# Functional universality in slow-growing microbial communities arises from
thermodynamic constraints

Ashish B. George1,2, Tong Wang1,3,4, and Sergei Maslov1,3,5∗ 1Carl R. Woese
Institute for Genomic Biology, University of Illinois at Urbana-Champaign,
Urbana, IL 61801, USA.
2Department of Plant Biology, University of Illinois at Urbana-Champaign,
Urbana, IL 61801, USA.
3Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL
61801, USA.
4Brigham and Women’s Hospital and Harvard Medical School, Boston, MA 02115,
USA.
5 Department of Bioengineering, University of Illinois at Urbana-Champaign,
Urbana, IL 61801, USA.  ∗<EMAIL_ADDRESS>
###### Abstract

The dynamics of microbial communities is incredibly complex, determined by
competition for metabolic substrates and cross-feeding of byproducts. Species
in the community grow by harvesting energy from chemical reactions that
transform substrates to products. In many anoxic environments, these reactions
are close to thermodynamic equilibrium and growth is slow. To understand the
community structure in these energy-limited environments, we developed a
microbial community consumer-resource model incorporating energetic and
thermodynamic constraints on an interconnected metabolic network. The central
ingredient of the model is product inhibition, meaning that microbial growth
may be limited not only by depletion of metabolic substrates but also by
accumulation of products. We demonstrate that these additional constraints on
microbial growth cause a convergence in the structure and function of the
community metabolic network—independent of species composition and biochemical
details—providing a possible explanation for convergence of community function
despite taxonomic variation observed in many natural and industrial
environments. Furthermore, we discovered that the structure of community
metabolic network is governed by the thermodynamic principle of maximum heat
dissipation. Overall, the work demonstrates how universal thermodynamic
principles may constrain community metabolism and explain observed functional
convergence in microbial communities.

## Introduction

Over half of earth’s prokaryotic biomass resides in ocean sediments and deep
soil falkowski_microbial_2008 ; whitman_prokaryotes_1998 . In many of these
natural environments and anaerobic bioreactors, communities grow under energy-
limited conditions due to the absence of strong electron acceptors, like
oxygen or nitrate, and strong electron donors, like glucose
jessen_hypoxia_2017 ; jorgensen_feast_2007 ; leng_review_2018 ;
hoh_experimental_1997 ; nobu_catabolism_2020 ; bradley_widespread_2020 . Hence
species in these communities are forced to harvest energy required for biomass
growth from low free energy reactions conrad_thermodynamics_1986 ;
bradley_widespread_2020 ; hickey_thermodynamics_1991 ; jackson_anaerobic_2002
; larowe_energetics_2019 ; larowe_thermodynamic_2012 . Growth in these
environments can be very slow—division times are measured in weeks and
years—instead of minutes and hours used for growth in the lab
larowe_thermodynamic_2012 ; lomstein_endospore_2012 ; jorgensen_feast_2007 ;
park_impact_2010 ; sottile_comparative_1977 . These long timescales and
difficulty in culturing these species in a lab environment make experimental
investigation of these communities challenging. Models and theory of energy-
limited microbial communities can help uncover their organizational principles
and shared emergent properties and drive understanding.

Models and theories inspired by MacArthur’s consumer-resource model have
helped understand many of the principles and properties governing microbial
communities structured by nutrient-limitation macarthur_species_1970 ;
posfai_metabolic_2017 ; tikhonov_collective_2017 ; goldford_emergent_2018 ;
marsland_minimum_2020 ; dubinkina_multistability_2019 ;
wang_complementary_2021 . However, models of communities in low-energy
environments, structured by energy-limitation, need to incorporate important
additional details. First, microbial growth in low-energy environments is
determined by energy assimilation rather than nutrient uptake. Second, the low
free energy reactions utilized to drive growth are subject to thermodynamic
constraints. And third, reactions need to be explicitly modeled to track their
thermodynamic feasibility, rather than just species preference for resources.
Here we propose and study a minimal model of microbial communities that
accounts for these crucial details to understand the emergent properties of
slow-growing communities in energy-limited environments.

Recently, a few studies have attempted to incorporate thermodynamics into
community models groskopf_microbial_2016 ; cook_thermodynamic_2021 . These
studies focused on community diversity, showing that thermodynamics enables
communities to overcome the competitive exclusion principle and stabilize high
diversity on a single substrate. In contrast, here we focus on the emergent
properties of the communities in low-energy environments, such as the
metabolic network structure and function of the community.

Simulations of our model generated communities that shared many features of
natural communities. Strikingly, communities assembled from separate species
pools in replicate environments realized the same metabolic network and
performed similar metabolic functions at the community-level despite stark
differences at the species level. This resembles the observed convergence in
community function despite taxonomic divergence, seen in anaerobic
bioreactors, oceans, and other environments fernandez_how_1999 ;
louca_decoupling_2016 ; louca_function_2018 ; peces_deterministic_2018 .

Analyzing the model to understand how functional convergence arises, we
discovered that thermodynamic principles govern community-level metabolic
network structure and function in slow-growing, energy-limited communities. We
derived the thermodynamic principle of maximum dissipation, which, we show,
determines the community metabolic network selected by ecological competition
in energy-limited communities. This thermodynamic principle, along with
physical constraints, shape the metabolic environment created by the community
and the metabolic functions it performs. Further, the derivation of the
maximum dissipation principle provides a concrete example in which communities
are structured by thermodynamic optimization, an idea that has been
conjectured in ecology but never proven dewar_theoretical_2014 .

Overall, our results highlight the crucial role of thermodynamic constraints
in defining community metabolism and function of energy-limited microbial
communities. The results provide an explanation for the observed convergence
in microbial community function, serve as a concrete example of thermodynamic
optimization in community ecology, and make predictions for the community
metabolic network and resource environment.

## Results

### Model of microbial communities in energy-poor environments

Figure 1: Model of communities in energy-limited environments. A) Species
harvest energy from reactions (grey arrows) that consume higher energy
resource (substrate) to produce a lower energy resource (product). Reactions
connecting any pair of the four resources $R_{0},R_{1},R_{2},R_{3}$ can be
utilized by a species, making the space of all possible reactions a fully
connected network. B) A species can utilize a reaction by allocating a part of
its overall enzyme budget to the corresponding, reaction-specific enzyme.
Species differ in both the manner of enzyme allocation as well as their
overall enzyme budgets. C) The reactions in low-energy environments are
thermodynamically reversible. The flux $J$ in a reversible, enzyme-catalyzed
reaction between substrate $S$ and product $P$ is determined by three factors:
1) Enzyme capacity, which is the amount of enzyme available. 2) Enzyme
occupancy, which measure the fraction of free enzyme available to catalyze the
reaction, determined by the concentration of substrates and products. 3)
Thermodynamic inhibition due to accumulation of products. Since low-energy
reactions are reversible, the net flux in the forward direction will decrease
as products accumulate. The strength of this inhibition is controlled by the
heat dissipated in the reaction, $Q$.

To understand slow-growing microbial communities in energy-limited
environments, we develop a model that incorporates crucial features of growth
in these environments: energetic-limitation of growth, thermodynamic
constraints on reactions, and explicit modeling of reaction fluxes.

In the model, species grow utilizing energy harvested from chemical reactions
that convert a higher energy resource (substrate) to a lower energy resource
(product) (Fig. 1A). A reaction can be understood as a coarse-grained
description of catabolism jin_thermodynamics_2007 ;
wachtel_thermodynamically_2018 . The resources are labeled in the order of
decreasing standard state energy as $R_{0},R_{1},R_{2},...$. A species can
utilize reactions connecting any pair of resources; the allowed reactions make
a directed, fully-connected network. The product of one reaction can act as
the substrate of another, facilitating cross-feeding interactions between
microbes.

