The Energetic Cost of Building a Virus
Gita Mahmoudabadi
1
, Ron Milo
2
, Rob Phillips
1,3
1 Department of Bioengineering, California Institute of Technology, Pasadena, CA
91125, USA.
2 Department of Plant and Environmental Sciences,
Weizmann Institute of
Science, Rehovot 7610001, Israel.
3 Department of Applied Physics, California Institute
of Technology, Pasadena, CA 91125, USA.
1
Abstract
Viruses are incapable of autonomous energy production. Although many experimental
studies
make it clear that viruses are parasitic entities that hijack the host
’s
molecular resources, a
detailed estimate for the energetic cost of viral synthesis is largely lacking. To quantify the
energetic cost of viruses to their hosts, we enumerated
the costs associated with two very
distinct but representative DNA and RNA viruses, namely, T4 and influenza. We found that for
these viruses, translation of viral proteins is the most energetically expensive process.
Interestingly, the cost of building a
T4 phage and a single infl
uenza virus are nearly the same
.
Due to influenza’s higher burst size, however, the overall cost of a T4 phage infection is only
2
-
3
% of the cost of an influenza infection. The costs of these infections relative to their host’s
estimated energy budget
during the infection
reveal that a T4 infection consumes
about
a
third
of its host’s energy budget, whereas an influenza infection consumes
only
1%. Building o
n our
estimates for T4, we
show how the energetic costs of double
-
stranded DNA viruses scale with
virus size, revealing that the dominant cost of building a virus can switch from translation to
genome replication above a critical virus size. Lastly, using our
predictions
for the ene
rgetic cost
of viruses, we provide estimates for the strengths of selection and genetic drift acting on newly
incorporated genetic elements in viral genomes
,
under conditions of energy limitation
.
Significance Statement
Viruses rely entirely on their ho
st as an energy source. Despite numerous experimental studies
that demonstrate
the capability
of
viruses
to
rewir
e
and undermin
e
the
ir
host
’s
metabolism
, we
still largely lack a
quantitative understanding of an infection’s energetics
. And yet, the energeti
cs
of a viral infection is at the center of broader
evolutionary and physical
questions
in virology.
By
enumerating the energetic costs of different viral processes, we open
the door
to quantitative
predictions about viral evolution.
For example, w
e predic
t that for the majority of viruses,
translation will serve as the dominant cost of building a virus, and that selection, rather than
drift, will govern the fate of new genetic elements within
viral
genomes.
Key Words
viral energetics, viral evolution,
T4
, influenza
,
cellular
energetics
2
Introduction
Viruses are biological ‘entities’ at the boundary of life. Without cells to infect, viruses as we know
them would cease to function, as they rely on their hosts to replicate. Though the extent of this
relianc
e varies for different viruses, all viruses consume from the host’s energy budget in
creating the next genera
tion of viruses. There are many
examples of viruses that actively
subvert the host transcriptiona
l
and translational processes in favor of their ow
n replication
(1)
.
This viral takeover of the host metabolism manifests itself in a variety of forms such as in the
degradation of the host’s genome or the inhibition of the host’s mRNA translation
(1)
. These
examples suggest that a viral infection requires a considerable amount of the host
’s
energ
etic
supply
. In support of this view are experiments on T4
(2)
, T7
(3)
,
Pseudoalteromonas
phage
(4)
,
and
Paramecium bursaria
chlorella
virus
-
1
or PBCV
-
1
(5)
, demonstrating the viral burst size to
correlate positively with the host growth rate. In the case of PBCV
-
1, the burst size is r
educed
by 50% when its photosynthetic host, a freshwater algae, is grown in the dark
(5)
. Similarly,
slow growing
E. coli
with a doubling time of 21 hours affords
a T4 burst size of just one phage
(6)
, as opposed to a burst size of 100
-
200 phages during optimal growth conditions
.
