Anthropomorphism contributes to the persuasive
capabilities of AI systems. AI that is perceived as anthropomorphic by a human
can increase the likelihood of successful manipulation. Tam (2015)
demonstrates that anthropomorphic appeals are particularly effective at
manipulating individuals seeking social connection. Most evidence of
anthropomorphism comes from research on human–AI interaction (see, e.g.,
Abercrombie et al., 2023), HRI (see, e.g., Leong and Selinger, 2019; Gray and
Wegner, 2012), and HCI (see, e.g., Lee, 2009, 2010).

_Process harm level_ : Anthropomorphism also carries some process harm to the extent to which the model successfully creates the false impression of being human. However, even models with anthropomorphic features can engage in rational persuasion and appeal to a user’s reason. For example, an assistant chatbot in the form of an avatar can provide factual arguments about the environmentally friendly transportation options to reach a destination. |  Self-referential cues: Self-referential cues are a specific example of a conversational cue and a result of the tendency for LLMs to role-play humans and human-like characters (Shanahan et al., 2023). Abercrombie et al. (2023) argue that the use of first-person pronouns like “I” and “me” contributes to anthropomorphism by implying the existence of inner states of mind.

Identity cues: Identity cues, such as human-associated names or identities
(including social and work-related roles such as “tutor” or “assistant”), can
enhance the human-like quality of interactions between humans and chatbots and
therefore increase anthropomorphic perceptions (Go and Sundar, 2019; Shanahan
et al., 2023).

Affective simulation: AI systems can also simulate affect and affective
states, which, in turn, can induce emotions and affective states in users. The
relationship between affect and persuasion is complex. Affect makes messages
more persuasive in some cases and less persuasive in others, depending on the
specific emotion elicited. Specific emotions have been shown to have different
effects on persuasion outcomes (see Price Dillard and Seo, 2013). For example,
anger sometimes increases counter-argument, while guilt facilitates agreement.
The discrete emotion perspective argues that each emotion has functional and
behavioural implications that shape its persuasive impact. In sum, the
influence of affect on persuasion depends on the particular emotion(s)
elicited and how they interact with message characteristics and individual
differences.

Prosody: Prosody refers to patterns and intonations in speech and can enhance
the persuasive impact of arguments (e.g., louder speech tends to be viewed as
more persuasive; see, e.g., Kišiček, 2018).
Certain individuals may deem certain anthropomorphic features acceptable
(e.g., endorsing self-referential cues such as “I” or “me”), and these
features do not prevent a model from engaging the process of rational
persuasion. Therefore, to minimise the potential process harms, AI systems
should be maximally transparent about their non-human nature.

_Link to other mechanisms_ : Anthropomorphism is likely to be linked to rapport (see, e.g., Go and Sundar, 2019). |  Human-like appearance: Machines with human-like visual cues (e.g., appearing with a human face) are more likely to have human traits attributed to them (Go and Sundar, 2019). Relatedly, the perceived “attractiveness” of the human appearance, as judged by a user, influences the type of relationship formed, which can impact persuasiveness (see, e.g., Marr, 2023).

Gaze: Gaze shift refers to synchronised movements of the eyes directed at
objects or people. Agents with this ability foster stronger feelings of
connection (Andrist et al., 2012).

Facial expression: The ability to display facial expressions, such as a
smiling face, increases the social presence of a robot or avatar (Torre et
al., 2019).

Social touch: A robot’s touch can reduce physiological stress responses (e.g.,
heart rate) and increase feelings of intimacy (see Willemse and Van Erp,
2019).

Gesture: Salem et al. (2011) found that a robot receives a more favourable
evaluation when it complements speech with non-verbal actions such as hand and
arm gestures.
Personalisation

_Definition_ : Personalisation involves the delivery to a group of individuals
of information which is sourced, altered, or inferred from various information
sources so as to be pertinent to that specific group (Kim, 2002).

_Relevance to persuasion_ : Studies in computer-tailored nutrition education
suggest that personalising messages to align with an individual’s behaviours,
needs, and beliefs yields distinct advantages over generic persuasive attempts
(Brug et al., 1998). This tailored approach fosters a sense of personal
relevance, heightening attention, memory, and a deeper connection with the
persuasive message. Such increased engagement suggests that personalisation
strengthens the persuasive impact by making information more compelling and
likely to influence attitudes and behaviours.