Species utilize a reaction by producing the corresponding, reaction-specific
enzyme. A species allocates a portion of its total enzyme budget to any number
of the possible reactions. We allow total enzyme budgets to vary, as in real
species milo_cell_2016 ; this also avoids potential degenerate behavior seen
in community models with fixed enzyme budgets posfai_metabolic_2017 . Thus a
species is characterised by its enzyme allocation strategy and total enzyme
budget (Fig. 1B). Through the explicit connection of species to reactions,
substrate consumption can create different products depending on the enzyme
used, like in real microbes krieger_metacyc_2004 . This contrasts with
microbial consumer-resource models, where substrate consumption by a species
leads to a fixed mixture of products, i.e., all species use the same reactions
and differ only in their consumption preferences marsland_minimum_2020 ;
marsland_available_2019 ; fant_eco-evolutionary_2021 .

From a reaction converting substrate $S$ to product $P$ with standard-state
energies $\mathcal{E}_{S}^{0}$ and $\mathcal{E}_{P}^{0}$, a species
assimilates $\mathcal{E}^{\mathrm{ATP}}$ energy. This energy, stored in ATP or
other forms, is constrained by reaction stoichiometry, and so is assumed to be
species-independent.

The harvested energy drives the proportional growth of new biomass. The
remaining energy is dissipated as heat $Q_{SP}$. $Q_{SP}$ is is defined as

$Q_{SP}=\mathcal{E}_{S}^{0}-\mathcal{E}^{\mathrm{ATP}}-\mathcal{E}_{P}^{0},$
(1)

which can also be understood as the negative free energy difference under
standard conditions, $\Delta G^{0}$.

The flux through the reaction is determined by reversible Michaelis-Menten
kinetics cornish-bowden_fundamentals_2012  :

$J_{S\to
P}=k_{\mathrm{cat}}E\frac{\frac{S}{K_{S}}}{1+\frac{S}{K_{S}}+\frac{P}{K_{P}}}\left(1-\frac{P}{S}\;\mathrm{exp}\left[-\frac{Q_{SP}}{RT}\right]\right),$
(2)

where $E$ is the enzyme concentration, $k_{\mathrm{cat}},K_{S},K_{P}$ are
enzyme-specific parameters describing the chemical kinetics, $T$ is the
temperature, and $R$ is the gas constant. In thermodynamic parlance,
$\frac{P}{S}\;\mathrm{exp}\left[-\frac{Q_{SP}}{RT}\right]$ represents the free
energy difference after accounting for resource concentration gradient,
$\Delta G^{\prime}=\Delta G^{0}+RT\log\frac{P}{S}$. Note that our results will
apply to a general stoichiometric ratio of substrate and product beyond $1:1$
as well (see SI); we omit discussion of this scenario in the main text for
clarity.

Eq. 2 can be understood as a product of three terms noor_note_2013 . The first
term specifies the maximal reaction rate, which is proportional to amount of
enzyme allocated to the reaction, $E$. The second term describes the
saturation level of the enzyme; the flux increases linearly at low substrate
concentrations and saturates at high substrate concentrations. The last (and
most crucial for our purposes) term describes thermodynamic inhibition, i.e.,
how the net rate of a reversible reaction decreases as products accumulate and
the ratio $P/S$ increases. The strength of the thermodynamic inhibition is
controlled by the heat dissipated in the reaction. This thermodynamic
inhibition of microbial growth has been quantitatively validated in the lab
and in situ conditions jin_new_2003 ; hoehler_thermodynamic_1998 ;
hoh_experimental_1997 ; westermann_effect_1994 . If product accumulation is
severe enough to reverse the reaction direction, we assume that species down-
regulate enzyme production to prevent energy loss from catalyzing the reverse
reaction.

The dynamics of species and resources are driven by these reaction fluxes.
Species grow in proportion to the energy they assimilate from the reactions
catalyzed by their enzymes. The concentration of a resource decreases due to
consumption in a reaction and increases due to production in a reaction.
Additionally, the entire system is diluted at rate $\delta$, which represents
the dilution rate of the bioreactor or the dilution by sedimentation in oceans
arndt_quantifying_2013 . This dilution of species biomass can also be extended
to account for the maintenance energy requirements of a species (see SI). The
precise equations describing species and resource dynamics are detailed in
Methods. We also obtained similar results in a model without explicit dilution
of resources and only species maintenance costs(see SI); we omit discussion of
this model in the main text for clarity.

Communities in natural and industrial environments are the result of years of
ecological competition and succession. To model such communities that emerge
from ecological competition, we studied community assembly from a large and
diverse species pool in an environment consisting of $6$ resources, labelled
in the order of decreasing standard-state energies as $R_{0},R_{1}...,R_{5}$.
The environment was supplied with the most energy-rich resource $R_{0}$ at
high concentrations compared to the typical $K_{S}$. The other lower energy
resources were generated as products in some of the 15 reactions that could be
utilized by species for growth. The energy assimilated from a reaction was
chosen to be a random fraction (between $15\%$ and $85\%$) of the energy gap
between product and substrate of that reaction. Enzymatic parameters
describing reaction kinetics, were chosen from lognormal distributions,
motivated by empirical observations bar-even_moderately_2011 . Since we are
interested in slow-growing communities, we chose a small dilution rate so as
to not drive any slow-growing species to extinction. After introducing species
from the pool into the environment, many species went extinct from competition
and simulations settled down to a steady-state community comprised of the
survivors.

### Emergent metabolic structure and function in slow-growing, energy-limited
communities

To study the features shared across slow-growing communities in energy-limited
environments, we repeated the community assembly experiment from five separate
pools of $600$ species each. Each species allocated its enzyme budget, chosen
from a lognormal distribution, to a random subset of the 15 possible
reactions. Species were not shared across pools. We also varied enzymatic
parameters (chemical kinetic parameters) to vary between pools. The
environment and its energetics was shared across the experiments, i.e., the
resource supply, resource energies, and energy uptake in each reaction (which
is constrained by stoichiometry) was the same across experiments. Simulations
of all pools converged to a steady-state maintained by a community of the
surviving species.

Figure 2: Functional convergence despite taxonomic variation. We simulated the
model to obtain the final community that arose as the outcome of competition
between a large number of species. We repeated this community assembly
experiment from five separate pools of $600$ species each. A,B) The metabolic
networks in the final communities obtained from two separate species pools are
similar. From all possible reactions (grey arrows), the same subset of
reactions are active (i.e., carry a positive flux) in the final communities
(colored arrows). On each reaction arrow, the size of the circles show the
flux carried in the reaction and the pie-chart on shows how this flux is
shared between species. The manner in which species contribute to the flux
differs between pools. C) The flux through the community metabolic network is
similar across communities from different species pools. The theoretical
prediction (Eq. (6)) matches simulations. The reactions in the bar plot are
colored according to the arrow colors in panels A,B (pools 1 and 2). D) The
relative abundance of species in the final communities. The species in the bar
plot colors are colored according to the pie-charts in panels A,B (pools 1 and
2). The relative abundance is not proportional to the flux catalyzed by the
species because the energy-yield per unit flux differs between reactions. For
example, the green species from pool 1 (panel A) and the pink species from
pool2 (panel B) catalyze a large flux but have a low relative abundance due to
the low energy yield of the reaction (panel C).

We analyzed the final steady-state communities to find emergent properties of
energy-limited communities that were shared across pools that differed in
species and enzyme content. We identified three properties of the communities
that resemble observations in natural communities:

Concurrent community metabolic networks: Only a subset of the 15 possible
reactions were active (i.e., carried nonzero flux) in the final communities
(colored arrows in Fig. 2A). This subset of reactions was shared across
communities, despite starting from different species pools (Fig. 2A,B). Hence,
the reactions utilized by the surviving species were determined by the
environment. Furthermore, the metabolic network structure was constrained. The
in-degree of each node was $1$, i.e., each resource was produced by only a
single reaction.

Functional convergence: We compared the metabolic functioning of the
communities obtained from the different species pools. The function performed
by the community was defined as the flux through the active reactions in the
final community. These fluxes were strikingly similar across pools (radius of
circles in Fig. 2A,B and Fig. 2C). Thus communities converged in the metabolic
function they performed despite having been assembled from different species
pools.