There are many other
experimental
studies
(
discussed
in the
SI section I)
(7
-
11)
that
demonstrate viruses
to be
capable of rewiri
ng the host metabolism
. These fascinating
observations led us to
ask the following
question
s:
what
is the energetic cost of a viral infection
,
and what is
the energetic burden of a viral infection on the host cell?
To our knowledge, the first
attempt to address
these problems
is provided through a kinetic model of the growth of Qß
ph
age, which demonstrates that
Qß growth is energetically optimal
(12)
. A more recent study
performed numerical simulations of the impact of a phage T7 infection on its
E. coli
host,
yielding
very interesting insights into the time course of the metabolic demands of a viral
infection
(13)
.
To further explore the energetic requirements of viral synthesis, we made careful estimates of
the energetic costs for two viruses with very different characteristics, namely the
T4 phage and
the influenza A virus. T4
phage
is a double
-
stranded DNA (dsDNA) virus with a 169 kb genome
that infects
E. coli
. The influenza v
irus is a negative
-
sense, single
-
stranded RNA virus (
-
ssRNA)
with a segmented genome that is 10.6 kb in total leng
th. The influenza virus is a eukaryotic virus
infecting various animals, with an average burst size of 6000
(14)
. Similar to many other dsDNA
viruses, T4 phage infections yield a relatively modest burst size, with the majority of T4 phages
resulting in a b
urst size of approximately 200
(15)
. To determine
the energetic demand of
3
viruses on their hosts, the cost estimate for building a single virus has to be multiplied by the
viral burst size and placed in the context of the host’s energy budg
et
during the viral infection
.
Concretely, the costs associated with building a virus can be broken down into the following
processes that are
common to the
life
-
cycle
s of many viruses: 1) viral entry 2) intracellular
transport, 3) genome replication
,
4) transcription, 5) translation, 6) assembly and genome
packaging, and 7) exit.
Detailed estimates for all of these costs are provided in the SI.
Our
strategy
was
to examine each of these processes for both viruses in parallel, comparing and
contrasting t
he energetic burdens of each of the steps in the viral
life
-
cycle
.
Results
By estimating the energetic costs of influenza and T4 life
-
cycles, we show that surprisingly the
cost of synthesizing an influenza virus and a T4 phage are nearly the same (Table
1). The
outcome of the analysis to be discussed in the remainder of the paper is summarized pictorially
in Figure
1
for bacteriophage T4 and Figure
2
for influenza. For both viruses, the energetic cost
of translation outweigh
s
other costs
(Table 1, Figure
s 1, 2, 3)
, though
as we will show at the end
of the paper, since translation scales with the surface area of the viral capsid and replication
scales as the volume of the virus, for double
-
stranded DNA phages larger than a critical size,
the replication co
st outpaces the translation cost.
Our
results will be provided
in terms of two
different energetic cost definitions
described in detail as part of
SI section
s
II
-
IV
.
To briefly summarize
, in our first definition of energetic cost, termed
direct cost
or
퐸
!
, we will
only account
for hydrolysis of
ATP molecules
(and equivalent molecules, such as GTP)
required
during
viral synthesis
. This definition will include costs
such as those
incurred during the
synthesis and polymerization o
f building blocks
(
SI Fig
ure 1A, steps 3 and 4; SI section II)
. In
our second definition, termed
total cost
or
퐸
!
, we not only account for the
direct cost
s, but also
for the
opportunity cost
of building blocks
,
퐸
!
,
required
during
viral
synthesis (
SI
Figure 1A,
steps 1
-
4
; SI s
ections II
-
IV
)
; hence,
퐸
!
=
퐸
!
+
퐸
!
.
We define the
opportunity
cost
of a building
block as the number of ATP molecules that
could have been generated had the building block
not been synthesized
. The full definition and derivation of these two cost components can be
found in the
SI (
SI
sections
II
-
IV
, SI table
5
, SI Figure
1
, SI Figure 2
)
.