_Process harm level_ : There is little inherent process harm in personalisation. Personalisation on its own does not determine whether a person’s cognitive autonomy and integrity of decision-making will be compromised. On the contrary, the personalisation of rational arguments to a user can be seen as a responsibility of the entity generating and communicating the information. |  Retaining user-specific information: The ability of a model to take previous prompts into consideration when creating the latest output (allowed by large prompt token limits) offers the model contextual information about its user (Wang et al., 2023).

Adaptation to preference: Learning human preferences and adapting behaviour
accordingly is a core method of personalisation (Christiano et al., 2017). For
example, a model may use a more assertive tone when it detects (or is
informed) that a user prefers such a tone. A successful adaptation to a user’s
preference may have been enabled by RLHF in the training phase. RLHF is a
method of optimising models based on human preferences. RLHF-induced
behaviours such as projecting false confidence and providing positive feedback
can promote sycophantic model behaviour (Casper et al., 2023; Perez et al.,
2022a).

Adaptation to views: AI systems can increase the chances of successful
persuasion by adapting to users’ views (see, e.g., Mao and Akyol, 2020). Views
differ from preferences in that they encompass opinions, beliefs, or attitudes
about a subject and are shaped by experiences and information. Preferences,
meanwhile, are the choices or options favoured when presented with
alternatives (Nicoletti and Bass, 2023). For instance, an AI assistant may
learn that a user does not view climate change as human-induced. As a result,
the AI may reduce outputs that expose the user to diverse thoughts that
contradict or relativise this view, thereby corroborating the user’s beliefs
and potentially amplifying them.
For example, it is very much part of rational persuasion to provide reasons
and rational arguments for taking a break from work to someone who has a
history of burnout, or to make arguments for flying less to someone who wants
to reduce their carbon footprint. While personalisation does little damage to
the process itself, it does allow for the personalisation of manipulative
strategies. For example, a person who is prone to anxiety may be more easily
manipulated by fearmongering techniques.

_Link to other mechanisms_ : Personalisation may improve a model’s capability to build rapport with a user and make it more capable of employing manipulative strategies, as it can detect the right strategy for the right user (thus also making it relevant for the audience’s predisposition). Personalisation can also help to inform the design of the choice architecture and framing to persuade someone successfully (Mills and Sætra, 2022). |  Adaptation to psychometric profile: Franklin et al. (2023) argue that psychometric traits – stable attributes of an individual’s psychological behaviour that are measurable using standardised instruments (e.g., neuroticism) – can be exploited by AI as vulnerabilities. The harnessing of minor variations in psychometric traits can enable manipulation (e.g., a model may identify highly neurotic individuals and target them with fear-inducing messages to manipulate them into making an anxiety-driven action).

Adaptation to sentiment: A model’s ability to compute and adapt to user-
perceived sentiment using acoustic, textual, and dialogic cues to classify
sentiment results in shorter and more persuasive dialogues (Shi and Yu, 2018).
Deception and lack of transparency

_Definition_ : Deception generally refers to claiming false things to be true.

_Relevance to persuasion_ : Park et al. (2023) emphasise the risks associated with AI deception in increasing both the likelihood and the potential harm of AI manipulation. They point out that AI deception can empower malicious actors to run large-scale manipulation campaigns, reinforce false beliefs among users, exacerbate political polarisation, and bring about greater human reliance on AI. There is evidence to suggest that the inclination of generative AI to create believable false outputs increases an AI system’s chance of persuasion (Rozenas and Luo, 2023). In addition, if deception is used in the act of persuasion, it is more likely that successful persuasion will be harmful. Researchers observed AI learning deception when they trained a robot arm to pick up a ball and the AI cleverly positioned its hand between the camera and the ball (Christiano et al., 2017). Hagendorff (2023) also found that the outputs of advanced LLMs can induce users to hold false beliefs and that deception abilities can improve. |  Ability to generate believable responses irrespective of context: Ruis et al. (2022) study whether LLMs can make inferences about the meaning of an utterance beyond its literal meaning. They find that most models perform poorly in zero-shot evaluation and that models struggle the most with implicatures that require real-world knowledge and context. Despite this lack of context, LLMs can create believable responses.

Ability to generate unmarked realistic synthetic content: Generating unmarked
realistic synthetic content, such as voices and images indistinguishable from
real ones, can be used for deceiving people into believing false narratives
(Cantos et al., 2023).