Taxonomic divergence: Bolstered by the convergence in metabolic network
structure and function across pools, we measured the species abundances and
functional roles in the communities. The functional role of a species was
quantified as the reaction flux catalyzed by it. We found that species
contributed to the reaction fluxes idiosyncratically across pools (pie charts
in Fig. 2A,B). Some reactions were performed by multiple species while others
were performed by only one, and this breakup of reaction fluxes between the
species varied between pools. The relative abundance of the species is
determined by product of the metabolic flux catalyzed by a species and the
energy assimilated per unit flux, which differed between reactions. The
relative abundance is shown in Fig. 2D. Thus the relative abundance and
functional roles of the species did not converge across the different pools.

Taken together, these observations mirror the ‘functional convergence despite
taxonomic divergence’ observed in many natural communities fernandez_how_1999
; louca_decoupling_2016 ; louca_function_2018 . We investigated the model
analytically to understand why these slow-growing, energy-limited communities
share these emergent properties. We uncovered fundamental thermodynamic
principles governing functional convergence in these energy-limited
communities, which we explain in the next section.

### Principle of maximum heat dissipation explains selected community
metabolic network

We first sought to understand why the same metabolic reactions are realized in
the final community across species pools. We were able to make analytical
progress by focusing our attention on slow-growing communities growing on low-
energy reactions. At steady-state, the biomass growth in communities replaces
loss by dilution, $\delta$. In slow-growing communities, the growth at steady-
state is much smaller than the maximum growth rate of the species
$g_{\mathrm{max}}$. Motivated by conditions in ocean sediments and
bioreactors, the substrate concentration in the resource supply in simulations
was larger than the typical $K_{S}$ mentges_long-term_2019 ;
arndt_quantifying_2013 ; jessen_hypoxia_2017 ; fernandez_how_1999 . The high
substrate levels in the supply mean that growth was primarily slowed by the
accumulation of products.

Figure 3: The maximum dissipation principle determines the community metabolic
network. In a system with four resources, we assemble the community metabolic
network by considering the production of each resource sequentially to
understand the governing thermodynamic principles. A) The sole path from the
supplied resource, $R_{0}$, to the next-highest energy resource $R_{1}$. The
path dissipates $Q_{01}=0.4$ units of energy as heat. B) The steady-state
community with reaction $R_{0}\to R_{1}$ maintains resource concentrations
such that $\frac{R^{*}_{1}}{R^{*}_{0}}\approx\mathrm{exp}\left(0.4/RT\right)$.
C) The two possible paths from $R_{0}$ to the next resource, $R_{2}$, that
could be added to the community. The paths $R_{0}\to R_{2}$ and $R_{0}\to
R_{1}\to R_{2}$ dissipate 0.5 and 0.7 units of energy as heat. D) The path
that dissipates more heat, $R_{0}\to R_{1}\to R_{2}$, is selected in the final
community because species utilizing this path will drive concentration of
$R_{2}$ higher (such that
$\frac{R^{*}_{2}}{R^{*}_{0}}\approx\mathrm{exp}\left(0.7/RT\right)$) than
species utilizing $R_{0}\to R_{2}$ E) The three possible paths from $R_{0}$ to
$R_{3}$, that could be added to the community. We do not consider the path
$R_{0}\to R_{2}\to R_{3}$ because we have already found that the maximally
dissipative path to $R_{2}$ is $R_{0}\to R_{1}\to R_{2}$ and not $R_{0}\to
R_{2}$. F)The path that dissipates most heat, $R_{0}\to R_{1}\to R_{3}$, is
selected in the final community because it can drive the concentration
gradient $R_{3}/R_{0}$ highest (such that
$\frac{R^{*}_{3}}{R^{*}_{0}}\approx\mathrm{exp}\left(1.0/RT\right)$). Thus,
the active reactions in the final community network will be determined by the
paths to each resource that dissipates the most heat.

Since growth is slowed down by product accumulation, we can relate the
concentrations of substrates and products of an active reaction in the final
steady-state community. Fig. 3A shows an example of a reaction $R_{0}\to
R_{1}$ in a community with four resources. If the reaction is active in the
final steady-state community, then we have:

$\frac{R^{*}_{1}}{R^{*}_{0}}=e^{Q_{01}/RT}\;+\mathcal{O}\left(\frac{\delta}{g_{\mathrm{max}}}\right),$
(3)

where $R^{*}_{1},R^{*}_{0}$ are the steady state concentrations of the
resources and $Q_{01}$ is the heat dissipated in the reaction $R_{0}\to
R_{1}$. This condition implies that reactions are slowed down to near
thermodynamic equilibrium due to product accumulation. The first (and leading
order) term depends only on the thermodynamics of the reaction. The second
term, $\frac{\delta}{g_{\mathrm{max}}}$, which contains all the properties
specific to the species and enzyme, is only a small correction.

We now consider the production of the second resource, $R_{2}$, which can be
produced via two possible reaction paths (Fig. 3C). To analyze this scenario,
we derive a crucial extension to Eq.(3) that applies to reaction paths,
composed of multiple reactions, that are active in the final community (see SI
for derivation). If a reaction path proceeding from $R_{i}$ to $R_{j}$ is
active in the final community, we have:

$\frac{R^{*}_{j}}{R^{*}_{i}}=e^{Q_{i\Rightarrow
j}/RT}\;+\mathcal{O}\left(\frac{\delta}{g_{\mathrm{max}}}\right),$ (4)

where $Q_{i\Rightarrow j}$ refers to the sum of the heat dissipated in the
reactions along the path from $R_{i}$ to $R_{j}$. Again, note that the
species- and enzyme- specific properties are only a small correction. This
equation provides us different values for $\frac{R^{*}_{2}}{R^{*}_{0}}$ for
each of the paths considered in Fig. 3C. Since both values cannot hold
simultaneously, only one of the two paths can be realized in the final
community. Thus the in-degree of any node in the network is always $1$, as
seen in Fig. 2A,B.

To understand which of the two paths is selected in the final community, we
can consider the competition of two species utilizing reactions $R_{1}\to
R_{2}$ and $R_{0}\to R_{2}$ added to the community with reaction $R_{0}\to
R_{1}$ shown in Fig. 3B. The species utilizing the reaction $R_{1}\to R_{2}$
(and hence path $R_{0}\to R_{1}\to R_{2}$) will drive product accumulation
until $\frac{R^{*}_{2}}{R^{*}_{0}}\approx e^{0.7/RT}$, while the species
utilizing the reaction $R_{0}\to R_{2}$ will drive product accumulation until
$\frac{R^{*}_{2}}{R^{*}_{0}}\approx e^{0.5/RT}$. Since
$e^{0.7/RT}>e^{0.5/RT}$, the former species can invade and grow in the steady-
state environment of the latter, driving the product accumulation to levels
where the latter cannot grow. Thus the species utilizing the path dissipating
more heat is able to invade and displace its competitor, and create conditions
that cannot be invaded by the other. Hence, the path to $R_{2}$ that
dissipates more heat is realized in the final community (Fig. 3D).

The same argument can be extend to resources with multiple paths leading to
them, such as $R_{3}$. We consider three paths to $R_{3}$ in Fig. 3E. Note
that we exclude the path $R_{0}\to R_{2}\to R_{3}$ since we previously found
the maximally dissipative path to $R_{2}$; this is an application of Prim’s
algorithm to find the maximal spanning tree in a network prim_shortest_1957 .
Comparing the heat dissipated among the three paths, we find the maximally
dissipative path, $R_{0}\to R_{1}\to R_{3}$. A species utilizing this path is
able to raise the concentration of $R_{3}$ high enough so as to make the other
reactions infeasible, driving competitors relying on the paths extinct. Thus
the principle of maximum dissipation governs the selection of the community
metabolic network in slow-growing, energy-limited communities.

### Functional convergence from thermodynamic principles

The principle of maximum heat dissipation explains why the same reactions are
realized in the final communities across pools. But it does not explain the
convergence in reaction fluxes across pools.