The distinction between these two different energetic cost definitions is that under the
direct cost
defin
ition, we attribute energy only to the hydrolysis of ATP
-
equivalent molecules, whereas
4
under the
total cost
definition, we also attribute an energetic cost to the
building blocks that are
usurped from the host during viral synthesis. Both energy definition
s have physical significance.
For example, the
direct cost
definition only accounts for ATP (and
ATP
-
equivalent) hydrolysis
events, thereby giving us insight into heat production and power consumption of a viral infection.
The
total cost
definition, on the
other hand, is aligned with traditional energetic cost estimates
made from growth experiments in chemostats and allows for a
clear
comparison between the
cost of an infection and the cost of a cell.
To
help the reader discern
between
opportunity
and
direc
t
costs
, we will signify the former in units of ^P
and the latter in the units of ~P
.
When
reporting
total cost
estimates, we will simply use P to signify the sum of
opportunity
and
direct
cost
s.
Moreover, in formulating our estimates, we will generally e
stimate the cost of a certain viral
process for a single virus, and then multiply this cost by the viral burst size to determine the
infection cost of a given process. Subscript
v
will denote the cost estimates made for a single
virus, and the subscript
i
will refer to a cost estimate made for an infection.
We
relegate the
energetic cost estimates for
all viral process
to the
SI
sections
V
-
XI
.
The
direct
,
opportunity
and
total cost
s of
T4 and Influenza
.
To get a sense for the numbers,
here we provide
ord
er
-
of
-
magnitude
estimates of both the costs of
translation and replication
and refer the interested reader to the SI
sections II
-
XI
for full details
.
As detailed in the SI Tables
1 and 2, b
oth T4 and influenza are comprised of about
10
6
amino acids
.
W
e can
estimate the
total cost
of translation
by appealing to a few simple facts. First, the
average
opportunity cost
per amino acid is
about 30 ^P
. Second, the
average
direct cost to produce amino acids from
precursor
metabolites
is
2 ~P
.
Finally, each polypeptide bond incurs a direct cost of 4
~P
.
We
can see that
the
total cost
of
an
amino acid is approximately 36 P (30 ^P + 6 ~P). As a result,
the
translational cost of an influenza virus and a T4 phage
both fall
between
10
7
to 10
8
P
(T
abl
e
1)
.
The cost of viral replication can be approximated in a similar fashion
:
we have to
consider that
the T4 genome is comprised of
roughly
4 x10
5
DNA
bases
and that the influenza genome is
composed of
an order of magnitude fewer
RNA bases (
≈
10
4
).
The
total costs of a DNA
nucleotide and an
RNA
nucleotide
, including the opportunity costs
as well as
the direct costs of
synthesis and polymerization,
are
approximately
50 P
(SI section II
-
IX
, SI Figure 1, SI Figure 2
,
SI Table 5
)
.
As a result
of T4’s longer genome length
,
its
total cost of replication
(
≈
10
7
P)
is
5
about an order of magnitude higher than that of an influenza
genome
(Table 1, Figure 1, Figure
2, SI section VII)
.
The direct, opportunity and total cost estimates of different vira
l processes during T4 and
influenza infections are summarized in
Figure
s 1
-
3
and Table 1.
The
overall
cost of a T4
infection is obtained by summing the costs of replication
(
퐸
!"#
/
!
)
, transcription
(
퐸
!"
/
!
)
,
translation
(
퐸
!"
/
!
)
, and genome pac
kaging
(
퐸
!"#$
/
!
)
required during the infection
(SI sections V
-
XI, Table 1, Figure 1
, Figure
3).
These costs
together amount to
≈
3 x 10
9
~
P
, 8
x 10
9
^P, and
1
x 10
10
P, respectively
(SI sections V
-
XI, Table 1, Figure 1
, Figure
3
)
.
The total cost of a T4
infection is also
equivalent to the aerobic respiration of
≈
4 x 10
8
glucose molecules
by
E. coli
(26
P
per glucose
,
(16)
). Alternatively, it is equivalent to
≈
2 x 10
11
k
B
T
(assuming 1 ATP = 20
k
B
T on average)
(17)
.