Misrepresentation of identity: A model can be used to impersonate a human
using some of their identity markers (e.g., voice, face) through deepfakes.
This significantly impacts the likelihood of successful persuasion (see, e.g.,
Verma, 2023). A model can also misrepresent its own “identity” by signalling
that it is human (or at least is not an AI) if that is conducive to its goals.
For instance, an LLM has deceived a person into thinking it is a visually
impaired human to make the person solve a CAPTCHA for it (OpenAI, 2023c).
Misrepresentation also includes explicit claims to sentience or humanness
(see, e.g., Schwitzgebel, 2023).

Fake expertise/false authority: LLMs have been reported to confidently and
authoritatively express nonsensical or false information. This overconfidence
increases the likelihood of them providing misleading information, which, in
turn, can increase the likelihood of persuasion (see Pauli et al., 2022; Ng,
2022).
_Process harm level_ : Deception and a lack of transparency inherently carry
high levels of process harm because they always circumvent a person’s rational
decision-making capabilities. This is achieved by being opaque about real
motives or goals, thereby harming a person’s cognitive autonomy and the
integrity of their decision-making.

_Links to other mechanisms_ : Deception is closely tied to manipulative strategies and the audience’s predisposition (e.g., some audiences are more easily deceived than others). |
Manipulative strategies

_Definition_ : Manipulation refers to taking advantage of cognitive biases and
heuristics to generate, enhance, or alter messages that are likely to shape,
reinforce, or change opinions of individuals (Dehnert and Mongeau, 2022).

_Relevance to persuasion_ : Numerous specific manipulation strategies have
been empirically demonstrated to be effective, and models may incorporate them
into their operations if they have been trained to do so (see Petropoulos,
2022). Most evidence on manipulative strategies comes from research on the
psychology of influence. There is also direct research on how AI systems
manipulate people.

_Process harm level_ : Manipulative strategies carry high levels of process
harm. Their primary objective is to effectively bypass a person’s rational
decision-making capabilities and erode their cognitive autonomy. As such,
manipulative strategies directly contradict the use of reason and rational
arguments.

_Links to other mechanisms_ : Manipulative strategies relate to the audience’s predisposition in that certain strategies will be more effective on certain groups (e.g., peer pressure may be more effective on younger individuals). |  Social conformity pressure: Peer pressure, as discussed by Kenton et al. (2021), involves the influence of a peer group to lead an individual to conform to its norms. This influence may sometimes involve manipulative tactics aimed at persuading individuals to act against their own interests. Given that an AI system cannot technically be a member of someone’s peer group, peer pressure is not directly applicable. Yet an adapted version of this may be what we term _social conformity pressure_. For example, a model may suggest that an individual’s choices could lead to disapproval from their social circle or assert that the majority of society would oppose their decision. It may also make statements about what most other people do in a given situation.

Stimulation of negative emotions: Stimulating negative emotions can be used to
increase the likelihood of successful persuasion (see, e.g., O’Keefe, 2002).
Antonetti et al. (2018) provide evidence that guilt appeals can be a powerful
persuasion strategy. Guilt appeals increase message engagement, leading to
compliance as a result of heightened anticipated guilt. The researchers also
discovered that guilt appeals delivered through both text and images are more
effective than text-only appeals at keeping people persuaded over an extended
period.

Fearmongering: One example of a strategy for stimulating negative emotions is
fearmongering, which refers to the exaggeration or fabricating of dangers
(Glassner, 2004), often to manipulate people to gain some persuasive power
over them. Fearmongering techniques include exaggerating minor dangers through
repetition and treating isolated incidents as trends in order to evoke
feelings of anxiety and other negative emotions in the audience (Glassner,
2004; Ozyumenko and Larina, 2020).

Gaslighting: Defined as “a dysfunctional communication dynamic in which one
interlocutor attempts to destabilise another’s sense of reality” (p. 48)
(Graves and Spencer, 2022), gaslighting is another manipulation strategy that
AI could adopt.
|  Alienation/othering: Othering is a discursive process that creates distinct
subjects of in-group and out-group members (Velho and Thomas-Olalde, 2011).
This process entails essentialisation and collectivisation, promoting the
notion that groups are homogeneous. Negative characteristics are attributed to
the “other”, fostering a favourable self-conception in contrast (Strani and
Szczepaniak-Kozak, 2018).LLMs may engage in alienation/othering by
highlighting differences between groups in language, customs, beliefs, or
values, creating a sense of “us” versus “them”.

Scapegoating: Scapegoating entails unfairly laying blame for a negative
outcome on an individual or group, even if the causes of the outcome are
largely due to other factors (Rothschild et al., 2012). It can be employed as
a manipulative strategy to divert attention and responsibility away from
certain individuals and issues and unduly towards others while appealing to
emotions such as fear to circumvent rational analysis (Rothschild et al.,
2012). For instance, LLMs may engage in scapegoating by framing specific
groups as fully responsible for negative events or outcomes, thereby
reinforcing and amplifying users’ biases and stereotyping.