To understand how this convergence in fluxes arises, we build on results in
Eq. (4) to derive the concentration at steady state of $R_{0}$,

$R_{0}^{*}=\frac{h_{0}}{1+\sum_{j=1}^{M}e^{Q_{0\Rightarrow
j}/RT}}\;+\mathcal{O}\left(\frac{\delta}{g_{\mathrm{max}}}\right),$ (5)

where $h_{0}$ is the steady state concentration of $R_{0}$ in absence of any
consumption and $Q_{0\Rightarrow j}$ is the heat dissipated in the reaction
path to $R_{j}$ realized in the community (see SI). Using Eq. (4), we can
obtain the the steady-state concentrations of all resources:

$R_{i}^{*}=\frac{h_{0}}{1+\sum_{j=1}^{M}e^{Q_{0\Rightarrow
j}/RT}}e^{Q_{0\Rightarrow
i}/RT}+\mathcal{O}\left(\frac{\delta}{g_{\mathrm{max}}}\right).$ (6)

These equations imply that the resource concentrations at steady-state are
determined to leading order by thermodynamics alone. The surviving species
grow to abundances that allow them to maintain the environmental resource
concentrations at these thermodynamically-determined values. Note that these
equations resemble the Boltzmann-Gibbs distribution in statistical physics,
now realized in an ecological context.

The fluxes in the steady-state community can be calculated by conserving
resource flux along the chemical reaction network. The outflow from a terminal
resource without any outgoing reactions, $R_{T}$, is solely determined by
dilution and equal to $\delta R^{*}_{T}$. At steady state, this outflow is
balanced by the reaction flux into the terminal resource. This can be used to
calculate the flow from resources producing a terminal resource. Iterating
this procedure, we can calculate the total flux into any resource $R_{i}$,
$I_{i}$, as

$I_{i}^{*}=R_{i}^{*}\delta+\sum_{j\;\text{downstream
of}\;i}R_{j}^{*}\delta+\mathcal{O}\left(\frac{\delta}{g_{\mathrm{max}}}\right),$
(7)

where the sum is over all resources, $R_{j}$, that appear downstream of
$R_{i}$ in the reaction network. This theoretical prediction matches
simulations (Fig. 2 A). Importantly, the steady-state resource concentrations
and reaction fluxes are independent of enzyme budgets, enzyme allocation, and
details of the chemical kinetics—none of the associated parameters
($E,k_{cat},K_{M},K_{S}$) appear in the equations to leading order (Eq.6).
Hence there is strong selection for choosing the maximally dissipative network
and converging to the thermodynamically constrained fluxes; selection on the
species-specific properties is weaker. Thus, we observe functional
convergence, driven by the shared reaction thermodynamics across experiments,
despite taxonomic divergence, in terms of how species conspire to maintain the
community function.

Note that a community utilizing the maximally dissipative reactions can still
experience species turnover. For example, an invading species that allocates
more enzyme to the maximally dissipative reactions can displace a resident.
However, this invasion will have only a very small effect (of order
$\frac{\delta}{g_{\mathrm{max}}}$) on the community metabolic function and
steady-state resource environment. Hence communities can continuously
experience species turnover while maintaining their metabolic functions, as
seen in bioreactors fernandez_how_1999 ; peces_deterministic_2018 .

## Discussion

Microbial community models have successfult exposed the organizational
principles and universal, emergent behavior of microbial communities
structured by nutrient limitation macarthur_species_1970 ;
posfai_metabolic_2017 ; tikhonov_collective_2017 ; goldford_emergent_2018 ;
marsland_minimum_2020 ; dubinkina_multistability_2019 ;
wang_complementary_2021 . However, in many natural and industrial
environments, microbial communities grow under energy-limited conditions and
are forced to use low free energy reactions to drive their
growth.jessen_hypoxia_2017 ; jorgensen_feast_2007 ; leng_review_2018 ;
hoh_experimental_1997 ; nobu_catabolism_2020 ; bradley_widespread_2020 ;
conrad_thermodynamics_1986 ; bradley_widespread_2020 ;
hickey_thermodynamics_1991 ; jackson_anaerobic_2002 ; larowe_energetics_2019 ;
larowe_thermodynamic_2012 . Here, by explicitly modeling the thermodynamic
inhibition of microbial catabolism and energy-limitation of growth, we have
developed a minimal model of microbial communities in low-energy environments.
We used the model to investigate the emergent properties of slow-growing
microbial communities assembled in low-energy environments. Strikingly, model
simulations displayed the ‘functional convergence despite taxonomic
divergence’ observed in many communities fernandez_how_1999 ;
louca_decoupling_2016 ; louca_function_2018 . We demonstrated that functional
convergence in our model originates from the fundamental thermodynamic
constraints on microbial growth; previous approaches have shown functional
convergence in models of nutrient-limited communities due to shared metabolic
constraints between species fant_eco-evolutionary_2021 . Further, we
demonstrated that community metabolic network structure in slow-growing
communities assembled by ecological competition over long periods of time is
determined by the thermodynamic principle of maximum dissipation. Importantly,
network selection by maximum dissipation manifests through ecological
competition and is not expected in isolated microbes.

For simplicity, we demonstrated our main results using a minimal model of
energy-limited communities. In the supplementary text, we show that our
results hold more generally. In particular, we demonstrate that our results
apply in the following scenarios: First, if reaction stoichiometry varies
beyond $1:1$ in the model (see SI Sec.6). Second, if maintenance energy
requirements of the cell are incorporated in the model; the maintenance energy
flux requirement resembles biomass dilution, and so our results apply as long
as this requirement is small (see SI Sec.5). And third, a model without
explicit dilution of resources, where cells uptake resources for anabolic
processes in addition to catabolism (see SI Sec.7).

Figure 4: Functional convergence and the strength of thermodynamic constraints
decreases in fast growing communities. A),B),C) The realized community
metabolic networks at slow growth rate, intermediate growth rate, and fast
growth rate respectively. All three communities were obtained from the same
species pool, and the steady-state growth rate was varied by changing the
dilution rate, $\delta$. The dashed lines indicate that the active reaction in
the community agrees with the prediction based on maximum dissipation
principle. In the slow-growing community, the active reactions match the five
reactions predicted from the maximum dissipation principle; in the middle
community 3 of the active reactions match the prediction; in the fast-growing
community only 2 of the active reactions match the prediction. D) The fraction
of reactions correctly predicted by the maximum dissipation principle,
averaged across 10 different species pools in the same environment. The
accuracy decreases as the growth rate increases. E) The functional distance
between two communities was quantified by the Jensen-Shannon distance between
the two community flux vectors. The average functional distance increases with
the growth rate. Thus, the observed functional convergence decreases as the
communities grow faster. The dashed line indicates the average distance
between two random flux vectors. A random flux vector had the same length
(15), and had each element picked from a uniform distribution between 0 and 1.
The colored boxes in panels D and E correspond to the growth rates shown in
the panels in A,B,C. The maximum growth rate, $g_{max}$, was used to normalize
the steady-state growth rate. $g_{max}$ was defined as the growth rate
obtained on an irreversible reaction between consecutive resources, without
any energy lost as heat, by a species investing its entire budget in the
reaction (see Methods).

An important assumption in our theoretical derivation of the maximal
dissipation principle and thermodynamic explanation of functional convergence
was that communities were slow-growing. But what happens when growth rate
increases? Our theoretical analysis predicts that differences in species’
enzyme budgets and allocation, and in enzymatic parameters, will start to
matter as growth rate increase, and will cause greater differences in the
community metabolic network structure and function of communities from
different pools. To study community metabolic network structure and function
as the steady-state growth rate increases, we simulated community assembly
from 10 separate pools of 600 species at different dilution rates $\delta$.
Since the growth rate of a community at steady-state is equal to the dilution
rate, these simulations provided us with 10 different final communities at
each steady-state growth rate.