Similarly, the cost of an influenza infection is obtained by adding up the costs of entry
(
퐸
!"#$%
)
,
intracellular transport
(
퐸
!"#$%&'
/
!
)
, replication
(
퐸
!"#
/
!
)
, transcription
(
퐸
!"
/
!
)
, translation
(
퐸
!"
/
!
)
,
and exit
(
퐸
!"#$
/
!
)
required during the infection
(SI sections
V
-
XI
,
Table 1, Figure
2
, Figure
3
).
These processes
have a cumulative cost of
≈
8 x 10
10
~
P
,
5
x 10
11
^
P and 6 x 10
11
P
,
resp
ectively.
The
sum of costs in an influenza infection is
equivalent to the aerobic respiration of
≈
2
x 10
10
glucose molecules
by a eukaryotic cell
(
32
P
per glucose).
It is also
equivalent to
≈
10
1
3
k
B
T
.
It is interesting to note that for both viral infections the opportunity cost components
are the dominant component of the total costs.
The
direct cost
of a
T4 phage infection is therefore only
≈
3
% of the
direct cost
of an influenza
infection
. Similarly
, the
total cost
of a T4 phage infection is
only
≈
2% of the
total cost
of an
influenza infection
even though
individually
a T4 phage and an influenza virus have comparable
energetic costs.
To
contextualize these numbers
, the host energy
budget
(or the host energetic
cost, depending on the viewpoint of a virus versus a cell)
during the infection has to be taken
into account.
The
total cost
of a cell is experimentally tractable
through gr
owth experiments in chemostats, in
which
cultures
are
main
tain
ed
a
t a
constant growth rate. The number of glucose molecules
taken up per cell per unit
time can be determined. The number of glucose molecules can then
be converted to an
energetic supply by assuming typical
conversion rate
s
of 26
P or 32
P per
6
gluco
se
molecule
depending on the organism
(16)
.
This
energetic cost
es
timate will be a
total
cost
estimate because not all glucose molecules
taken up by the cell
are fully metabolized
to
carbon dioxide and water to generate
ATPs.
During the cellular
life
-
cycle
,
the cell has to double
its number of building blocks prior to di
vision, and to do so,
a fraction of
glucose molecules
take
n
up
is
diverted
away from
energy production towards biosynthesis pathways
. Hence,
cellular energetic cost estimates that are derived from chemostat experiments are
total cost
estimates
because they
report on the combined
opportunity
and
direct cost
s of a cell
(SI section
II
-
IV)
.
Based on chemostat growth
experiments
(18)
,
the
total cost
of a bacterium and a mammal
ian
cell with volumes
of
1
휇푚
!
and
2000
휇푚
!
, respectively,
are
≈
3 x 10
10
P and
≈
5 x 10
13
P, during
the course of their viral infection
s
(
SI section
XII
)
.
A simpler estimate
for arriving at the
total cost
of
E. coli
during its
30
-
minute
doubling time
is by considering the dry weight of
E. coli
(
≈
0.
6
pg)
(
(19)
, B
NI
D
100089
)
.
Given
that about half of the cell’s dry weight is comprised of carbon
(
(19)
,
B
NI
D 100649
)
, an
E. coli
is composed of
≈
2
x 10
10
carbons, supplied from
≈
3
x 10
9
glucose
molecules,
since each glucose contributes 6 carbons. With the 26 P per glucose conversion
for
E. coli
, this is equivalent to a
total
cost
of
≈
7
x 10
10
P, which is
similar
to the
number obtained
from chemostat growth experiments
(18)
(SI
section XII
).
Moreover, w
e estimate the fractional
cost of a viral infection
as the ratio of
total cost
of an
infection,
퐸
!
/
!
, to the
total cost
of the host during the infection,
퐸
!
/
!