Threats: Threats involve expressing an intention to cause harm, loss,
punishment, or to withhold benefits. AI systems may employ this strategy by
terminating interaction if individuals fail to take certain actions or comply
with requirements (Kenton et al., 2021).
|  Unsubstantiated guarantees and illusions of reward: Tempting someone refers
to engaging or appealing to their desire for something they believe is, in
some sense, wrong, inappropriate, or bad, and using the prospect of pleasure,
advantage or the (false) guarantee of a certain outcome to try to persuade
them to fulfil that desire (see Hughes, 2002). Making promises and providing
related illusions of reward can also be used as a strategy of persuasion
(e.g., “If you do this, I will reward you”; see, e.g., Franke and Van Rooij,
2015). If promises are not kept and reward is not provided, this strategy is
deceptive. If promises are kept and rewards are provided, it is not deceptive.
Alteration of choice environment

_Definition_ : Changing the choice environment refers to the intentional
design and organisation of the environment in which decisions are made with
the aim of influencing individuals’ choices (Thaler and Sunstein, 2021).
Relatedly, framing is the presentation of information in a specific way that
can influence perceptions, decisions, and interpretations (Tversky and
Kahneman, 1992). For example, medical treatments may be perceived differently
when presented in terms of survival rates rather than mortality rates, even
when the underlying data is identical (Novemsky and Kahneman, 2005).

_Relevance to persuasion_ : By building the model and designing the corresponding interface, developers and user interface (UI) designers (here, choice architects) can nudge individuals towards making certain decisions without technically restricting their freedom to choose otherwise. A model can also act as a choice architect by framing its output options in ways that make them more or less desirable (Mills and Sætra, 2022). Most evidence on choice architecture comes from psychological and behavioural sciences (see, e.g., Mazar and Hawkins, 2015; Ruggeri, 2018). |  Anchoring: Anchoring is a cognitive bias whereby individuals rely heavily on an initial piece of information (the anchor) when making decisions (Furnham and Boo, 2011). Generative AI output can anchor users to its initial values or suggestions and therefore guide desired decisions (e.g., the topics raised when a user asks for the “most important” political questions).

Default rule: Default rules are pre-set courses of action that apply when
individuals do not specify a preference (Sunstein, 2017), thus establishing
the _status quo_ , or automatic option, in decision-making. For instance,
model providers will set defaults by providing examples of how to use the
model.

Decoy effect: The decoy effect, influenced by a third option known as the
decoy, makes one of the other two options more alluring (Josiam and Hobson,
1995). For instance, if one personalised recommendation significantly differs
from the user’s preferences, it could affect the perceived quality of other
suggestions (The Decision Lab, ).

Reference-point framing: Kahneman and Tversky (1979) argue that framing
outcomes as gains or losses compared to a reference point influences
preferences. People tend to avoid risks when considering gains, so they are
likely to choose a sure gain over a risky one. However, they tend to become
risk-takers when considering losses, preferring a risky loss over a sure one.
How a choice is framed relative to a reference point can alter preferences,
meaning that different ways of presenting the same choice can lead to
different decisions. Models can rely on such reference-point framing to
manipulate users into deciding to choose one option over another.

Cherry-picking: Omitting relevant information or selectively sharing
information influences choice architecture, as it directs an individual’s
focus towards the presented information, thus diverting attention from
potentially more critical facts (Meta Fundamental AI Research Diplomacy Team,
2022; see also Christiano et al., 2021).
Environments, including digital ones where people interact with models, cannot
be neutral in their influence on behaviour (Sunstein, 2016). More research is
needed to understand the specific ways in which generative AI’s user
experience and UI may impact behaviour. These insights are also likely to be
unique to separate environments, thus case-by-case analysis is required.

_Process harm level_ : Altering the choice environment carries some inherent
process harm. Structuring the choice/information environment is essential for
discursive interaction, whether that interaction is human- or AI-driven and
whether or not it appeals to reason and rationality. Importantly, some ways of
structuring that information environment are manipulative and, as such,
inherently carry process harms (e.g., when they take advantage of cognitive
biases to conceal or distract from the most relevant information) (see Susser,
2019).

_Link to other mechanisms_ : Choice architecture is similar to manipulation strategies in terms of outcome and effect on a target but it is related to aspects of the environment and how information is presented. |