Fig. 4A,B,C depicts three final communities obtained, at three different
dilution rates from the same species pool. The maximum dissipation principle
predicts all 5 reactions correctly in the slow-growing community, which grows
at $1\%$ of the maximum possible growth rate (dashed lines indicate reactions
predicted correctly). At an intermediate growth rate, the maximum dissipation
principle predicted 3 out of the 5 reactions correctly. Finally, for the fast-
growing community, which grew at $30\%$ of the maximum possible growth rate, 2
out of 5 reactions were predicted correctly. The accuracy of the predictions
by the maximum dissipation principle, defined as the average fraction of
reactions predicted correctly across the 10 species pools, is shown in Fig.
4D. Communities deviate from the predictions at higher dilution rates due to a
combination of factors. First, due to the low energy yields of reactions on
the maximally dissipative path, species utilizing these reactions need to
catalyze a larger flux to achieve high growth rates than species utilizing
reactions with higher energy yields on competing paths. Second, due to the
variation in enzyme budgets and enzyme allocation strategies, a species
utilizing reactions on a maximally dissipative path can get out-competed by a
species with a larger enzyme budget allocated to reactions on a competing
path. Third, due to the variation in enzymatic parameters, a reaction on a
competing path might be preferred because it has better enzymes, (e.g. with
higher $k_{\mathrm{cat}}$).

As the idiosyncratic properties of species pools and enzymes start to play a
bigger role in determining the community metabolic network, functional
convergence weakens. Fig. 4E shows that the average distance between community
fluxes, or functional divergence, increases in fast-growing communities. The
dashed line shows the expected distance between two random flux vectors; this
distance is higher than the most functionally distant communities because the
random flux vectors are not subject to ecological and flux constraints.
Together, the observations in Fig. 4 show that the maximum dissipation
principle and functional convergence will be stronger in low-energy
communities that grow slowly. Intriguingly some published results hint at this
loss of functional convergence with faster growth. The functional stability of
communities in anaerobic bioreactors was analyzed in three different studies
fernandez_how_1999 ; peces_deterministic_2018 ; zhou_stochastic_2013 ,
operating at dilution times of 10 days, 15 days and 1 day. While the two
studies at the smaller dilution rates observed functional convergence, the
study at the highest dilution rate did not.

Microbes in low-energy environments face a trade-off between harvesting energy
efficiently, to increase biomass yield per unit reaction flux, and dissipating
more heat, to increase reaction flux. A microbe cannot grow at either
extreme—assimilating all the energy curbs growth because the reaction flux
will be zero, while dissipating all the energy curbs growth because energy
assimilated will be zero. Thus, microbes have to find a balance between these
opposing forces. Our results suggest that, at small dilution rates, the effect
of ecological competition will push microbes to evolve towards dissipating
more energy. However, in practice this evolutionary drive to decrease energy
assimilation will not continue forever. It will probably be limited by
biochemical constraints schink_syntrophism_2006 ; schink_energetics_1997 ;
lever_life_2015 ; hoehler_biological_2004 , such as the smallest energy unit
that can be assimilated by a species (one electron, one ATP, etc.), or when
reactions become limited by substrate depletion rather than thermodynamic
inhibition. In our simulations, to focus on the ecological properties of
energy-limited communities, a species at the lower-limit of energy
assimilation could survive at the smallest dilution rates considered. An
exploration of the evolutionary consequences of the selective pressures on
energy assimilation is reserved for future work.

Optimization principles grounded in thermodynamics have been used in microbial
metabolism to explain behavior at the cellular scale henry_thermodynamics-
based_2007 ; flamholz_glycolytic_2013 ; goldford_protein_2021 . At the
community level, optimization of thermodynamic quantities has been conjectured
to be a mechanism by which communities self-organize, motivated mostly by
verbal arguments and analogies with physical systems schneider_life_1994 ;
vallino_ecosystem_2010 . However, the question of which quantity should be
maximized, and under what conditions, remains actively disputed in the
literature dewar_theoretical_2014 ; meysman_ecosystem_2010 . By incorporating
ecological and thermodynamic principles, our model connects these two
disparate approaches toward understanding microbial communities. We derive the
thermodynamic optimization principle of maximum dissipation, which structures
slow-growing, energy-limited communities, providing a concrete example of
thermodynamic optimization in ecology.

Our results make predictions for the metabolic structure and resource
environment created by the communities in low-energy environments, based on
the thermodynamics of microbial metabolism. This requires knowledge of the
free energy differences and metabolomic data of the resource environment.
Although calculating the free energies of the many metabolites present in a
real environment is challenging, recent advances in computational methods make
the outlook promising noor_consistent_2013 ; jinich_quantum_2018 ;
jinich_mixed_2019 . Combining these methods with metabolomic data and
knowledge of microbial metabolism to predict metabolite composition in real
environments shaped by microbial communities is an exciting prospect for
future research.

Acknowledgements. The authors thank Avi Flamholz for valuable comments and
feedback on the manuscript. This research was supported in part by NSF Grant
No. PHY-1748958 and the Gordon and Betty Moore Foundation Grant No. 2919.02.

## Methods

### Species and resource dynamics

Species dynamics are determined the amount of reaction flux they can utilize,
the energy the assimilate from this to create biomass, and biomass loss due to
dilution. The dynamics of species $\alpha$ with abundance $N^{(\alpha)}$ is
described by

$\frac{dN_{\alpha}}{dt}=N_{\alpha}\left[\sum_{i,j\in\mathcal{X}}E^{(\alpha)}_{ij}\mathcal{F}_{ij}\mathcal{E}^{\mathrm{ATP}}_{ij}Y-\delta\right],$
(8)

where $F_{ij}$ is the flux of reaction $R_{i}\to R_{j}$ catalyzed per unit
enzyme, $E^{(\alpha)}_{ij}$ is the enzyme allocated to reaction $R_{i}\to
R_{j}$ by species $\alpha$, $\mathcal{X}$ is the set of all allowed reactions,
and $\delta$ is the dilution rate. The maintenance energy requirements of a
species can be accounted for by replacing $\delta$ with $\delta+m$ in Eq. 8,
where $m$ is the energy flux required for cell maintenance. Our results apply
in this scenario as well (see SI).

Resource dynamics are determined by their consumption and production via the
reactions catalyzed by the species, external supply, and dilution. The
dynamics of resource $i$ with concentration $R_{i}$ are given by

$\frac{dR_{i}}{dt}=h(R_{i})-\sum_{\alpha,j}N_{\alpha}E^{(\alpha)}_{ij}\mathcal{F}_{ij}+\sum_{\alpha,k}N_{\alpha}E^{(\alpha)}_{ki}\mathcal{F}_{ki}-\delta
R_{i}$ (9)

where $h(R_{i})$ is the resource supply. Only the top resource $R_{0}$ is
supplied, so $h(R_{0})=\delta h_{0}$ and zero otherwise. $h_{0}$ is the
concentration of resource in the supply.

### Simulation procedure

All species in a pool were introduced at the same initial density (=1) in an
environment with resource concentration of the supplied resource $R_{0}=h_{0}$
and all other resources at a very small concentration $10^{-10}$. The species,
reaction, and resource dynamics were simulated till they reached a steady-
state. At regular intervals, species that fell below an abundance threshold
had their concentration set to zero. The minimum allowed resource
concentration was $10^{-10}$ to prevent division by zero in Eq. (2). A steady-
state was reached if the maximum value of the vector
$\frac{1}{N_{\alpha}}\frac{dN_{\alpha}}{dt}$, measuring the logarithmic growth
rates, fell below $10^{-5}$.

### Simulation parameters

The enzyme budget of a species was chosen from a lognormal distribution with
lognormal parameters $\mu=1,\sigma=0.1$. A species utilized a random subset of
the 15 possible reactions. So species in the pool were not biased towards
extreme generalists or specialists. The enzyme budget was allocated to the
selected reactions uniformly, by using a Dirichlet distribution with the
dirichlet parameter, $\alpha=1$, for the selected reactions. There were 600
species in each of the 5 pools in Fig.2 and 10 pools in Fig. 4; species were
not shared across pools.