. For the
T4 infection with a
bu
rst size of 200 virions
,
퐸
!
/
!
≈
1 x 10
10
P
(Table 1)
and
퐸
!
/
!
≈
3 x 10
10
P, therefore the
fractional cost of the T4 infection is
≈
0.3
. Interestingly, a calorimetric study of a marine microbial
community demonstrated that 25% of the heat released by microbes is due to phage activity
(20)
–
an observation that resonates well with our estimate.
In contrast, the influenza infection
despite its
larger burst size
(6000 virions) and higher
퐸
!
/
!
(
≈
6 x 10
11
P)
has a fractional cost of
just 0.01.
In our estimates for heat production and power consumption
of a viral infection
, we will not
includ
e
the
total cost
of an infection as it contains the
opportunity cost
s; by definition, these
opportunity
cost
s do not represent direct expenditure of ATP
-
equivalent molecules and
therefore do not
substantially
contribute to heat production.
In contrast,
direct cost
estimates
capture only the number of ATP
-
equivalent molecules hydrolyzed during an infection
(S
I section
II)
.
7
T4 infection
has
a
direct cost
of
3 x
10
9
~
P
(Table 1)
. Assuming ATP hydrolysis
generates
-
30
kJ/mole, the heat generated during a T4 infection is
approximately
0.1
n
J
. An influenza infection
with a
direct cost
of 7 x
10
10
~
P
generates 4 nJ. While
influenza infection results in an order of
magnitude more heat, the average rate of heat production or the power of T4 and influenza
infections are surprisingly very similar. In half an hour, the T4 infection
results in the hydrolysis
of ATP
-
equivalent molecules
at a
n average
rate of
1
x 10
6
~
P
per second
.
In
half a day
, an
influenza infection
has an average ATP
-
hydrolysis rate of 2
x 10
6
~
P
per second
, which is nearly
the same rate as that of a T4 infection.
Put in terms of the more f
amiliar units of Watts, the
power of both viral infections is on the order of 100 fW.
Generalizing viral energetics for double
-
stranded DNA viruses
.
While we have concluded
that for the influenza virus and the T4 phage the translational cost outweighs
the replication
cost, the ratio of these two costs varies according to the dimensions of a virus. In the case of T4
and influenza, these two viruses had comparable dimensions and consequently were comprised
of a similar number of amino acids (SI Table
s
1 a
nd 2). However, due to the diminishing surface
area to volume ratio of a spherical object as it grows in size, the ratio of translational cost to
replication cost also diminishes with increasing radius of a spherical capsid.
This simple rule
govern
s not ju
st
nucleotide or amino acid composition of a virus, but more fundamentally, it
governs the elemental composition of viruses
with spherical
-
like geometries
(21)
.
The full derivation of replication and translational cost estimates
as a function of viral capsid
inner radius,
푟
,
can be found in the SI
section XIII
.
From these expressions, it is clear that the
translational cost of a virus scales with
푟
!
, whereas the replication cost scales with
푟
!
(Figure
4
). The critical radius
a
t which replication will outweigh translation in cost
is
59
nm
for
total cost
estimates
,
푟
!"#$
!
!"#
(
Figure
4, SI section XIII)
. For
the
direct cost
estimates, the critical radius,
푟
!"#$
!
!"#
,
is
42
nm
.
Interestingly,
a
survey of structural diversity
encompassing
2
,
600
viruses
inhabiting
the world’s oceans
reveals that the average outer
capsid radius is 28 nm
(22)
, which
is
much
smaller than the predicted critical
radii (Figure 4)
. As such, for the majority of viruses,
we predict
translation
is the dominant cost of
a viral infection
.
Furthermore, we provide genome replication to translation cost ratios for
about 30
different
double
-
stranded phages (
SI Table 3,
Figure
4
).
W
hile we have omitted calculations for the virus
tails, they can be si
mply treated as hollow cylinders and will further decrease the expected
8
replication to translation cost ratio for the tailed viruses.