The energies of resources $R_{0},R_{1},R_{2},R_{3},R_{4},$ and $R_{5}$ were
$5RT,4RT,3RT,2RT,1RT,$ and $0RT$. For each reaction, a random fraction between
$15\%$ and $85\%$ of the standard energy gap between product and substrate
($\mathcal{E}_{S}-\mathcal{E}_{P}$) was assimilated and the rest was
dissipated as heat. This assimilated energy, along with resource energies, was
fixed across the experiments with different species pools. The concentration
of $R_{0}$ in the supply, $h_{0}=80$. The chemical kinetic parameters
$K_{P}$,$K_{S}$, and $k_{cat}$ were chosen from lognormal distributions with
lognormal parameters $\mu=0.,\sigma=0.01$, and so, their mean was close to 1.
The energy to biomass yield factor, $Y=1$. The dilution rate, $\delta=0.01$ in
Fig. 2; this rate was small enough that a typical species would survive if it
was alone.

The Jensen-Shannon distance, used to measure functional distance between two
flux vectors in Fig. 4. It is the symmetrized analog of the Kullback-Leibler
divergence, and was defined as

$\mathrm{JSD}(f^{(a)},f^{(b)})=\frac{1}{2}\sum_{i}f^{(a)}\log\frac{f^{(a)}}{f^{(m)}}+\frac{1}{2}\sum_{i}f^{(b)}\log\frac{f^{(b)}}{f^{(m)}},$
(10)

where $f^{(a)},f^{(b)}$ are the two normalized flux vectors and $f^{(m)}$ is
an average flux vector defined as $(f^{(a)}+f^{(b)})/2$. We report the JSD
averaged over all pairs of communities in Fig. 4.

$g_{max}$ in Fig. 4 was defined as the growth rate obtained from an
irreversible reaction where a species invested its entire enzyme budget into
one reaction. Since this varies between reactions because reactions different
energy yields, we chose the energy gap between consecutive resources. It was
calculated as the product of mean $k_{cat}$, mean enzyme budget, energy gap
between consecutive resources ($=RT$), and biomass yield factor $Y$.

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# Haptic Interactions for Extended Reality
††thanks: This work was funded in part by the Research Foundation – Flanders
(FWO), IDLab (Ghent University – imec), Flanders Innovation and
Entrepreneurship (VLAIO), and the European Union.

Yentl Vermeulen1, Sam Van Damme1, Glenn Van Wallendael1, Filip De Turck1,
Maria Torres Vega1,2 1IDLab, Department of Information Technology (INTEC),
Ghent University - imec, Belgium
2eMedia Research Lab, KU Leuven, Belgium

###### Abstract

This research investigates whether the interaction methods of eXtended Reality
(XR)headsets can be improved by using haptic feedback. As a first and most
common technique, indirect interactions are considered. Indirect interactions
correspond to manipulations of virtual objects from a virtual distance using
pre-defined hand gestures. As a second interaction technique, direct
interaction (namely Direct Interaction Method (DIM)) has been implemented
where the user manipulates objects by virtually touching these with their
hands. A third interaction method extends the previous one with haptic
feedback (namely Haptic Enhanced Direct Interaction Method (HEDIM)). These 3
methods are compared with each other based on objective and subjective user
tests, also taking into account financial considerations. This research
concludes that the DIM improves upon the standard indirect method.
Additionally, it has been observed that haptic feedback could enhance the DIM
in specific situations. Nevertheless, when considering the current financial
cost, our subjects were not convinced of the small improvements haptic
feedback brings.

###### Index Terms:

Augmented Reality (AR), Head-Mounted Display, Haptic feedback

##  I Introduction

Current immersive systems lack tactile feedback when interacting with computer
generated objects. Users do not know when they are interacting with a virtual
object in eXtended Reality (XR)because they do not experience any feedback.
Additionally, immersive systems have no standard mechanism for interaction
comparable to what the computer mouse represents for the personal computer.
The computer mouse as an interface led to a breakthrough with the general
public and this is what XR is still waiting for [1]. Furthermore, the absence
of a direct interaction method is unnatural from the user’s perspective [2].

Since the interaction with an XR environment varies from one device to the
other, this study considers the HoloLens (first edition) and the Oculus Quest
2 as Head-Mounted Display (HMD). The interaction method of the Hololens will
serve as a baseline.

Currently, there are three methods to operate the HoloLens. Firstly, there is
gazing for selecting an item. A gaze is made when the user moves the whole
device, including their head, and try to aim the projected pointer on the
desired item. Secondly, the air tap is used to interact with the object on
which the pointer is projected. To perform an air tap, the user taps their
thumb and index finger together in sight of the camera. The third and final
option is a voice command, which is not standard integrated for all
applications.

This research will focus on the integration of two new interaction methods.
Firstly, the Direct Interaction Method (DIM)is proposed to make the standard
interaction method more natural. Secondly, this new interaction method is
extended with the Prime II Haptic Edition gloves from Manus and is
consequently named the Haptic Enhanced Direct Interaction Method (HEDIM).

The purpose of this research is to examine if these new interaction methods
improve the user experience, accuracy, and speed of performing frequently used
XR tasks in everyday life. As assignments, it is chosen to let the users type
a sentence on a virtual keyboard and construct a tower of virtual cubes. Both
assignments used in this research are visualized in Figure 1. After each set
of tests, the user will receive a questionnaire with subjective questions
about their preference of use, user experience, cybersickness and possible
irritations.

Figure 1: Visualization of the tasks to be performed by the subjects.
Assignments on the HoloLens (top row) and assignments on the Oculus (bottom
row).

##  II Taxonomy

To make it easier to understand how XR works, it is essential to know what it
refers to. Therefore, all terms used will be visualized and defined based on
the reality-virtuality continuum. This continuum is a continuous scale ranging
from the real environment to the completely virtual environment. It
encompasses all possible variations and compositions of real and virtual
objects and was first introduced in the research of Milgram and Kishino in
1994 [3]. The first version did not contain all contemporary terms; therefore,
an update is performed as shown in Figure 2. This study will only consider the
descriptions below as definitions to avoid misunderstandings, as some terms
are not strictly defined and are used interchangeably in different contexts.

Figure 2: Updated version of the reality-virtuality continuum.

  * •

EXtended reality (XR) is the term referring to all real-and-virtual combined
environments and human-machine interactions generated by computer technology
and wearables, where the X represents a variable for any current or future
spatial computing technologies [4]. XR can be understood as an umbrella term
that includes the entire reality–virtuality continuum and its extremes.

  * •

Mixed Reality (MR)or hybrid reality is a subset of XR and refers to everything
in the continuum except for all applications on the two extremes [3]. All
applications between the two extremes can be described as a combination of the
real and the virtual world, meaning that both realities are mixed. In non-
academic context, MR is often referred to as an extra step of AR where
holograms not just overlap the real world but in addition, they are
interactive and manipulable [5].

  * •

Augmented Reality (AR)is part of MR and lies between the two extremes. It
refers to an enhanced version of reality created by using technology to
overlay digital information on an image of something being viewed through a
device [3]. To retain the essential components and avoid limiting AR to
specific technologies three characteristics are often used, namely, it is a
combination of real and virtual content, it is interactive in real time and it
is registered in 3D [6].

##  III State of the art

Currently, HMD-companies use their own created interaction method for their
product. This creates confusion among users when a new product is purchased.
Additionally, their interaction method is never investigated in the public
scientific domain or compared with other methods to define the best possible
solution.

Despite the possibilities for daily use such as AR meetings with Microsoft
Mesh, users prefer to a personal computer for their daily use [7]. This
research will not compare the current interaction method of XR-devices with a
personal computer, but it will try to enhance the basic interactions used by
XR-devices based on common daily applications with an ultimate goal of
bringing XR-interactions closer to traditional PC interactions from a
productivity point of view.

Haptic feedback has been investigated in a lot of contexts [8]. Starting at
the hardware of the interface, it can be provided originating from different
sources, such as straight from the display device upon touching it [9], but
the focus of this work is rather on gloves worn during an AR-interaction. When
considering wearable haptic interfaces, there can be a focus on different
purposes of the haptic feedback, such as identifying objects [10] or
productivity as envisioned in this work. Looking from a different angle,
haptic interfaces can be used to simulate working with real-life tools [11]
[12]. Here, the difference is more subtle, but although we consider a keyboard
and cubes in our test which correspond to real life objects, it is not our
goal to make these feel like the real counterparts. In contrast to previous
work [13] where the interaction capabilities of different people are compared
to each other in a game like fashion, this study tries to quantify individual
differences in productivity when utilizing different interfaces. Finally, no
studies regarding the interest in buying an HMD and haptic feedback were
found. Consequently, this research investigates how much participants want to
spend on an HMD and whether they can estimate the value of the used HMD s.

##  IV Proposed solution

Because this research focuses on the basic interactions, the assignments for
the subjects are deliberately kept simple. Devising complex tests where the
user is pushed to the limit and is given a big explanation would only
negatively influence the results. That is why it was decided to perform a
simple keyboard task and building a virtual tower of blocks. These are tasks
that are straight forward for any user at first glance and require little or
no practice. Additionally, these assignments have the advantage that both the
three-dimensional and the two-dimensional space are tested.

###  IV-A System architecture

Firstly, a schematic visualization of the system architecture using the
standard interaction method of the HoloLens is shown in Fig. 3. On the right
in this image, the point of view of the user can be seen. It shows a couple of
cubes that can be constructed into a tower. Similarly, a virtual keyboard can
be placed in the AR environment. This environment is constructed using the
Unity game engine, which is installed on a personal computer. When an AR
environment is coded, it can be tested on the HoloLens. This can be done by
streaming the project or let it build completely standalone on the HMD. Due to
it can only be streamed wirelessly, streaming is only used for testing
purposes. If a user is testing the standalone version of an assignment on the
HoloLens, they can interact with the holograms using the standard HoloLens
interaction methods, such as gaze and air tap. In Unity, the HoloLens is coded
to perceive the hands of the user via the built-in cameras which recognize the
gestures via optical hand tracking.

Figure 3: Schematic visualization of the system architecture using the
standard interaction method of the HoloLens.

Similar to Fig. 3, a schematic visualization of the system architecture using
DIM is presented in Fig. 4. On the right, it is identical to the previous
figure because for both interaction methods the same assignments are used.
Different is that the user now wears an Oculus VR headset as HMD due to an
incompatibility between the HoloLens and the Manus gloves. The gloves are not
used in this interaction method but to enable a comparison with the haptic
gloves, DIM and HEDIM use the same code. In contrast with the HoloLens, the
project cannot be built to run standalone on the Oculus. Technically, this
would be a possibility but then the Intel RealSense and the Manus gloves
cannot be integrated. As both are essential for this research, it was required
to stream the project with a USB cable. Consequently, the project executes on
the personal computer.

Figure 4: Schematic visualization of the system architecture using DIM.

For the HEDIM, a schematic visualization of the system architecture is
displayed in Fig. 5. This system architecture is similar to the one of DIM
with the only difference being the haptic feedback. When the haptic gloves are
used, they need the Oculus controllers to be attached to them. Because the
gloves are not recognized as a person’s hand, optical hand tracking has become
impossible. Therefore, the connected Oculus controllers will send the location
of the hands via the HMD to the personal computer. The gloves itself are
wireless connected to the computer and they constantly send the shape of the
users’ hands to the computer. If a fingertip interacts with an AR hologram,
the computer will send a vibration signal that is felt by the user.

Figure 5: Schematic visualization of the system architecture using HEDIM.

###  IV-B Implementation of the interaction methods

As this research aims to improve standard interaction method, the test set-up
of HoloLens could therefore not be optimized. Only guidelines given in
Microsoft’s official documentation were used. For further research and
projects, it is essential to know in advance that Unity 2020 does not support
targeting HoloLens (1st gen) anymore [14]. The HMD remains supported in Unity
2019 LTS with Legacy Built-in XR for the full life cycle of Unity 2019 LTS
through mid-2022.

The integrated keyboard was used for the standard interaction method of the
HoloLens. An online notepad[15] was used for showing and to make typing
available for the user. Regarding the cube test set-up, the command design
pattern was used to implement the interaction method of the HoloLens and the
AR environment was fully implemented in Unity. This interaction method is
always performed from a distance, meaning without touching the virtual
keyboard or cubes. The used Unity version was Unity2017.4.40f1 because it was
the only version that allowed Holographic Remoting Player to be used. Without
it being documented anywhere, in newer versions no connection can be made to
the HoloLens without building the whole application.

In contrast with the interaction method of the HoloLens, both the DIM and the
HEDIM implemented on the Oculus were optimized as much as possible. Firstly,
both implementations are identical through reuse. The only difference is that
for the HEDIM the haptic gloves are activated. With this new interaction
method, it is now possible to touch, grab and directly interact with virtual
objects. When virtual object needs to be activated, moved or rotated the user
needs to be close enough to the hologram. For the implementation of this
interaction method, an observer design pattern was used where each fingertip
was observed by the corresponding hand. Because the Oculus device had problems
tracing the hands when the haptic gloves were worn, the prefab was slightly
modified for the haptic version. The standard optical hand tracking was
changed by the built-in hand tracking of the gloves. It should be noted that
apart from this nothing has changed in the way the interaction method works.

##  V Methodology

To obtain two objective performance parameters, the time and score of the user
per assignment for each interaction method is measured. This section will
discuss in detail how the subjects are evaluated on these parameters. For the
subjective parameters a questionnaire using Likert scale has been used.

For the keyboard test, each subject was requested to type a random sentence
that complied to the following self-imposed rules. First, the sentence had to
consist of a total of 30 characters. Second, it had to contain three special
characters that were not allowed to be in a row. Third, it also had to include
three numbers that had to be in a row. The remaining 24 characters had to
contain five capital letters that were also not allowed to occur
consecutively. The space character was not considered as a special character
and had therefore no additional conditions. Finally, the language of the
sentences was always English. To give each user the same difficulty, 3 fixed
sentences were chosen. These were randomly used for a different interaction
method for each user. We assembled the following sentences:

#HelloWorld<Test No Error-404

@Ghent is for me ToP-100 CitY^

>123 i LoVe auGmented-RealitY!

After exactly 4 minutes the test would be stopped. for each error in the
sentence or for each missing character, an error score was counted. This error
score was then added to the number of times delete was pressed during the
assignment to get the total number of errors. The error score for this
assignment is therefore the number of mistakes made. This means that a lower
error score is better than a higher one. A visualization of the set-up of the
keyboard test is presented in Fig. 6.

Figure 6: Visualization of the set-up of the keyboard test. (Keys are loaded
by runtime)

After successfully completing the assignment on the keyboard, the subjects
were presented with the cube test. The goal of this test was to make a tower
of six blocks high in the center platform. Blocks could fall when moving from
one of the two other platforms. When this happened, that cube was permanently
gone. This was deliberately done to prevent the user from building
indefinitely until time ran out. Additionally, it was also intended to give
users a real sense of grip while holding a cube and create frustration when
dropping one. A visualization of the set-up of the cube test is presented in
Fig. 7. The score was determined by subtracting the height (in number of
blocks) of the user’s largest tower from the requested height (i.e. six
blocks). Furthermore, two times the number of fallen cubes was added to this.
This gives the following formula:

Score = 6 - (tallest tower of the user) + 2 * (fallen cubes)

The score for this assignment is therefore again the number of mistakes made.
It was decided to give more weight to the fallen blocks in order to better
deduce how well the user could operate a block. This means both the grip while
holding a block, but also the precise placement of the block on top of the
tower in the three-dimensional space because blocks can still fall if the
tower is poorly built.

Figure 7: Visualization of the set-up of the cube test.