Although
we have calculated these
ratios for this select group of viruses, similar principles can be applied to modeling t
he
energetics of other viral groups.
Forces of evolution
operating on
viral genomes
.
Inspired by efforts to consider the
evolutionary implications of the cost of a gene to cells of different sizes
(18, 23)
, we were
curious whether similar considerations might be in play i
n the context of viruses.
For example,
we asked which evolutionary forces are prominently operating on neutral genetic elements that
are incorporated into viral genomes, either by horizontal gene transfer, gene duplication or other
similar types of events.
We further asked whether the viral size is a parameter of interest in the
tug of war between
different
forces of evolution. We will address these topics by assuming
that
the host lives in an
energy
-
limited environment
and that the viral infection,
consistent with our
findings for T4, consumes a substantial port
ion of the host energy budget.
By making these
assumptions, we
are able to treat
the energetic cost of a genetic element as a fitness cost.
For a genetic element to remain in the populatio
n, regardless of whether it is beneficial or not, it
must face the consequences of genetic drift which scales with the viral effective population size
,
푁
!
,
as
푁
!
!
!
.
We follow the treatment of
Lynch and Marinov
who argue that
the net selective
advantage
of a genetic element is
푠
!
=
푠
!
−
푠
!
,
where
푠
!
and
푠
!
den
ote the selective
advantage and
disadvantage, respectively
(Figure
5
B
)
. For a
genetic element
within a viral
genome
that is non
-
transcribed and non
-
translated
(Figure
5
C
)
,
only
the energetic
cost of its
replication poses a selective disadvantage. Assuming the
genetic element
provides no benefit to
the virus (
푠
!
=
0
), the net selective advantage can be stated as
푠
!
=
−
푠
!
, the absolute value of
which must be much greater than
푁
!
!
!
for sele
ction to operate effectively. Following Lynch and
Marinov and others
(23, 24)
, we make the simplifying assumption that a
neutral
genetic
element’s selection coefficient
,
푠
!
,
is proportional to its fractional energetic cost,
퐸
!
(Figure
5
C
)
.
In the case of a non
-
transcribed
genetic element
,
퐸
!
=
!
!"#
/
!
!
!
, where
퐸
!"#
/
!
corresponds to its
replication cost and
퐸
!
is
the sum of all costs of
a virus
(Figure
5
C
)
.
Given that replication cost scales as
푟
!
the effects of selection r
elative to genetic drift could be
different for viruses
of different sizes
. Consider Virus A, having a radius that is two times larger
than that of Virus B
(Figure
5
D
). Because both viruses
are assumed to
have radii
larger than
the
critical radi
us
,
we imag
ine the scenario in which
the cost of genome replication is the dominant
9
cost of synthesizing these vi
ruses. The fractional cost of a genetic element
in the smaller virus,
퐸
!
_
!"#$%
!
is then equal to
8
퐸
!
_
!"#$%
!
, where
퐸
!
_
!"#$%
!
is
the fractional cost of the genetic element
in the larger virus
. This is because the length of the genome is proportional to
푟
!
, and
consequently,
퐸
!
is inversely proportional to
푟
!
(Figure
5
D
)
.
Figure
5
E
and
SI Table 4
provide
퐸
!
estimates for
gen
etic elements
of different lengths (
1
–
10,000
base pairs) within
30 dsDNA
viruses.
To illustrate the effect of scaling in the example
provided above, we made the simplifying assumption that the viruses are large enough that their
퐸
!
are approximately eq
ual to their replication costs. However, for
퐸
!
values
in
Figure
5
E
and SI
Table 4, w
e provide more precise estimates, treating
퐸
!
as the sum of both the replication cost
and the translational cost of a virus. The cost of replicating a double
-
stranded genetic element
can be obtained
from
SI
Eq.
3
.
For
a 1 kb element
, which is about the average length of a
bacterial gene
,
the
direct
a
nd
total cost
s of
its
replication
per virus
,
퐸
!"#
/
!
,
are 3 x 10
4
~
P and 9
x 10
4
P, respectively
.
Both
direct
and
total cost
estimates
indicate that the
strength of selection
acting on a 1 kb, non
-
transcribed element range
s
from 2 x 10
-
2
-
7
x 10
-
6
(SI Table 4,
Figure 5E
)
when
considering viruses with radii ranging from ~2
0
nm to 400 nm
.
The difference between
direct
and
total
estimates of selection strength is minimal within this range of capsid radii and
continues to diminish as the capsids grow in
size.
To examine whether selection or genetic drift will decide the fate of
a genetic element
we need
to assess each virus’s effective population size. This is difficult
because
the effective population
size of most viruses is unknown and subject to gr
eat variability due to
several
environmental
factors
(25)
.
The current effective population size estimates regarding HIV, influe
nza,
dengue,
and measles fall within 10
1
to 10
5
(25
-
27)
. Based on the wide range of variation in these
effective population sizes, it is difficult to make conclusive
statements. It is, however, apparent
that the strength of selection on neutral
genetic elements
is a non
-
linear function of the viral
capsid radius and becomes much weaker as viruses get larger
(
Figure 5E
)
. In fact, for giant
viruses (
with outer radius,
R
> 200 nm
), assuming an
푁
!
!
!
=
10
-
5
, genetic drift could overpower
selection, allowing for the persistence of neutral
elements of lengths 100 bp or shorter
in the
population. For
the majority of
viruses (
R
=
2
8
±
6.5
nm,
(22)
),
however,
selection is likely to be
the domin
ant force and drift may only play a role for
genetic elements
that are just a few base
pairs long
(
Figure 5E
, SI Table 4).
10
Discussion
There have been several experiments that
imply
a viral infection requires a significant portion of
the host energy budget
(5, 6, 8, 10, 28
-
30)
.
Following
th
ese experimental hints
, we enumerated
the energetic requirements of two very different viruses on the basis of their
life
-
cycle
s, and
thereby estimated the energetic burdens of thes
e viral infections on the host cells. According to
our
total cost
estimates
, a T4 infection with a burst size of 200 will consume a significant portion
(about 30%)
of the
host energy supply
.
This result, demonstrating a significant fraction of the
host ene
rgy used by an infection, supports the experimental findings that the T4 burst size is
correlated positively with the host growth rate
(2, 6)
. It also lends further credence to the
hypothesis that auxiliary metabolic genes within phage genomes are not just evolutionary
accidents; rather, they have come to serve a functional role in
boosting the host
’s
metabolic
capacity, which translates into larger viral burst sizes
(8, 9, 30, 31)
.
These calculations make it
all the more interesting to develop high
-
precision, single
-
cell calorimetry techniques to monitor
energy usage during viral infections.
Perhaps the most promising support for T4’s
cost
estimat
e
is
the
observation that the maximum
T4 burst size is 1,000 virions
(15)
.
Using
the
total cost
to
make new viruses, at a burst size of 1,000, the viral infection would consume
17
0% of the host
energy
supply
,
consistent with the observed apparent upper limits on burst size.
While
there are several
fascinating
studies that explore the link between t
he host metabolism
and phage infections
(8, 11
-
13)
,
similar
studies focusing on viruses of multicellul
ar eukaryotes
are largely lacking.
To that end, we chose to estimate the energetic cost of a representative
virus for this category, namely, the influenza virus. The influenza virus and T4 phage are
functionally and evolutionarily very different viruses. Y
et, surprisingly, they have a very similar
per
-
virus cost, regardless of whether the
total
or the
direct cost
estimates are being considered.
This is
primarily
due to the fact that they have a similar translational cost, which dominates all
other costs. An
d, the
ir
comparable cost of translation
is
due to the fact that these viruses have
similar dimensions and are both composed of
about a million
amino acids. Perhaps even more
surprising is that both viral infections have very similar
average
power consumpti
ons,
on the
order
of
100
fW
, despite their different durations
.