##  VI Discussion of results

This section discusses results of this research. First, in Table I a summary
including statistical values of the error score of the tests is presented.
Thereafter, in Table II the similar statistical values are shown for the time
parameter. Next, a bar chart containing the financial preferences of the
subjects is displayed in Fig. 8. Finally, Fig. 9 contains a doughnut chart of
the most preferred interaction method and a doughnut chart of the assignment
where the haptic gloves were most useful.

Prior to discussing the results, it is valuable to analyze the test group. For
this study, a minimum of 20 people was envisioned and in total 22 subjects
were actually tested. It should be noted that all test subjects participated
voluntarily without compensation. Furthermore, no public call was made to find
participants. As a result, everyone who participated was either an
acquaintance or an employee of the research group. Nevertheless, none of the
subjects knew in advance the purpose of the study to ensure objectivity.

The age of the participants ranged from 16 years to 50 years old. An average
age of 25.95 years was obtained with a standard deviation of 8.82 years.
Similarly, the gender of the participants was well distributed. The research
included 10 women and 12 men, which corresponds to a distribution of 45.45%
women and 54.55% men.

TABLE I: Summary statistical values of the error score with the best (lowest) mean score per assignment in bold. Interaction method | Task | Mean | Std dev | Variance
---|---|---|---|---
HoloLens | K | 8.23 | 7.12 | 50.63
HoloLens | C | 3.32 | 3.53 | 12.49
DIM | K | 29.91 | 22.94 | 526.45
DIM | C | 2.59 | 3.81 | 14.51
HEDIM | K | 5.77 | 7.35 | 53.99
HEDIM | C | 1.86 | 2.34 | 5.48

The first thing that stands out in Table I is that the mean score of the HEDIM
is the lowest, thus the best, for both the assignments. For the cube
assignment, the same method without the haptic gloves, i.e. DIM, still
performed better than the standard interaction method of the HoloLens. For the
keyboard assignment, a significant higher mean value can be observed. When
normal distribution is assumed, for the keyboard assignment, a user using the
HEDIM has 57.77% chance to score better than the standard interaction method
of the HoloLens and 84.28% chance to score better than the DIM. Similarly for
the cube test, users have 63.5% chance to score better than using the standard
interaction method and 56.49% chance to score better than the DIM.

TABLE II: Summary statistical values of the time (in seconds) with the fastest mean time per assignment in bold. Interaction method | Task | Mean | Std dev | Variance
---|---|---|---|---
HoloLens | K | 182.23 | 53.90 | 2905.36
HoloLens | C | 169.64 | 64.36 | 4142.60
DIM | K | 158.14 | 50.57 | 2557.66
DIM | C | 62.00 | 37.29 | 1390.82
HEDIM | K | 81.27 | 29.25 | 855.74
HEDIM | C | 103.64 | 56.46 | 3187.32

By analyzing Table II, it cannot be easily concluded which interaction method
performs best. This is because DIM and HEDIM each perform superior on a
different assignment. On the other hand, the standard interaction method of
the HoloLens has the highest time for both tests. Consequently, this is the
worst interaction method in terms of speed. When normal distribution is
assumed, for the keyboard assignment, a user using the HEDIM has 90.75% chance
to finish earlier than the DIM and 95.10% chance to finish earlier than
standard interaction method. For the cube test, a user has a higher chance to
finish early with DIM. They have 73.08% chance to score a better time than
with HEDIM and 92.60% chance to score better than with the standard
interaction method.

Figure 8: Bar chart containing the financial preferences of the subjects.

By analyzing the graph in Fig. /reffig:money, it can be observed that 72.72%
is not willing to spend more than 1,500 euros on a computer and 100% is not
willing to spend more than 1,000 euros on a mobile phone. If the hypothesis is
correct, the users are not willing to pay more than 1.000 euros on an HMD and
definitely not more than €1.500. As the HoloLens is the only true AR device,
it is first analyzed. From all test subjects, 100.00% are not willing to pay
more than 1.500 euros and 90.91% are not willing to pay a maximum of 1.000
euros for it. Secondly, 90.91% do not want to pay more than 1.500 euros for a
VR HMD and 77.27% have a limit of 1,000 euros. From this, it can be concluded
that the majority do not want to spend more than they currently spend on a
cell phone or computer.

The HoloLens (First generation) was sold in 2016 for 3,000 dollars for a
developer’s kit and 5,000 for a commercial suite [16]. Nowadays, this is
respectively 2922.97 euros and 4871.63 euros. The price of the HoloLens 2 is
3500 dollars, meaning 3410.14 euros at the moment. The Oculus Meta Quest is
available between 449.99 and 549.99 euros depending on desired storage
capacity [17]. Since solely price ranges were asked and the price of the
HoloLens depends on the version, both the price range 2000-3000 euros and
above 3000 euros are approved. This results in 7 out 22 subjects or 31.82%
having correctly estimated the price. Similarly, for the Oculus Quest both the
price range 251-500 euros and 501-1000 euros are approved. As a result, 13 of
the 22 people or 59.09% were able to indicate the correct price range. Due to
the large distance between the boundaries of the price ranges and because only
45.45% of the total answers were correct, it is concluded that users are not
able to estimate the costs correctly for an HMD.

Before a final conclusion can be made whether the haptic feedback and the new
interaction method improves the standard interaction method of the HoloLens,
all participants were asked which interaction method they preferred for daily
use, and in which test they found the haptic gloves the most useful. The
result of their most desired interaction method is visible in Fig. 9. The name
of the HMD s was not used so that the users could only take into account the
interaction method and were not biased by the HMD s. Additionally, in Fig. 9,
it is displayed for which assignment the users found the haptic gloves most
useful.

Figure 9: Doughnut chart of the most preferred interaction method (left) and
doughnut chart of the assignment where the haptic gloves were most useful
(right)

It can be observed that the test subjects have no general preference in favor
or against haptic feedback. Nevertheless, the standard HoloLens interaction
method is clearly not preferred. This allows the study to conclude that both
the DIM and the HEDIM exceeds the standard method among users. When looking at
the preferences when only considering haptic feedback, the following result is
obtained: one user prefers the cube assignment, 16 users prefer the keyboard,
three users find both applications useful with haptic feedback and two users
do not find the haptic gloves useful anywhere. Users find the keyboard the
most useful application for haptic gloves. Additionally, HEDIM scored the
lowest mean time necessary for the keyboard task. In contrast, for the cube
assignment it was the DIM with the best time. However, one may wonder whether
gloves of 3,999 euros are worth buying if only used as a keyboard. This
research concludes that it is clearly not worth the financial cost. This
conclusion has also been confirmed by the Financial Hypothesis in which it was
concluded that people do not want to spend more than they currently spend on a
cell phone or computer solely on the HMD and, therefore, certainly do not want
to pay an extra 3,999 euros.

##  VII Conclusion

First, after analyzing the results, it was first concluded that the user
experience with all HMD s were equal and that the switch in HMD s was without
influence on the result of the further discussed conclusions. Second, this
research deduced from the gathered data that users have a slight preference
for using the DIM in general situations. For specific situations, users
preferred using the DIM for the cube assignment and using the HEDIM for the
keyboard task. This subjective perspective of the users could be supported by
the objective time measurements which scored the best for the cube assignment
when using the DIM and for the keyboard when using the HEDIM. For the score
parameter, it was concluded that using the HEDIM obtained the best result for
both assignments. It should be noted that despite the differences in the DIM
and the HEDIM, both outscored the standard interaction method of the HoloLens
each time. Last, this study determined that the majority of users do not want
to spend more than they currently spend on a cell phone or computer for an HMD
and users are not able to estimate the costs correctly of an HMD.

This research concludes as an end result that the DIM and the HEDIM have
proven to improve the standard method of the HoloLens. Additionally, it has
been established that haptic feedback enhances the DIM in certain situations.
Nevertheless, in this study, the haptic gloves only make a small improvement
that it is not worth the financial cost. As future work, we recognize that DIM
could still be improved in comparison with the haptic feedback by adding
software enhancements. As a result, the research concludes that, at this
moment, haptic feedback is useful for high-end personalized applications, but
not yet for daily use.

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