Even with
its higher burst size,
an
influenza
infection has a total cost that
is
just 1% of the
total
cost
of a eukaryotic cell
. This is because a typical eukaryotic cell is estimated to have much
higher energy supply than a typical bacterium under the same growth conditions. So far in our
estimates, we do not account for the possible inefficiencies at various stages of the viral
11
infection, which may drain more of the host energy than we estimated. Specifically, burst sizes
are typically reported from plaque assays, which count the number of infectious
virions
that
create plaques. However, we don’t have a good estimate for the numb
er of non
-
infectious
viruses that arise from faulty genome replication, transcription, or viral assembly, for example.
This point is especially important when considering RNA
-
based viruses such as influenza or
HIV, which have higher mutation rates
(10
-
4
-
10
-
6
mutations per base pair per generation;
(32)
)
compared to dsDNA viruses
such as T4 (10
-
6
-
10
-
8
mutations per base pair per generation;
(
(32)
).
As a
result of these higher error rates, RNA
-
based viruses may have greater hidden
costs associated with aborted viral synthesis or a greater fraction of faulty and non
-
infectious
virions.
Second, even infectious viruses cannot all be guaranteed to enter the
lytic cycle upon infecting
a host cell. In support of these statements is the finding that only about 50% of PBCV
-
1 viral
progeny are infectious
(5)
.
In fact
, onl
y 10% of influenza
-
infected host cells have been shown to
generate infectious virions
(33)
, demonstrating the cumulative inefficiency of an influenza
infection. Hence, counting pl
aques to measure viral burst sizes may be analogous to making
estimates of the human population by counting only individuals who have children. As such,
single
-
cell studies of viral infection could provide a detailed breakdown of inefficiencies at
various
steps of the viral life
-
cycle and enable more exact cost estimates.
We
further explore
other factors related to the
fractional cost
of influenza and T4 infections
in the SI section
XIV.
Finally, t
here
is a great need for estimates of the effective popul
ation sizes of different viruses
within their natural environments
. With current effective population size estimates for viruses it
appears that selection likely determines the fate of genetic elements for
the majority of
viruses
,
which have
on average
2
8
nm
radii
(22)
(
Figu
re 5E
, SI Table 4
). However, for larger viruses (
R
> 200 nm), the diminishing, fractional cost of a gene may enable the interference of genetic drift
to the extent that neutral genetic elements could persist in the viral population. The result of
such a ph
enomenon could be genome expansions in the form of gene duplication events,
cooption of previously noncoding
, horizontally transferred elements
into functional genes
and
regulatory domains
, and perhaps, even a trend towards greater autonomy over large
evol
utionary time
-
scales. This effect may explain the unusual number of duplication events in
the genome
s
of
gian
t
viruses such as that of the
Mimivirus
(34, 35)
. Perhaps this effect has also
allowed enough genomic expansion and novelty for certain large viruses to jump the barrier
between obligate entities and self
-
replicating organisms.
12
Acknowledgements
We are grateful to
David Balti
more,
Forest Rohwer, Thierry Mora, Aleksandra Walczak, Ry
Young, David Van Valen, Georgi Marinov, Elsa Birch, Yinon Bar
-
On and Ty Roach for their
many insightful recommendations. This study was supported by the National Science
Foundation Graduate Research
Fellowship (grant no.
DGE
‐
1144469),
The John Templeton
Foundation (Boundaries of Life Initiative, grant ID
51250
), the National Institute of Health’s
Maximizing Investigator’s Research Award (grant no. RFA
-
GM
-
17
-
002), the National Institute of
Health’s Exceptional Unconventional Research Enabling Knowledge Acceleration (grant no.
R01
-
GM098465), and
the National Sci
ence Foundation (grant no.
NSF PHY11
-
25915)
through
the 2015 Cellular Evolution course at the Kavli Institute for Theoretical Physics.